PETE_663_RESIST_THEORY.pdf

8/10/2019 PETE_663_RESIST_THEORY.pdf

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FORMATION EVALUATION

PETE 663

RESISTIVITY THEORY / SATURATION

Summer 2010


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IDEALIZEDLOG SET

= 0.30

= 0.35

= 0.07

R = 0.4

R = 0.3

R = 4

R = 8

Sand

Shale


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FOUR COMPONENTS OF SANDSTONE

MATRIXFRAMEWORK

(QUARTZ)

FRAMEWORK

(FELDSPAR)

CEMENT

PORE

Note different use of matrix

by geologists and engineers

0.25 mm

1. Framework

2. Matrix3. Cement

4. Pores

Engineering

matrix

Geologists Classification

Ayers, 2001


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FLUID SATURATIONS

Grain Water Gas Oil

Initially, water fills pores and wets the rock surface

Hydrocarbons migrate into the reservoir rock, displacing some water

Hydrocarbon distribution determined by gravity and capillary forces,and by wettability

Modified from NExT, 1999

and matrix


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RESISTIVITY OF ROCKS CONTAINING FLUID


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RESISTIVITY DEFINITION OF THE

OHM-METER

From Halliburton (EL 1007)


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RESISTIVITY

Resistivity

The voltage required to cause one amp to passthrough a cube having a face area of one

square meter

Units are ohm-m / m; usually ohm-m (.m)2

tyConductivi

1yResistivit =


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RESISTIVITY MEASUREMENT

Resistivity

( )( )

( )mL

mAohms

I

V

metersohmR

2*)(

=


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RESISTIVITY OF EARTH MATERIALS

tyConductivi

1yResistivit =

Incr

easing

Res

istivity

(1) Rock

(2) Gas

(3) Oil

(4) Fresh Water

(5) Salt Water

Inc

reasing

Co

nductivity


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Resistivity of water Porosity of the formation,

Pore geometry - tortuosity

Lithology of the formation

Degree of cementation, and

Type and amount of clay in the rock

FACTOR AFFECTING RESISTIVITY

From J. Jensen, PETE 321 Lecture Notes


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ELECTRICITY AND EARTH MATERIALS - 1

Conduction is by ions in water

Na+ and Cl- are very common

Other monovalent ions K+ and OH-

Common bivalent ions: Ca++, Mg++


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Water resistivity

controlled by

Ion concentrations

What type of ions

What temperature

Chart GEN-4 toconvert to NaCl

equiv

Chart GEN-5 fortemperature/resist

for NaCl

Electricity and Earth Materials - 2

From Schlumberger


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Resistivity

of NaClSolutions

____

GEN-5 H

orGEN-9 S

From Schlumberger


14/36From Schlumberger

Ca = 460 ppm

S04 = 1,400

Na + Cl = 19,000

TDS = 20,860

TDS = 20,850 ppm

0.81

0.45

(460)(0.81)+(1,400)(0.45)+(1)(19,000) = 20,000 ppm

T = 75 deg. F

H, GEN-4; SLB, GEN-8


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75 deg. F

SLB, GEN-9

H, GEN 5


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ARCHIES FIRST EQUATION

Relates rock resistivity to Rw

Ro

= F Rw

, where:

Ro = Resistivity of a rock that is 100%saturated with formation water

Rw

= Resistivity of formation water

F = Formation factor (formation resistivity factor)

As the salt water content increases, the formationresistivity will decrease.

A rock containing oil or gas will have a higherresistivity than the same rock completely saturatedwith salt water.

As the shale content increases, the rock matrix willbecome more conductive.


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Rt

Ro

Rw

Cube of water

having resistivity,

Rw

Non-shaly rock, 100% saturated

with water having resistivity,

Rw

Rock containing pores saturated

with water and hydrocarbons

Inc

reasing

Re

sistivity

(1) Rock

(2) Gas

(3) Oil

(4) Fresh Water

(5) Salt Water

Increasing

Conductivity

= 100%

Sw = 100%

= 20%

Sw = 100%

= 20%

Sw = 20%

SHC =80%

mw

o aR

RF

==


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The formation factor (F) depends on:

Porosity of the formation;Pore geometry;

Lithology of the formation;

Degree of cementation; and

Type and amount of clay in the rock.

