the effect of constant and variable eccentricity on the spacer performance during primary well...

1 Copyright © 2014 by ASME

Proceedings of the ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering

OMAE2014

June 8-13, 2014, San Francisco, California, USA

OMAE2014-24686

THE EFFECT OF CONSTANT AND VARIABLE ECCENTRICITY ON THE SPACER

PERFORMANCE DURING PRIMARY WELL CEMENTING

Muhammad Zulqarnain Graduate Student

Louisiana State University Baton Rouge, LA, USA

Mayank Tyagi Associate Professor

Louisiana State University Baton Rouge, LA, USA

ABSTRACT

Spacers are the intermediate fluids in the primary cementing

process, preceded by the mud and followed by the cement. They

help in mud removal, keep mud and cement separated and

prepare the annulus walls for a good cement bond. The focus of

this study is to analyze the spacer performance in keeping mud

and cement separated in the vertical and horizontal well

sections with eccentricity. Several combinations of eccentricity

variation and displacement rates are simulated using

Computational Fluid Dynamics (CFD) tool to analyze the

temporal and spatial fluid volume fraction distributions in the

annulus and validated against multi-fluid displacement

experiments. A 50 ft vertical section with annular gap of 1.5″

and casing standoff from 5% to 100% and a horizontal section

with variable eccentricity are studied. For initial conditions the

annulus is modeled as filled with mud and subsequently swept

by one annular volume of spacer and cement each respectively.

Mud and cement are treated as Herschel Bulkley fluids and

spacer as a Newtonian fluid.

Qualitative results from simulations are shown in the form

of volume fraction contour plots at different sections of the

annulus and quantitative results in the form of temporal and

spatial volume fraction of each fluid at specific planes in the

entire annulus. For a vertical annular section with constant

eccentricity, some unswept mud is observed on the narrow side

and eventually becomes trapped after the eccentricity is

increased above a threshold value. It is also observed that

increasing displacement rate helps in displacing some of this

trapped mud. After a threshold eccentricity value, the trapped

mud cannot be displaced and the spacer and cement follow the

path of least resistance and flow occurs mainly on the wider

side of the annulus. For a horizontal section with variable

eccentricity (maximum at the mid distance between

centralizers), the flow is observed to move towards wider side

around the center and then returning to the other side (narrow

part) after passing through middle section. Some trapped mud is

also observed in the vicinity of the middle section due to local

maximum eccentricity.

INTRODUCTION Conditioning of the drilling fluid, casing

centralization/standoff, flow rate, casing movement, formation

permeability, spacer design and contact time are some of the

most important parameters influencing the primary cementing

[9-11]. This study focuses on the performance of spacer in the

presence of eccentricity in vertical and horizontal well sections

and effect of flow rate.

Problems encountered during horizontal well cementing are

similar to those of vertical well cement job, but are exacerbated

by factors such as wellbore orientation, gravitational forces and

casing eccentricity. Solids settling are not limited to the drilling

mud, but also occur in the cement slurries if proper precautions

are not observed. Deposition of solids in the wellbore is one of

the most severe problems in horizontal wells [2]. Keller et al.

[2] conducted a series of lab experiments in which they

simulated the solid particle settling in a concentric annulus at

various wellbore orientations. They showed that even with

concentric annulus there was a huge difference in the

displacement efficiency, between the top and bottom section of

the annulus at different orientations. The problem was more

severe for certain combination of fluid properties and flow

rates.


Figure 1: Typical horizontal cemented wellbore cross

section [3]

There is an increased possibility of having narrow annular

channel on lower side and wider channel on other side of the

casing in horizontal well. Insufficient clearance on the narrow

side of the wellbore can result in portions of the well that are

not cemented properly or even not cemented at all. It is due to

the fact that due to excessive viscous forces have to be

overcome in order to mobilize the mud or settled cuttings on

narrow side while there is lower resistance on the wider side of

the annulus. Thus, fluid has the tendency to follow the path of

less resistance and move in the wider side of the annular path.

In some reported field studies [4], tops of the cement on the two

side of the annulus were separated by hundreds of feet.

If casing in the well is not centered, the velocity

distribution across the annulus is distorted, with the flow

favoring the wider side. This may lead to undesirable situations

where the flow regime can be laminar on the narrow side of the

annulus and turbulent on the wider side, because of the

azimuthal variation of local Reynolds number in the annulus

[3]. Pipe centralization can significantly aid in the efficient mud

displacement.

