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Annual Logging Symposium, June 4-7, 2006

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IDENTIFICATION AND EVALUATION OF FRACTURED

TIGHT-SAND OIL RESERVOIR IN DEEP ZONE OF BOHAI GULF

Shanjun Li1

, Ce Liu1

, Liang.C. Shen1

, Hanming Wang2

, Jian. Ouyang3

, and Genji. Zhang4

1ECE Department, University of Houston, 4800 Calhoun Rd., Houston, TX 77004 Email:

[email protected], [email protected], [email protected] of Houston, currently an employee of Schlumberger, Schlumberger, Houston TX,

Email:[email protected] National Petroleum Company, Email:[email protected]

4University of Petroleum, China, Email:[email protected]

Copyright 2006, held jointly by the Society of Petrophysicistsand Well Log Analysts (SPWLA) and the submitting authors.

This paper was prepared for presentation at the SPWLA 47thAnnual Logging Symposium held in Veracruz, Mexico June4-7, 2006.

______________________________________

Abstract

In this paper, three fracture models are considered. First,we study the plane fracture model that represents the

formation consisting of fractures with equal spacing

and opening. Second, the matchstick model in whichtwo sets of perpendicular plane fractures exist is

examined. Third, we also study the cubic one where

three sets of plane fractures perpendicular to each other.These models can be represented by a macro-

anisotropic medium using equivalent conductivity

theorem. Using a 3-D FEM codes, dual laterologresponses in the models may be computed.

The simulated results of plane fracture model show thattool response in the equivalent medium equals to that of

the original fracture-free medium only when the

spacing between fractures is small , and that deep

laterolog response (Rlld) is greater than shallowlaterolog response (Rlls) for large dip angles and Rlld is

smaller than Rlls for small dip angles.

The computed responses of the matchstick model show

that when the porosity of main set fractures is muchgreater than that of another set, the response of the

model has the same characteristics as the plane model;

and when the main fracture porosity decreases, Rllddecreases for large dip angles and increases for small

dip angles. Rlls decreases for large dip angles and

changes very little for small dip angles. Samecharacteristics are found in the response of cubic

situation.

An inversion code has been developed to computefracture porosity and dip angle from dual laterolog

response, and used to evaluate the fracture porosity anddip angle in tight-sand oil reservoir in Bohai Gulf.

A Well A was drilled in Dagang Oilfield in Bohai

Gulf in 1999. When drilling through a tight-sandformation with low porosity and low permeability,

more than 67 cubic meters of mud was lost. Oil testingof the reservoir with 12.2mm nozzle produced 543

cubic meters of oil and 90,500 cubic meters of gas daily.

Such high production in this kind of reservoir was

beyond expectation of all experts working on thisproject. Based on the characteristics of dual laterolog

curves and related geometrical data in this region, thislayer and two others were named as fractured reservoirs,

and their fracture porosity and dip angles were

computed by using the inversion code. Oil testing to

another reservoir obtained 220 cubic meters of oil and79,984 cubic meters of gas daily.

INTRODUCTION

Fractures provide the path for oil and gas to move inreservoirs. That is the main reason why the

permeability in the formation with fractures is much

higher than that without fractures. So the production of

oil and gas especially in low permeability formation ismainly depended on the existing of fractures. Thus the

exploration and development of fractured reservoirs isone of main goals for most oil companies. The ability to

identify fractures and to evaluate their porosity, dip and

strike angles become an important requirement for well

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logging analysts to acquire.

Interpretation of logs obtained by electrode-type tools

in fractured formations requires special attention. A

fractured formation is an electrical anisotropic medium,

which means that the conductivity is different indifferent directions. Because of this property, it is

difficult for log analysts to identify and evaluate

fractures if standard interpretation routines are used.Some features in the dual laterolog responses in

fractured reservoirs have long been one of the keyproblems that log analysts wish to resolve. To this end,

using a 3-D FEM code, Sibbit et al. (1985) computed

the dual laterolog response of a single fracture when the

fracture dip angle is 0o or 90o. Philippe et al. (1990)derived the conductivity tensor formula for a medium

containing parallel fractures with equal aperture andspacing. They also obtained approximate dual laterolog

responses in a fractured medium with an arbitraryorientation angle. By means of a 3-D FEM code, Wang

et al. (1998) computed dual laterolog responses in many3-D cases, including those in parallel fractured

formations. Using azimuthal electrical sondes,Mousatov et al. (2003) discussed the property of

azimuthally fractured formations.

