ARCHIE EQUATIONARCHIE EQUATION

F . F . RwRw

SwSw n n ==RtRt

•• Basic assumptionBasic assumption ::–– Non Non shalyshaly (clean) (clean)

fromationsfromations–– HomogeneusHomogeneus intergranularintergranular

porosityporosity•• Where:Where:

–– SwSw = water saturation of the = water saturation of the uninvadeduninvadedzone (Archie method)zone (Archie method)

–– RmfRmf = = resistivityresistivity of the mud filtrate at of the mud filtrate at formation temperatureformation temperature

–– RxoRxo = shallow = shallow resistivityresistivity from Laterologfrom Laterolog--8*, 8*, MicrophericallyMicropherically Focused Log*, or Focused Log*, or MicrolaterologMicrolaterolog* *

–– f f = porosity= porosity–– a = a = tortuositytortuosity factor factor –– m = cementation exponent m = cementation exponent –– n = saturation exponent which varies n = saturation exponent which varies

from 1.8 to 2.5 but is normally equal to from 1.8 to 2.5 but is normally equal to 2.02.0

aaFF ==

ΦΦmm

Archie Equation for Archie Equation for SwSw & & SxoSxo

•• Water saturation (Water saturation (SwSw) of reservoir’s ) of reservoir’s uninvadeduninvaded zonezone is calculated by the is calculated by the Archie (1942) formula.Archie (1942) formula.

a . a . RwRwSwSw n n ==

ΦΦmm . . RtRt

•• Where:Where:

SwSw = water saturation of the = water saturation of the uninvadeduninvaded zone zone (Archie method)(Archie method)

RwRw = = resistivityresistivity of formation water at of formation water at formation temperatureformation temperature

RtRt = true = true resistivityresistivity of formation (i.e. of formation (i.e. RIldRIld or or RLLdRLLd corrected for invasion)corrected for invasion)

ΦΦ = porosity= porositya = a = tortuositytortuosity factor factor m = cementation exponent m = cementation exponent nn = saturation exponent which varies from = saturation exponent which varies from

1.8 to 2.5 but is normally equal to 2.01.8 to 2.5 but is normally equal to 2.0

•• Water saturation of a formation’s Water saturation of a formation’s flushed zone (flushed zone (SxoSxo)) is also based on is also based on the Archie equation, but two variables the Archie equation, but two variables are changed:are changed:

a . a . RmfRmfSxoSxo n n ==

ΦΦmm . . RxoRxo

•• Where:Where:SwSw = water saturation of the = water saturation of the uninvadeduninvaded zone zone

(Archie method)(Archie method)RmfRmf = = resistivityresistivity of the mud filtrate at of the mud filtrate at

formation temperatureformation temperatureRxoRxo = shallow = shallow resistivityresistivity from Laterologfrom Laterolog--8*, 8*,

MicrophericallyMicropherically Focused Log*, or Focused Log*, or MicrolaterologMicrolaterolog* *

f f = porosity= porositya a = = tortuositytortuosity factor factor m m = cementation exponent = cementation exponent n n = saturation exponent which varies from = saturation exponent which varies from

1.8 to 2.5 but is normally equal to 2.01.8 to 2.5 but is normally equal to 2.0

•• Water saturation of the flushed zone Water saturation of the flushed zone ((SxoSxo) can be used as an indicator of ) can be used as an indicator of hydrocarbon hydrocarbon moveabilitymoveability..

Archie Equation for Archie Equation for SwSw & & SxoSxo

PenentuanPenentuan RwRw..!!!..!!!

•• Ratio MethodRatio Method•• RwaRwa Method Method •• SP MethodSP Method•• Picket Picket CrossplotCrossplot MethodMethod•• HingleHingle CrossplotCrossplot MethodMethod•• AnalisisAnalisis contoconto air air formasiformasi•• KatalogKatalog RwRw (database (database seluruhseluruh duniadunia))

PenentuanPenentuan RwRw : Ratio Method: Ratio Method•• The Ratio Method identifies hydrocarbons from The Ratio Method identifies hydrocarbons from

the difference between water saturations in the difference between water saturations in the flushed zone (the flushed zone (SxoSxo) and the ) and the uninvadeduninvadedzone(Swzone(Sw). ).

