Compute Saturation SWE & SWT

Generalities

The calculation of water saturation is one of the most troublesome aspects of Shaly Sand log analysis.

Many equations have been developed over the years based on known physical principles or on empirically derived relationships.

SW can be determined if one or more measurements can be made that are strongly influenced by the fluid properties.

Resistivity measurements are, by far, the most commonly used measurement to determine SW.

In the very earliest days of well logging, it was recognized that the presence of hydrocarbons was indicated by anomalously high resistivity in porous intervals.

The presence of clay can suppress resistivity and sometime mask the hydrocarbon effect.

We will review here some of the methods used to calculate SW from resistivity data.

There are two general groups of Water saturation equation commonly used today and both have strong suites of followers.

 

Equations by Group

1- Vshale or resistivity model equations (Uses PHIE)

Laminar Simandoux Modified Simandoux Poupon Leveaux Fertl & Hammack. Indonesia Etc.

  2- Cation Exchange or conductivity model equations (Uses PHIT)

Waxman-Smits Modified Waxman Smits

Juhasz Dual Water Charlebois etc.

 

What equation to use:?

It is generally accepted that conductivity models using PHIT will give results that are more consistent than resistivity type equations however conductivity models have inherent problems to the users for the following reasons:

 

PHIT cannot be measured without calibration with core analysis since the dry clay matrix points does not exist in nature and is therefor not seen by the logs.

Different laboratory methods to calculate PHIT in clays will give different PHIT for the same core.

It can take months before sufficient core results are available to determine the actual PHIT.

Oil companies do not always take cores in the shales and the PHIT from low volume clays in a sand do not necessarily have the same properties as in the adjacent shales.

The determination of QV and the establishment of a correlation between logs and QV is not always evident and can induce errors.

 

Recommendations:

1. In a development field, and provided sufficient core results are available in the zone of interest only, we recommend the use of a conductivity saturation equation to determine SWT and SWE

2. Resistivity model equations should preferably be used in all wildcat wells or where insufficient core results can be used to determine PHIT accurately.

Input Logs:

PHIE PHIT VCLAY

Input log should all be environmentally corrected before proceeding here below.

Output curves:

SWE SWT

Zone parameters:

a m n a1 m1 n1 RW RCLAY B

 

Earth electrical conductance

Electrical currents can flow in various ways.

1. Metallic conductance is probably understood by most. It requires that a voltage potential exist across a conductor (light bulb) and that the conductor be comprised of elements which have “free” electrons that can be passed from one atom to another.

2. Ionic conductance is not so well understood. Current flow though a conductive ionic medium (e.g. salt water) requires the actual movement of charged ions (Such as Na+ and Cl-) through the medium (water). The SP measurement is derived from this phenomenon. However, when an alternating current is induced in the medium, the direction of the potential is constantly reversing. The Cations and Anions are still in motion but their behaviour is different.

 

When a field reaches a peak in one direction, the displacement of the charged ions is set to a maximum. As the field collapses and then builds in the reverse direction, the ion displacement is in the opposite direction. At higher frequencies, the distance travelled by an ion between ‘+’ and ‘-‘peaks becomes extremely small. Thus, it can be seen that the conductance in the formation is due to the ability of charged ions to migrate through the water within the pore spaces.

The presence of hydrocarbon impedes the movement of charged ions.

Many electrical tools measure conductivity but, traditionally, resistivity is recorded on the log. Thus most equations have been written in terms of resistivity instead of conductivity.

Resistivity is the reciprocal of conductivity.  R = 1/C

R = resistivity in Ohm2/m

C = Conductivity in mhos

Resistivity tools measure resistivity as a series circuit

Conductivity tools measure conductivity as parallel circuits.