In this paper, three geological fracture types areintroduced: plane model, matchstick model, and cubic

model. It is shown that formations containing thosefractures can be treated as equivalent to some

homogeneous anisotropic media. Formula for the

effective conductivity tensor for each fracture model is

presented. Then dual laterolog responses in thosefractured formations are computed and discussed.

MODEL OF PLANE FRACTURE

A formation with plane fractures is consisted of parallel

fractures of equal aperture and spacing, as shown in

Figure1. Let dbe the fracture spacing, the fractureaperture,

bthe conductivity of the rock matrix, and

f

the conductivity of the fluid in the fracture, theequivalent conductivity tensor (Philippe and Roger,

1990) of this formation containing plane fractures with

zero dipping angle is

=

0

0

0

0

00

00

00

zzp

yyp

xxp

(1)

where

ffbfxxp += )1(0

, (2a)

ffbfyyp += )1(0, (2b)

)1(10

+=

f

bf

b

zzp

, (2c)

andd

f+

=

is defined as the fracture porosity. Note

that definition of the fracture porosity used here isdifferent from that used in (Philippe and Roger, 1990).In above equationsthe z-axis coincides with the normal

to the fracture plane and the x- and the y- axes are

parallel to the fracture plane.

Figure 1 Model of the plane fractures

The relative dip angle of the fracture is defined as theangle between the normal of the plane fracture and the

reference z-axis that is also the borehole axis. Then theconductivity tensor (Philippe and Roger, 1990) of the

dipping fractured formation is

=zzzx

yy

xzxx

0

00

0 , (3)

where

+= 2000 sin)( xxpzzpxxpxx , (4a)

0yypyy =, (4b)

= 2000 sin)( xxpzzpzzpzz , (4c)

== cossin)( 00 zzpxxpzxxz . (4d)

Note that due to the symmetry of the plane fracture, the

conductivity tensor is independent of the strike or the

azimuthal angle.

MODEL OF MATCHSTICK FRACTURES

A formation containing matchstick type of fractures is

consisted of two sets of plane fractures, as shown in

Figure 2. One set of plane fractures is horizontal orparallel to the XOY plane in the chosen coordinate

system shown in Figure 2. The other set of the plane

fractures is vertical or parallel to the YOZ plane. Herepoint O represents the origin of the coordinate system.

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Let a be the ratio of the horizontal fracture porosity to

the total fracture porosity. Assume first that the dippingangle of the fracture is zero. As shown in Appendix I,

the three diagonal elements of the conductivity tensor in

(1) can be expressed as follows:

ff

f

bf

b

fxxm a

a

a

+

+=

)1()1(1)1(0

(5a)

ffbfyym += )1(0(5b)

ff

f

bf

b

fzzm a

a

a

+

+= )1(

)1(1

])1(1[0

(5c)

Figure 2 Model of the matchstick fractures

In a similar case where one set of plane fractures isparallel to the XOY plane and the other is parallel to the

XOZ plane, the three diagonal elements are also given

by (5) with:0zzm

given by (5c). Furthermore,

0xxmand

0yymexchange their positions, i.e., the former is

given by (5b) and the latter by (5a).For the dipping case, the conductivity tensor is

same as (3), with the0xxp,

0yyp, and

0zzpin (4) replaced

by0xxm,

0yymand

0zzmin (5).

MODEL OF CUBIC FRACTURES

A formation is said to have cubic fractures if it isconsisted of three sets of plane fractures. These

fractures are parallel to the XOY, YOZ, and XOZplanes, respectively, as shown in Figure 3.

Let a be the ratio of the porosity of the main fractures

(the ones parallel to the XOY plane) to the total fracture

porosity. Let b be the ratio of porosity of the fracturesparallel to the YOZ plane, to the total fracture porosity.

