Electromagnetic Propagation (EPT1) Log Interpretation



Electromagnetic Propagation (EPT1) Log Interpretation

on the Computer

By Andy May2

1Mark of Schlumberger

2Senior Staff Geologist, Kerr McGee, Oklahoma City

Dielectric logging has been available commercially from

Schlumberger and other logging companies for over 10 years. These

tools are very useful in evaluating formations drilled with oil-

based mud, formations that contain fresh water, and in thin-bedded

reservoirs. In particular, in wells drilled with oil-based mud,

these tools can be invaluable when used to find the top of the oil-

water transition zone. Dielectric tools are also used to correct

for the effect of invaded oil on density and induction logs.1.

Yet, interpreting dielectric logs continues to be very difficult.

The mathematics that describe the tool's response are very complex.

In addition, a battle over which of several complex interpretation

methods is best has been raging in the technical journals for over

ten years.

Unlike the more commonly used logging tools, it is difficult for

the practicing geoscientist and log analyst to get a "feel" for the

EPT. The mathematics that describe the theory of microwave logging

are not the straightforward linear and logarithmic functions that

we associate with density or electric logs. Instead, difficult

functions of complex numbers describe dielectric log response.

These functions fill dielectric logging papers with greek letters

and equations that only die-hard mathematicians could love.

The purpose of this paper is not to present anything new, but to

present a concise synthesis of dielectric log theory, and a

practical, accurate, and up-to-date computer algorithm for

interpreting dielectric logs. The intent is to give the reader

that "feel" for the tool that is so important in interpreting a

log. While researching this paper the author tried just about

every technique proposed for interpreting the dielectric logs, but

only one is presented here.

The "Modified CRIM" method, originally published by Dahlberg and

Ference4, with a few original modifications, is the basis for the

program presented in this paper. Essentially the same algorithm was

independently developed at Schlumberger and published as the CTA

method by Chardac2, Cheruvier and Suau3. The jury is still out on

the subject of the "correct" way to interpret the EPT, but this

method leads the pack today.

Dielectric Logging Theory

EPT porosity is the quantity calculated using the tool

measurements. This porosity(þept) is equivalent to the water-filled

porosity in the near borehole region. This is the volume of water

in the flushed zone, which is equal to porosity(þ) times the

flushed zone water saturation (Sxo). The tool works because the

relative dielectric permittivity (î') of water is about 78 and the

relative dielectric permittivity of oil, gas, and sedimentary rock

is very low, normally less than 10.

A rock's complex dielectric permittivity describes the rock's

electrical properties. This is the quantity that the EPT tool

attempts to measure. The complex dielectric permittivity is

defined as:

î* = î' - (å/þ)i ......................(1)

Where (þ) is the angular frequency (2ãþfrequency), (å) is the

conductivity, (î') is the effective permittivity, and (i) is the

square root of (-1). The equation shows that at low frequencies

(like those used in induction logging) the imaginary part of (î*),

the rock's conductivity, dominates the electrical properties of the

rock. Further, it shows that at very high frequencies the real

part of (î*), or the rock's effective permittivity, is dominant.

Equation (1) has one other property, when the rock's conductivity

is very small compared to the frequency, the complex dielectric

permittivity is a real number and is easily evaluated. This is

true of a non-conductive rock matrix filled with fresh water and

oil or gas. In these situations all the normal methods of

evaluating the EPT work very well. These methods include the TPO

method9, the Complex Refractive Index Method (CRIM)9, and the Hanai-

Bruggeman-Sen(HBS)7,8 method.

Early workers on the dielectric logging tool hoped that the very

high frequencies used by the tool would allow the computation of

water saturation independently of Rw. This is essentially the

assumption made when using the TPO equation. In practice, ignoring

Rw can only be done when Rw is greater than about 0.2 ohms at 75þ

F. In this higher Rw range any of the equations cited above can be

used to evaluate þept. When Rw is less than 0.2 either CRIM or the

more general HBS equations must be used.

Figure 1 shows the effect of salinity on þept. The center line is

an assumed Sxo. The lower line is the computed Sxo if the water

has a salinity of 60,000 PPM. The upper line is the computed Sxo

at 200,000 PPM. The potential error is over 20 at 50% Sxo in this

hypothetical case. The error is very small at low Sxo's,

encouraging the use of the EPT in oil-based mud systems.