NOMENCLATURE

ID Inner diameter

OD Outer diameter

ρs Density of spacer

ρm Density of mud

ρc Density of cement

Re Reynolds Number

τ Time for one annular sweep

μs Viscosity of spacer

μm Viscosity of mud

μc Viscosity of cement

μp Plastic Velocity

τy Yield Stress

CFD Computational Fluid Dynamics

VOF Volume of Fluid

Φs Spacer Volume Fraction

φm Mud Volume Fraction

φc Cement Volume Fraction

SIMULATION METHODOLOGY A commercially available CFD package Fluent

TM

based on unstructured finite volume formulation of non-

Newtonian Navier Stokes equations is used [1]. Volume of

Fluid method (VOF) has been implemented in this study to

track the fluid volume fractions in each cell of

computational domain and reconstruct the interface [6],

between different fluids. VOF method tracks the volume of

each fluid in all cells containing portions of the

interface. The geometric reconstruction scheme is used to

reconstruct the interface in the cells where more than one

fluid is present. This reconstruction scheme represents the

interface between fluids using a piecewise-linear approach. It

assumes that the interface between two fluids has a linear slope

within each cell, and uses this linear shape for calculation of the

advection of fluid through the cell faces. The position of linear

interface relative to the center of each partially-filled cell is

based on information about the volume fraction and its

derivatives in the cell. The volume fraction in each cell is

calculated using the balance of fluxes calculated during the

previous step. For further details on governing equations and

numerical method, reader is referred to [1] and [7].

VALIDATION STUDY Experimental results of Tehrani et al. [5] were used for the

validation of numerical study. The experimental setup consisted

of two coaxial cylindrical tubes. The ID and OD of the annulus

were 1.57 inches and 1.97 inches respectively, creating a

concentric gap of 0.20 inches. Total axial length of the tubes

was 9.8 ft. Comparison for both concentric and ecentric cases

were made. The simulated values for the displacement

efficiency and experimental measured value eccentric (e = 0.5)

case with similar and different density fluids are shown Figure2.

A satisfactory agreement is obtained between the experimental

data and the calculated values of displacement efficiency.

Figure 2: Comparison of the simulation results (lines) for

displacement efficiency with the experimental data (symbols)

of Tehrani et al. [5]


NUMERICAL SIMULATION SETUP

Horizontal Setup with Variable Eccentricity

Casing was assumed to be supported by two centralizers at both

ends and had uniformly distributed load on it. It was assumed

that the horizontal well was completed with 8.5" of open hole

having 5.5" OD P-110 casing. The spacing between the

centralizers was varied to achieve maximum eccentricities of

0.15, 0.3 and 0.6 at centeral ponit of casing. Casing section

length, maximum deflection at center and eccentricity are given

in Table 1.

Table 1: Casing Deflection and Corresponding Eccentricity

Section

Length (ft)

Air inside and outside casing

Max.

deflection (in) Eccentricity

48.29 0.90 0.60

40.61 0.45 0.30

34.15 0.23 0.15

Mud had the density and rheological properties of ρ = 10.2

lb/gal, μp = 34 cP, τy = 13 lb/100ft2 and cement had the density

and rheological properties of ρ = 15.8 lb/gal, μp = 34 cP, τy = 4

lb/100ft2 respectively.

Herschel Bulkley rheological model was

used for mud and cement, while the spacer was treated as

Newtonian fluid. Reynolds number for Herschel Bulkley fluid

was calculated by the procedure given by Antonino Merlo et al.

[14]. A pump rate of 10 bbl/min corresponds to Reynolds

number of 3304 was used. Corresponding critical Reynolds

number for turbulence was 1309, resulting in turbulent flow

regime. A two-equation (k-ϵ) turbulent model was used with

standard wall function with default setting for this model. It was

also ensured that the grid clustering along the walls met the wall

distance y+ requirements for the selected turbulence model.

Three variable eccentric cases (Table 2) were considered with

spacer density and viscosity either equal to mud or cement for a

fixed displacement rate corresponding to Reynolds number

3304. All fluids enter the computational domain from the left

and exit from the right.

Figure 2: Computational domain to show the casing (green

surface) inside the wellbore (grey surface) having emax = 0.60 at

the center of the annulus.

Table 2: Different density and rheological properties for spacer

fluid in the horizontal setup with variable eccentricity (12

simulation cases) at fixed Reynolds number (displacement rate).

Case emax ρs

(lbm/gal)

μs

(Cp)

Sub

Cases Re

1 0.15

10.2 78 1a

3304 49 1b

15.8 78 1c

49 1d

2 0.30

10.2 78 2a

3304 49 2b

15.8 78 2c

49 2d

3 0.60

10.2 78 3a

3304 49 3b

15.8 78 3c

49 3d

Vertical Setup with Constant Eccentricity

A 50 ft. vertical section with annular gap of 1.5″ and casing

standoff from 5% to 100% were also simulated in this study.

