Crain's Petrophysical Handbook

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ENVIRONMENTAL CORRECTIONS for RESISTIVITY LOGS

Correction Basics Borehole Corrections Invasion Corrections Diameter of Invasion

ENVIRONMENTAL CORRECTIONS FOR RESISTIVITYWater saturation calculations require a good value for formation resistivity,commonly called true resistivity or Rt, as well as shale corrected porosity(PHIe), and the shale content (Vsh). Therefore, the resistivity log may needsome environmental corrections before use in the saturation equations.

The corrections on this page are for older style induction logs and laterologs,and are shown for illustration purposes only. Use the appropriate charts forthe specific tool that was run on your well. Note that invasion corrections,covered in the next Section, apply only to water zones and oil zone caseshave not been published anywhere. On modern array induction logs, invasioncorrections for both water and oil zone cases are applied by the service company to create Rt and Rxo curves. Thesealgorithms have not been published.

Commercial log analysis software may use generic or obsolete environmental corrections, so care in the use of thesecorrections is required. No software package has individual corrections for every possible tool type from all servicecompanies.

Borehole corrections for mud salinity and hole diameter should be applied first, if needed. Most computer aided loganalysis software has this capability. Fortunately, borehole corrections can often be safely ignored when the log isrun in a good borehole with a good mud system. The newest array induction logs attempt to produce Rt with allcorrections applied. Do not over correct your data by applying the corrections a second time.

BOREHOLE ENVIRONMENT CORRECTIONS TO RESISTIVITYFor those who insist on superfluous detail, formulae are provided here for the deep induction log for no standoff andfor 1.5 inches standoff (the usual case):

Crain's Petrophysical Handbook - ENVIRONMENTAL CORRECTIONS... https://www.spec2000.net/14-swenvir.htm

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Borehole correction for deep induction - standoff = 0.0 inches


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Borehole correction for deep induction - standoff = 1.5 inches

Note that the abbreviations shown above are those used in this FORTRAN program and do not conform toabbreviations used in this Handbook. Hole size is in inches and correction to the code for metric dimensions isrequired. Charts for these formulae are given below for various tool types.


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Borehole correction for medium induction log


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Borehole correction for deep induction log

Borehole correction for deep laterolog (dual)


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Borehole correction for shallow laterolog (dual)

Borehole correction for laterolog (single)

It is instructive to determine the borehole corrections for some typical cases and run a sensitivity study with one ofthe saturation equations to see if the corrections have a measurable impact.

RESDc1 - Induction Log Borehole CorrectionsThe borehole signal for induction logs is subtracted from the induction conductivity measurement and reciprocatedto obtain corrected resistivity. 1: RESDc = 1000 / (1000 / RESD - BHGD) 2: RESMc = 1000 / (1000 / RESM - BHGM)

WHERE: BHGD = deep resistivity correction (mS/m) BHGM = medium resistivity correction (mS/m) RESD = deep resistivity reading (ohm-m) RESDc = deep resistivity corrected for borehole effect (ohm-m) RESM = medium resistivity reading (ohm-m) RESMc = medium resistivity corrected for borehole (ohm-m)


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COMMENTS:The values for BHGD and BHGM are to be taken from charts similar to those shown below, or from curve fits to thesecharts. Some computer programs use a look-up table. These charts are for Schlumberger’s 6FF40 tool. Differentcharts and look-up tables are needed for other induction logging tool designs.

RESDc2 - Laterolog Borehole CorrectionsThe borehole correction for laterologs is a correction factor which is divided into the original log reading to obtainthe corrected value. 3: RESDc = RESD / CFD 4: RESMc = RESM / CFM 5: RESEDITFLAG$ = "BH"

WHERE: CFD = borehole effect correction factor for deep laterolog CFM = borehole effect correction factor for shallow laterolog RESD = deep resistivity reading (ohm-m) RESDc = deep resistivity corrected for borehole effect (ohm-m) RESM = medium resistivity reading (ohm-m) RESMc = medium resistivity corrected for borehole (ohm-m)

COMMENTS:The values for CFD and CFM are to be taken from appropriate charts, or from curve fits to these charts. Somecomputer programs use a look-up table. These charts are for Schlumberger’s DLL tool. Different charts and look-uptables are needed for other laterolog tool designs.

INVASION CORRECTIONSThe second correction is for the effects of invasion of mud filtrate into the formation. Knowledge of the invasionprofile can be used to correct the deep resistivity log for this effect. The profile knowledge comes from the mediumand shallow resistivity data when compared to the deep resistivity. Correction charts are available for various tooltypes, and are usually known as Tornado Charts due to the shape of the lines on the graph.