Two researchers7,8 have compared both the HBS þept and the CRIM þept

to laboratory measured water volumes, in various rock types and

with waters of varying salinities. These studies were

inconclusive, since one author determined that CRIM was a better

method7 and the other determined that the HBS method was superior8.

But, the studies did show that the CRIM þept was an acceptable

estimate of Sxo under ideal laboratory conditions. The program

presented in this issue uses a derivative of CRIM. The form of the

equations used is very different from the equations presented in

the original CRIM paper9, and so the method used is often called

the Complex Time Average (CTA) method. But, the two methods are

equivalent, as demonstrated elsewhere3,4. The key equations, that

connect the log readings used in the CTA method and the dielectric

permittivity values used in CRIM are:

î'/î0 = 0.09018 (Tpl2 - (Att/60.03)2)................(2)

î"/î0 = (å/þ)/î0 = Att þ Tpl/333.5..................(3)

Tpl is the log propagation time in nano-seconds/meter, Att is the

plane-wave corrected log attenuation in dB/meter. We have divided

the two parts of the complex dielectric permittivity (î' and î") by

the permittivity of a vacuum î0 (8.854 x 10-12) to turn them into

relative dielectric permittivities. This makes the numbers easier

to handle. Typically when one sees a value of dielectric

permittivity quoted for a substance (eg. 79 for water) the number

is a relative dielectric permittivity.

The CTA equations have two common variables, salinity and þept. The

solution process used in the computer program solves for these two

values using the EPT log measured Tpl and Att. The equations are:

þept = (Tpl - Tpm + þt(Tpm-Tphc)) / (Tpw-Tphc).....(4)

þept = Att/Attw....................................(5)

Figure 2 shows how Tpw (the Propagation Time of water in

nanosec/m), Attw (the Attenuation of water in Db/m), and salinity

are related. As salinity (the values posted next to the squares on

the line) increases, the values for Tpw and Attw also increase.

Each salinity predicts a unique pair of Attw and Tpw values and

vice-versa. Thus after equation 4 is used to compute þept, this

value can be used to compute Attw with equation 5. The new value of

Attw predicts a new salinity. The new salinity is used to reenter

equation 4 with a revised Tpw, to compute a new þept. This cycle

continues until the values of salinity and þept stabilize.

Iterating in this fashion will solve the two equations for both

salinity and þept, if the data is accurate.

A second look at Figure 2 and at equations 4 and 5 shows that this

function is somewhat unstable. Notice that as Tpw increases þept

decreases, which in turn causes Attw and salinity to increase.

Thus, if the Att measurement is only slightly in error, the

solution process can proceed up the graph and fly off the end.

The EPT and its sister dielectric logging tools are very sensitive

to mudcake and borehole rugosity5,6. In particular, the attenuation

measurement can be affected severely by the borehole environment,

dipole effects, signal scattering, and spreading loss6. The newer

EPT-G tool can be corrected more accurately for these effects5 than

the older EPT-D. The author has no experience with this new tool,

but if it works as described, it will result in far better answers

when using the program presented in this issue. As Dahlberg and

Ference4 have noted the full CTA method(or any other iterative

method) can give inaccurate results, due to erroneous log measured

attenuations. Cheruvier and Suau3 also made this point.

The attenuation measurement is the additional information used in

CRIM (or CTA) to account for the salinity of the water. It is also

the weakest measurement. That is why the computer program allows

the log analyst to limit the range of salinities considered by the

solution process. Limiting the salinity range as much as possible,

will improve the computer program's accuracy. In water-based muds

the EPT will "see" a salinity that is close to that of the mud

filtrate and in oil based muds the salinity seen will be similar to

the formation water salinity.

Well Example

The accuracy of þept under appropriate logging conditions is

acceptable. In the example wells, the tool was used to pick the

top of the oil-water transition zone. Figure 3 is a graph showing

the Rt derived Sw in well A and the EPT derived Sw from the same

well and an offset, Well B. The EPT Sw is lower than the induction

Sw in the transition zone because the wells were drilled with oil-

based mud and the invading fluid is oil. All three water

saturation curves come together and flatten out at approximately

7912 ft. subsea. This is the top of the oil-water transition zone

based upon the EPT and supporting core data. The sudden increase

in Sw, at 7900 ft, in well B is due to a shale.