SwSw RxoRxo / / RtRt(( ))22 ==

SxoSxo RmfRmf / / RwRw

•• Where:Where:

SwSw = water saturation = water saturation uninvadeduninvaded zonezone

SxoSxo = water saturation flushed zone= water saturation flushed zone

RxoRxo = formation’s shallow = formation’s shallow resistivityresistivity from Laterologfrom Laterolog--8*, 8*, MicrosphericallyMicrospherically Focused Log*, or Focused Log*, or MicrolaterologMicrolaterolog**

RtRt = formation’s true = formation’s true resistivityresistivity ((RIldRIld or or RLLdRLLdcorrected for invasion)corrected for invasion)

RmfRmf = = resistivityresistivity of the mud filtrate at formation of the mud filtrate at formation temperaturetemperature

RwRw = = resistivityresistivity of the formation water at formation of the formation water at formation temperaturetemperature

PenentuanPenentuan RwRw

F . F . RmfRmfSxoSxo n n ==

RxoRxo

aaFF ==

ΦΦmm

SwSw RxoRxo / / RtRt(( ))22 ==

SxoSxo RmfRmf / / RwRw

F . F . RwRwSwSw n n ==

RtRt

•• didalamdidalam formasiformasi kandungkandung air (air (SwSw= 100%)= 100%)

SwSw = 1= 1Ro = Ro = RtRt

Where : Where : Ro : Ro : resistivitasresistivitas dalamdalam formasiformasi kandungkandung airair

SwSw = = SxoSxo = 1= 1SehinggaSehingga–– DiDi daerahdaerah asliasli : Ro = F . : Ro = F . RwRw–– DiDi daerahdaerah rembesanrembesan : : RxoRxo = F. = F. RmfRmf

MakaMaka, ,

: Ratio Method: Ratio Method

RwRw = = RmfRmf . Ro/. Ro/RxoRxo

…….for example:.for example:•• Based on the logs reading, we assumes Based on the logs reading, we assumes

that the water bearing zone is at that the water bearing zone is at 3012.40 meter with parameters as 3012.40 meter with parameters as follows:follows:

T T = 68.5 = 68.5 ooFFRmfRmf = 0.374 = 0.374 ohm.mohm.m @ 68.5 @ 68.5 ooFF (surface)(surface)BHTBHT = 295 = 295 ooFF @ 3292 m @ 3292 m TT = 275.763 = 275.763 ooFF @ 3012.4 m@ 3012.4 m

RmfRmf = 0.09964 = 0.09964 ohm.mohm.m @ 3012.4 m@ 3012.4 mRtRt = 9.89 = 9.89 ohm.mohm.m @ 3012.4 m@ 3012.4 mRxoRxo = 6.17 = 6.17 ohm.mohm.m @ 3012.4 m@ 3012.4 m

•• The final water The final water resistivityresistivity ((RwRw) at ) at 3012.4 m is 0.15971 3012.4 m is 0.15971 ohm.mohm.m, which is , which is calculated from:calculated from:

RwRw = = RmfRmf ((RtRt / / RxoRxo))RwRw = 0.09964 ( 9.89 / 6.17 )= 0.09964 ( 9.89 / 6.17 )RwRw = 0.15971 = 0.15971 ohm.mohm.m

PenentuanPenentuan RwRw : Ratio Method: Ratio Method

R2 = R1[(T1 + 6.77) / (T2 + 6.77)] OF

•• didalamdidalam formasiformasi kandungkandung air air ((SwSw = 100%)= 100%)

SwSw = 1= 1Ro = Ro = RtRtRwaRwa = Ro / F= Ro / F

•• In waterIn water--bearing zones (bearing zones (SwSw = 100%), = 100%), then calculated then calculated RwaRwa value is equal to value is equal to RwRw. However, if hydrocarbons are . However, if hydrocarbons are present, present, RtRt will be greater than Ro, and will be greater than Ro, and RwaRwa will be greater than will be greater than RwRw ((FertlFertl, , 1978).1978).