FORMATION FACTOR


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For a clean formation (no shale), the formation factor can

usually be empirically correlated with porosity.

a = constant 1.0 for most formations

m = cementation factor 2 for most formations

Common values

F = 0.8/2 (Tixier) or 0.62/2.15 (Humble) for sandstones

F = 0.8/2 for carbonates

m

aF

=

FORMATION FACTOR


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FormationResistivity

Factor

VersusPorosity

mw

o a

RRF

==

As

increases, more ofthe rock volume is

comprised of pores

filled with conductive

fluid

Therefore, Ro and Fdecrease

RELATION OF FORMATION FACTOR


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RELATION OF FORMATION FACTOR

TO VOLUMETRIC POROSITY


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RESISTIVITY FACTOR TO SHALINESS

The formation factor (F) is constant for a clean

sand; F decreases for shaly sand as value of Rwincreases.


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SATURATION

Amount of water per unit volume = Sw

Amount of hydrocarbon per unit volume = (1 - Sw)

Matrix

Water

Hydrocarbon(1-Sw)

Sw


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Relates Sw to Rt

If Rt = R0, then the formation is 100% saturated

with formation water. However, if Rt > Ro, thenthe formation contains oil or gas.

General formula:

t

m

w

t

w

t

on

w

R

Ra

R

RF

R

RS

**===

For clean sands, n = 2 is common.

Like a and m, n is measured in the lab.

ARCHIES SECOND EQUATION


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LAB EVALUATION OF N


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Archies equation is based on the following

relationships

How Archies Equation Works

Rock type 1

Rock type 2

1000

100

10

1 .01 .1 1.0

FR

When water saturation is 100%


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Determining Rw Directly: from measured water sample

Indirectly: from openhole well logs

SP logs

Pickett plotsRwa technique


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Rw Using the Rwa Technique

t

m

waRR


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Example Log

GRC0 150

SPCMV-160 40

ACAL6 16

ILDC0.2 200

SNC0.2 200

MLLCF0.2 200

RHOC1.95 2.95

CNLLC0.45 -0.15

DTus/f150 50

001) BONANZA 1

10700

10800

10900


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Rw Using Pickett Plots

For water sands

n1

tm

w

w R

Ra

S

/

wwt SlognRaloglogmRlog

wt aRloglogmRlog

y InterceptxSlope


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Well: Bonanza 1

Zone: 10690.000 - 10980.000 ft

Date: 27 Apr 1998 @ 11:31

VCL < .3Deep Induction

5000.01 0.1 1 10 100

Porosity

0.0

1

0.1

1

Ap

parentRt

0.2

200

0.6

32456

2

6.3

24555

20

63.2

45553

1.00

Rw = 0.073

a = 1

m = 2

n = 2

Example Pickett Plot

Pi k tt Pl t S l ti F S


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Pickett Plot Solution For Sw

1.00

.8

.6

.4

.2

.1

Well: Bonanza 1

Zone: 10690.000 - 10980.000 ft

Date: 27 Apr 1998 @ 11:32

VCL < .3Deep induction

5000.01 0.1 1 10 100

Porosity

0.0

1

0.1

1

Ap

parentRt

0.2

200

0.6

32456

2

6.3

24555

20

63.2

45553

Rw = 0.073

a = 1

m = 2

n = 2


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SUMMARY - RESISTIVITY

Resistivity important property

Depends on ions in water

Water resistivity depends onConcentration

Temperature Ion species

Archies First Equation relates rock

resistivity to Rw Archies Second Equation relates Sw to Rt

Documents

PETE_663_RESIST_THEORY.pdf