The various estimates of water saturation above the top of the

transition zone are compared in Table 1. The Sw's estimated with

the induction log are listed first. In well A the high

resistivities result in a very low estimate of Sw (5.5%) using core

derived values of M and N. Using the same values of M and N the

induction log indicates that well B had an irreducible Sw of 14.5%.

The core measured Sw's, from both the center of the cores (the

vertical plugs taken from well B) and plugs taken from the edge of

the cores (the horizontal plugs) all cluster around 10%.

One would ordinarily assume that the EPT estimates of Sw, above the

transition zone, are valid. Above the top of the oil-water

transition zone, the invading oil from the mud will not move the

connate water since the rock is at irreducible water saturation.

Yet, compared to the Rt and core measured Sw's, the EPT values are

low.

Oil and gas have very low relative dielectric permittivities and

low propagation times (Tpl). The Tpl of the oil-based mud

filtrate, used to drill the example wells, is 4.7 ns/m. This can

cause the EPT signal to "short circuit" through the mud that lies

between the EPT pad and the borehole wall. The example wells have

a very thin mudcake, less than one-eighth inch thick, typical of

wells drilled with oil-based mud, but still some "short-circuiting"

occurs. This has caused the EPT Sw's in the example wells to be

too low, the effect is discussed in the literature5,9. In the

example wells, and in other area wells, the effect is a constant

offset that can be corrected by comparing the EPT Sw's to core

data.

The Program

The main program asks the user for the necessary constants, for the

input file name and for the output file name. If the output file

name is "*" then the program sends the output to the screen.

The first constant requested is the Tpl of the matrix(TPM). This

value can be measured from cores or obtained from a chartbook. To

process the supplied test data, use the sandstone value of 7.2

ns/m. The second and third constants requested are the minimum and

maximum salinity values. These values constrain the solution

process. The function CTA will attempt to solve for salinity and

þept, these minimum and maximum values will keep the solution

process from "going wild," as discussed above, when it encounters

incorrect attenuation values.

Next the main routine asks for the formation temperature in degrees

Fahrenheit. Using the temperature, an array is initialized by the

function LOSS that is used by the function CTA to compute salinity

from water attenuation. Finally the hydrocarbon propagation time

will be requested. This value can be input directly or as a

hydrocarbon density1 in g/cc.

After obtaining the input constants from the user, the main routine

goes into a loop. The input data are read, one depth at a time,

using format 1000. The variables read are described in the

comments preceding the read statement. All of the variables are

not used by the program, some are supplied only for the reader's

information.

Immediately after reading each line (or depth) of data, the value

of KPPMIN (the minimum salinity) is reset to the input value KPPM.

This is done because the function CTA returns the computed salinity

in KPPMIN each time it is called.

After calling CTA to do the computations, the main program calls

either PRTVAL to write the results to a file, or SCRVAL to write

the results to the screen. The variable PAGESZ controls the

placement of the page headings. To remove the page headings

altogether, enter a PAGESZ of zero.

The Calculations

The calculations are performed with the function CTA. The function

returns Sxo. KPPM, the computed salinity, is returned as the

variable KPPMIN. The work of the function is done in the DO loop.

The function calls EPSWA in each loop to compute the values of TPW

(the water propagation time) and ATTW (the water attenuation)

associated with the current estimate of KPPM. The first estimate

of KPPM tried is KPPMIN, the minimum salinity expected by the user.

EPSWA is a function modified from one published by Dahlberg and

Ference4. It is used here with their permission. This function

uses a complex, but accurate, method to compute TPW and ATTW for

water of a particular salinity and temperature.

Next, TPLMET is called to compute Sxo from the TPL and TPW

supplied. This estimate of Sxo is then used to compute ATTW with

the second of the CTA equations. The function SALIN converts the

ATTW to salinity using the table previously built by the function

LOSS.

The computed salinity (SAL) is carefully constrained to the user

defined limits with the next three statements. Convergence is

achieved when the current estimate of salinity is within 10% of the

previous estimate or when the current estimate of Sxo is within

one-half of one percent of the previous estimate.