 

The equation for total conductance in a parallel circuit is

CT = C1 + C2 +   Cn                                                   EQ 1

The equation for total conductance in a series circuit is

CT =  1 / (1/C1 + 1/C2 +   1/Cn)                                EQ 2

For total resistance in a parallel circuit we get

RT =  1 / (1/R1 + 1/R2 +   1/Rn)                               EQ 3

For total resistance in a series circuit we use:

RT = R1 + R2 +    Rn                                               EQ 4

 

Various Shaly Sand models differ in the manner in which the two current paths are defined. Generally, the formation water in the pore space is treated as one current path and the clay network is treated as the second current path.

 

Basics

Archie characterized the conductivity of porous media having a non-conductive matrix as a function of the porosity and of the conductivity of the saturating fluid.

Archie’s equation is in the form:

F = a/PHI^m                                                                  EQ 5

The conductivity of a clean sand saturated with a conductive brine can be defined as:

Co = CW/F                                                                        EQ 6

Where

Co:    Conductivity of a 100% water saturated rock

CW   Conductivity of the saturating brine

F       Formation resistivity factor

PHI:  Porosity

a and m are constants

Where electrical current can be conducted by a second path, the above equation becomes invalid. This condition exists where the matrix is conductive of where a second conductive path exists in the pore network. Clay provides such a conductive path. Where clays are present, the conductivity can be expressed as

Co = K * CW/F + X                                                              EQ 7

Where

K Interactive clay function (Unity in many models)

X The additional conductivity due to the presence of clay

Analysis of Eq. 7 will show that, for any given value of ‘X’, the magnitude of the shale effect decreases as the formation water conductivity ‘CW’ increases.

Thus, where formation waters are very saline, the contribution of the shale term becomes relatively small.

Conversely, where formation water conductivity is low (formation water is fresh) the contribution of the shale term is relatively large.

It is then obvious that accurate characterization of the shale term becomes increasingly important as formation waters become fresher. It is in the brackish and fresh water applications that most shaly sand analysis models encounter difficulties.

Nearly every shaly sand log analysis model is in basic agreement with EQ 7, however they differ in the manner in which ‘X’ and ‘F’ are derived.

We address here only some of the most commonly used equations.

Elements of the water saturation models

There are two different approaches to compute SW in Shaly Sand models

1-“V-Shale or resistivity Models” These are the most commonly used today as they can use recorded logs input only.

2-“Cation Exchange or Conductivity Models” These models can give better results as they can be matched closely to laboratory measurements. It is not as popular as the cost of doing the laboratory tests and the lack of core data often precludes the use of these models.

 

The “V-Shale Models” work reasonably well in sands where the water is very saline.

The “V-Shale Models” fail to account for significant non linear changes in formation conductivity as a function of conductivity where fluid conductivity is less than a certain critical value.

However this non-linearity can be overcome using advanced techniques such as the dual clay resistivity option.

The -“Cation Exchange Models” are based on the Waxman-Smits or derivatives of it.

The Waxman-Smits and Modified Waxman-Smits equations have much in common and the question of the value of one relative to the other has sparked lengthy and sometimes bitter debates.

However, both equations account for non-linear changes in conductivity in the fresh to brackish water reservoirs. Since they also account for the linear conductivity changes in the saline reservoirs, they are more acceptable as general Shaly Sand models.

The Waxman-Smits model was the first technique to demonstrate broad application based upon core and core data from a variety of reservoir conditions.

The Modified Waxman-Smits model was later proposed as a practical application of the lessons learned from the Waxman-Smits model.

The Waxman Smits model can give better results but must be calibrated against core data which is not always available. This problem will be discussed in more details further down this presentation.

