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OTC-26639-MS

Behind Casing Inspection Using Active Gamma-Gamma TechniqueYike Hu, and Weijun Guo, Halliburton

Copyright 2016, Offshore Technology Conference

This paper was prepared for presentation at the Offshore Technology Conference Asia held in Kuala Lumpur, Malaysia, 22–25 March 2016.

This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents

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Abstract

During the completion of well drilling, cement is pumped into the annulus behind the casing to provide

zonal isolation and a pressure barrier. The cement integrity inside the annulus is crucial for environmental

and safety concerns. This paper describes a subsurface evaluation technique to evaluate the cement

integrity behind the casing using an active gamma-gamma technique.

The target was a layered structure consisting of single or multiple layers of casing, cement in the

annulus, and formation. The tool in use includes a radioactive gamma source and a gamma ray detector,

which is designed to be sensitive only to the annular space away from the inner casing. Monte Carlo

N-particle (MCNP) simulation based on high-energy photons transport was conducted to simulate the

energy spectrum that would be measured by the gamma ray detector. Cement channels were represented

by the void located in the annulus, which is characterized in volumetric terms and the localized area

coverage of the voids. The detector responses change with different cement integrities. There are two

attributes describing the gamma ray spectrum: count rates (CR) ratio and dipping point value. Through

extensive computer modeling, the correlation between cement integrity and spectrum information was

established, which are in terms used when generating equal CR-ratio curve and equal-dipping point curves.

When investigating cement of unknown integrity, its gamma ray response is recorded by the detector and

processed by algorithms. The dipping point value (Edip) and count rates ratio (CRratio) can be computed from

the as-recorded gamma ray spectrum, and a volume-position chart can be generated in which the equal CR-ratio

curve and equal-dipping point curve are plotted. The cement integrity information, the amount and the position

of the void, are found simultaneously as the intersection of those two curves.

As compared to the conventional acoustic methods used in cement evaluation, this paper proposes anevaluation method using nuclear technology. The new method provides a data processing methodology to

determine the void amount and position inside the cement, which could be used to image the void channel

inside the cement.

Introduction

During the cased-hole completion operation, cement is placed behind the steel pipe to create the barrier

to prevent pressure communication between the formation and wellbore. The quality of the cement inside

the annular space is of critical importance to meet the health, safety, and environment (HSE) standards.

The monitoring of the cement integrity plays an undisputable role in the well economics and management



plan. To maximize production efficiency, the proper zonal isolation requires a full coverage of cement in

the annular space without channeling. Poor cement integrity could also lead to well corrosion. It is

important to provide high-quality indicators for operators to make early intervention decisions without

incurring a large operational cost.

The cement quality issue may occur for the following reasons:

●

Poor bonding between the inner steel casing and cement● Channeling or cracks within the cement annulus

● Void space between the cement and formation or poor bonding between the cement and outer steel

casing for scenarios of multiple casing

In this paper, the research study of using an active gamma-gamma measurement to determine the

location and amount of cement void is presented. The theory section describes the fundamental physics

behind the measurement technique. The modeling section defines the problem in detail and discusses how

to simulate the gamma ray spectrum using computer modeling. The analysis of the modeling results

reveals the connection between the spectrum characteristics and cement integrity. Two attributes are

defined to evaluate cement integrity given a gamma ray spectrum. The measurement results for both

regular and thick steel casing are reported in a large borehole completion environment. A new spectros-

copy feature of dipping point is illustrated to show its effectiveness to solve for both the void/crack amount and location behind casing.

Theory

With a chemical radioactive source, such as Cs-137, the high-energy gamma ray can penetrate through a

thick wall of dense materials and still return a meaningful signal. The high-energy gamma ray interacts

with material in three major ways: photoelectric absorption, Compton scattering, and pair production. Pair

production occurs at energy higher than 1 MeV, which is beyond the energy range of the Cs-137 source.

The photoelectric absorption and Compton scattering are the two relevant interactions. The photoelectric

absorption occurs when the incoming gamma ray interacts with atoms, which strongly depend on the

gamma ray energy and the atomic number (Z) in the material. The Compton scattering is the interaction

between high-energy photons and individual electrons.The probability of interactions is described by a constant called cross section. The cross section

depends on the energy of the incoming radiation, the type of interaction, the material, the angle between

the incoming radiation direction, and the resultant radiation direction. The interactions result in the

attenuation law of gamma ray intensity:

(1)

Where N is the existing number of photons, e is electron density of the materials, and x is the distance

gamma ray travels. This attenuation law is the fundamental physics governing the tool measurement.