Sometimes the log data does not fit inside the body of lines on the chart. A pragmatic solution is to lower the deepresistivity by a an offset based on the difference between the logarithm of the shallow resistivity and the logarithm ofthe medium resistivity. An example is shown below. The equations to run standard invasion corrections follow. Notethe warning at the end of this section.

Original logs showing deep invasion on resistivity, with hydrocarbon volume (shaded red) and water saturationbased on the deep resistivity as recorded.

Invasion corrected deep resistivity (dashed purple) is a linear shift of the logarithm of the original deep resistivity(dashed red). Note that the water zone now looks wet, the zone no longer triggers a pay flag, and original

hydrocarbon -- water contact is now more clearly defined in this depleted reservoir.

In the above example, the need for invasion corrections is inferred from the fact that no oil or gas was produced fromthe perforations annotated at the top of the zone. If hydrocarbons had been produced, the deep resistivity wouldneed to be increased. The published Tornado Charts for induction logs never increase resistivity, so they are meantonly for wet or depleted intervals.


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RESDc3 - Invasion Correction for Induction LogsThe invasion corrections for dual induction logs are computed as follows: 6: IF RESD < RESM 7: AND IF RESM < RESS 8: THEN H = RESS / RESD - 1 9: B = RESM / RESD - 1 10: C = H / B 11: D = 0.59 * H - 2.21 * C + 1.35 12: E = -1.44 * H + 2.47 * C - 2.76 13: G = - 0.5 * (D ^ 2 - 4 * E) ^ 0.5 + D) 14: IF RESD >= RESM 15: OR IF RESM >= RESS 16: THEN G = 1.0 17: RESDc = G * RESD

WHERE: B = intermediate term C = intermediate term D = intermediate term E = intermediate term G = intermediate term H = intermediate term RESD = deep resistivity log reading (ohm-m) RESDc = deep resistivity log reading corrected for invasion (ohm-m) RESM = medium resistivity log reading (ohm-m) RESS = shallow resistivity log reading (ohm-m)

COMMENTS:If the medium and deep resistivity logs read the same value, then either no correction is needed because invasion isvery shallow, or no correction is possible because invasion is extremely deep. These formulae are shown graphicallybelow. Newer tools need different charts.

RESDc is often called Rt, the "true" resistivity - see warning below.


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Invasion correction for dual induction

CRAIN'S OPINIONATED OPINIONCAUTION: The invasion correction for induction logs as defined by service company charts always

reduces Rt. This is fine in a water zone but is dead wrong in oil or gas zones, where Rt is usualy too lowdue to invasion of water. Lowering it even more is just too dumb for words. Therefore, DO NOT apply

invasion corrections from these charts in hydrocarbon zones. Most software allows you to turn off theseoffensive corrections.

Below is a sample sensitivity analysis that shows the correction factor Rt/RESD is greater than 1.0 for many realsituations. The same factor (Rt/Rild) on above graph is never greater than 1.0.

SENSITIVITY ANALYSIS

WATER SATURATION AND RESISTIVITY WITH INVASION

Archie's EquationSw = (A * RW@FT / (PHIe ^ M) / Rt) ^ (1 / N)

Assume A=1.0, M = N = 2.0Sw = (RW@FT / (PHIe ^ 2) / Rt) ^ 0.5

Rearrange termsSw^2 = (RW@FT / (PHIe ^ 2) / Rt)

Solve for Rt in uninvaded oil zoneRt= (RW@FT / (PHIe ^ 2) / Sw^2)


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Solve for Rxo in invaded oil zoneRxo= (RMF@FT / (PHIe ^ 2) / Sxo^2)

Solve for R0 in uninvaded water zoneR0= (RW@FT / (PHIe ^ 2)

Assume RESD gets 50% of signal from invaded zone and 50% from uninvaded zoneRESD = 1 / ((1 / Rt + 1 / Rxo) / 2)

Solve for SWa in invaded oil or water zoneSwa = (RW@FT / (PHIe ^ 2) / RESD) ^ 0.5

Multiply deep resistivity (RESD) by Rt/RESD ratio to obtain Rt from RESD

INVADED OIL ZONE Sw=0.25 RMF@FT=1.000 Sxo=0.6 Sxo=0.8 Sxo=1.0 Sw=1.0

RW@FT PHIe Rt Rxo R0 RESD SWa Rt/RESD Rt/RESD Rt/RESD Rt/RESD0.25 0.25 64.0 44.4 4.0 52.5 0.28 1.22 1.78 2.50 0.630.25 0.15 177.8 123.5 11.1 145.7 0.28 1.22 1.78 2.50 0.630.10 0.25 25.6 44.4 1.6 32.5 0.22 0.79 1.01 1.30 0.550.10 0.15 71.1 123.5 4.4 90.2 0.22 0.79 1.01 1.30 0.550.03 0.25 7.7 44.4 0.5 13.1 0.19 0.59 0.65 0.74 0.520.03 0.15 21.3 123.5 1.3 36.4 0.19 0.59 0.65 0.74 0.52