ARCHIE

The very earliest research established that for a formation with constant porosity and water salinity, an increase in resistivity indicated the presence of hydrocarbons. Archie quantified this relationship as:

SW^n = F * RW /RT                                                                EQ 8a

or

SW^n = F * CT/CW                                                                 EQ 8b

Where:

F          Formation resistivity Factor

RW      Formation water resistivity

CT       Conductivity of the formation

RT       Resistivity of the formation

SW      Formation water saturation (fraction)

n          Saturation exponent

EQ 8 can be rewritten as:

CT = K * CW * SW^n / F                                                           EQ. 9

Formation Factor F

The key to this relationship is the Formation resistivity factor which is defined in equation 10

F = Ro/RW                               Eq 10  or       F = CW / Co                            EQ 10b

Where:

Ro Resistivity of the shale free formation 100% saturated with water of resistivity RW

Co Conductivity of the shale free formation 100% saturated with water of conductivity CW

Electrical current will flow through any conductor if there is a difference in voltage across this conductor. Salt water is a good conductor while Quartz is a good insulator.

Thus, when a potential is applied across a clean-sand (no Clay) with salt-water filling the pore space, all of the current will flow through the water in the pores.

High porosity sands with large pore throats will flow currents easily (low resistance) but sands with low porosity will restrict or block off the flow of current (high resistance to currents).

This restriction of the flow path is referred as the tortuosity of sand. More tortuous flow paths will result in higher resistivity and higher formation resistivity factor.

Water Saturation

In a clean water-wet sand, (SW =1.0) and EQ 8 and 10 become

Ro/RW * RW/RT = 1.0 = Ro/RT   or  CW/Co * CT/CW = 1.0 = CT/Co       EQ 11

For clean sands where Ro = RT and Co = CT, EQ 8 can be rewritten as:

SW^n = Ro/RT = CT/Co                                                                       EQ 12

EQ 12 states that the ratio of the resistivity of a wet formation Ro to its resistivity measured while only partially saturated RT can be related to SW by an exponent n.

The ratio RT/Ro is referred to as the “resistivity index”

Since there is a large number of logging tools which measure RT it should be obvious that, knowing n we can calculate SW if we can determine Co or Ro.

Determining Co or Ro from F

We can determine Co or Ro if we know RW or CW and can determine the formation resistivity factor F from another down-hole measurement.

Fortunately there is a known relationship between F and PHI

F = a/PHI^m                                                                                      Eq 13

Where

PHI     Porosity

m        Cementation exponent

a          Porosity intercept

With F derived from porosity, we can solve Co or Ro in terms of F and CW or RW by rewriting EQ 10

Ro = F*RW    or   Co CW/F                                                           Eq 14a, b

Determining F from porosity

EQ 13 shows that F can be determined from the porosity if the values of a and m are known.

For most beginners, the values of a and m can be confusing and need to be carefully explained.

The values of a and m are best derived by cross plotting the log of porosity versus the log of the formation factor.

The value of F is obtained from log or core analysis. A core sample is saturated with a brine of known RW. The resistivity of the water saturated core is measures and the resistivity of the water saturated sample Ro is divided by the resistivity of the saturated brine RW. The resulting ratio plot F is then plotted against the porosity as measured on the sample.

Figure 1

Figure 1 illustrates the cross plotting of F versus Porosity from core. The value of m is the slope of the best fit line through the data and a is the intercept where porosity is set to 100%. The value of m is referred to as the ‘cementation factor’ or the ‘tortuosity factor’ because it increases with the complexity of the current path through the pore network.

Figure 2

Figure 2 illustrates the effect of variation in PHI, m and RW on Ro and F

 

Saturation exponent n

Having determined F then Ro and having measured RT and PHI we are now ready to determine SW. This last step requires knowledge of the exponent n.

The value of n is empirically derived and can be estimated either from well logs or core studies.

In practice, n is often used as a ‘fudge factor’ to satisfy the whims of management if reserves are a little low.

The exponent n is used to take into account such variables as the electrical properties of the water/oil interface, the wettability of the matrix and increased current paths.

If the matrix is partially oil wet so that the thin veneer of formation water is interrupted, (see Figure 3) then ‘n’ can be significantly altered. Figure 4 shows the effect or varying ‘n’ on the final SW.

Figure 3

Figure 4

The saturation exponent n can be estimated from core analysis.

Once the core porosity has been measured, it is saturated with a brine of known resistivity.