When the high energy photon enters the materials in front of the source, its energy is reduced as a result

of the scattering process, and the number of photons decreases because of the photoelectric absorption.

Some of the photons finally escape the materials and get scattered into the detector. The energy spectrum

recorded in the detector is an energy distribution of count rates.

The material information is embedded in the spectrum. The distinctive features of the spectrum are the

amplitude and shape. An equivalent description of amplitude is the total count rates. It sums the total

number of photons within an energy range. When there is certain void existing inside cement, the overall

cement volumetric properties change. Depending on where the void is located, the void affects the shallow

layer (close to casing) or deep layer (away from casing) differently, which means there is nonuniformity

in material distribution in the radial direction. As the photons travel from shallow layers into deep layers

and some of them get scattered back, they contain the volumetric information along the entire travelling

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path. And the deeper it penetrates, the lower the energy remains when the photons are scattered back. To

obtain good statistic precision and keep substantial depth of investigation, the count rates of photons in

an intermediate energy level are chosen to extract volumetric information. On the other hand, the spectrum

shape describes a change of photon number with respect to energy. For the photons traveling into deep

layers of material, less energy was deposited in the detector. Suffice it to say that the spectrum in the

high-energy end corresponds to photons travelling in the shallower layer in the material. The high-energy end

of the spectrum contains radial distance information (material distribution in the radial direction). The changein the number of photons with respect to energy reflects the material property change in the radial direction.

Although both the count rates and spectrum shape are influenced by the material volumetric property and the

nonuniformity of material distribution in the radial direction, as demonstrated below, they are not equally

affected, which provides a unique method to identify the void volume and position simultaneously.

Model and Methods

Monte Carlo N-particle modeling (Briesmeister 2000) has been widely used in the well logging

industry to generate the detector response in downhole situations (Watson 1983; Moake 2011) thanks to

its convenience to vary wellbore parameters and credibility in simulating real-world results. In the

application of gamma-gamma technique, it accounts for the transport process of high-energy photons bymodeling the tool body, casing, cement, and formation behind.

The tool used in the cement evaluation is a nuclear tool, consisting of a radioactive source (Cs-137),

a scintillator crystal detector [NaI(Tl)], and necessary shielding, which prevents high-energy photons from

transmitting through the tool body to arrive at the detector without interactions with surroundings. The

entire tool body is packaged inside a pressure housing to meet the temperature and pressure requirement

for downhole application. Openings in the housing (collimator) are properly designed to allow the high- energy

photons to pass through. When the high-energy photons are emitted from the chemical source, they interact

with materials in front of the tool, that is, casing, cement, and formation. A portion of the high-energy photons

are scattered into the scintillator crystal and are detected. By changing the design parameters of the tool body,

the detected high-energy photons contain information about the cement only, so-called formation-independent

cement evaluation. The tool design features short-detector source spacing, small-detector collimator size, and downward-angled detector collimator. More details about the tool design can be found in Hu and Guo (2015).

Fig. 1 is the schematic of one such tool placed in a cased-hole environment.

Figure 1—Schematic of tool design used in the formation independent cement evaluation.

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This paper studies the void, its volume, and its position inside the cement sheath behind the casing. It

aims to provide a method to derive information about how much void exists inside the cement sheath and

where it is located. The detector responses were modeled for a series of void structures. In this paper, the

word position and location are used interchangeably. The word amount and volume are also used

interchangeably.

The void structures are associated with two attributes: position and amount. To define the position of

a void inside the cement sheath, the annular space behind the casing is segmented into 10 parts. Each part

takes up 10% of the annulus thickness. The void position is defined as the location of the front surface

of a cement void (the side closing to casing). The grid lines mark the positions. The outer casing surface

is defined as position 0. Position 0.1 is defined as 10% of the cement thickness away from the outer casing

surface. Position 0.2 is defined as 20% of the cement thickness away from the outer casing surface. As

on the positions continue, the final position, which is on the end of the annular space, is at position 1.0.

The grid lines are shown in Fig. 2. With this definition, any void located inside the cement sheath can be

labeled with a position. For example, when the front surface of the cement void is located at a distance

of t 1 away from the casing outer surface, it is gives this cement void a position label , where t is the

total thickness of the annular space behind casing. Likewise, the cement position label indicates how much

cement lies in front of the void space. For example, when a certain cement void locates at x position inside

the cement sheath, it means the front surface of the cement void is located at a distance of x t from the

casing outer surface.

