PetEvalCh7.pdf

7Saturation Determination7

CONTENTS

1 INTRODUCTION

2 DETERMINATION OF SATURATION INCLEAN FORMATIONS

3 RESISTIVITY VS POROSITY CROSSPLOTS

4 MICRORESISTIVITY VS POROSITYCROSSPLOTS

5 LOGARITHMIC OVERLAYS

6 RO AND F OVERLAY

7 RESISTIVITY RATIO METHODS

8 SHALY FORMATIONS

APPENDIX - DETERMINATION OF Rw

LIST OF INTERPRETATION CHARTS FORCHAPTER 7

12

LEARNING OBJECTIVES

Having worked through this chapter the Student will be able to:

1. Determine the saturation of a rock using various techniques.

2. Describe the Archie Equation and define the terms in the equation.

3. Describe the source of the formation resistivity factor and typical values for n,m and a.

4. Describe the potential errors in the results from the Archie equation.

5. Describe the technique and the assumptions used for deriving saturation froma crossplot of resistivity logs and porosity logs.

6. Describe the technique and the assumptions used for deriving saturation fromRwa.

7. Describe the technique and the assumptions used for deriving saturation fromlogarithmic overlays.

8. Describe the technique and the assumptions used for deriving saturation fromRo overlay and F overlay.

9. Describe the technique and the assumptions used for deriving saturation fromResistivity Ratio Methods.

10. Describe the Impact of Shale on the determination of saturation.

11. Describe the Laminated sand-shale models, the Dispersed Shale Model and thetotal shale model.

Institute of Petroleum Engineering, Heriot-Watt University 3


1 INTRODUCTIONWater saturation is the fraction (or percentage) of the pore volume of the reservoir rockthat is filled with water. It is generally assumed, unless otherwise known, that the porevolume not filled with water is filled with hydrocarbons. Determining water andhydrocarbon saturation is one of the basic objectives of well logging.

2 DETERMINATION OF SATURATION IN CLEAN FORMATIONS

All water saturation determinations from resistivity logs in clean (nonshaly) formationswith homogeneous intergranular porosity are based on Archies water saturationequation, or variations thereof. The equation is:

Swn =

F RR

w

t

whereR

wis the formation water resistivity (see Appendix 1),

Rt is the true formation resistivity (see Chapter 4),and

F is the formation resistivity factor.

F is usually obtained from the measured porosity of the formation through therelationship shown in Chart Por-1.

F = a / m

For Sxo

, the water saturation in the flushed zone, a similar expression exists:

Sxon

= F RR

mf

xo

whereR

mf is the mud filtrate resistivity, andR

xois the flushed zone resistivity.

In these equations, the saturation exponent n is usually taken as 2. Laboratoryexperiments have shown that this is a good value for average cases. The values of aand m in Equation 2 are subject to more variation:

in carbonates, F = 1/2 is usually used;in sands, F = 0.62/2.15 (Humble formula), orF = 0.81/2 (a simpler form practically equivalent to the Humble formula).

Equation 1 (with n = 2) is solved, in nomograph form, in Chart Sw-1.

Within their normal range of application, these two ways of expressing the Humbleformula yield quite similar results.

Equation 1Archies water saturationequation

Equation 2Formation ResistivityFactor

Equation 3Water saturation in theflushed zone

14

While the Humble formula is satisfactory for sucrosic rocks, better results are

obtained using F = 1/2.2 to 1/2.5 in compact or oolicastic rocks. In some

severely oolicastic rocks, m may even be as high as 3.

The accuracy of the Archie equation (Equation 1 and 3) depends in large measure,of course, on the accuracy of the fundamental input parameters: R

w, F, and R

t. The deep

resistivity measurement (induction or laterolog ) must be corrected, therefore, forborehole, bed thickness, and invasion. The most appropriate porosity log (sonic,neutron, density, or other) or combination of porosity and lithology measurementsmust be used to obtain porosity, and the proper porosity-to-formation factor relation-ship must be used. Finally, the R

w value should be verified in as many ways as possible:

calculation from the SP curve, water catalogue, calculation from nearby water-bearing formation, and/or water sample measurement.

Humble Equation Procedure:

Step 1: Determine from porosity acoustic, density or Neutron log.

Step 2: Determine F from Humble Formula

Step 3: Determine Rt from deep reading resistivity (induction or laterolog) log

corrected for borehole, bed thickness and invasion.

Step 4: Determine Rw from Appendix 1 of Chapter 7

Step 5: Determine Sw from the Archie Equation (Equation 1)

Chart Sw-1 may also be used to solve Equation 3 for the flushed zone watersaturation. To do this, the R

xo reading is inserted on the R

t leg of the nomograph and

the Rmf value is inserted in the Rw leg. Chart Sw-1 is constructed using the Humble

porosity-to-formation factor relationship. For any other porosity-to-formation factorrelationship the nomograph should be entered with the formation factor.

Flushed Zone in Humble Formula Procedure:

Step 1: Determine f from porosity acoustic, density or Neutron log.


Step 3: Determine and use Rxo from shallow resistivity log in place of Rt from deep reading resistivity log

Step 4: Determine and use Rmf in place of Rw

Step 5: Determine Sw from the Archie Equation (Equation 1)



Resistivity vs Porosity CrossplotCombining Equation 1 and 2, the Archie saturation equation may be written

Swn =

a R R

w

m

t

If n and m are equal to 2, and a = 1, then

S = R .w w / Rt

Equation 5 shows that for Rw constant, S

w is proportional to ; 1/Rt. S

w is the

quantity of water per unit volume of formation. To emphasise the proportionalitybetween and 1/Rt, Equation 5 may be rewritten:

= RS

Rw

w t

1

For a 100% water-saturated formation, Sw = 1 and R

t = R

o. If R

o for water-saturated

formations is plotted on an inverse square-root scale versus , all points should fallon a straight line given by = Rw/Ro.

Furthermore, the points corresponding to any other constant value of Sw will also fall

on a straight line, since in Equation 6 the coefficient,Rw/Sw, is constant for constantvalues of R

w and S

w.

Instead of an actual Rt value, it is usually satisfactory to plot the log reading of the deep

resistivity device provided the readings are not much influenced by invasion of otherenvironmental factors (e.g., from a deep induction log or deep laterolog).

Figure 1 shows several points plotted over an interval in which formation-waterresistivity is constant (as indicated by constant SP deflections opposite the thick, cleanpermeable beds). Assuming that at least some of the points are from 100% water-bearing formations, the line for S

w = 1 is drawn from the pivot point ( = 0, R

t = )

through the most north-westerly plotted points. The slope of this line defines the valueof R

w. As shown on Figure 1, for = 10%, R

o = 6.5 ohm-m. For this formation, the

most appropriate F - relation is F = 1/2. Thus, for = 10%, F = 100. Since Rw =

Ro/F, R

w = 6.5/100 = 0.065 ohm-m as shown.