Only eccentricity and Reynolds number were varied while

keeping all of the other parameters same (Table 3). The hole

and casing geometry and fluid properties were same as were for

the concentric vertical cases [8].

Table 3: Vertical section setup and flow conditions at different

eccentricity and Reynolds number (15 simulation cases)

Case e ρs = ρm

(lbm/gal)

μs = μw

(cp)

Sub

case Re

4 0.05 13.11 1

4a 100

4b 167

4c 400

5 0.25 13.11 1

5a 100

5b 167

5c 400

6 0.5 13.11 1

6a 100

6b 167

6c 400

7 0.75 13.11 1

7a 100

7b 167

7c 400

8 0.95 13.11 1

8a 100

8b 167

8c 400

Inlet Outlet


From the vertical simulations of concentric annulus, it was

found that the spacer performs best when it has the same density

as of mud and viscosity equal to that of water [7]. Therefore,

the density and viscosity of spacer were fixed to be that of mud

and water respectively. With increasing eccentricity, the

yielding fluid behavior becomes very important, and therefore

the fluid theologies of mud and cement were modeled with

Herschel Bulkley rheological model.

RESULTS AND DISCUSSION

Interpreting of the volume fraction plots

Instantaneous average volume fractions of three fluids

involved (mud-spacer-cement) are reported in the last one third

annular sections for the horizontal configurations and in the last

10 ft section of vertical configurations. These “exit” sections

are referred as observation section in the following discussion.

Presumably all fluids could have significant volume fractions in

the annulus for this particular section. In an ideal situation, if

the spacer were to act as a fluid plug by not only physically

separating the mud and cement but also helping in easy removal

of mud from the annulus, the highest displacement efficiencies

could be achieved with φc =1.

In a representative temporal sequence plot (Fig. 3), volume

fractions of three fluids are plotted against the fluid annular

sweeps: first half annular volume sweep of spacer followed by

one annular volume sweep of the cement. Three important

instances on these plots to describe the effectiveness of the

spacer in separating mud and cement along with the efficiency

of the displacement process are: i) spacer and cement

breakthrough times, ii) the slopes of spacer and cement fraction

curves, and iii) the plateau region attained by the spacer curve.

Figure 3: Temporal fluid volume fraction variation in

observation section of the annulus.

If the spacer were to act like a plug between cement and

mud, then it should breakthrough at the observation section no

earlier than t = 0.66 τ and its volume fraction should approach

1.0 at about t = τ ideally, where τ is the time for one annular

sweep. Earlier breakthrough times of spacer imply that it would

have penetrated (or mixed) into the mud volume ahead of it due

to interfacial instabilities [12, 13]. Similar arguments are also

true for cement volume sweep except that ideally it should

breakthrough at t = 1.16 τ and should attain the maximum

volume fraction of 1.0 at about t =1.5 τ. The plateau region

within one annular volume being pumped would imply that no

further improvement in placed volume fraction could be

obtained by pumping more fluid volume and would hold true

for both spacer and cement.

Horizontal configuration with variable eccentricity

Results of only cases 1 and 3 are discussed here and for

detailed discussion with other cases, the reader is referred to

[7].

Case1 emax=0.15: Two representative subcases a & d

were selected (Table 2) as it was found that altering the spacer

viscosity does not influence the flow behavior while the density

changes had significant effects on the displacement process and

the value of the final cement volume fraction in the annulus.

Temporal volume fraction variations in the observation section

are shown in Figure 4.

Figure 4: Temporal fluid volume fractions variation in the last

one third sections of the annulus for different spacer densities

(Table 2: 1a – top, and 1d - bottom).

For subcase (a) when both the spacer and mud have the

same densities and viscosities, the spacer breaks through in the

observation section at about the ideal breakthrough time of 0.66

τ, showing that the interface between spacer and mud is stable.

The annulus in this simulation is only 34 ft long, for very long

annular sections, the result could be different. The spacer curve

Cement

breakthrough

Spacer Plateau

region

Spacer

breakthrough

(a)

(d)


does not have a plateau region, which emphasizes the need for

more spacer volume should have been pumped and only half

annular volume was not sufficient to achieve the plateau regime.

The cement breakthrough time is slightly delayed primarily due

to the presence of more volume of other fluids (mud and spacer)

ahead of it.