Figure 2—Define the position grids inside cement sheath. The entire cement sheath is segmented into 10 parts. The casing outer

surface is defined as position 0. Position 0.1 is defined as 10% of annular spacing away from the casing outer surface. Position 0.2 is

defined as 20% of annular spacing away from the casing outer surface. As on the position continues, position 0.9 is defined as 90%of annular spacing from the casing outer surface. The last grid coincides with the end of the annular space, which is defined as position

1.0.

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The amount of cement void is defined as a certain percentage of the total cement volume filling

the annular space behind the casing. For example, 20% of cement void means the void takes up 20%

of the annular space volume. This assumes the cement void is continuously distributed in the

azimuthal direction in the field of view of the tool and in the longitudinal direction between the

source and detector spacing.

To determine how much void locates at which position inside the annular space, the MCNP codes

were used to simulate the gamma ray spectra from a series of structures with increasing amount of

voids at different position. Since the void position is defined as the front surface of the void volume,

the maximum amount of void is limited by its position, shown in Table 1. Fig. 4 illustrates how the

void amount is propagating at a given position. Position 0.2 is set as an example. The void amount

begins increasing from 10% void gradually to 80% of void. The maximum amount of void allowed at position 0.2 is 80%.

Figure 3—A certain amount of void locates inside the annular space. The void amount is characterized as a percentage of the annular

volume.

Table 1—Structures of different cement integrities used in

MCNP modeling.

Void Position Void Volumetric Amount

0 0% (Full-cement)

0 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 100%

0.1 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%

0.2 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%

0.3 10%, 20%, 30%, 40%, 50%, 60%, 70%

0.4 10%, 20%, 30%, 40%, 50%, 60%

0.5 10%, 20%, 30%, 40%, 50%

0.6 10%, 20%, 30%, 40%

0.7 10%, 20%, 30%

0.8 10%, 20%

0.9 10%

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For the convenience of discussion, the amount and positon combination associated with a void is

labeled as (x%, y). It means that the void takes up x% of the annular space with its front surface (the side

closing to casing) located at position y. Take cement integrity (40%, 0.2) for example; it is a void that

takes up 40% of the annular space locating at position marker 0.2.A few parameters were chosen for the well completion profile in the modeling. The casing thickness

is 0.5 in. The cement annular spacing is 1.5 in. The casing OD is 9 5/8 in. The casing weight is 53.5 lb/ft.

Although in a real situation the void space could be filled with brine, mud sediments, or water, for the

purpose of illustration, the void was filled with fresh water in the MCNP modeling.

Results

The spectrum measured in the detector depicts the energy distribution of count rates. It contains

information about the materials with which the high-energy photons interact during their traveling path.

Fig. 5 illustrates two representative cases of cement integrities: good cement (full cement inside the

annular space) and bad cement (cement with certain amount of void inside). The simulated spectrum fromeach scenario is presented in the left panel of Fig. 6.

Figure 4—Schematics for increasing void amount a given position inside the cement annular space. Voids in this example have a

position of 0.2.

Figure 5—Schematic of different cement integrities in cased-hole. The left depicts a good cement situation: full cement inside the

annular space. The right depicts a bad cement situation: some void space inside of the cement.

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As the left panel of Fig. 6 shows, compared to the good-cement spectrum, the sample spectrum fromcement with some void is different in amplitude and shape. The amplitude difference can be captured by

summing the count rates in the intermediate energy range from 150 keV to 250 keV. The other

not-so-obvious feature in this plot is that the spectrum shape at 300 keV to 500 keV is also different. A

transformation is required to amplify the difference, as shown in the right panel of Fig. 6.

The transformation takes the following steps:

1. Normalize both spectra to make the total count rates under the curve equal to 1.

2. Take the normalized full-cement spectrum as the standard spectrum.

3. Subtract the standard spectrum from the normalized sample spectrum. The difference is defined as

spectrum difference. This technique highlights the shape change, as shown in the right panel of

Fig. 6.

The most striking feature in the spectrum difference plot is that there is a dipping point in the sample

spectrum curve at the high-energy range. The dipping point is defined as the energy E dip where the

spectrum difference value is at a minimum. Mathematically speaking, the dipping point is the turning

point where the first order derivative of the spectrum difference curve changes from negative to positive.