With similar method of treating0xxm,

0yymand

0zzm, the

three diagonal elements in the conductivity tensor given

in (1) take the following forms:

ff

f

bf

b

fxxc b

b

b

+

+= )1(

)1(1

])1(1[0

(6a)

ff

f

bf

bfyyc ba

ba

ba

+++

+= )()1()1(1

])(1[0

(6b)

ff

f

bf

b

fzzc a

a

a

+

+= )1(

)1(1

])1(1[0

(6c)

Figure 3 Model of cubic fractures

Let0xxc,

0yyc, and

0zzcin (6) replace

0xxp,

0yypand

0zzp

in (4), the conductivity tensor of the cubic fractureformation with a dipping angle is obtained. It is easily

seen by comparing formulas (2), (5), and (6) that theplane model and the matchstick model are two special

cases of the cubic model.

SUMMARY OF 3-D FEM FORMULATION

When the dual laterolog response problem isformulated in terms of the FEM, the energy functional

is defined first (Zhang, 1986):

21 = . (7)

In (7),dVJE= 2

11

and it is the half of power

consumption in the medium;=

UI2

is the power

supplied by the electrodes; Jis the current density; Eis

the electric-field strength;EI

is the current emitted by

the electrode E; andEU

is its potential.

Y

Z

X

Y

Z

X

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In this paper tetrahedral elements are adopted. The

field strength in a tetrahedral element assumes aconstant value expressed in terms of the linear

combination of the potential values at the four nodes of

the tetrahedron. As shown in Appendix II, the half

power consumption 1 in element e of a homogeneousanisotropic medium with conductivity tensor (3) is

Vzxffzffb

yffb

V

xffb

dEEE

EE

]cossin)(2))(sin(

))(())(cos[(

22

2222

11

+++

+++=

(8)

whereeV

is the volume of the element e, andxE,

yE, and

zEare the three components of the electric field

strengthE.

For an inhomogeneous element, in which both the rock

matrix and the fracture are present, the half powerconsumption functional )(1

e in that element e is

2+= fb, (9)

where )(eb

is the power consumption in the matrix, and

efb

e

b VEE )1(2

1)( = .(10a)

Also, )(ef

is the power consumption in the fracture. In

Appendix III, taking into account the continuity of the

potential and the continuity of the normal component ofthe current density at the boundary between the fracture

and the matrix, the power in the fracture can be derivedto take the following form

effnf

f

be

f VEEE

])[(

2

1 22

)( +=. (10b)

It is proved in Appendix IV that the power consumption

defined by (8) for a homogeneous anisotropic mediumis equal to that defined by (9) for the plane fractures.

The above statement is valid on the conditions that boththe aperture and the spacing approach zero, with their

ratio kept at a constant value, and that the aperture is

infinitesimal with respect to the spacing. This means

that the formation with plane fractures can be treated asa macroscopic homogeneous anisotropic medium under

those conditions. This assertion is verified by actual

numerical computation in formation with planefractures, as we shall see later.

LATEROLOGS IN PLANE FRACTURES

Figure 4a and 4b show the influence of fracture spacing

on laterologs in the plane fractures. The abscissa

represents position of tools center and the ordinaterepresents the deep laterolog response computed with

3-D FEM. Curves labeled Rlld1 and Rlls1 are deep and

shallow laterologs with the fracture spacing equal to 1

m. Similarly, Rlld2 and Rlls2 are for 0.5 m spacing;Rlld3 and Rlls3 for 0.25 m spacing; and Rlld4 and

Rlls4 for 0.125 m spacing. It is assumed that the

resistivity of the rock matrix is 140 ohm-m and thefracture is filled with 0.18 ohm-m borehole mud. The

size of the borehole is 6 inches in diameter and the

fracture porosity is 1 %. The equivalent conductivitytensor corresponding to these parameters is listed in

Table I. These parameters are used throughout this

paper unless stated otherwise.

(a) Deep laterologs

(b) Shallow laterologs

Figure 4 Laterolog responses in a formation

with plane fractures.

