2 Archie Equation SwWater saturation (Sw) of a reservoir’s uninvaded zone is calculated by the Archie (1942) formula.Where:Sw＝ water saturation of the uninvaded zone (Archie method)Rw＝ resistivity of formation water at formation temperatureRt＝ true resistivity of formationΦ＝ porositya ＝ 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)
3 Archie Equation Sw (Cont.) The uninvaded zone’s water saturation (Sw), determined by the Archie equation, is the most fundamental parameter used in log evaluation.But, merely knowing a zone’s water saturation (Sw) 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.
4 Archie Equation SxoWater saturation of a formation’s flushed zone (Sxo) is also based on the Archie equation, but two variables are changed:Where:Sxo＝ water saturation of the flushed zoneRmf＝ resistivity of the mud filtrate at formation temperatureRxo＝ shallow resistivity
5 Archie Equation Sxo (Cont.) Water saturation of the flushed zone (Sxo) can be used as an indicator of hydrocarbon moveability.For example, if the value of Sxo is much larger than Sw, then hydrocarbons in the flushed zone have probably been moved or flushed out of the zone nearest the borehole by the invading drilling fluids (Rmf).
6 Ratio MethodThe Ratio Method identifies hydrocarbons from the difference between water saturations in the flushed zone (Sxo) and the uninvaded zone (Sw).When water saturation of the uninvaded zone (Sw) is divided by water saturation of the flushed zone (Sxo), the following results:
7 Ratio Method – without knowing porosity When Sw is divided by Sxo, the formation factor (F＝a/Φm) is cancelled out of the equation because formation factor is used to calculate both Sw and Sxo.This can be very helpful in log analysis because, from the ratio of (Rxo/Rt)/(Rmf/Rw), the geologist can determine a value for both the moveable hydrocarbon index (Sw/Sxo) 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.
8 Ratio Method -- moveable hydrocarbon index Formulas for calculating the moveable hydrocarbon index and water saturation by the Ratio Method are:If the ratio Sw/Sxo is equal to 1.0 or greater, then hydrocarbons were not moved during invasion.Whenever the ratio of Sw/Sxo is less than 0.7 for sandstones or less than 0.6 for carbonates, moveable hydrocarbons are indicated (Schlumberger, 1972).
9 Ratio MethodTo determine water saturation (Sw) 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:
10 Ratio MethodWhere: Swr ＝ water saturation uninvaded zone, Ratio Method
11 Ratio Method – Quality 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 Sw (Archie) ≈ Sw (Ratio)the assumption of a step-contact invasion profile is indicated to be correct,all values determined (Sw, Rt, Rxo, and di) are correct.
12 Ratio Method – Quality check (2) If Sw (Archie) ＞ Sw (Ratio)the value for Rxo/Rt is too low.Rxo is too low because invasion is very shallow, or Rt is too high because invasion is very deep.Also, a transition type invasion profile may be indicatedSw (Archie) is considered a good value for Sw
13 Ratio Method – Quality check If Sw (Archie) ＜ Sw (Ratio)the value for Rxo/Rt is too high because of the effect of adjacent, high resistivity bedsan annulus type invasion profile may be indicatedor Sxo ＜ Sw1/5
14 Ratio Method – Quality check In the case of Sw (Archie) ＜ Sw (Ratio), a more accurate value for water saturation can be estimated using the following equation (from Schlumberger, 1977):Where:(Sw)COR ＝ corrected water saturation of the uninvaded zoneSwa ＝ water saturation of the uninvaded zone (Archie Method)Swr ＝ water saturation of the uninvaded zone (Ratio Method)
15 Bulk Volume WaterThe 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 (Sw irr).
16 Bulk Volume WaterWhen a zone is at irreducible water saturation, water calculated in the uninvaded zone (Sw) 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).
17 Bulk Volume WaterA formation not at irreducible water saturation (Sw irr) will exhibit wide variations in bulk volume water values.Figure 39 illustrates three crossplots of porosity (Φ) versus Sw 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.
19 Permeability From Logs Log-derived permeability formulas are only valid for estimating permeability in formations at irreducible water saturation (Sw irr; Schlumberger, 1977).The common method for calculating log-derived permeability is the Wyllie and Rose (1950) formulas.
20 Permeability From Logs 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＝Sw× 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 .
21 Permeability From Logs The Wyllie and Rose (1950) method for determining permeability utilizes the following two formulas:Where:K1/2 ＝ square root of permeability (K is equal to permeability in millidarcies)Φ＝ porositySw irr ＝ water saturation (Sw) of a zone at irreducible water saturation