For other Sw values, R

t and R

o are related by the equation R

t = R

o/ . For S

w = 50%, = 4,

and Rt = 4 R

o. This relation establishes the line for S

w = 50%.

Equation 4Archies water saturationequation - modified

Equation 5Simplified Archie's watersaturation equation

Equation 6Porosity from Archie'sequation

16

On Figure 1, for the same porosity as before ( = 10%), Rt = 4, R

o = 4 x 6.5 = 26 ohm-

m gives a point that defines the line for Sw

= 50%.

Other Sw

lines may be defined in asimilar manner.

Charts Appendix A3 and A4 provide blank grids for making resistivity-porositycrossplots. Chart A4 is used when F = 1/2 is the more appropriate formation factor-porosity relationship and Chart A3 is used when F = 0.62/2.15 is more appropriate.

If the matrix composition remains constant over the formations under investigation,the basic measurement from the sonic, density, or neutron logs can be plotted directlyversus R

t with similar results. This is possible because of the linear relationship

between porosity and bulk density, sonic transit time or neutron hydrogen indexresponse. An example of a sonic-induction crossplot is shown in Figure 2. The transittime has been plotted against the induction resistivity for several levels. The north-westerly points define the 100% water saturation line. The transit time value at the

Figure 1Resistivity-PorosityCrossplot for determiningRw and Sw



point where this line intersects the horizontal line of infinite resistivity is the matrixtransit time, t

ma. In Figure 2, t

ma is found to be approximately 47.5 ms/ft (156 ms/m),

corresponding to a matrix velocity of 21,000 ft/sec (6,400 m/s).

By knowing tma

, a porosity scale, from Chart Por-3, and a scale of formation factor(e.g., from F = 1/2 using Chart Por-1) can be easily derived. A vertical line drawnthrough F = 100 (or = 10) intersects the water line at R

o = 5 ohm-m; accordingly,

Rw

(= Ro/F) is 0.05 ohm-m.

The lines for other Sw values are straight lines, determined as previously described,

radiating out from the Rt = , t

ma = 47.5 pivot point.

Density and neutron logs can be crossplotted against resistivity in a manner identicalto the sonic logs. For density logs, the intersection of the 100% water line with theinfinite resistivity line yields the matrix density value,

ma. For neutron logs, the

intersection defines the matrix hydrogen index, or apparent matrix porosity. Knowledgeof matrix density or hydrogen index permits the b or N scale to the rescaled in andF units. With the F scale defined, R

w can be calculated as for the sonic-resistivity

crossplot, and lines of constant water saturation can be constructed in a similarmanner.

These resistivity-versus-porosity crossplots require that formation water resistivity beconstant over the interval plotted, that lithology be constant, that invasion not be deep,and that the measured porosity log parameter (i.e., t, b, N) can be linearly related toporosity. This last condition implies that the time average transform for theconversion of t into porosity is appropriate.

Figure 2Sonic-Induction Crossplot

18

The neutron-resistivity crossplot is not as satisfactory in gas-bearing formations as thesonic- or density-resistivity crossplots. The apparent porosity measured by theneutron log in gas zones is often much too low. This results in pessimistic S

w values

in gas zones. Indeed, in a gas zone, the neutron-resistivity may indicate a porous gas-bearing zone, the neutron-resistivity may indicate a porous gas-bearing zone to be nearzero porosity and 100% water bearing. In contrast, the sonic- or density-resistivitytends to be slightly optimistic in gas zones (i.e., porosities may be slightly high andwater saturations slightly low).

Resistivity vs Porosity Crossplot Procedure:

Step 1: Determine for a number of zones from porosity acoustic, density orNeutron log.

Step 2: Determine the resistivity Rt of the zones from a deep reading resistivity

log

Step 3: Plot the values of (on a linear scale) versus Rt (on an inverse square rootscale).

Step 4: Draw a line through the average points in the northwest part of the plot. If

water zones are present in the zone this line represents the water (or

100% Sw) line. The values of Rt along this line represent the resistivity

of the water-saturated formations, Ro. The extrapolation of this line to

zero conductivity defines the matrix travel time.

Step 5: Check the matrix value derived in Step 4 against the value of matrix travel

time derived from other sources. This is a good check for errors in the

100%Sw line.

Step 6: For other Sw values, R

t and R

o are related by the equation R

t = R

o/ .

For Sw = 50%, = 4, and R

t = 4 R

o. This relation establishes the line

for Sw = 50%. Calculate the relationship between Rt and Ro for various

values of Sw from the equation. Plot the values of Ro for Sw = 10%,

20%, 30% and 50%, using the above relationship, for a set of porosities.

Step7: Determine Sw in the zones of interest, from the position of the plotted

points in relation plot saturation lines.

Microresistivity vs Porosity CrossplotsA resistivity-porosity plot can also be made using the values from a shallow-investigation resistivity log, such as the microlaterolog or MicroSFL log. If themicroresistivity log reads substantially R

xo, 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-resistivityplot does not give a clear answer because of hydrocarbon saturation. The F R

mf lineshould be easier to determine since S

xo is usually fairly high even in hydrocarbon-

bearing formations.

Figure 3 shows a resistivity-porosity plot in which both the deep induction readingand the microlaterolog at the same levels are plotted in a series of water-bearingformations. The porosity values were derived in this case from a neutron-densitycrossplot. The plots from the two logs define two trends corresponding respectivelyto S

w = 1 (using deep induction) and S

xo = 1 (using microlaterolog data). The points

not in these trends can be divided into two groups.

1. Points whose microlaterolog readings fall on the Sxo

= 1 line but whose deep induction log readings fall below the S

w = 1 line (Points 2, 9, 10) are probably

the result of either deep invasion or adjacent-bed effect in which RID is greater than R

t.

2. Points whose induction log readings fall on the Sw = 1 line but whose

microlaterolog points fall above the Sxo

= 1 line are possibly due to shallowinvasion in which RMLL is lower than Rxo.

Resistivity-porosity plots are thus often more informative if the short-spaced resistivityvalues are also plotted. Not only does this permit an appreciation of invasion effectsbut it may also indicate moved oil.

Rwa

Comparison

Figure 3Resistivity-porositycrossplot showing pointsfrom deep induction andmicrolaterolog.S

w = 1 and S

xo = 1 lines are

shown. (After Baird, 1968)

110

If water saturation is assumed to be 100%, the Archie water saturation equation(Equation1) reduces to

Rwa = RF

RF

t ID

The term Rwa

is used in Equation 7, rather than Rw, to indicate that this is an apparent

formation water resistivity. It is only equal to Rw in 100% water-bearing formations.