140=bR(ohm.m),

fm RR ==0.18(ohm.m), bore-

hole size is 6(inch),f=1%. Curve 1 is for 1 m

fracture spacing. Similarly, curve 2 is for 0.5

m, curve 3 for 0.25 m, and curve 4 for 0.125mfracture spacing, respectively.

In both Figures 4a and 4b, it is seen that laterolog

readings in the fractured formations oscillate when the

tool moves along the borehole. The amplitude of the

10

100

1000

-2 -1 0 1 2

Position(m)

Rlld(ohm.m

)Rlld1

Rlld2

Rlld3

Rlld4

10

100

1000

-2 0 2

Position(m)

Rlls(ohm.m

) Rlls1

Rlls2

Rlls3

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oscillation decreases with the fracture spacing. The logs

are smoothly varying with depth without observableoscillation when the fracture spacing is reduced to

0.125 m. As far as laterolog is concerned, the medium

containing plane fractures with spacing less than or

equal to this margin can be regarded as macroscopicallyhomogeneous anisotropic medium.

Figure 5 shows responses of dual laterolog in twomedia. The first is a medium containing plane fractures

and the other is a homogeneous anisotropic medium.The abscissa represents the dip angle. The ordinate

represents Rlld1 and Rlls1, which are the deep and

shallow laterologs in a homogeneous anisotropic

medium. The curves Rlld2 and Rlls2 are the deep andthe shallow laterologs in a medium with plane fractures.

It is seen in Figure 5 that the dual laterolog responses inthe medium with plane fractures and those in the

anisotropic medium are indistinguishable for all dipangles. Of course, the conductivity tensor of the

anisotropic medium is set equal to the effectiveconductivity tensor of the medium with plane fractures.

The fracture spacing is 0.125 m.

Figure 5 Comparison between the duallaterolog responses in the plane fracture

formation and in a homogeneous anisotropicmedium with various dip angles.

Rlld1 and Rlls1 are deep and shallow responses

in a homogeneous anisotropic medium

respectively. Rlld2 and Rlls2 are deep andshallow responses in the medium with plane

fractures. Both media have the same equivalentconductivity tensor. Borehole size is 6(inch).

For the plane fracture formation,

bR=140(ohm.m),

fm RR ==0.18(ohm.m),

f=1%,

and spacing =0.125(m).

Figure 5 also displays the fact that the deep laterolog

reads lower than the shallow one for nearly horizontal

fractures. For nearly vertical fractures, the opposite is

true. Also, when the fracture dip is in the range from30o to 74o, the rate of variation of dual laterologs with

respect to the dip angle is the greatest. The critical

angle at which the deep and the shallow logs read the

same value is within this range. Both the deep and theshallow readings are affected primarily by the

horizontal conductivity at zero dip. At 90-degree dip,

these readings are approximately determined by thegeometric mean of the horizontal and the vertical

conductivities. These characteristics are common tolaterolog responses in anisotropic media (Wang et al.

1998). Figures 4 and 5 also verify the equivalence

between a medium with plane fractures and a

macroscopic homogeneous anisotropic medium in asfar as dual laterolog response is concerned.

(a) Deep Laterolog

(b) Shallow laterolog

Figure 6 The relationship between fractureporosity and shallow laterolog apparent

conductivity

bR=140(ohm.m),


Borehole size is 6(inch). Clls0, Clld0, Clls30,

Clld30, Clls60, Clld60, Clls80, Clld80, Clls90and Clld90 are shallow and deep laterolog

apparent conductivity computed when fracturedip is 0o, 30o, 60o, 80o and 90o respectively.

10

100

0 10 20 30 40 50 60 70 80 90

Fracture Dip(degree)

Ra(ohm.m

) Rlld1

Rlls1

Rlld2

Rlls2

0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.1

Fracture Porosit y(%)

Clld(s/m)

Clld0

Clld30

Clld60

Clld80

Clld90

0

0.05

0.1

0.15

0.2

0.25

0.3

0.350.4

0 0.05 0.1

Fracture Porosi ty(%)

Clls(s/m)

Clls0

Clls30

Clls60

Clls80

Clls90

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Figure 6a shows the relationship between the deep

laterolog reading and the fracture porosity for the planefracture model. The abscissa represents the fracture

porosity, and the ordinate is the apparent conductivity

reading of the deep laterolog. The curves labeled as

Clld0, Clld30, Clld60, Clld80 and Clld90 are deeplaterolog readings expressed in conductivity units when

fracture dip is 0o, 30o, 60o, 80o, and 90o, respectively. It

is seen that the deep conductivity reading increasesalmost linearly as the fracture porosity is increased.

