You are on page 1of 7


Predicting Mud Removal during Cementing A New and Simple Approach

Mark Savery and Robert Darbe, Halliburton

Copyright 2007, AADE

This paper was prepared for presentation at the 2007 AADE National Technical Conference and Exhibition held at the Wyndam Greenspoint Hotel, Houston, Texas, April 10-12, 2007. This conference
was sponsored by the American Association of Drilling Engineers. The information presented in this paper does not reflect any position, claim or endorsement made or implied by the American Association
of Drilling Engineers, their officers or members. Questions concerning the content of this paper should be directed to the individuals listed as author(s) of this work.

Perhaps the most important factor engineers and operators
should consider for successful oilwell cementing is adequate
drilling-fluid removal, or mud displacement. To optimize
mud displacement, the primary technique used today is to
pump a spacer fluid with modified rheology that creates a
beneficial fluid-fluid interface. However, the extent to which
this material property hierarchy affects one fluid displacing
another fluid is often unknown, especially in wells where the
casing is offset from center. Therefore, this paper addresses
the question: To what extent will changing density,
modifying viscosity, or doing both have on mud displacement
efficiency in both concentric and eccentric annuli?
To better describe this influence of rheological hierarchy,
volume-fraction vs. time curves derived from computational
fluid dynamic (CFD) simulations are used to accurately
describe the mud removal process. A test matrix covering
typical ranges of densities and viscosities was established and
several geometric models, each with different casing standoff
percentages, were created in a finite element grid generation
program. Initial conditions were set to simulate mud with predetermined rheological properties sitting static in the annulus.
A spacer fluid, also with programmable rheological properties,
was then automated to begin displacing the mud at the inlet.
The simulations were allowed to run until 99% of the mud was
removed from the model. The displacement efficiencies in
both the wide side of the annulus and narrow side of the
annulus were used as a basis for contour plots. These contour
plots, which can span casing standoffs from 0% to 100%,
allow the user to quickly assess the relative influence density
changes and viscosity changes have on displacement
efficiency. Upon review, this novel method of data
presentation gives a cementer a powerful and simple tool to
efficiently design a spacer fluid for optimal mud removal.
The present study describes a method of using empirical
parameters to accurately describe the mud removal process.
This method encompasses two main concepts. The first
concept relates to using volume-fraction vs. time curves to
estimate the rate of mud displacement in a wellbore annulus.
These curves may be derived from CFD simulations,
experimental tests, real-world cement jobs, or combinations
thereof. For this study the curves were derived using CFD
simulations, but an experimental model using sensors could be

used to measure the amount of fluid being displaced as a

function of time. A commercial CFD package was used for
this proof-of-concept study, but any computer programming
code capable of modeling fluid flow in a geometric domain
may be considered. Previously, a validation study of the
commercial CFD code was performed employing a full
scheme of physical tests.1
The second concept relates to plotting the rate of mud
displacement as a function of any two or any three
cementing parameters. A cementing parameter is one that
is critical for optimally designing a successful mud removal
process. These parameters include, but are not limited to,
casing standoff, pump rate, mud properties, displacing fluid
properties, and casing movement.
Combining these two concepts creates a unique tool that
can help design fluid systems to optimize mud displacement.
First, a partitioned, geometric model (Fig. 1) of a 5-ft
concentric setup was created in a mesh generation program.
The dimensions were OD = 6.5 in., ID = 5 in., and annular gap
= 0.75 in. Next, initial conditions were set to simulate mud
with predetermined rheological properties (modeled Bingham
Plastic) sitting static in the annulus. A displacing fluid, also
modeled Bingham Plastic, was then programmed to begin
flowing 4-bbl/min at the inlet in an attempt to displace the
mud. It is important to mention that, for the concentric case,
the displacing fluids velocity profile was described by a true
Bingham Plastic velocity profile as prescribed by a userdefined function.1,2 Finally, the simulation was allowed to run
until more than 99% of the mud was removed from the model.
Displacement efficiency curves were plotted showing the
percent displacing fluid by volume at any time in the model.
Also recorded was the time required to completely displace
the 5 feet of mud.
Concentric Case
Fig. 2 shows the volumetric displacement efficiency in the
5-ft concentric model as a function of flow time and
rheological properties including density, yield point (YP), and
plastic viscosity (PV). As expected, there are differing degrees
of displacement rates (the slope of these curves) between the
nine different rheological hierarchies. For instance, the best
case scenario when the mud is displaced most rapidly (i.e. the
steepest slope and fastest time to 100%) occurs when a dense


displacing fluid with high rheology displaces a less dense mud

with low rheology. The worst case scenario, where the
displacing fluid is less dense and less viscous than the mud,
shows a longer time to 100% and a flatter slope. Both of these
observations are intuitive and reinforce current industry best
Fig. 3 takes the final times of plots like Fig. 2 and more
easily describes the rheological hierarchy influence. It shows
the different time requirements to arrive at 99% displacement
efficiency. For this case, 25 simulations in a concentric
annulus were run to cover a wide range of possible densities
and apparent viscosities. To arrive at the apparent viscosity,
the volume average shear rate (VASR) first needed to be
estimated using Eq. 1:


h2 w

where Q is the volumetric flow rate, h is the annular gap, and

w is the average circumference between the 6.5-in. OD and the
5-in ID. The apparent viscosity, , can then be found from Eq.