In hydrocarbon-bearing formations, Rwa

computed from Equation 7 will be greaterthan R

w. Indeed, by combining Equations 1 and 5, the relationship between S

w, R

wa,

and Rw can be shown to be

S Rw wa = Rw / .

The Rwa

technique can, therefore, be useful for identifying potential hydrocarbon-bearing zones and for obtaining R

w values.

In practice, Rwa

is obtained by simply dividing the deep induction resistivity (or deeplaterolog resistivity) by the formation factor obtained from a porosity log or acombination of porosity logs. To be most effective, either a continuous R

wa computation

is made over a long interval of the borehole or many individual manual computationsare made so as to approximate a continuous computation.

For manual computation of Rwa

, the logs are divided into sections of consistentlithology, shaliness, and R

w. The SP curve is most useful for this, but the GR,

resistivity, and other curves should be consulted. The log readings, deep resistivityand porosity (t, b, or N), are read and tabulated, and the corresponding values of Rwaare calculated. Various charts are helpful in these calculations. For example, ifporosity is obtained from the FDC* formation density or Lith-Density* log, ChartPor-5 can be used for porosity calculation, Chart Por-1 can be used to convertporosity to formation factor, and Chart Sw-1 (in reverse starting at S

w= 100%) can

be used to make the Rwa

computation.

Since the Rwa

technique, as normally applied, requires that deep resistivity (Rdeep) Rt,invasion must be shallow enough that the deep resistivity reads essentially the sameas the true resistivity. In addition, R

w should be constant or vary in a consistent and

recognisable manner over the interpreted intervals, lithology should be essentiallyconstant and known, and permeable zones should be reasonably clean (i.e., shale free).If these conditions are fulfilled, the calculated R

wa values will approximate R

w values

in clean water-bearing sands. Usually, an Rwa

value at least three times that of Rw is

needed to indicate possible hydrocarbon potential; that corresponds to a watersaturation of less than 60%.

A useful feature of the Rwa

method is that foreknowledge of Rw

is not needed; indeed,if some reasonably clean water zones are included in the computations, their R

was are

Rw.

Equation 7

Equation 8



A continuous log of Rwa

can be recorded at the wellsite using resistivity and porositylogs. Figure 4 is an example computed from the BHC sonic log and induction-SFLlog combination. The R

wa combination indicates the lower sand to be predominately

water bearing with a good show of hydrocarbons at its top. Rw is indicated to be about

0.08 ohm-m by the consistent Rwa

computations over Interval C. Rwa

reaches 0.6 ohm-m at Level B in the top of this zone. That corresponds to a water saturation of 37%.The entire upper sand, Interval A, is indicated as hydrocarbon bearing by the R

wa

computations, assuming it contains formation water similar to that of the lower zone.Similar SP deflections in the two zones suggest this is the case.

A continuous Rwa

log provides ready visual identification of water- and hydrocarbon-bearing formations, changes in R

w, in lithology, etc.

Rwa to Rw Comparison Procedure:Step 1: Determine for a number of zones from porosity acoustic, density or

Neutron log.


Step 3: Determine the resistivity Rt of the zones of interest from a deep readingresistivity log

Figure 4Rwa Curve recorded onISF/sonic log

112

Step 4: Calculate Rwa from Equation 7.

Step 5: Determine the value of Rwa (assumed to be Rw) in clean water-bearingzones.

Step 6: Determine the values of Rwa in zones suspected on being hydrocarbonbearing.

Step 7: Calculate Sw in the hydrocarbon bearing zones of interest from Equation 8.

7.3 LOGARITHMIC OVERLAYS

Logarithmic scaling of resistivity and porosity logs is useful for wellsite interpreta-tions because of the properties of logarithms.

1. The logarithm of the product of two numbers is equal to the algebraic sum of the logarithms of the two numbers.

2. The logarithm of the quotient of two numbers is equal to the algebraic difference of the logarithms of the two numbers.

3. The logarithm of a number raised to the power, n, is equal to the product of n times the logarithm of the number.

On logarithmic scaling, the logarithm of a curve reading is proportional to the distancefrom the unity index line to the curve. Thus, near the bottom of Figure 5, the lengthof Line A is proportional to the logarithm of the deep resistivity measurement.Similarly, Line B is proportional to logarithm of F at the same level. The algebraicseparation between the two curves, Length A - Length B (= Length C) is proportionalto the algorithm of the ratio, Rdeep/F. Since Length A is less than Length B, thelogarithm of the ratio, in this case is negative. This means the value of the ratio is lessthan one. Then, measuring the Length C to the left of the index line and reading fromthe logarithmic scale, the value of the ratio is about 0.4.

For field use it is more convenient to evaluate the quotient (corresponding to theseparation, Length C) by using a transparent plastic logarithmic overlay scale applieddirectly to the separation between the curves.

Log F- Log Rdeep OverlayInstead of computing a continuous R

wa curve or a series of R

wa values, as explained

earlier, the formation factor, F, can be recorded directly (or traced) on logarithmicscale on the resistivity log. Then, log F could be compared to log Rdeep . WritingEquation 7 in terms of logarithms,

log log log R = R - Fwa deep Equation 9



Thus, log Rwa

, on a logarithmic scale, is simply the algebraic separation between thetwo curves, Rdeep and F.

To read the value of Rwa

, a transparent overlay scale of Exponent 1 is used. (Exponent1 means that the logarithmic scale is identical to the one on the field log.) At any givenlevel on the log the unity index line of the overlay is placed on the F curve. Then R

wa

is read directly from the position of the Rdeep curve relative to the scale. As shown inthe scales in Figure 5, R

wa is about 2.2 ohm-m for the upper level and about 0.027 ohm-

m for the lower level.

The value of F could be derived from any porosity log. The sonic log is most popularbecause it is more compatible with the resistivity log in shaley sands and it readilyrecognises gas zones but does not handle shaly sands very well. It is necessary, ofcourse, to record the F log on a logarithmic scaling that matches that of the resistivitylog.

RO and F OverlayIt would be just as easy to produce an R

o curve, for comparison with the Rdeep curve,

Figure 5The log Rdeep - log Foverlay

114

by adding the logarithm of Rw to the logarithm of F. This is done by shifting the F curve

a distance corresponding to the logarithm of Rw in respect to the resistivity grid. Thus,

since Ro = FR

w,

log log log R F Ro w= +

In case Rw is not known, this could be done by shifting the F curve until it overlays the

Rdeep curve in suspected water-bearing zones.