Similar relationship between the shallow laterolog andthe fracture porosity is seen in Figure 6b. This behavior

is expected because the rock is highly resistive so that

the fluid in the fracture mainly contributes the overall

conductivity of the formation. The characteristics of thematchstick fractures and the cubic fractures are similar

to that of the plane fracture case in this regard.

LATEROLOGS IN MATCH STICK FRACURES

Figure 7 shows the relationship between fracture dipangle and the dual laterolog responses in a formation

containing matchstick fractures. Figures 7a, 7b, 7c, and7d are computed when the porosity ratio a is 0.9, 0.8,

0.7, and 0.6, respectively. Recall that a is the ratio of

the horizontal fracture porosity to the total porosity. It

is seen that in general the deep laterolog reading ishigher than the shallow reading in nearly vertical

fractures and lower in nearly horizontal fractures. Butthe difference between the deep and the shallow

responses becomes smaller when the ratio a is

decreased. Note that when a = 0.5, the horizontal

fracture is equal in porosity to the vertical fracture andthe readings at zero degree dip is the same as those at

90-degree dip.

(a) a=0.9

(b) a=0.8

(c) a=0.7

(d) a=0.6

Figure 7d Dual Laterolog response in

matchstick fracture formation

bR=140(ohm.m),


f=1%,

Borehole size is 6(inch).

(a) Deep Laterolog


Figure 8 Dual laterolog responses in matchstick

fracture formation for various a ratios.

The curves labeled as Rlls1 through Rlls4correspond to a ratio of 0.9, 0.8, 0.7, and 0.6,

respectively.fm RR =

=0.18(ohm.m),f

=1%.

bR=140(ohm.m), Borehole size is 6(inch).

10

100

0 10 20 30 40 50 60 70 80 90

Fracture Dip(degre e)

Ra(ohm.m

)Rlld1

Rlls1

10

100

0 10 20 30 40 50 60 70 80 90


Ra(ohm.m

)Rlld1

Rlls1

10

100

0 10 20 30 40 50 60 70 80 90


Ra(ohm.m

)Rlld1

Rlls1

10

100

0 10 20 30 40 50 60 70 80 90


Ra(ohm.m

)

Rlld4

Rlls4

10

100

0 10 20 30 40 50 60 70 80 90


Rlld(ohm.m

)Rlld1

Rlld2

Rlld3

Rlld4

10

100

0 10 20 30 40 50 60 70 80 90


Rlld(ohm.m

)Rlld1

Rlld2

Rlld3

Rlld4

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10

100

0 10 20 30 40 50 60 70 80 90


Ra(ohm

.m

) Rlld4

Rlls4

10

100

0 10 20 30 40 50 60 70 80 90


Ra(ohm.m

) Rlld1

Rlld2

Rlld3

Rlld4

Figure 8a summarizes the deep laterolog responses

shown in Figure 7a through Figure 7d for various aratios. The curves labeled as Rlld1 through Rlld4

correspond to a ratio of 0.9, 0.8, 0.7, and 0.6,

respectively. It is seen that the deep laterolog readings

in 90-degree dipping fractures decrease with decreasinga ratio. Deep laterolog readings increase with a ratio in

zero-degree dip fractures. Figure 8b shows similar

behavior for the shallow laterolog readings. The curveslabeled as Rlls1 through Rlls4 correspond to a ratio of

0.9, 0.8, 0.7, and 0.6, respectively. It is seen that theshallow laterolog readings in 90-degree fractures

decrease with decreasing a ratio but the shallow

laterolog readings are insensitive to the ratio in zero-

degree dip fractures.