The resistivity of the fully brine saturated core sample is then measured.

Some of the fluid is then removed and the resistivity again measured.

The amount of fluid removed is carefully measured so that the partial saturation can be calculated.

After several repetitions the measured data are plotted as in figure 4.The slope of the line is the saturation exponent n.

Several samples representing a wide range of porosities and facies type for a particular reservoir should be so measured in order to obtain a statistically significant value of n.

A separate n for each facies should be expected for most shaly sand reservoirs.

Effect of clay and salinity on the Archie equation

The Archie equation works relatively well as long as salinity is high and there exists only one current path through the formation.

However, the presence of trace amounts of clay minerals provides a second current path and requires alteration of EQ 8.

The Archie equation will be in error in clean sands if the formation water salinity is extremely low. This is due to surface conductance effects.

Reservoirs having extremely fresh water cannot properly be evaluated using conventional resistivity logs. However a growing number of dielectric constant and electromagnetic propagation tools offer means of evaluating very fresh water reservoirs.

Evolution of shaly sand models

Numerous approaches have been taken over the years to predict Ro for shaly sands.

We will not go into details here but Table 1 and Table 2 list some of the earlier efforts to develop reliable SW equations.

For more background information we refer you to:

“SPWLA Shaly Sand reprint” Section III by Patchett and Herrick

“The evolution of Shaly Sand Concepts in Reservoir Evaluation” by Paul F Worthington (1985)

Cation exchange models

The publication in 1967 of the Waxman-Smits equation opened a new era in formation evaluation.

This equation removed some of the errors associated with RCLAY (from adjacent shales) techniques.

This model requires extensive coring and core analysis and thus is not universally accepted as an economic mean of calculating SW.

‘Clavier et Al’ attempted to incorporate the concept of the Waxman-Smits approach into a general model that requires minimal core data. Ref: “The Theoretical and Experimental Basis for the Dual Water Model for the interpretation of Shaly Sands” SPE Journal, 1984.

Waxman Smits

Hill and Milburn (1950) established the relationship of cation exchange capacity CEC and the suppression of resistivity on water bearing shaly sands.

Waxman and Smits (1967) refined the relationship propose by Hill and Milburn and presented a general equation for SW which required CEC data for core analysis.

Waxman and Thomas (1974) expanded the model with explanations of the influence of partial saturation by hydrocarbons and of the influence of temperature on the resistivity of shaly sands.

Koerperich (1975) focused on the application of the Waxman-Smits model to solve for SW in reservoirs containing fresh and brackish water.

Juhasz (1979) ties the various Waxman-Smits concepts together with modern logging measurements to illustrate the use of the Waxman-Smits model to derive SW directly from logs.

Waxman-Smits Overview, summary:

A parallel conductance path exists in shaly sands

Some of the electrical currents will flow though the cations associated with the clay and some will pass through the salt solution in the pore system.

Knowledge of the boundary between the clay associated water and the pore water is not necessarily in this model because the equation treats the two waters as a mixture.

This is possible because the formation resistivity factor used in the model reflects the net conductivity from the two current paths.

The conductivity through the cation system is expressed by the terms B and QV. B is temperature and salinity dependent.

QV quantifies the cation concentration per volume of formation water.

The ion concentration is usually expressed in equivalents per litre.

The combined term B*QV expresses the conductivity due to the presence of compensating cations in the water filling pores.

The conductivity of a wet shaly sand can be expressed as:

 

Co = CW/F1 + B*QV /F1                                                                 Eq 15

Where F1is the formation factor for the Waxman Smits model

Because the equation treats the two conductance paths as a mixture having a common F, SW cannot be solved in terms of the resistivity index.

Instead, SW must be included in the body of the equation to balance the mixture relationship. Thus the Waxman-Smits equation can be written in the familiar form:

CT = CW * SW^n1 /F1 + B * QV*Sw^(n1-1)/F1                                 Eq 16

Conductivity of wet shaly sands

Figure 5

Figure 5 is a plot of the relationship of the conductivity of a water saturated rock as a function of the conductivity of the saturating fluid.