•• The The RwaRwa curve is plotted as a dashed curve is plotted as a dashed line along with the SP curve. The line along with the SP curve. The RwaRwacurve will deflect to curve will deflect to the leftthe left in in wet wet zoneszones and and to the rightto the right in in hydrocarbonhydrocarbon--bearing zonesbearing zones

PenentuanPenentuan RwRw : : RwaRwa MethodMethod

F . F . RmfRmfSxoSxo n n ==

RxoRxo

aaFF ==

ΦΦmm

SwSw RxoRxo / / RtRt(( ))22 ==

SxoSxo RmfRmf / / RwRw

F . F . RwRwSwSw n n ==

RtRt

WBZWBZ

WBZWBZ

RwaRwa MethodMethod

SP Method (:SP Method (:RxoRxo / / RtRt curve)curve)

..remember that SP equation is:SP = SP = --K x log (K x log (RmfRmf / / RwRw))

In water zones (Sw = 1.0)Rxo = F x Rmf and Ro = F x Rw

From the above equations, the SP equation can be rewritten as:SP = -K x log (Rxo / Ro)

Where:K K = 60 + (0.133 x formation temperature)= 60 + (0.133 x formation temperature)RxoRxo = shallow = shallow resistivityresistivity from Laterologfrom Laterolog--8*, 8*, MicrosphericallyMicrospherically Focused Log*, or Focused Log*, or MicrolaterologMicrolaterolog* x * x Ro Ro = wet = wet resistivityresistivity (Ro = (Ro = RtRt when when SwSw = 100%)= 100%)

In water-bearing zones, the measured values for Rxo and Ro (Rt for Sw = 100% ; RIld or RLLd) can be used to calculated a value for SP. This calculated value for SP should duplicate the measured value of SP from the spontaneous potential log in a wet zone. The presence of hydrocarbons results in Rt values which are greater than Ro. This means that when SP is calculated from Rxo and Rt values, it will be lower than the measured value of SP.

Pickett Crossplot Method

The Pickett crossplot (Picket, 1972) is one of the simplest and most effective crossplotmethod in use. This technique not only gives estimates of water saturation, but can also help determine:

(1) formation water resistivity (Rw),

(2) cementation factor (m), and

(3) matrix parameters for porosity logs (Dtma and rma).

The Pickett method is based on the observation that true resistivity(Rt) is a function of porosity (f), water saturation (Sw), and cementation factor(m). A Pickett crossplot is developed by plotting porosity values with deep resistivity (RIld or RLLd) values on two-by three cycle log-log paper

Hingle Crossplot•• The procedure for constructing a The procedure for constructing a HingleHingle

crossplotcrossplot to determine water saturation to determine water saturation is:is:

–– Select the correct Select the correct corssplotcorssplot graph paper graph paper (sandstone or carbonates).(sandstone or carbonates).

–– Scale the X axis on a linear scaleScale the X axis on a linear scale–– Plot deep Plot deep resistivityresistivity values (values (RIldRIld or or RLLdRLLd) on the Y axis versus the porosity ) on the Y axis versus the porosity log data.log data.

–– Construct a straight line through the Construct a straight line through the most northwesterly points , and most northwesterly points , and extrapolate this line until it intersects extrapolate this line until it intersects the X axisthe X axis

–– At the intersection point of the X axis At the intersection point of the X axis and the Ro line, determine the matrix and the Ro line, determine the matrix value and scale the X axis in porosity value and scale the X axis in porosity units.units.

–– Calculate a value for Calculate a value for RwRw from any from any corresponding set of f and Ro values.corresponding set of f and Ro values.

–– Determine lines of constants Determine lines of constants SwSw based based on the formula :on the formula :

Formation Water Test Method

Metoda formation water test merupakan metoda penentuan Rwberdasarkan jumlah air formasi yang telah dites pada sumurtertentu. Kemudian dilakukan penentuan kadar Cl- (dalam ppm), dan diplot pada Resistivity of NaCl Solution Chart untukmendapatkan nilai Rw.

0.15

Resistivity of NaCl Solution Chart

271.88oF

0.150.15

Resistivity of NaCl Solution Chart

271.88oF

…for example: This Water Test method is based on the amount of water formation that was tested in DST-2 (2949-2956 m) in KRT-1. The amount of Cl- is 13215 ppm with depth temperature 271,88 oF. Using Resistivity of NaCl Slutionchart, water resistivity is found approximately 0.15 ohm.m.