LATEROLOGS IN CUBIC FRACTURES

Figure 9 shows the relationship between fracture dipangle and dual laterolog responses in a formation with

cubic fractures. Figure 9a is computed for ratios a and

b equal to 0.9 and 0.05, respectively. Recall that a is the

ratio of the horizontal fracture porosity to the totalporosity andb is the ratio of porosity of YOZ fractures

to the total porosity. These a andb ratios are 0.7 and

0.15, respectively in Figure 9b; 0.6 and 0.2 in Figure

9c; and 0.4 and 0.3 in Figure 9d, respectively. Thesefigures display similar characteristics as those of

matchstick fractures shown in Figure 7. That is, whenthere are mainly horizontal fractures, as in the case of

Figure 9a, the deep laterolog reads higher than the

shallow laterolog near 90-degree dip and the readings

are just the opposite near the 0-dip angle. When thefracture volumes are nearly equal in all three directions,

as in the case of Figure 9d, the deep and shallowlaterolog readings are almost the same.

(a) a=0.9, b=0.05

(b) a=0.7, b=0.15

(c ) a=0.6, b=0.2

(d ) a=0.4, b=0.3

Figure 9 Dual laterolog responses in cubic

fracture formation for various a andb ratios.

bR=140(ohm.m),


f=1%.

Borehole size is 6(inch).

(a) Deep laterolog


Figure 10b Dual laterolog responses in cubic

fracture formations with different a andb ratios.

Figure 10a summarizes the deep laterolog curves shown

in Figure 9. It is seen that the deep laterolog reading incubic fractures with 90-degree dipping angle decreases

with decreasing ratio a and increasing ratio b. The

10

100

0 10 20 30 40 50 60 70 80 90


Ra(ohm

.m

) Rlld1

Rlls1

10

100

0 10 20 30 40 50 60 70 80 90

Fracture Dip(ohm.m)

Ra(ohm

.m

) Rlld2

Rlls2

10

100

0 10 20 30 40 50 60 70 80 90


Ra(ohm

.m

)Rlld3

Rlls3

10

100

0 10 20 30 40 50 60 70 80 90


Ra(ohm.m

) Rlls1

Rlls2

Rlls3

Rlls4

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trend is just the opposite at the other end, that is, at

zero-degree dip. Similarly the shallow laterologreadings shown in Figure 9 are summarized Figure 10b.

It is seen that the shallow reading in 90-degree cubic

fractures decreases with decreasing ratio a and

increasing ratio b, with the opposite trend seen at zero-degree dip.

Application of Laterolog Response to Fracture

Evaluation

The software has been used in oilfield, China, to

evaluate fracture porosity and dip in carbonate and tight

sand formation. As an example, in this paper we only

give an application in tight sand formation.

In late 1999, Dagang oilfield drilled a well designatedas the A well here. When drilling from *923m through

*233m, more than 67 cubic meters of mud was lost.Interpretation of well logs showed low porosity and low

permeability, and formation water saturation computedfrom logs was very low in the region. So the layers in

this region were interpreted as water layers by Dagangoilfield well logging company. However, the oil testing

from *220m through *233m with 12.2mm opening of

pipeline given 543 cubic meters oil and 90,500 cubic

meters gas one day. Such high production in the lowporosity and low permeability zone was beyond the

expectation of all experts working on this project. Butthe use of dual laterologs can explain the unusual result.

Figure 11 shows dual laterolog data of three layers of

the A well from *930m through *230m. We can see thepositive difference between the deep and the shallow

laterolog responses. Also, the deep laterolog reading isgreater than the shallows. These observations coincide

with the characteristics of dual laterolog responses

computed above when the fracture dip angle is higher.

Based on some geometry data in this oilfield, weidentified the reservoir as a fractured one, and

interpreted other three reservoirs as fractured ones from*933m through *178m. Using the simulation software

of dual laterolog response in fractured reservoir, for

which the results are shown in Table 3.2. According to

the interpretation results, Dagang oilfield tested the

reservoir from *933m through *936m, resulting in 220cubic meters of oil and 79,984 cubic meters of gas. The

test data proved the correctness of the interpretation.Later, Dagang oilfield did image logging in this region,

which also confirmed our interpretation.