The solid line shows a typical shale response.

The slope of the line is the formation resistivity factor F

At higher conductivities the relationship is linear.

At lower fluid resistivity (Fresh water) the relationship is non-linear and any slight increase in fluid conductivity results in a sharp increase in rock conductivity.

Water saturation less than 100%

The Waxman-Smits general equation for saturation can be expressed as:

 

SW^n1 = F1*RW / (RT * (1.0 + RW * B * QV / SW))          Eq 17a

or

SW^n1 = F1*CT / (CW * (1.0 + B * QV /(CW * SW)))         Eq 17b

The term QV

QV is expressed as cation concentration per unit volume of fluid in the pore space. (Equivalents per litre or meq/m)

QV is derived from laboratory measurements of the cation exchange capacity of the rock (CEC)

CEC is expressed as milli-equivalents per gram of sample.

To determine QV, CEC must be corrected for density and porosity by the relationship:

QV = CEC * RHOMA * (1.0-PHIT) / PHIT                                         EQ 18

Where

PHIT      = Total Porosity which includes clay associated water

RHOMA =  Matrix density

EQ 18 should be applied with caution as the matrix density used in the relationship must include the proportional clay and clean matrix densities. This is best achieved by obtaining matrix density values from pieces of the same core samples on which the CEC measurements are made.

Where no CEC is available, Lavers has suggested the following relationship:

QV = Aq * PHIT^Bq                                                      EQ 19

Where

PHIT Total Porosity which includes clay associated water

Aq Constant:  Default =   0.0029

Bq Exponent: Default = -3.0590

This is the value of QV used by PETROLOG when an external QV is not supplied as an input curve.

This relationship was used in the North Sea initially however can be modified for other locations.

The term B

B quantifies the conductance of the clay exchange cation as a specific temperature and a specific cation concentration.

Juhasz (1981) published the expression linking B with Salinity and temperature as:

B = (-1.28 + 0.225 * T - 0.0004059 * T^2) / (1.0+RW*0.045* T - 0.27) EQ 20

Where

B      Is expressed in mho.m-1/meq.cm-3

RW  Formation water resistivity at formation temperature

T      Temperature in DegC

B is automatically computed as a Zone Parameter in PETROLOG whenever BHT or RW is changed in a zone. B can also be modified manually by the user in the zone control file. Gravestock (1991)

The term F1 = (Waxman-Smits Formation factor)

According to Waxman and Thomas F1 is temperature independent.

The reciprocal of the slope Co/CW line is F1

It is essential to determine the slope on the linear section of Co/CW (see Fig 5) because the term B accounts for the curved portion.

The method to determine F1 is as follows

1. Saturate a core is a brine of a given salinity and measure Co2. Flush the core and replace with a brine of different salinity and measure Co again3. Repeat above as many time as necessary to trace the Co vs. CW plot and derive F1

This method is often referred to as ‘The Waxman-Smits multiple salinity method’.

This is an expensive and time consuming exercise.

The term F1 (Hoyer & Spann method)

‘Hoyer and Spann’ (1975) in their paper ‘Comments on Obtaining Accurate Electrical Properties of Cores’ established this simple relationship of F1 vs. F where F is determined from a single measurement of Co vs. CW.

F1 = F * (1.0 -RW*B*QV) = F * (1.0 - B*QV/CW)                           EQ 21

Where

F Formation resistivity factor from a single measurement of CW/Co

F1 Waxman-Smits Formation resistivity factor

The values of B and QV used in EQ 21 should be determined from the same core at the same temperature that was used to measure F in the laboratory.

The terms a1, m1 (Waxman-Smits intercept and cementation exponent)

Once a few F1 have been calculated using cores with different porosities, the values of a1 and m1 can be determined using the same conventional method to determine a and n. See figure 1.