Apparent water saturation would be determined from the separation between Ro and

log Rdeep. Since = RO/RT RO/Rdeep.

2 S R Rw deeplog log logo

Thus, the separation between the Ro and Rdeep curves on a logarithmic scale will be

approximately twice the logarithm of Sw. S

w can be obtained by using a logarithmic

overlay in which one decade of Sw is equal in length to two decades of Rdeep or F. The

scaling is designated on Figure 6 by the expression Exponent 0.5.

To use the transparent overlay scale, the unity index line is placed on the Rdeep curve;S

w is read from the resulting position of the R

o curve on the scale. At the upper level

of Figure 6, Sw is indicated as about 11%.

The F overlay is a variation of the Ro overlay. S

w is determined by the separation on

the logarithmic scale between FR (as derived from the deep resistivity) and F. FR isdefined as:

Figure 6The R

o overlay

Equation 10

Equation 11



FR = RR

RR

deep

w

t

w

The meaning of FR in terms of Sw is seen by replacing Rt /Rw with FR in the Archie watersaturation equation to give

FR F

Sw2

In terms of logarithms, Equation 12 becomes

log log log R Rdeep w FR =

and Eq. 13 becomes

2 = F - Fw Rlog log logS

Thus, the log FR curve is found by shifting the logarithmic Rdeep curve by a distanceequal to log R

w (Figure 7). If R

w is not known, this shift could also be determined by

making the shift such that the FR and F curves overlay in water-bearing zones.

The Sw scaler used on the transparent overlay to read S

w is the same one used in Figure 6.

On Figure 7, Sw at the upper level is again indicated to be about 11%.

In the Ro overlay technique, the F curve is shifted relative to the Rdeep curve an amount

equal to log Rw. S

w (or more exactly, log S

w) is the resulting separation between the

two curves. In the F overlay technique, the Rdeep curve is shifted relative to the F curvean amount equal to log R

w.

Equation 12

Equation 13

Equation 14

Equation 15

116

4 RESISTIVITY RATIO METHODS

In resistivity ratio methods, it is assumed that a formation is divided into two distinctregions, a flushed or invaded zone and a non-invaded zone. Both zones have the sameF, but each contains water of a distinct resistivity (R

mf or Rz in the invaded zone andR

w in the non-invaded zone). The resistivities of the two zones must be measurable

or derivable from logs, and methods for determining the resistivity of the water in eachzone must be available.

Because of the necessary assumptions, the resistivity ratio methods have limitations,but when no porosity or formation factor data are available, they are sometimes theonly choice. The principal limitation arises from the inability of any resistivity deviceto measure either R

xo or R

t totally independent of the other. Simply put, invasion must

be deep enough to allow a shallow-investigating resistivity device to measure Rxo

butnot so deep that a deep resistivity device cannot measure R

t.

Another difficulty appears when hydrocarbons are present. In this case, someknowledge or assumption of the value of the flushed or invaded zone saturation isnecessary.

Flushed Zone MethodIf n = 2 is assumed and Equation 1 is divided by Equation 3,

SS

RR R

w

xo

t

mf w

2//

= Rxo

Figure 7The F overlay (log F-logFR).

Equation 16



This equation gives the ratio of Sw to S

xo, and no knowledge of formation factor or

porosity is needed. Rxo

may be found from a MicroSFL log, Rt from an induction or

laterolog, and Rmf /Rw from a measured values or from the SP curve.

The ratio Sw/S

xo,is valuable in itself as an index of oil movability. If S

w/S

xo = 1, then

no hydrocarbons have been moved by invasion, whether or not the formation containshydrocarbons. If S

w/S

xo is about 0.7 or less, movable hydrocarbons are indicated. The

value of Sw/S

xo along with and S

w, is useful in evaluating reservoirs.

To determine Sw

from Equation 16, Sxo

must be known. For moderate invasion andaverage residual oil saturation, an empirical relation between S

xo and S

w has been found

useful: Sxo

= Sw

1/5. Inserting this into Equation 16 gives:

S RR Rw

t

mf w =

Rxo //

58

Chart Sw-2 provides a solution of Equation 17 using the values of Rxo

/Rt and R

mf/Rw.Preferably, the chart is entered with R

mf/Rw; optionally, the SP can be used. Provisionis also made in the upper right portion of the chart for using values of S

or (residual oil

saturation) other than those given by the fifth-root relation.

The relationship Sxo

= Sw

1/5 is strictly empirical and may differ appreciably from the

actual case.

Invaded Zone MethodThe invaded zone method is useful for water saturation determination when only anES, IES, or other early resistivity log is available and no porosity log or formationfactor data exist. For application of the method, Ri /Rm must be at least 10.

Archies equation for the invaded zone is

Si2 =

FRT

z

t

where Rz is the resistivity of the water in the invaded zone. Because of incomplete

flushing, Rz is a mixture of mud filtrate, R

mf, and formation water, Rw.

Studies of many logs suggest that Si and Sw are related by

Si = Sw1

2

Dividing the non-invaded zone water saturation equation (Equation 1) by Equation19 and using the relationship presented in Equation 19 yields an expression for S

w:

S RR Rw

t

z w

= Ri /

/Equation 20

Equation 17

Equation 18

Equation 19

118

To use Equation 20, Rt is taken from a deep resistivity device such as a deep induction

or deep laterolog (corrected as necessary for borehole effect and bed thickness). Riis taken from a shallow resistivity device such as Laterolog 8, 16-in. normal, or SFL(corrected for borehole effect and bed thickness).

Rz is given by the relationship

1Rz

= z

R +

- z

Rw mf1

where z is the fraction of the invaded zone pore water, which is formation water, and1 - z is the fraction that is mud filtrate. Experience has indicated that z varies from0.075 in cases of normal invasion to 0.035 in cases of deep invasion or vuggyformations.

Figure 8 solves Equation 20. It is entered with Rmf /Rw on the appropriate z scale and

Ri/Rt (oblique lines) to determine Sw. When Ri/Rt is close to unity, some caution isrequired. The formation may be extremely invaded or there may be little invasion, orit may be dense and impermeable. On the other hand, many good hydrocarbon-bearing reservoirs will have Ri /R 1.0.

Porosity BalanceTo verify that invasion falls within the limits required by the resistivity ratio methods,the porosity balance can be used. It requires an independent value of porosity; thiscan be obtained from cores, logs, reservoir analysis, etc. This porosity check can

Figure 8Empirical resistivity-ratiomethod. (Ref. 4)

Equation 21



verify the applicability of the ratio method and the validity of the Sw value derived. If

the porosity check indicates the ratio method results are in error, the porosity balancewill indicate how the error can be corrected.