In Table 2, Section, Thk, LLd, LLs, Por, pf , Def and

FR represent region of reservoir, thickness of layer,

deep laterolog, shallow laterolog, formation porosity,

fracture porosity, interpretation definition and fractured

reservoir, respectively.

Salt mud was used with salinity 40,000mg/l. The mud

resistivity under earth is 0.05 m . Rock matrix

resisitivities were computed with Archies formula.

Those parameters were used to compute the fractureporosity and dip listed in Table 2.

CONCLUSIONS

In this paper we study three fracture models: the plane

fractures, the matchstick fractures, and the cubicfractures. It is shown that formations containing these

fractures can be modeled as anisotropic media. The

equivalent conductivity tensors for these fracturemodels are presented. The equivalence between these

fracture models and the corresponding homogeneous

anisotropic media are mathematically established and

numerically verified. By means of 3-D FEM, duallaterolog responses in various fracture models are

computed and studied. The 3-D simulation can even beused in cases where those fractures are dipping with

respect to the borehole axis. The results presented in

this paper are useful for interpreting laterologs infractured reservoirs. The software has been used by

oilfield company of China to evaluate fracture porosity

and dip in carbonate and tight sand formation and goodresults have been obtained.

Acknowledgments

This research is supported by a consortium of Aramco,

Baker Hughes, BP, Chevron E & P TechnologyCompany, ConocoPhillips, ExxonMobil Upstream

Research Company, Halliburton Energy Service,

Precision Energy Service, Shell E & P Technology

Company and Statoil.

REFERENCES

A.Mousatov, E.Pervago, and E.Kazatchenko, 2003,

Feasibility of Azimuthal Electrical Sondes for the Study

of Anisotropy in Fractured Formation, Paper YY, inTransactions of 44th Annual Logging Symposium:

Society of Professional Well Log Analysts.

Sibbit, A. M., Faivre, O., 1985, The dual laterolog

response in fractured rocks, paper T, in 26th Annual

Logging Symposium Transactions: Society ofProfessional Well Log Analyst, p. T1-34.

Philippe, A. P., Roger, N. A., 1990, In situ

measurements of electrical resistivity, formation

anisotropy and tectonic context, paper M, in 31st

Annual Logging Symposium Transactions: Society ofProfessional Well Log Analyst, p. M1-24.

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Wang, H. M., Shen, L. C. and Zhang, G. J., 1998, DualLaterolog Response in 3-D Environments, paper X, in

39th Annual Logging Symposium Transactions:

Society of Professional Well Log Analyst, p. X1-13

Wang Hanming and Shen, Liang C., 2001, Dual

Laterolog Responses in Anisotropic Crossbedding

Formation: Petrophysics, v.42, n.6, November-December, p. 624-632.

Zhang Genji, 1986, Electrical Well Logging vol. 2,

Petroleum Industrial Press, Beijing, China.

About the Author

Shanjun Li received the PhD degree in ElectricalEngineering from University of Houston, USA in 2004,

Ms degree in geoscience and BS degree in applied

mathematics from University of Petroleum, China in1993 and 1986, respectively. He worked as an

instructor in the Department of Mathematics of the

University of Petroleum from 1986 to 1990, as anengineer in Exploration Research Center of Tarim

Basin during 1993-1995, and as an associate professor

in the Department of Exploration of University ofPetroleum from 1996-2001. From 2005 to present, he is

a post doctoral fellow. His research interest is in

electrical logging theory and reservoir parameterevaluation.

Ce, Liu received the BS and MS and PhD degrees inradio engineering from Xian Jiaotong University, Xian,China, in 1982, 1984 and 1988, respectively. He has

been with the Department of Electrical and ComputerEngineering, University of Houston, TX, since 1988,

where he is currently an Professor and Director of Well

Logging Laboratory and Subsurface Sensing

Laboratory. From 1997 to 1998, he was on sabbaticalleave with Compaq Computers, Houston, TX, as a

Senior RF Architect. His research areas include EMsubsurface sensing, well logging, EM tomography,

sensor development, ground penetrating radar, RF

circuit design, and wireless telecommunication systems.

Dr. Liu is a licensed Professional Engineer and amember of SPWLA, EEGS, and SCA.