The porosity values used to determine a1 and m1 are total porosity PHIT which must be obtained by a dehumidified core analysis procedure.

The terms n1 (Waxman-Smits saturation exponent)

n1 should be measured with high conductivity water.

The practice is to saturate a core with 100% brine (SW=1.0) and then remove gradually a percentage of the brine for partial saturations. See "Saturation Exponent" above.

Modified Waxman Smits Equation

This equation is based on the Juhasz model and makes do without the BQV and uses the apparent bound water resistivity. Rwb Rwa where VCLAY = 100%

Rwb is the bound water resistivity using PHICP from the D-N Z-Plot.

Two sets of equations are used:

1- When RW > Rwb

Ro = F * Rwb * RW / (Rwb * (1 - VCLAY) + Vclay * RW)

SWT = (Ro/RT)^(1/n)

2- When RW <= Rwb

X = VCLAY * (Rwb - RW) / (2 8 Rwb)

SWT = (X^2 + F * RW)/RT)^(1/n) + X

Note that if RW = Rwb, the equation becomes a simple Archie formula since X = 0

Charlebois Equation

This is an alternative equation to the Waxman-Smits that computes the conductivity of the bound water in relation to the volume of clay.

This is a dual water model that calculates RW1 as a function of the proportion of clay bound water Rwb and formation water RW. This equation will give best results when the Rwa-vs GR points fall on a relatively straight line in a water bearing interval. Rwa is plotted on a logarithmic scale.

Figure 5

Rwa is computed using the PHIT apparent from the Density Neutron X-Plot assuming that SW= 1.0 and using the Archie equation

SWT = F * RW/RT  = 1.0   with F = a/PHIT^n

From these two equations we then get

Rwa = (PHIT^n)/(a * RT)

The blue line in figure 1 starts at (GRclean, RW)and ends at (GRclay, Rwb)and  represents the 100% water saturation line.

RW1 can be calculated as a function of VCLAY using the following equation:

RW1 = 10^(VCLAY*Log10(Rwb) + (1-VCLAY)* Log10(RW))

The Archie Equation is thereafter used to compute SWT:

SWT = F * RW1 /RT

The F, a and m used in this cation exchange type equation are the same as those used in the resistivity type saturation equations.

Effect of non-sodium cations

Ions of different elements have different mobilities.

The relationship established by Waxman-Smits applies only to sodium chloride systems.

Where magnesium and calcium are present as anions in either of the two current paths, the value of B will be in error.

“Robertson and Stokes’ (1959) and ‘Nightingale’ (1959) published a table of the equivalent conductivities of some common ions as follows:

TABLE 1

They also report that the counter ion equivalent conductance for calcium ion (Ca) is 0.54 that for Na+.

From this, one may conclude that ‘B’ for low salinity clay water systems where calcium is the predominant cation may be predicted by a partitioning equation based upon the sodium and calcium content of the water. However this is not stated in their papers.

They do present an empirical method of deriving ‘Bmax’ for non sodium cations.

- The slope and intercept of the Co/CW plot are determined by ‘The Waxman-Smith multiple salinity; method using the non sodium brine.(e.g. CaCl)

- If QV is measured independently, then ‘Bmax’ for calcium can be derived from the B * QV intercept

Fresh Water applications

No data exists for fresh water (RW >1.0) (see Figure 5).

This problem is further enhanced by the fact that calcium and magnesium anions frequently occur in high concentration in fresh where RW > 1.0 in both the clay associated water and the free formation water.

More studies and data need to be supplied in fresh formation water regarding the derivation of B for the use in the Waxman-Smits equation.

QV vs. CEC (Juhasz approach)

The Juhasz paper “The central role of QV and Formation water salinity in the evaluation of shaly sands” provides a table of average CEC and density values for the more common clay minerals and suggest an equation to derive QV from logs and CEC

 

QV = (VCLD * RHOCLD * CEC)/PHIT                                EQ 22

Where

PHIT:          Total Porosity which includes clay associated water

RHOCLD:  Dry clay density taken from tables or lab measurements.