INVADED OIL ZONE Sw=0.25 RMF@FT=0.50 Sxo=0.6 Sxo=0.8 Sxo=1.0 Sw=1.0


INVADED OIL ZONE Sw=0.25 RMF@FT=0.25 RMF@FT Sxo=0.6 Sxo=0.8 Sxo=1.0 Sw=1.0


INVADED OIL ZONE Sw=0.25 RMF@FT=0.10 RMF@FT Sxo=0.6 Sxo=0.8 Sxo=1.0 Sw=1.0



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NUMERICAL EXAMPLE:1. For example, the data for Sand D gives:RESS = 2.0RESM = 1.5RESD = 1.0H = 2.0 / 1.0 - 1 = 1.0B = 1.5 / 1.0 - 1 = 0.5C = 1.0 / 0.5 = 2.0D = 0.59 * 1.0 - 2.21 * 2.0 + 1.35 = -2.48G = - 0.5 * (2.48 ^ 2 - 4 * 0.74) ^ 0.5) - 2.48) = 0.35RESDc = 0.35 * 1.0 = 0.35

Thus, invasion is so deep that the dual induction reads nearly three times too high. If this is a water zone, thecorrection is reasonable. If it is hydrocarbon bearing, the correction makes no sense.

RESDc4 - Invasion Correction for LaterologsThe invasion corrections for dual laterologs are computed as follows: 18: IF RESD / RESS <= 1 19: THEN RESDc = 1.7 * RESD - 0.7 * RESM 20: IF RESD / RESM >= 1.1 21: THEN RESDc = 1.1 * RESD 22: C = RESM / RESS * (RESD - RESS) / (RESD - RESM) 23: IF C = 1 / 1.7 24: THEN RESDc = RESD 25: IF C # 1 / 1.78 26: THEN RESDc = 2.18 * C * RESD / (1.78 * C - 1) 27: OTHERWISE RESDc = RESD

WHERE: C = intermediate term RESD = deep resistivity log reading (ohm-m) RESDc = deep resistivity log reading corrected for invasion (ohm-m) RESM = medium resistivity log reading (ohm-m) RESS = shallow resistivity log reading (ohm-m)

COMMENTS:If the medium and deep resistivity logs read the same value, then either no correction is needed because invasion isvery shallow, or no correction is possible because invasion is extremely deep. These formulae are shown graphicallybelow. Newer tools need different charts.


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Invasion correction for dual laterolog

This chart can raise or lower the Rt. Use the correction only if the correction raises Rt. The reader is encouraged torun a sensitivity analysis, similar to the one shown earlier for induction logs, for the laterolog in a salt mud case anda fresh mud case.

NUMERICAL EXAMPLE:1. Assume a dual laterolog had been run, the log might have read:RESD = 2.0RESM = 1.5RESS = 1.0C = 1.5 / 1.0 * (2.0 - 1.0) / (2.0 - 1.5) = 3.00RESDc = 2.18 * 3.00 * 2.0 / (1.78 * 3.00 - 1) = 3.00

CALCULATING DIAMETER OF INVASIONThe invasion correction described above can also be used to calculate an apparent invasion diameter (Di). On somemodern logs, this result is calculated by the service company. The generic formulae are:


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Di - Diameter of InvasionFor dual induction logs: 30: C = (RESM / RESDc) * (RESD - RESDc) / (RESM - RESD) 31: Di = 33 * (C + 1) - min (100, 10 ^ (0.5 * C - 0.04))

For dual laterolog: 32: IF RESDc / RESD > 1 33: THEN Di = 10 ^ (RESDc / RESD - 1) 34: IF RESDc / RESD < 1 35: THEN Di = 160 * (1 - RESD / RESDc) 36:: OTHERWISE Di = 0.0

WHERE: Di = diameter of invasion (inches) RESD = deep resistivity log reading (ohm-m) RESDc = corrected deep resistivity reading (ohm-m) RESM = medium resistivity log reading (ohm-m)

COMMENTS:Di is in inches; multiply by 25.4 to get millimeters.

If RESDc / RESD = 1; Di cannot be determined.

While diameter of invasion is not used to correct other data, it is a useful quality control indicator.

NUMERICAL EXAMPLE:1. Data for Sand D gives:RESS = 2.0RESM = 1.5RESD = 1.0RESDc = 0.35 from previous example

C = (1.5 / 0.35) * (1.0 - 0.35) / (1.5 - 1.0) = 5.57Di = 33 * (5.57 + 1) - min (100, 10 ^ (0.5 * 5.57 - 0.04)) = 116 inches

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