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B ASIC WELL L OGGING A NALYSIS – L OG I NTERPRETATION Hsieh, Bieng-Zih Fall 2009 1

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A RCHIE E QUATION S W Water saturation (S w ) of a reservoir’s uninvaded zone is calculated by the Archie (1942) formula. Where: S w ＝ water saturation of the uninvaded zone (Archie method) R w ＝ resistivity of formation water at formation temperature R t ＝ true resistivity of formation Φ ＝ porosity a ＝ tortuosity factor (1.0 for carbonates; 0.81 for consolidated sandstone; 0.62 for unconsolidated sandstone) m ＝ cementation exponent (2.0 for carbonates and consolidated sandstone; 2.15 for unconsolidated sandstone) n ＝ saturation exponent (normally equal to 2.0) 2

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A RCHIE E QUATION S W (C ONT.) The uninvaded zone’s water saturation (S w ), determined by the Archie equation, is the most fundamental parameter used in log evaluation. But, merely knowing a zone’s water saturation (S w ) will not provide enough information to completely evaluate a zone’s potential productivity. A geologist must also know whether: (1) hydrocarbons are moveable, (2) water saturation is low enough for a water- free completion, (3) the zone is permeable, and (4) whether (volumetrically) there are economic, recoverable hydrocarbon reserves. 3

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A RCHIE E QUATION S XO Water saturation of a formation’s flushed zone (S xo ) is also based on the Archie equation, but two variables are changed: Where: S xo ＝ water saturation of the flushed zone R mf ＝ resistivity of the mud filtrate at formation temperature R xo ＝ shallow resistivity 4

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A RCHIE E QUATION S XO (C ONT.) Water saturation of the flushed zone (S xo ) can be used as an indicator of hydrocarbon moveability. For example, if the value of S xo is much larger than S w, then hydrocarbons in the flushed zone have probably been moved or flushed out of the zone nearest the borehole by the invading drilling fluids (R mf ). 5

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R ATIO M ETHOD The Ratio Method identifies hydrocarbons from the difference between water saturations in the flushed zone (S xo ) and the uninvaded zone (S w ). When water saturation of the uninvaded zone (S w ) is divided by water saturation of the flushed zone (S xo ), the following results: 6

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R ATIO M ETHOD – WITHOUT KNOWING POROSITY When S w is divided by S xo, the formation factor ( F ＝ a/ Φ m ) is cancelled out of the equation because formation factor is used to calculate both S w and S xo. This can be very helpful in log analysis because, from the ratio of (R xo /R t )/(R mf /R w ), the geologist can determine a value for both the moveable hydrocarbon index (S w /S xo ) and water saturation by the Ratio Method without knowing porosity. Therefore, a geologist can still derive useful formation evaluation log parameters even though porosity logs are unavailable. 7

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R ATIO M ETHOD -- MOVEABLE HYDROCARBON INDEX Formulas for calculating the moveable hydrocarbon index and water saturation by the Ratio Method are: If the ratio S w /S xo is equal to 1.0 or greater, then hydrocarbons were not moved during invasion. Whenever the ratio of S w /S xo is less than 0.7 for sandstones or less than 0.6 for carbonates, moveable hydrocarbons are indicated (Schlumberger, 1972). 8

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R ATIO M ETHOD To determine water saturation (S w ) by the Ratio Method, you must know the flushed zone’s water saturation. In the flushed zone of formations with moderate invasion and “average” residual hydrocarbon saturation, the following relationship is normally true: by substituting the above equation in the relationship: 9

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R ATIO M ETHOD Where: S wr ＝ water saturation uninvaded zone, Ratio Method 10

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R ATIO M ETHOD – Q UALITY CHECK After the geologist has calculated water saturation of the uninvaded zone by both the Archie and Ratio methods, he should compare the two values using the following observations: (1) If S w (Archie) ≈ S w (Ratio) the assumption of a step-contact invasion profile is indicated to be correct, all values determined (S w, R t, R xo, and d i ) are correct. 11

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R ATIO M ETHOD – Q UALITY CHECK (2) If S w (Archie) ＞ S w (Ratio) the value for R xo /R t is too low. R xo is too low because invasion is very shallow, or R t is too high because invasion is very deep. Also, a transition type invasion profile may be indicated S w (Archie) is considered a good value for S w 12

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R ATIO M ETHOD – Q UALITY CHECK If S w (Archie) ＜ S w (Ratio) the value for R xo /R t is too high because of the effect of adjacent, high resistivity beds an annulus type invasion profile may be indicated or S xo ＜ S w 1/5 13

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R ATIO M ETHOD – Q UALITY CHECK In the case of S w (Archie) ＜ S w (Ratio), a more accurate value for water saturation can be estimated using the following equation (from Schlumberger, 1977): Where: (S w ) COR ＝ corrected water saturation of the uninvaded zone S wa ＝ water saturation of the uninvaded zone (Archie Method) S wr ＝ water saturation of the uninvaded zone (Ratio Method) 14

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B ULK V OLUME W ATER The product of a formation’s water saturation (Sw) and its porosity ( Φ ) is the bulk volume of water (BVW). If values for bulk volume water, calculated at several depth in a formation, are constant or very close to constant, they indicate that the zone is homogeneous and at irreducible water saturation (S w irr ). 15

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B ULK V OLUME W ATER When a zone is at irreducible water saturation, water calculated in the uninvaded zone (S w ) will not move because it is held on grains by capillary pressure. Therefore, hydrocarbon production from a zone at irreducible water saturation should be water-free (Morris and Biggs, 1967). 16

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B ULK V OLUME W ATER A formation not at irreducible water saturation (S w irr ) will exhibit wide variations in bulk volume water values. Figure 39 illustrates three crossplots of porosity ( Φ ) versus S w irr for three wells from the Ordovician Red River B-zone, Beaver Creek Field, North Dakota. Note, that with increasing percentages of produced water, scattering of data points from a constant value of BVW (hyperbolic lines) occurs. 17

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P ERMEABILITY F ROM L OGS Log-derived permeability formulas are only valid for estimating permeability in formations at irreducible water saturation (S w irr ; Schlumberger, 1977). The common method for calculating log-derived permeability is the Wyllie and Rose (1950) formulas. 19

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P ERMEABILITY F ROM L OGS Before these formulas can be applied, a geologist must first determine whether or not a formation is at irreducible water saturation. Whether or not a formation is at irreducible water saturation depends upon bulk volume water (BVW ＝ S w × Φ ) values. When a formation’s bulk volume water values are constant, a zone is at irreducible water saturation. If the values are not constant, a zone is not at irreducible water saturation. 20

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P ERMEABILITY F ROM L OGS The Wyllie and Rose (1950) method for determining permeability utilizes the following two formulas: Where: K 1/2 ＝ square root of permeability (K is equal to permeability in millidarcies) Φ ＝ porosity S w irr ＝ water saturation (Sw) of a zone at irreducible water saturation 21

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H OMEWORK #6 -- L OG I NTERPRETATION 23

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H OMEWORK #6 24 Rxo Rt

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H OMEWORK #6 – L OG I NTERPRETATION DepthRxoRt Φ Sw Sxo Sw/SxoSwrBVWK 7600 7610 7620 …. 7840 7850 25 Information: Consolidated sandstone a = 0.81 m = 2.0 n = 2.0

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