In other words, the dipping point is the point where the first order derivative of the spectrum difference

curve equals zero. In this case, the high-energy range is chosen to be from 300 keV to 500 keV.

In order to systematically study the correlation between the spectra characteristics and cement

integrities, the simulated spectra for a series of voids of different amounts at different positions are plotted

in the following figures.

Fig. 7 plots the spectra for a series of void amounts at position 0. The spectrum from full-cement with

legend 0-0 per is also plotted as reference. At position 0, the void amounts can be increased from 10%

all the way up to 100% by 10% volume increments. The 100% void amount is equivalent to a no-cement

situation. The left panel in Fig. 7 presents the simulated spectra. The major feature in this plot is that the

magnitude for the spectrum from 150 keV to 250 keV is clearly different as the cement void amount

changes. The sum of the count rates at this energy range increases as the void amount increases. Using

the transformation discussed above, the spectra are transformed to spectrum difference and shown in the

right panel in Fig. 7. As expected, each spectrum difference curve has a dipping point. Moreover, the

dipping point is moving as the cement void amount changes. In particular, it shows the dipping points are

moving toward smaller values when the amount of void increases inside cement.

Figure 6—Left panel: gamma ray spectra from the two cement integrities shown in Fig. 5. Right panel: Transformation of spectrum in

the left panel to amplify the spectrum feature.

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The same data processing was applied to the spectra simulated at other positions when the cement void amount increases, as shown in Figs. 8 through 16. Similar to what were observed in Fig. 7, there are two

key findings:

1. At a given position, when the amount of void increases, the total count rates within the energy

range from 150 keV to 250 keV are increasing.

2. At a given position, when the amount of void increases, the dipping point value E dip decreases.

Figure 7—Detector spectra from cased hole with different amount of voids inside cement at position 0. The left panel plots the

simulated gamma ray spectra. The right panel plots the normalized spectra subtracted by the normalized full cement spectrum.

Figure 8 —Detector spectra from cased hole with different amount of voids inside cement at position 1. The left panel plots the


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Figure 9 —Detector spectra from cased hole with different amount of voids inside cement at position 2. The left panel plots the


Figure 10—Detector spectra from cased-hole with different amount of voids inside cement at position 3. The left panel plots the




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Those two findings hold true for all the spectra modeled at all positions inside cement.

Discussion

The observations from the modeling results are quantified further. First the count rates in the intermediateenergy range from 150 keV to 250 keV for each spectrum are summed.

(2)

As the full-cement situation describes good cement integrity without any void inside, the spectrum

from the full-cement situation is chosen as the standard spectrum.





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(3)

A new parameter can be defined as CR-ratio, which is the ratio of the summed count rates of the

previous two equations.

(4)

Taking the ratio of count rates between any spectrum and the standard spectrum rescales the count rates

in the intermediate level for all spectra to a value around 1.0.

Fig. 17 shows a plot of the CRratio versus the cement void amount at each position. To avoid confusion,

the cement void amount is labeled by percentage while the void position is marked by number. As the

figure shows, for the same position when the void amount increases, CRratio increases. For the same

amount of void, when its position increases (moving away from casing), CRratio is decreasing. This

indicates that a given CRratio could correspond to either a large void amount at a large position or a small

void amount at a small position.

Next, the dipping points E dip from all cement void amounts at every position are plotted in Fig. 18. For

the same position when the cement void amount increases, the dipping point value E dip decreases. For the

same cement void amount when its position increases (away from casing), the dipping point E dip

decreases. This indicates that a given dipping point value could correspond to either a small void amountat a large position or a large void amount at a small position.

Figure 17—Count rates ratio versus cement void amount at each position inside the cement sheath. (Casing thickness: 0.5 in.)

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The observations from Fig. 17 and Fig. 18 are critical as they provide clues to determine the amount

of void and its position simultaneously from its gamma ray spectrum. The logics are as follows:

1. The gamma ray spectrum from a full-cement situation of a well completion profile is chosen as the

reference spectrum.

2. The gamma ray spectrum is measured from structure of unknown cement integrity of the same

well completion profile.

3. CRratio and dipping point value E dip is obtained from the gamma ray spectrum of the unknown

structure.

4. For a given CRratio, its corresponding void amount monotonically increases as the position marker

increases. This curve is called the equal-CR-ratio curve, which can be extrapolated from Fig. 175. For a given dipping point value, its corresponding void amount monotonically decreases as the

position marker increases. This curve is called as the equal-dipping point curve, which can be

extrapolated from Fig. 18.