Liang C. Shen received the PhD degree in applied

physics from Harvard University in 1976. He then

joined the faculty of the University of Houston and is

now a professor in the Department of Electrical andComputer Engineering. He served as the Department

Chairman from 1977 to 1981. He was a full-timeresearch consult at Gulf Oil Exploration and Production

Company during 1981-82, and ARCO oil and Gas

Company during 1990-91. Dr. Shen founded the Well

Logging Laboratory in 1979 to do research inelectromagnetic properties of reservoir rocks. He has

published a textbook and more than 90 technical

papers. He is a fellow of IEEE and a recipient of the

SPWLA Gold Medal for technical achievement. He hasserved as an associate editor for Geophysics, Radio

Science, and IEEE Transactions on Geoscience and

Remote Sensing.

Hanming Wang received PhD degree from WellLogging Laboratory of University of Houston in 1999.

He is a senior research scientist of Schlumberger Sugar

Land Product Center. He is interesting in well logging

modeling, inversion and log analysis. He is a number ofSPWLA, SPE and SEG.

Jian Ouyang is a counselor of CNPC. He was a vice

general geologist of Exploration Bureau of CNPC.

Genji Zhang received his B.S. degree in 1952 fromTsinghua University, Beijing, China. He works with the

University of Petroleum, Shandong, China. Hisresearch interest is in electromagnetic field in

inhomogeneous media and geotomography. Mr. Zhang

is a member of the Petroleum Society of China and

Geophysical Society of China.

APPENDIX I

In X direction, the formation, as shown in Figure2, canbe treated as serial conductors of the matrix with

conductivity,

)1()1(1 +f

bf

b

a

obtained from (2b)

with fracture porosityfa )1(

, and fractures with

porosityfa. With formula (2a), the conductivity in X

direction0xxmcan be computed with the following result:

ff

ff

bf

b

fxxm

a

a

a

+

+=

)1()1(1

)1(0

(A1)

Similarly, in Y direction, the conductivity0yym

can be

computed with the following result:

ffbfyym += )1(0. (A2)

In Z direction, the formation can be considered as serial

conductors of the matrix with conductivity,

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)1(1 +f

bf

b

a

obtained from (2c) with fracture

porosityfa

, and fractures with porosityfa )1(

. The

conductivity in Z direction 0zzm con be computed withthe following result:

ff

f

bf

b

fzzm a

a

a

+

+= )1(

)1(1

])1(1[0

(A3)

APPENDIX II

In a fractured reservoir, becausef

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Table 1 Diagonal conductivity tensor elements when fracture (dip angle = 0)

Off diagonal elements are equal to zero.

Fracture modelxx (s/m) yy (s/m) zz (s/m)

Plane Fracture 0.062 0.063 0.0072

a=0.9 0.057 0.063 0.013

a=0.8 0.052 0.063 0.018

a=0.7 0.046 0.063 0.024

Matchstick

Fracture

a=0.6 0.040 0.063 0.029

a=0.9, b=0.05 0.060 0.060 0.013

a=0.7, b=0.15 0.054 0.054 0.024

a=0.6, b=0.2 0.052 0.052 0.029

CubicFracture

a=0.4, b=0.3 0.046 0.046 0.040

Table 2 Interpretation results of A well in Dagang oilfield

Section Thk LLd LLs Por pf Dip Def Test Results

m m m m % % (O

) daym /3

*933-*936 4 8 4.5 15 1 85 FR 220 oil and 79,984 gas

*158-*165 7 8 4.5 13 1 85 FR*172-*178 6 9 6 13 1.05 85 FR

*220-*226 6 5 3 13 1.9 80 FR 543 oil and 90,500 gas

3 12 9 13 0.27 70 FR

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Figure 11 Dual laterolog data of A well from *930m through *230m

0 Gr/API 150

0 SP/mv 100

2 Rlld/ohm.m 20

2 Rlls/ohm.m 20

Dept

h(m)

#*28 layer

Pf=1%

Dip Angle

=85 degree

#*51 layer

Pf=1%

Dip Angle

=85 degree

#*55 layer

Pf=1%Dip Angle

=80 degree

*930

*940

*160

*220

*230

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