Volume fraction contours in the last one half part of the

annulus are shown in Figure 5. Most of the unswept mud and

spacer is present at the top side of the annulus near the exit.

Gravity influences fluid segregation as well as casing sagging

leading variable eccentricity of the annulus. Due to gravity, the

mud and the spacer being lighter than cement will override in

the top part of the annulus while the cement will be displacing

these fluids. At the center of the casing section (max. deflection

point), the top side has an expansion and the lower side has

reduction in the flow area, but overall the flow cross-sectional

area remains constant. After the middle region, the top side has

reduction in flow area and the lower side has expansion in the

flow area. Due to this geometry of the annulus with variable

eccentricity, a decrease in pressure occurs at the top side in the

middle and increase in pressure on the lower side at middle.

After the middle section, the pressure on the top side increases

and on lower side decreases. The consequences of such a

pressure distribution on the flow field are to move fluids

upward and towards the exit to move further downstream.

Therefore, unswept mud and spacer are present towards the top

side near the exit.

Figure 5: Planer and cross-sectional view of fluid volume

fraction contours in the last one half section of the annulus for

cases (1a) and (1d) respectively.

When the spacer density is increased to reach cement

density, the spacer breakthrough time is little bit delayed and

the cement breaks in earlier as compared to the case (1a). Due

to differential density effects, the mud displacement process is

improved and the spacer volume fraction attains higher value of

0.88 as compared to 0.78 for case (1a). Unswept spacer fraction

after one cement annular flow increase and is evident in the

volume fraction contour plot. Due to its increased density, the

spacer is also left on the lower side of the annulus alongside

both annular walls.

Case 3 emax = 0.6: With increase of the casing deflection due

to sagging at the center, the flow field is dramatically altered.

The upward push for the moving fluid is reflected in the upward

curvature of streamline plots both for case (3a) and (3d) shown

in Figure 6.

Figure 6: Streamline plot colored by mixture volume fraction in

the entire annular section for cases (3a) and (3d) respectively.

Delay in the cement breakthrough time occurs due to the

differential density effects between the spacer and the cement.

The spacer overrides on the cement and mostly fills the upper

portion of the annulus and due to restriction in the flow path in

the lower part of the annulus, the cement lags behind the

expected breakthrough time. Same phenomenon contributes in

the early breakthrough of spacer in conjunction with the annular

length.

Figure 7: Temporal fluid volume fraction variation in last one

third sections of the annulus for subcases (a) and (d)

respectively

A more severe case occurs when the spacer has same

density and viscosity as cement. A large quantity of unswept

spacer is present on the lower side of the annulus (Fig. 8). In

(3a)

(3d)

(1a)

(1d)


this case, the differential density effects are not present and the

cement on the lower side has not reached a cross sectional plane

at the 75% of the annular length while the cement on the upper

side has already reached the exit.

Figure 8: Planer and cross-sectional view of fluid volume

fraction contours in the last one half section of the annulus

Vertical configuration with constant eccentricity

Results of only two cases 5 and 8 are presented and

discussed here and the reader is referred to [7] for details on

comparative results and analysis. In this set of simulations the

50 ft. section is further divided into subsection (I, II, III, IV &

V) each of 10 ft length and the fluid volume fractions are

averaged over these sections. In this way, different sections near

exit can be compared with each other in terms of number of

fluid sweeps in each section and the volume fractions of

unswept fluids. For example, when the spacer front based on

average velocity reaches to the end of annular section, the

section (I) is swept by 4 times while section (V) is swept only

once by the spacer.

Case 5 e=0.25: Variation of various fluid volume

fractions for different Reynolds number (100 for case 5a and

400 for case 5c) are shown in Figure 9. The increase in the

spacer volume fraction is clearly visible with increasing

Reynolds number. One significant observation is that the spacer

can be seen in the narrow side of the annulus for the Reynolds

number of 400, while for the lower Reynolds number (100) only

the mud is present in the section (IV), Figure 10. It implies that

for some eccentric cases in which the eccentricity is not very

severe, the mud displacement efficiency can be enhanced by

increasing displacement rate. The spacer left over after one

annular sweep increases with displacement rate but increase is

not as significant as was in the case of low eccentric case of

0.05. The spacer maximum fraction reached in this case is

around 0.8 which is less then as compared 0.85 with

eccentricity of 0.05, this is due to the reason that more mud is

present in the observation section at all times during the sweep.

Comparison of fluid volume fractions in different sections

(I-V) with the increasing Reynolds number showed that the mud

fraction left in section (IV) increased (Figure 10).