For comparison with the independent value of porosity, t, a porosity value,

c, is

derived from Swc

. (Swc

is the value of Sw from the ratio method chart. The subscript

t stands for the true value and the subscript c for the calculated value.) This is doneby computing a formation factor, F

c, from the relation

F RRc

t

w

= Swc2

and then deriving c using the appropriate F - relationship from Chart Por-1. Then:

1. If c =

t, the ratio method solution is correct and S

wc = S

w.

2 If c >

t, then F

c is too low and S

wc is too low. The ratio R

xo/R

t or Ri/Rt is too

low, probably because invasion is either deeper or shallower than one of theresistivity measurements can handle. The shallow resistivity (R

xo or Ri) is too low

because of shallow invasion or the deep resistivity (Rt) is too high because of deep

invasion.

a) If Rshallow/Rdeep < 1.4 and the induction was used for Rt, use RID = Rt in Equation 1

to find Sw.

b) If Rshallow/Rdeep > 1.4 and FRz > Rshallow, invasion is shallow. Use Rdeep = Rt in

Equation 1 to find Sw.

c) If Rshallow/Rdeep > 1.4 but FRz < Rshallow, invasion is deep. Equation 18 is solved

for Sw

(with Sw

= Si2).

3. If c >

t, then S

wc is too high. This occurs when R

xo/R

t or Ri /Rt is too high, as

might happen in the case of annulus. Equation 18 is used for Sw

determination (with Ss = Si2).

Invasion-Corrected Ratio MethodsThe uncertainty in invasion diameter can be eliminated by correcting the log databefore using it in a resistivity ratio interpretation method. This requires at least threeresistivity measurements of different depths of investigation.

The three resistivity measurements (corrected for borehole effect and bed thickness)are entered in the appropriate invasion correction chart and R

xo/R

t obtained. For

example, for the DIL-SFL data, Chart Rint -2b would be used (dependent on the Rxo

/R

m ratio). R

xoR

t is obtained, and ideally R

t, from the R

t/RID value. Rxo/Rt can then be

entered into Chart Sw-2 or Equation 16 to determine Sw.

The invasion correction charts generally assume a step profile of invasion. If atransition profile (one in which mud filtrate and formation water are intermixed) or anannulus profile exists, the R

xo/R

t and R

t /RID values given by the charts may be in error.

The porosity balance may be used to detect and correct the error. An independent

Equation 22

120

source of porosity, such as a porosity log, is required.

Rather than compare porosity computed from the ratio method saturation with trueporosity measured by the porosity log, the ratio method water saturation, S

wR, (i.e., Swfrom Equation 18) is compared to the Archie water saturation, S

wA, (i.e., Sw fromEquation 1). If S

wA and SwR are equal, the assumption of a step-contact invasion profileis verified, and all values found (S

w, R

xo/R

t, R

t/RID, Rt, di) are considered good.

If SwA > SwR, either invasion is very shallow or a transition type of invasion profile is

indicated. In these cases, SwA is considered the better value for Sw. If SwA < SwR, an

annulus type of invasion profile is indicated. In this case, a more accurate value canbe estimated using the relation:

Sw = S SSwA

wA

wR

14

Rxo

/Rt OverlayLogarithmic scaling of resistivity logs makes it possible to read saturations byoverlaying one resistivity log over another. This is done by applying a resistivity-ratiomethod directly on the logs and using a simple procedure involving the separationbetween the curves.

The equation for the water saturation ratio method was given in Equation 17. Thesimplest case is for R

mf = Rw; then Equation 17 reduces to Sw (Rx0/Rt)5/8 . To obtainS

wa a transparent overlay is used that corresponds to Exponent 5/8. This means that

the length of a decade on the log scale is

times as long as a decade on the overlay scale.The unity index line of the overlay scale is placed on the deep resistivity curve, andS

w is read on the overlay scale from the shallow resistivity curve, and S

w is read on the

overlay scale from the shallow resistivity curve. Figure 9 illustrates the method. Sw

is indicated to be 24%.

When Rmf Rw (usually Rmf > Rw), the procedure for finding Sw involves an additional

step. The value of Rmf / Rw must be known, or the Rdeep curve can be shifted to make

it coincide with the Rshallow curve in known water zones. In the lower zone of Figure 10,

expected to be water bearing, this shift is indicated as a; it suggests an Rmf / Rw value

of 3. The entire Rdeep curve is shifted by this amount to the right (or the Rshallow curveshould be shifted to the left by the same amount). The unity index line of the Exponentoverlay scale is placed on the shifted Rdeep value, and the value of Sw is read from theposition of the shallow resistivity curve on the overlay scale. S

w is indicated to be 14%.

Equation 23



Figure 9S

wa from logarithmic

resistivity overlay, case ofR

mf = Rw

122

Rxo

/Rt QuicklookThe R

xo/R

t quicklook can be used to identify hydrocarbon-bearing formations and to

indicate hydrocarbon movability (producibility). When Sw/S

xo is 1 in a permeable

zone, the zone will produce water or be non-productive regardless of water saturation.An S

w/S

xo is 1 in a permeable zone, the zone will produce water or be non-productive

regardless of water saturation. An Sw/S

xo significantly less than 1 indicates the zone

is permeable and contains some hydrocarbons, and that the hydrocarbons have beenflushed (moved) by invasion. Thus, the zone contains producible hydrocarbon.

Equation 16 can be written as

SS

RR R

w

xo

t

mf w SP

= Rxo /

/( )

12

which shows that an indication of Sw/S

xo can be obtained by comparing R

xo/R

t with R

mf/R

w, where the subscript SP emphasises that R

mf/Rw is derivable from the SP. Equiva-lently, the comparison can be between log R

xoR

t and the SP curve for an indication of

log Sw/S

xo.

The log Rxo

/Rt is computed from a comparison of the deep and shallow resistivity

measurements or from all three resistivity measurements or from all three resistivitymeasurements and is used as an overlay comparison curve with the SP. Separations

Figure 10Logarithmic resistivityoverlay, case where R

mf/Rw 1.

Equation 24



between the log Rxo

/Rt curve, properly scaled to match the SP, and the SP curve provide

a quicklook location of producible hydrocarbons.

Originally, log Rxo

/Rt was computed from RLL8/RID or RSFL/RID. Use was made of the

observation that over a wide range of invasion diameters (from about 20 to 100 in.)R

xo/R

t depends primarily on the value of RLLS/RID or RSFL/RID (Figure 11). The

relationship employed for the LL8 device was

R R Rxo t ID/ 1.85 / . = RLL8( ) 0 85

For the SFL device, it was

R R Rxo t ID/ 1.45 / . = RSFL( ) 0 45

Much more sophisticated algorithms are now used to obtain Rxo

/Rt. All three

resistivity measurements of the DIL-SFL tool are employed. As a result, thecomputed R

xo/R

t values more closely duplicate the values given by the relevant

invasion correction chart and by Figure 11 over a greater range of invasion diameters.