CEC:           Average CEC for clay minerals known to be in the formation. (For 100% clay of this type)

VCLD:         Volume of dry clay from logs.

The proposed method to determine VCLD is:

 

VCLD = (PHIN - PHID)/HICLD                                        EQ 23

Where

PHIN:       Neutron porosity corrected for lithology and hydrocarbons

PHID:       Density porosity

HICLD    Hydrogen index of the average dry clay mineral mixture in the formation.

TABLE 2

Table 2 is a typical table with the hydrogen index for the major clay minerals

Tables of saturation equations

TABLE 3

TABLE 4

Table 3 an 4  lists a few saturation equations expressed with resistivity input

TABLE 5

TABLE 6

Table 5 an 6  lists a few saturation equations expressed with conductivity input  

References:

G.E. Archie 1942 “The electrical resistivity log as an aid in determining some reservoir characteristics” Trans AIMI 146 54-62

Paul. E. Worthington: “The Evolution of Shaly-Sand Concepts in Reservoir Evaluation”, “The Log Analyst”, Jan-Feb 1985

Charles R. Berg: “Effective-Medium Resistivity Models for Calculating Water Saturation in Shaly Sands”, “The Log Analyst” May-Jun 1996

I. Juhasz: “The Central Role of Qv and Formation Water Salinity in the evaluation of Shaly Formations.”, “The Log Analyst” Jul-Aug 1979

D.I. Gravestock “Behaviour of Waxman-Smits Parameter ‘B’ in High Rw, High Temperature Reservoirs”, “The Log Analyst, Sep-Oct 1991

H. Crocker K. Kutan: “Log Interpretation in the Malay Basin” , SPWLA 25th Annual logging symposium July 8-11 1980

E. C. Thomas: “Determination of Qv from membrane Potential measurements on Shaly Sands”, SPE AIME Sept 1986

Fertl W.H. and Hammack: G.W> 1971 “A comparative look at water saturation computations in shaly pay sands”, “ Trans SPWLA 12th Annual Logging Symposium R1-17

Comparative results of saturation equations:

We have constructed a pseudo data set containing a constant PHI, RT (water = 1 and Rclay = 60.0) and a variable GR as shown in Figure 5

Figure 6

Figure 6 shows the pseudo log with the GR from 20 to 120 API in track 1. RT and the compute Rwa are in track 3 PHIT = 0.35 is in track 4.

Figure 7

Figure 7 is the Rwa vs GR Z=Plot with the Vclay, Vsand PHIE and SW shown on he right hand track.

Figure 8 - 8a

Figure 8 shows the SW computed using the Indonesia equation. The 100% is fine at Vclay = 0.0 however this equation add oil due to the presence of clays. There are insufficient corrections due to the presence of high resistivity clays in this example. Figure 8A shows the SW results using the Laminar equation. SW is over corrected in this case.  

Figure 98, 9a

Figure 9 shows SW computed using the Simandoux equation Figure 9a shows SW computed using the Fertl & Hammack equation  

Figure 10

Figure 10 shows the Modified Waxman Smit SW equation results Figure 10a shows the Waxman Smits results using a, m, n and F1 instead of a1, m1, n1 and F1. High resistivity clays can appear as oil if the BQV is incorrectly calculated.

Figure 11

Figure 11.0 shows the SW computed using the Charlebois equation. It gives the perfect fit since this equation has been designed for logs that displays a typical Rwa vs GR as shown in figures 5 and 6

Figure 12

Figure 12 shows the different SW calculated in an example where PHIT = 0.316 and RT = 10 Using a = 1, m = 2 and n = 2 we get in the clean sand: With Rw = 0.01 we get: PHIT = PHIT = 0.316 and F = 1.0 / (0.316^2) = 10.0   SW = SQRT ( F* RW /RT) = 0.10

  Ass saturation equations give similar results where Vclay < 30%.