Figure 9: Temporal fluid volume fraction variation in last 10 ft

sections of the annulus for cases (5a) and (5c) respectively.

Figure 10: Comparison of different fluid volume fractions along

the 50 ft. vertical section.

The lower three sections (I-III) in both cases indicate perfect

cement job. The top section (V) has a large fraction of bypassed

mud along with some fraction of spacer as well. The decrease in

cement fraction in the section (V) with increasing displacement

rate can be explained by the fact that depending on the

displacement rate the interfaces of cement-spacer and spacer-

mud behave differently. Both Rayleigh-Taylor [12] and

Saffman-Taylor [13] instabilities grows and mixing of fluids

occurs and as a result, some of the spacer is also left behind,

while below a certain critical displacement rate the instabilities

does not grow rapidly and the sweep is good. The ratio of mud

to cement is used to define the green (φm /φc ≤ 0.5), yellow

(0.5< φm /φc < 0.1) and red (φm /φc ≥ 0.1) coloring for the

sections shown in Figure 10.


Case 8 e=0.95: As the eccentricity increased from 0.25 to

0.95, it can be observed (Figure 11) that in the given three

sections, the volume fraction of unswept mud decreases. The

reason for this decrease is the immobile fluid in a very narrow

gap. Since the volume fraction is calculated as the average in

the cross-sectional area and section length, the flow

contributions of wide section compared to narrow section are

very large. Most of the flow takes the path of wider side and the

mud is confined or static in the narrow gap. A major difference

from the previous cases with lower eccentricity is that the small

amount of unswept mud is observed even in the lowest two

sections as well (Fig. 11).

Figure 11: Fluid volume fraction in different sections (left –

first 10 ft., middle – 20 to 30 ft. section, right – last 10 ft.) for

the case 8c.

The severity of unswept mud on the narrow side of the

annulus can be seen in Figure 11. The continuous volume

fraction distribution (i.e. layer or channel of mud) starting from

entrance section to exit section of the annulus is present. If the

cement job in this high eccentricity annulus were evaluated in

only terms of the displacement efficiency, it might provide

completely misleading interpretation in terms of goodness of

the cement job.

The effect of increasing the displacement rate on various

fluid volume fractions in the observation section is shown in

Figure 12. With increasing the Reynolds number from 100 to

400 the flat plateau region attained by the spacer is raised from

0.66 volume fraction of spacer to 0.7 and correspondingly mud

fraction flat region is decreased from 0.32 to 0.29, showing

slight improvement in the mud sweep efficiency at higher rates.

Figure 12: Temporal fluid volume fraction variation in last

section for cases (8a) and (8d) respectively

CONCLUSIONS AND FUTURE DIRECTIONS

Mud displacement efficiency is not a good indicator of

the severity of mud left in the annulus, for eccentric

geometries even a small fraction of left over mud may

be occupying a large region along the narrow side of

the annulus.

Gravitational segregation of different density fluids

along with variable eccentricity flow path in horizontal

well section makes the cement displacement

challenging. Due to variable eccentricity the flow on

the top side experiences an expansion in the flow area

and then contraction, while on the lower side the fluid

encounters reduction in flow area at the center. These

geometric variations combined with differential

density, viscosity and displacement rates result in a

complex flow fields.

Maximum cement volume fraction after one and half

sweep was obtained with spacers lighter than cement.

Even for smaller length horizontal sections, gravity

segregation of fluids was observed and its effects were

significant, resulting in the unswept mud along the top

portion of the annulus towards the exit.

For the case with maximum casing deflection resulting

in eccentricity of 0.6, the spacer with same density as

cemented performed very poorly, resulting in a

continuous spacer layer on the lower side of annulus.

In this study, the spacer volume pumped for horizontal

section is only half of the total annular volume and for

vertical section, it is exactly one annular volume followed

0′

10′

20′

30′

40′

50′


by one annular volume of cement. For the future extension

of such simulation study, it is suggested that the simulation

should be carried out to the point such that the spacer

fraction in the annulus reaches an asymptotic value with

minimum residual mud to better understand and quantify

the phenomenon. Similarly, the total pumped cement

volume fraction must be increased with simulation time to

achieve its asymptotic value.

ACKNOWLEDGMENTS Authors are thankful to Prof. A. K. Wojtanowicz and Prof.

J. R. Smith at the Craft & Hawkins Department of Petroleum

Engineering, LSU, for the valuable discussions. Authors would

also like to express their gratitude for Chevron Emerging

Faculty Fund for providing the financial support for (M.Z.) to

carry out this research work.

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the effect of constant and variable eccentricity on the spacer performance during primary well...

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