To interpret the Rxo

/Rt quicklook curve, the impermeable zones must be eliminated by

reference to the SP, GR, or microlog curves or by resistivity ratios. Then, if the SP

Figure 11Plot illustrating stronginterdependence of RLL8/RIDand R

xo/Rt

in the range of di valuesfrom 20 to 100 in.

Equation 25

Equation 26

124

and Rxo

/Rt (actually - K log R

xo/R

t) curves coincide in a permeable zone, the zone will

most probably produce water. If however, the Rxo

/Rt curve reads appreciably lower

(i.e., to the right) than the SP, the zone should produce hydrocarbons. An Rxo

/Rt value

less than the SP amplitude indicates movable hydrocarbons are present.

The Rxo

/Rt quicklook technique is applicable to fresh mud conditions (R

xo > R

t) in

formations where invasion falls within the limits demanded by the Rxo

/Rt computation.

For the simpler computation technique using Equation 25, that is about 30 to 70 in.;for the more sophisticated techniques, that is between 20 and 120 in. Even in the morerestrictive case, however, any errors are optimistic. In other words, water zones mayappear to be hydrocarbon productive. This constitutes a safeguard against overlook-ing pay zones, and is considered a desirable feature in any quicklook approach.

The Rxo

/Rt technique efficiently handles variations in formation water resistivity, R

w,

and in shaliness. Any change in Rw is reflected similarly into both the computed R

xo/

Rt and the SP amplitude. Thus, comparing the two curves still permits formation fluid

identification. Shaliness also affects the two curves in a similar manner. All otherthings remaining constant, shaliness reduces the R

xo/R

t value and the SP amplitude.

Finally, the Rxo

/Rt quicklook technique does not require porosity data nor use of any

F - relationships.

Figure 12 is an example of a shaly gas sand at 3760 through 3788 ft and several water-productive sands with varying amounts of shaliness. The productive gas sand isidentified by the separation between the R

xo/R

t and SP curves. Water-productive zones

are shown by lack of separation. In shaly water zones the variation in the SP curve isessentially the same as the variation in the R

xo/R

t ratio - a result of the same shale; so,

the comparison is not significantly disturbed by shaliness. Neither is it disturbed byvariations in R

w.

Figure 12Example of (R

xo/Rt)QL curve

used for comparison withSP to identify zones withmovable hydrocarbons.



Estimates of water saturation and saturation ratio in clean formations can be made bycomparing the R

xo/R

t and SP curves. Equation 24 permits S

w/S

xo to be estimated and

Equation 17 (assuming Sxo

= Sw) permits S

w to be estimated.

7.5 F-MOP MOVABLE OIL PLOTThe F-MOP plot uses two resistivity curves and a porosity curve recorded onlogarithmic scale to show hydrocarbon saturation and movability. The recordedcurves are Fdeep, Fxo, and F (from a porosity log), where

Fdeep = RR

FS deepw

w

2

Fxo = RR

FS xomf

xo

2

and

F = am

On a logarithmic scale, the apparent formation factor curves, Fdeep and Fxo, are locatedby shifting the corresponding resistivity curve by log R

w or log R

mf, whichever isappropriate. The F curve is a log curve recorded at the proper sensitivity andpolarity.

For an estimate of hydrocarbon movability the Sxo

value is compared with the Sw value.

Values of Sw

are found, as shown in Figure 13, with a logarithmic overlay ofExponent 0.5 applied to the separation between the F and Fdeep curves. Values ofS

xo are found in the same manner by applying the scale between the F

xo and F curves.

In each case, the unity index line of the overlay scale is placed on the Fxo

or Fdeep curve.

Equation 28

Equation 29

Equation 27

126

8 SHALY FORMATIONS

Shales are one of the more important common constituents of rocks in log analysis.Aside from their effects on porosity and permeability, this importance stems fromtheir electrical properties, which have a great influence on the determination of fluidsaturations.

Shales are loose, plastic, fine-grained mixtures of clay-sized particles or colloidalparticles and often contain a high proportion of clay minerals. Most clay minerals arestructured in sheets of alumina-octahedron and silica-tetrahedron lattices. There isusually an excess of negative electrical charges within the clay sheets. The substitutionof Al+++ by ions of lower valence is the most common cause of this excess; the structureof the crystal remains the same. This local electrical imbalance must be compensatedto maintain the electrical neutrality of the clay particle. The compensating agents arepositive ions - cations or counterions - which cling to the surface of the clay sheets ina hypothetical dry state. The positive surface charge is usually measured in terms ofmilli-ions equivalents per 100 grams of dry clay minerals and is called the cationexchange capacity (CEC). When the clay particles are immersed in water, theCoulomb forces holding the positive surface ions are reduced by the dielectricproperties of water. The counterions leave the clay surface and move relatively freelyin a layer of water close to the clay water interface) and contribute to the conductivityof the rock.

Figure 13The F MOP



Since the Archie water saturation equation, which relates rock resistivity to watersaturation, assumes that the formation water is the only electrically conductivematerial in the formation, the presence of another conductive material (i.e., shale)requires either that the Archie equation be modified to accommodate the existence ofanother conductive material or that a new model be developed to relate rock resistivityto water saturation in shaley formations. The presence of clay also complicates thedefinition or concept of rock porosity. The layer of closely bound surface water onthe clay particle can represent a very significant amount of porosity. However, thisporosity is not available as a potential reservoir for hydrocarbons. Thus, a shale orshaley formation may exhibit a high total porosity yet a low effective porosity as apotential hydrocarbon reservoir.

The way shaliness affects a log reading depends on the amount of shale and its physicalproperties. It may also depend on the way the shale is distributed in the formation.Shaley material can be distributed in the formation in three ways.

1. Shale can exist in the form of laminae between which are layers of sand. Thelaminar shale does not affect the porosity of permeability of the sand streaksthemselves. However, when the amount of laminar shale is increased and the amountof porous medium is correspondingly decreased, overall average effective porosity isreduced in proportion.

2. Shale can exist as grains or nodules in the formation matrix. This matrix shale istermed structural shale; it is usually considered to have properties similar to those oflaminar shale and nearby massive shales.

3. The shaly material can be dispersed throughout the sand, partially filling theintergranular interstices. The dispersed shale may be in accumulations adhering to orcoating the sand grains, or it may partially fill the smaller pore channels. Dispersedshale in the pores markedly reduces the permeability of the formation.

All these forms of shale can, of course, occur simultaneously in the same formation.