The program has been tested with the wells used as examples in this

paper and with many other wells drilled with both oil-based and

water-based muds. When properly used the program gives very good

results. The key to successful use is determining KPPMAX and

KPPMIN. Generally, set the range closely around the salinity of

the mud filtrate when processing wells drilled with water-based

muds. Set the range closely around the formation water salinity

when processing wells drilled with oil.

The best salinity range to use can be more accurately set by

running trials on a selected subset of the data. The EPT

attenuation measurement is the reason that the program seldom

converges and the reason why the salinity range is required. If

the attenuation measurement is accurate the program will converge

at the proper salinity, if it is off the program will not converge.

If the program does not converge, the higher estimated salinity

(KPPMAX) will probably be the value used. But the minimum value

may be used in zones of high Sw. The attenuation measurement is

most accurate when the borehole walls are smooth, the mudcake is

thin, and the volume of water (þept) is greater than 0.1. Under

these conditions, the user should see several intervals where the

program reaches convergence on a salinity. These values can be

used to select an appropriate range for KPPMIN and KPPMAX.

References

1. Boyeldieu, C., Coblentz, A., Pelissier-Combescure, J.,

"Formation Evaluation in Oil Base Mud Wells," SPWLA Symposium,

June, 1984, paper BB.

2. Chardac, J. L. M., "EPT Applications in the Middle East,", SPE

13737, SPE 1985 Middle East Oil Technical Conterence, March,

1985.

3. Cheruvier, E. and Suau, J., "Applications of Microwave

Dielectric Measurements in Various Logging Environments,"

paper MMM, 1986 SPWLA Symposium Transactions.

4. Dahlberg, K. E., and Ference, M. V., "A Quantitative Test of

the Electromagnetic Propagation Log (EPT) for Residual Oil

Determination," SPWLA Symposium Transactions, June, 1984.

5. Freedman, R. and Grove, G. P., "Interpretation of EPT-G Logs

in the Presence of Mudcakes," SPE 18116, Presented at the 1988

SPE Conference, Oct., 1988.

6. Gilmore, R. J., Clark, B., Best, D., "Enhanced Saturation

Determination Using The EPT-G Endfire Antenna Array," Paper K,

1987 SPWLA Symposium.

7. Shen, L. C., Savre, W. C., Price, J. M., Athavale, K.,

"Dielectric Properties of Reservoir Rocks at Ultra-High

Frequencies," Geophysics, Vol. 50, No. 4, April, 1985, p. 692-

704.

8. Sherman, Michael M., "The Calculation of Porosity from

Dielectric Constant Measurements: A Study using Laboratory

Data," The Log Analyst, Jan.-Feb., 1986, p. 15-24.

9. Wharton, R. P., Hazen, G. A., Rau, R. N., and Best, D. L.,

"Electromagnetic Propagation Logging: Advances in Technique

and Interpretation," SPE 9267, Presented at the 1980 SPE

Conference, Sept., 1980.

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º Table 1 º

º Comparison of Sw Estimates, Above Transition Zone º

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º Well Rt Sw EPT Core Core º

º CTA Sw Vert. Sw Horiz. Swº

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º Well A 5.5 4.7 -- 8.3 º

º Well B 14.5 6.1 10.4 12.5 º

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C***************************************************************************

C EPT SW COMPUTATION PROGRAM *

C *

C COMPUTES EPT SW USING THE CTA METHOD *

C *

C BY ANDY MAY *

C MARCH 2, 1990 *

C *

C Compiled, linked and tested with Microsoft Fortran 4.1 *

C OS/2 Version *

C *

C Command lines: FL /AM /c /G2 EPT.FOR *

C LINK /ST:4096 EPT *

C***************************************************************************

C

CHARACTER TITLE*80, TITLE2*80

CHARACTER FNAME2*80

INTEGER LINES, PAGENO, PAGESZ

C

REAL KPPM, KPPMIN, KPPMAX

COMMON /PRINT/ LINES, PAGENO, TITLE, TITLE2, PAGESZ

C

CHARACTER FNAME*80

C

C*******************************************************

C* FORMATS AND INITIALIZATION OF PRINT VARIABLES *

C*******************************************************

C

100 FORMAT(A80)

200 FORMAT(F10.0)

300 FORMAT(' Enter the output file name or an asterisk ("*") to'

1 ' send the output to the screen')