6. Plot the equal-CR-ratio curve and the equal-dipping point curve in a volume-position plot. The

intersection of both curves gives the value for the amount and position of the void.

7. A few boundary conditions are required to help ensure a physically meaningful result: the cement

void amount should be larger or equal to 0% and smaller or equal to 100%, the cement void

position should be larger or equal to 0 and smaller or equal to 1, and the sum of void amount and

void position marker should be less than or equal to 1.

Take the cement integrity (40%, 0.2) for example; it has a CRratio

of 1.15 and dipping point value E dip

355 keV . For a CRratio of 1.15, from Fig. 17, it could correspond to cement integrity combinations such

as (25%, 0), (30%, 0.1), (40%, 0.2) and (60%, 0.3). For a dipping value of 355 keV, from Fig. 18, it could

correspond to cement integrity combinations such as (15%, 0.4), (30%, 0.3), (40%, 0.2), (60%, 0.1) and

(70%, 0). The equal-CR curve and equal-dipping point curve can be drawn in the same volume-position

chart, as shown in Fig. 19. Clearly those two curves intersect at one point, of which the coordinate is (40%,

0.2). This means the spectrum with a CRratio of 1.15 and a dipping point of 355 keV corresponds to cement

integrity of 40% of void amount locating at a position marker of 0.2. This is exactly the cement integrity

used in this example.

Figure 18—Dipping point value versus cement void at each position inside the cement sheath. (Casing thickness: 0.5 in.)

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A more sophisticated method is required to obtain the position and amount for cement void accurately.

It is herein described as follows:

In Fig. 17, the curve for every position can be fitted with a second polynomial,

(5)

Eq. 5 establishes the relation between the CR-ratio and void amount.In Fig. 18, the curve for every position can be fitted with a linear approximation,

(6)

Eq. 6 establishes the relation between the dipping point value and void position.

The fitting coefficients from Fig. 17 and Fig. 18 are listed in Table 2. With those coefficients, one cancompute the void amount and position combination for every CRratio and every dipping point value E dip,

which in turn plots the equal-CR radio curve and equal-dipping point curve in a volume-position chart.

In the volume-position chart, the intersection point of equal-CR-ratio curve and equal-dipping point

curve is the void inside cement. Since the void amount has physical meaning, the void amount should

always be within the range from 0 to 1. The fundamental physics rule requires the equal CR-Ratio to be

Figure 19—Equal-CR-ratio curve and Equal-dipping point curve for a gamma ray spectrum with dipping point at 355 keV and CR-ratio

of 1.15.

Table 2—Coefficients for CR ratio void amount dependence and

dipping point (E dip) void amount dependence.

Position a b c1

c0

0 -0.3767 0.7255 -60.0 324.0

0.1 -0.3637 0.6282 -30.0 327.0

0.2 -0.3516 0.5307 -33.0 336.0

0.3 -0.3073 0.4262 -48.0 350.4

0.4 -0.2877 0.3453 -68.6 368.0

0.5 -0.2314 0.2551 -70.7 378.9

0.6 -0.334 0.2407 -78.9 393.6

0.7 -0.3141 0.1811 -72.0 397.7

0.8 0 0.0693 -78.9 412.4

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The void amount and position for the unknown structure are identified as the coordinates of the

intersection point. The results are listed in Table 4, and the errors compared to the true values are also

presented. The error is shown as the percentage of the full annular spacing. As Table 4 shows, all errors

are well within 2% of the entire annular spacing.

Case Two

Discussion above was based on the modeling results from 0.5-in. casing. The applicability of this method

was also studied for thick casing (0.8-inch.). Similar to the 0.5-in. casing situation, a series of structures

of different void amounts at different positions were modeled. The count rates ratio (CRratio) versus

Figure 21—The equal-CR_ratio curve and equal-dipping point curve for all tested structures in the volume-position plot. The

intersection point corresponds to the void amount and void position for the tested structure.

Table 4—The void amount and position estimated using the

volume-position plot for testing structures. (Casing thickness:

0.5 inch)

Structure Position Amount Position error Amount error

A 0.01 16% 1% 1%

B 0.21 37% 1% 2%

C 0.40 16% 0 1%

D 0.37 21% 2% 1%

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cement void amount at each position is presented in Fig. 22. The dipping point value ( E dip) versus cement

void amount at each position is presented in Fig. 23. The three observations from 0.5-inch casing situation

are still valid in the 0.8-in. casing situation.