Over the years, a large number of models relating resistivity and fluid saturations havebeen proposed. Many have been developed assuming the shale exists in a specific

Figure 14Forms of shale classified bymanner of distribution information. Pictorialrepresentations above,volumetric representationsbelow.

128

geometric form (i.e., laminar, structural, dispersed) in the shaly sand. All these modelsare composed of a clean sand term, described by the Archie water saturation equation,plus a shale term. The shale term may be fairly simple or quite complex; the shale termmay be relatively independent of, or it may interact with, the clean sand term. All themodels reduce to the Archie water saturation equation when the fraction of shale iszero; for relatively small amounts of shaliness, most models and methods yield quitesimilar results.

Only a very few of these models will be reviewed here in order to provide some flavourand understanding for the evolution of shaly sand interpretation logic.

Laminated Sand-Shale Simplified ModelIn this laminar shale model, R

t, the resistivity in the direction of the bedding planes,

is related to Rsh (the resistivity of the shale laminae) and to Rsd (the resistivity of the

clean sand laminae) by a parallel resistivity relationship,

1R R

VRt sd

lam

sh

= - Vlam1 +

where Vlam is the bulk-volume fraction of the shale, distributed in laminae, each ofmore-or-less uniform thickness.

For clean-sand laminae, Rsd = Fsd Rw/Sw2 , where Fsd is the formation resistivity factor

of the clean sand. Since Fsd = a /sd2 , (where sd is the sand-streak porosity) and

= (1 - Vlam) sd (where is the bulk-formation porosity), then

11

2

RS

V aRVRt

w

lam w

lam

sh

=

2( )

+

To evaluate Sw

by the laminated model,

Rt, R

w, , Vlam, and Rsh must be determined.

For the determination of Rt, the problem is the same as for clean formations. If R

w is

not known, its determination usually involves looking at a nearby clean sand andsolving for R

w using the SP measurement or, if the formation is water bearing, using

the resistivity and porosity measurements.

For the determination of and Vlam, a combination of porosity logs can be used. Forexample, as illustrated in Figure 15, a crossplot of N and b from a density log iseffective. The triangle of the figure is defined by the matrix point, water point, andshale point. In this example, the matrix point is at N = 0 (the neutron log was scaledin apparent sandstone porosity) and

ma = 2.65 g/cm3 (quartz matrix). The shale point

is at N = 50 pu and sh = 2.45 g/cm3. These values were taken in a nearby thick shalebed; it is assumed that shale laminae in the shaly sand under investigation are similarto the nearby massive shale beds. The water point is, of course, located at N = 100pu and b = 1 g/cm3. The matrix-water line and shale-water line are linearly dividedinto porosity; the matrix-shale line and water-shale line are linearly divided into shalepercentages.

Equation 30

Equation 31



Point A, plotted as an example, corresponds to log readings of b = 2.2 g/cm3 and N= 33 pu. Interpretation by the lines on the plot yields = 23% and V

sh (or Vlam) = 16%.

Direct use of this crossplot assumes 100% water saturation in the zone investigatedby the tools. Since oil has a density and hydrogen content normally not greatlydifferent from water, this crossplot technique can be used with acceptable accuracyin oil-bearing formations. The presence of gas or light hydrocarbon, however,decreases N and decreases b. This would cause the point to shift in a north-westerlydirection. When gas or light hydrocarbon are present, an additional shalinessindicator, such as GR or SP data, is needed in order to evaluate the amount of the shift.

Using the laminated model, an equation for Rxo

analogous to Equation 31 could bewritten. S

xo would replace S

w and R

mf would replace Rw. The other terms (, Vlam, Rsh)remain the same in the two equations. Assuming S

xo = S

w1/5

(as in the flushed-zone ratiomethod) and the ratio of the PSP (SP deflection in the shaley sand) to the SSP (SPdeflection in a nearby clean sand of similar formation water) is a measure of shaliness,Vlam, water saturation could be calculated from RxoRt and PSP in the shaley sand andSSP (or R

mf/Rw) in a nearby clean sand. Chart Sw-2 performs the calculation.

Dispersed Shale Simplified ModelIn this model, the formation conducts electrical current through a network composedof the pore water and dispersed clay. As suggested by L. de Witte, it seems acceptableto consider that the water and the dispersed shale conduct an electrical current like amixture of electrolytes.

Figure 15Neutron-density crossplotshowing matrix, water, andshale points,scaled for determination ofV

sh and porosity.

130

Development of this assumption yields

1R

qR

S qRt shd

im

w

= Sa

im2

im +

where,im is intermatrix porosity, which includes all the space occupied by fluids anddispersed shale,Sim is the fraction of the intermatrix porosity occupied by the formation-water,dispersed-shale mixture,q is the fraction of the intermatrix porosity occupied by the dispersed shale,

andR

shd is the resistivity of the dispersed shale.

Also, it can be shown that Sw = (Sim - q)/(1 - q) where Sw is the water saturation in the

fraction of true effective formation porosity:

Combining these relations and solving for Sw yields

S

R R

w

w w

=

aR R

+ q R

R -

q R R

- q

w

im2

t

shd

shd

shd

shd( ) +( )2

2 21

Usually, im can be obtained directly from a sonic log since dispersed clay in the rockpores is seen as water by the sonic measurement. The value of q can be obtained froma comparison of a sonic and density log. Indeed, if , sh ma, then qSV (D - SV)/, where SV and D are the sonic and density derived porosities, respectively. In thiscase, D approximates , the effective porosity available for fluid saturation.

The value of Rshd is more difficult to evaluate. It is usually taken as equal to Rsh in

nearby shale beds. Fortunately, its value is not too critical if it is at least several timesgreater than R

w. In fact, when R

w is small compared to R

shd and the sand is not too shaly,Equation 33 can be simplified to a form independent of R

shd:

Sw =

aR R

+ q

-

q

- q

w

im2

t

2

4 21

Total Shale RelationshipBased upon the above ideas, laboratory investigations and field experience, it has beenfound that a simple relationship of the following form works well for many shalyformations independent of the distribution of the shale and over the range of S

w values

encountered in practice:

Equation 32

Equation 33

Equation 34



11R Vt sh

= S

a R +

V SR

w

w

sh w

sh

2 2

( )

In using this equation, Rsh is taken equal to the resistivity of the adjacent shale beds

and Vsh is the shale fraction as determined from a total shale indicator.

In recent years, it is equations of the form of Equation 33 and 35 that have gained thewidest acceptance in the evaluation of shaly sands. These equations have a generalform

1 2R

S St

w w= + ,

where denotes a predominant sand term that is dependent on the amount of sand, itsporosity, and the resistivity of the saturating water. The sand term always reduces toArchies water saturation equation when the shale fraction is zero. denotes apredominant shale term that depends on the amount and resistivity of the shale.