400 FORMAT(I10)

C

TITLE =' DEPTH PHIT SW SXOCTA KPPM CORE'

TITLE2=' (FEET) (XPLOT) (RT) CTA SW SW '

C

LINES = 0

PAGENO = 0

IERR = 0

C

WRITE(*,'(A)') ' Enter the number of lines per page or screen'

READ (*,400) PAGESZ

C

C***************************************

C* ASK FOR FILE NAMES *

C***************************************

C

WRITE(*,'(A)') ' Enter the input file name'

READ (*,100) FNAME

OPEN(UNIT=10,FILE=FNAME,STATUS='OLD', ERR=9000)

C

WRITE(*,300)

READ (*,100) FNAME2

IF (FNAME2(1:1) .NE. '*')

1 OPEN(UNIT=20, FILE=FNAME2, STATUS='NEW', ERR=9000)

C

C***************************************

C* PICK UP CONSTANTS FROM SCREEN *

C***************************************

C

WRITE(*,'(A)') ' Enter the matrix propogation time'

READ(*,200) TPM

C

WRITE(*,'(A)') ' Enter the minimum water salinity in Kppm'

READ(*,200) KPPMIN

KPPM = KPPMIN

C

WRITE(*,'(A)') ' Enter the maximum water salinity in Kppm'

READ(*,200) KPPMAX

C

WRITE(*,'(A)') ' Enter the formation temperature'

READ(*,200) FT

C

C ...BUILD ARRAY OF KPPM AND ATTW VALUES FOR CTA FUNCTION

CALL LOSS(FT)

C

WRITE(*,'(A)') ' Enter the hydrocarbon propogation time'

WRITE(*,'(A)')' or, if unknown, enter hydrocarbon density in g/cc'

READ(*,200) TPHC

C

C ...THE FOLLOWING EQUATION IS FROM BOYELDIEU, ET. AL., 1984

IF (TPHC .LT. 1.3) TPHC = 3.3 + 1.6*(TPHC - 0.2)/0.7

C

C**************************************************************

C* LOOP THROUGH THE INPUT DATA, QUIT AT THE END-OF-FILE *

C**************************************************************

C

C**************************************************************

C* READ A LINE OF INPUT DATA FROM THE INPUT DISK FILE *

C* *

C* DEPTH: MEASURED DEPTH, NOT USED IN THE PROGRAM LOGIC. *

C* SUBSEA: SUBSEA DEPTH, NOT USED IN PROGRAM LOGIC. *

C* PHIT: TOTAL POROSITY, USED TO COMPUTE EPT SXO, THE EQ *

C* IS SXO = PHIEPT/PHIT, NOTE THE PROGRAM *

C* ASSUMES THIS VALUE IS WHOLE NO. PERCENT *

C* PHIE: EFFECTIVE OR SHALE CORRECTED POROSITY, NOT USED *

C* IN PROGRAM LOGIC. *

C* SW: RT COMPUTED SW, NOT USED IN PROGRAM LOGIC. *

C* SWE: SHALE CORRECTED SW, NOT USED IN PROGRAM LOGIC. *

C* TPL: RAW EPT PROPOGATION TIME IN NANOSEC/M. *

C* USE TPL FROM EPT-D AND TPPW FROM EPT-G *

C* ATTEV: SPHERICAL SPREADING LOSS CORRECTED EPT *

C* ATTENUATION. FOR EPT-G USE VALUE CALLED EAPW. *

C* FOR EPT-D USE THE FOLLOWING EQUATION TO CORRECT *

C* THE READING: *

C* ATTEV = EATT - 45 - 1.3*TPL - 0.018*TPL*TPL *

C* CORESW: CORE MEASURED SW, NOT USED IN PROGRAM LOGIC *

C**************************************************************

C

500 READ(10, 1000, END=3000, ERR=9000)

1 DEPTH, SUBSEA, PHIT, PHIE, SW, SWE, TPL, ATTEV, CORESW

1000 FORMAT(F8.0, F9.0, 5F7.0, F9.0, F7.0)

C

C...CTA METHOD

KPPMIN = KPPM

SXOCTA = CTA(TPM, TPHC, PHIT*0.01, TPL, ATTEV, KPPMIN,

1 KPPMAX, FT)*100.0

C

C...PRINT RESULTS

IF (FNAME2(1:1) .NE. '*') THEN

CALL PRTVAL(DEPTH, PHIT, SW, SXOCTA, KPPMIN, CORESW, IERR)

ELSE

CALL SCRVAL(DEPTH, PHIT, SW, SXOCTA, KPPMIN, CORESW)

ENDIF

IF (IERR .EQ. 1) GO TO 9000

C

C...LOOP FOR NEXT SET OF VALUES.