1. For a given CRratio, its corresponding void amount monotonically increases as the position marker

increases. This curve is called the equal-CR-ratio curve.

2. For a given dipping point value E dip, its corresponding void amount monotonically decreases asthe position marker increases. This curve is called as the equal-dipping point curve.

3. As the CRratio and the dipping point value are obtained from the same structure, it only corresponds

to one void amount and position combination. Therefore, the cross point from the equal-CR-ratio

curve and the equal-dipping point curve gives the amount and position for the void.

From Fig. 22, the equal-CR-ratio curve can be extrapolated for a given CRratio. From Fig. 23, the

equal-dipping point curve can be extrapolated for a given dipping point value E dip. And the void

information is obtained from the volume-position chart, which plot both of the equal-CR-ratio curve and

equal-dipping point curve.

Figure 22—Count rates ratio versus cement void amount at each position inside the cement sheath. (Casing thickness: 0.8 in.)

Figure 23—Dipping point versus cement void at each position inside the cement sheath. (Casing thickness: 0.8 in.)

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A series of test structures of different cement integrities were modeled using the 0.8-in casing. They

are A: (15%, 0), B: (35%, 0.2), C: (15%, 0.4), and D: (20%, 0.35). Using the method described in Case

1, the position and void amount for each structure are estimated and listed in Table 5. As it shows, the

accuracy in the estimation does not decrease because of the increasing thickness of casing. The

measurement sensitivity is maintained even with thicker casing.

Conclusion

This paper studied how to use the spectrum from a gamma-gamma technique to evaluate the cement

integrity in cased-hole situations. A series of structures of different amount of cement voids located atdifferent position inside cement sheath were constructed to represent different cement integrities. Monte

Carlo N-particle simulation was utilized to model their gamma ray detector response.

Analysis reveals that there are two attributes characterizing the gamma ray spectrum feature, count rates

ratio (CRratio) and dipping point value ( E dip). Using the full-cement spectrum as the reference spectrum, the

count rates ratio (CRratio) is a value obtained by dividing the sum of count rates of a given spectrum in an

intermediate energy range by that of the reference spectrum. The dipping point value is the energy corre-

sponding to the turning point of spectrum difference (normalized sample spectrum subtracts the normalized

reference spectrum) at a high energy range. Together, CRratio and dipping point E dip describe the entire

spectrum shape. For a given cement integrity inside the cased-hole, a CRratio and E dip can be computed from

its gamma ray spectrum. For a given well completion profile, the CRratio dependence on void amount and void

position, and the E dip dependence on void amount and void position can be pre-established through computer simulation or lab measurement. The equal-CR_ratio curve and equal-dipping point curve are extrapolated from

the database and plotted in a volume-position chart. The amount and position of the void can thus be

determined simultaneously. From case studies, the error of determining the void amount and void position with

such method is less than 2% of the entire annular spacing.

AcknowledgmentsThe authors thank Halliburton for allowing the publication of this work.

ReferencesBriesmeister, J.F. 2000. MCNP - A General Monte Carlo N-Particle Transport Code, Version 4C . Los Alamos National

Laboratory. http://permalink.lanl.gov/object/tr?whatinfo:lanl-repo/lareport/LA-13709-M (accessed 26 August2016).

Hu, Y. and Guo, W. 2015. Behind-Casing Cement Void Volumetric Evaluation. Presented at the SPE Thermal Well

Integrity and Design Symposium, Banff, Alberta, Canada, 23-25 November. SPE-178447-MS. http://dx.doi.org/

10.2118/178447-MS.

Moake, G.L. 2011. Using Computer Modeling to Generate Accurate Pe Equations. Presented at the SPWLA 52nd Annual

Logging Symposium, Colorado Springs, Colorado, 14-1 May. SPWLA-2011-MMM.

Watson, C.C. 1983. Numerical Simulation of the Litho-Density Tool Lithology Response. Presented at the SPE Annual

Technical Conference and Exhibition, San Francisco, California, 5-8 October. SPE-12051-MS. http://dx.doi.org/

10.2118/12051-MS.

Table 5—The void amount and position estimated using the

volume-position plot for testing structures. (0.8 inch casing)

Structure Position Amount Position error Amount error

A 0 16% 0 1%

B 0.2 35% 0 0

C 0.39 15% 1% 0

D 0.37 22% 2% 2%

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