Although the general form of shaly sand interpretation models may be quite similar,the methods of determining the amount of shale and its resistivity may differ greatly.

APPENDIX 1 - DETERMINATION OF RW

In addition to formation factor or porosity, values of formation water resistivity,

Rw, and mud filtrate resistivity, R

mf, are needed for the water saturation

calculations. Mud resistivity, Rm, mudcake resistivity, R

mc, and R

mf are generally

measured at the time of the survey on a mud sample from the flowline or mud pit.

These values are recorded on the log heading. If a measured value of Rmf

or Rmc

is

not available. Since the resistivity of a material is a function of temperature, Rm.

Rmf

, and Rmc

must be corrected to formation temperature (Chart Gen-9). Rw canbe determined in a number of ways:

from the SP Log from water saturation equation in a 100% water-bearing formation from produced water samples from water catalogues

1.1 RW from the SP Log

In a clean formation, the static SP (SSP) curve value is

SSP K RR

mfe

we

log =

where,K =temperature-dependent constant = 61 + 0.133 T degrees FT =Formation Temperature, degrees F

Equation 35

Equation 36

Equation 37

132

Rmfe = Resistivity of Mud Filtrate

Rwe

=Equivalent Formation Water Resistivity

Knowing the formation temperature, the static SP value recorded opposite a porous,permeable, nonshaly formation can be transformed into the resistivity ratio R

mfe/RweChart SP-1 performs this translation graphically. Charts SP-1 and -2 solve the aboveSP equation for R

w

Procedure:Step 1: Identify a permeable, water bearing zone near to the hydrocarbonbearing zone of interest.

Step 2: Determine the formation temperature at the zone of interest.The formation temperature can be found from either:

direct measurement (if the zone is at total depth and maximum temperaturereading is used); or

the bottom hole temperature, total depth and average surface temperatureand Chart Gen-6.

Step 3: Correct the Rm and Rmf resistivity values for the formation temperaturefound in Step 2.The values of R

m and R

mf can be found on the log heading. For predominantly NaClmuds: if R

mf at 75 degrees F is greater than 0.1 ohm-m, use Rmfe = 0.85 Rmf at formationtemperature; if R

mf at 75 degrees F is less than 0.1 ohm-m use the NaCl (solid) curvesof Chart SP-2 to derive a value of R

mfe value corrected to formation temperature fromChart Gen-9.

For freshwater gypsum muds, the dashed lines of Chart SP-2 are used to convert Rmf

to Rmfe.

Step 4: Draw the shale base line on the SP Log.The shale base line in fresh mud environments will generally be the line

established by the maximum SP deflections to the right. This shale base line is not

necessarily perpendicular to the depth lines on the log due to drifting with depth.

Usually, over limited sections, this drift is negligible. If a significant change in the

base line occurs, use the average shale base line.

Step 5: Mark out the bed boundaries on the SP Log.The bed boundaries on the SP Log are the inflection points on the curve. The

inflection point (or maximum slope) on the curve occurs due to maximum current

flow in the well bore at the boundary. The apparent bed thickness from the SP is

used, not the bed thickness indicated on some other log. Sometimes it is difficult

to pick a bed thickness if there are large shale beds within the sand. A judgement

decision must be made under these circumstances as to the real thickness of the

bed.



Step 6: Read the maximum SP value for the permeable zone of interestThe SP value is the millivolt reading indicated on the log, from the shale base line

to the maximum deflection on the SP in the permeable bed.

Step 7: Correct the SP value in Step 6 for thickness and resistivity effectsChart SP-4 is a generalised correction chart for the SP. It corrects for bedthickness and resistivity effects on the SP amplitude. Notice on Chart SP-4 thatlow resistivity, thick beds require little to nor correction. If the bed is thick

enough, the SP will have reached maximum amplitude. On this particular chart,

the resistivity value from the short normal is used as Ri. A focused log (from the

dual induction) also can be used.

Step 8: Determine the mudfiltrate to apparent formation water resis-tivity ratio, R

mf/RweChart SP-1 relates the corrected SP deflection, formation temperature and the

ratio of the resistivity of the mud filtrate to apparent formation water resistivity for

a sodium chloride solution (Rwe

). Determine Rmfe

/Rwe

from this chart

Step 9: Determine Rwe

Rwe

is obtained from the Rmfe

/Rwe

ratio determined from Chart SP-1 by dividing

Rmfe

by the Rmfe

/Rwe

ratio. The correlation in Chart SP-1 is based on formation

water containing only sodium chloride, NaCl.

Step 10: Correct Rwe for to that for a more realistic salt content anddetermine R

w

Correct Rwe

to Rw for the average deviation from sodium chloride solutions

found in formation water. Chart SP-2 corrects for high salinitys and normalconcentrations of calcium, magnesium and other divalent ions, as well as theinfluence of formation temperatures.

1.2 Rw from water saturation equation in a 100% water-

bearing formation

When the water saturation is assumed to be 100%, the Archie water saturation

equation reduces to:

Rw = Rt/F

Where Rt is from a deep-investigation resistivity log, and F is computed from aporosity log reading.

Equation 38

134

If we assume all zones are water bearing and generalise this equation we have:

Rwa

= Rt/FR

The values of Rwa

can be calculated for a number of water bearing zones and if the samethen the value of R

wa can be assumed to be equal to R

w. If R

wa is calculated mistakenly

in a hydrocarbon zone then Rt will increase and if the porosity is unaffected by thepresence of hydrocarbons then the value of R

wa will increase.

Procedure:

Step 1: Identify a permeable, water bearing zone near to the hydrocarbonbearing zone of interest.

Step 2: Read the resistivity of the zone of interest from a deep investigationresistivity log.

Step 3: Determine the Formation Resistivity Factor, FDetermine porosity from the acoustic, density or Neutron Log. Calculate F from the

Humble formula.

Step 4: Determine Rwa

from Equation 39 above

Step 5: Compare values of Rwa

.

The values in the water bearing zone should be similar. The lowest value of Rwa

isgenerally the value of R

w. If the calculated value of R

wa at a particular depth is over

three times that of Rw determined in a definite water bearing zone then the zone is

potentially hydrocarbon bearing.

Equation 39



LIST OF INTERPRETATION CHARTS FOR CHAPTER 7

Chart POR-1Chart POR-3Chart POR-5

Chart SW-1Chart SW-2

Chart Rint-2b

Chart SP-1Chart SP-2Chart SP-4

Chart Gen-6Chart Gen-9

Chart Appendix A3Chart Appendix A4

PetEvalCh7.pdf

Documents

Transcript of PetEvalCh7.pdf