GO TO 500

C.....................................................................

C

C********************************************

C* PROCESSING AND PRINTING FINISHED, STOP *

C********************************************

C

3000 CONTINUE

STOP

C

C*****************************************************************

C* AN ERROR OCCURRED WHILE OPENING, READING OR WRITING TO A FILE *

C*****************************************************************

C

9000 WRITE(*,'(A)') ' I/O ERROR'

STOP

END

C

SUBROUTINE PRTVAL(DEPTH, PHIT, SW, SXOCTA, KPPM, CORESW, IERR)

C

C************************************************************************

C* PRINT RESULTS TO A FILE *

C* *

C* PARAMETERS: *

C* *

C* DEPTH - MEASURED DEPTH OF VALUES *

C* PHIT - THE TOTAL POROSITY OF THE ROCK (PERCENT) *

C* SW - WATER SATURATION FROM RT *

C* SXOCTA - SXO FROM THE CTA METHOD *

C* KPPM - COMPUTED SALINITY *

C* CORESW - CORE SW USING DEAN-STARKE METHOD *

C* IERR - I/O ERROR FLAG: IF 0 OK; IF 1 ERROR *

C* *

C************************************************************************

C

REAL KPPM

CHARACTER TITLE*80, TITLE2*80

INTEGER LINES, PAGENO, PAGESZ

C

COMMON /PRINT/ LINES, PAGENO, TITLE, TITLE2, PAGESZ

C

1000 FORMAT(1X, 'PAGE ',I3)

2000 FORMAT(1X,A79)

3000 FORMAT(5F10.2, F8.2)

C

C...NEW PAGE?

IF ( (LINES .EQ. PAGESZ .OR. LINES .EQ. 0)

1 .AND. PAGESZ .GT. 0) THEN

C

C****************************

C WRITE OUT TITLE LINES *

C****************************

C

LINES = 0

PAGENO = PAGENO + 1

WRITE (20,1000, ERR=9000) PAGENO

C

WRITE(20, 2000, ERR=9000) TITLE, TITLE2

LINES = LINES + 3

C

ENDIF

C

C*************************

C WRITE OUT RESULTS *

C*************************

C

WRITE (20, 3000, ERR=9000) DEPTH, PHIT, SW, SXOCTA, KPPM, CORESW

LINES = LINES + 1

C

RETURN

C

9000 IERR = 1

RETURN

END

C

SUBROUTINE SCRVAL(DEPTH, PHIT, SW, SXOCTA, KPPM, CORESW)

C

C************************************************************************

C* PRINT RESULTS TO SCREEN *

C* *

C* PARAMETERS: *

C* *

C* DEPTH - MEASURED DEPTH OF VALUES *

C* PHIT - THE TOTAL POROSITY OF THE ROCK (PERCENT) *

C* SW - WATER SATURATION FROM RT *

C* SXOCTA - SXO FROM THE CTA METHOD *

C* KPPM - COMPUTED SALINITY *

C* CORESW - CORE SW USING DEAN-STARKE METHOD *

C* *

C************************************************************************

C

C

REAL KPPM

CHARACTER TITLE*80, TITLE2*80, ENTER*4

INTEGER LINES, PAGENO, PAGESZ

C

COMMON /PRINT/ LINES, PAGENO, TITLE, TITLE2, PAGESZ

C

1000 FORMAT(1X, 'PAGE ',I3)

2000 FORMAT(1X,A79)

3000 FORMAT(5F10.2, F8.2)

C

C...END OF SCREEN?

IF (LINES .EQ. PAGESZ .OR. LINES .EQ. 0) THEN

WRITE(*,'(A)') ' >>>> Press enter to continue. ................
................

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