+ PV .2

It was observed that each simulation required a different time

to arrive at complete displacement efficiency. Notice the
general trend toward the upper right of longer times to 99%
mud displacement, which makes intuitive sense. A thin, light
fluid would take longer to displace a thick, heavy fluid. Upon
review, this data can give the job designer a powerful tool to
efficiently select the displacing fluid. Using the 25 data points
in Fig. 3, a contour plot (Fig. 4) can be created to describe
displacement phenomena and to access the relative influence
of both density changes and apparent viscosity changes. Two
new terms are introduced Eqs. 3 and 4:
Density Ratio =

Density of Displacing Fluid d

Density of Mud
m ..3

Apparent Visc. Ratio =

Apparent Visc. of Mud

= m
Apparent Visc. of Displacing Fluid d 4

Using these two terms, a contour plot like Fig. 4 can help
answer the question: To what extent will changing density,
modifying viscosity, or doing both have on displacement
efficiency? To properly answer this question, it is necessary
to first set the two axes on a 1:1 scale. The legend shows the
time required for 99% mud displacement, but this could
conceivably show any percentage desired by the user. The yaxis shows the degree of density difference between the
displacing fluid and mud. The x-axis shows the degree of


apparent viscosity difference between the displacing fluid and

mud. A value of 1.0 on either axis means the two fluids are
equal in that variable. The value at plot location [1,1]
describes a mud with density of 12.5 lb/gal and apparent
viscosity of 108.5 cP being displaced by a fluid with the exact
same properties. This is indicated by the black star on Fig. 4,
which geometry confirms should fall on the 45 line. In this
case, a time of 4 to 5 seconds to fully displace 5 feet of mud at
4 bbl/min is expected if the material properties of both fluids
were equal.
Geometric Proof
The y-axis of Fig. 4 shows the dimensionless variable
d/m and the x-axis shows the dimensionless variable m/d.
It should be noted that only the numerators change in these
relationships, as the denominators remain constant at m = 12.5
lb/gal and d = 108.5 cP, respectively. Assume a similar plot
with three lines drawn from the origin. This gives the
simplified plot of Fig. 5. Line CL1, which has an angle greater
than 45, can be analyzed using Eq. 5:

m 1 sin(60)


d 1
Thus for every 1.73% change in the density ratio, the same
impact can be achieved by changing the apparent viscosity
ratio 1%. In other words, when the slope of the contour line is
>45, the apparent viscosity ratio dominates. The best practice
would be to adjust the apparent viscosity ratio first (i.e. make
the displacing fluid more viscous or the mud less viscous).
This, of course, should be done only if cost-practical. The
analysis of CL2, which has an angle less than 45, yields:

m 2



d 2
Thus for every 1% change in the apparent viscosity ratio, the
same impact can be achieved by changing the density ratio
0.58%. In other words, when the angle of the contour line is
<45, the density ratio dominates. The best practice would be
to adjust the density ratio first (i.e. make the displacing fluid
more dense or the mud less dense).
Eccentric Case
The procedure described above may also be used to
investigate eccentric conditions when the wide-side flow tends
to travel faster vs. the narrow-side flow. A difference,
however, is the use of a constant inlet velocity profile in the
CFD code as opposed to a Bingham Plastic velocity profile.
The reason: Bingham Plastic profiles are ill-defined in


Predicting Mud Removal During Cementing A New and Simple Approach

eccentric cases. Instead, a constant velocity inlet boundary

condition was used at a flow rate of 4 bbl/min.
Because the geometry was no longer symmetric, a
volumetric approach (as done in the concentric case) by itself
would be inefficient to thoroughly define displacement
efficiency. To solve this problem, two 2-D grid faces, one for
the wide side and one for the narrow side, were incorporated
into the model to capture the entire displacement phenomena
(Fig. 6). As each simulation progressed, the displacement time
to 99% was calculated across the entire volume and along
these 2-D grid faces. Thus, a new term is introduced for
eccentric cases:
Displacement Time Ratio

Time Required to Displace a Point on the NARROW side

Time Required to Displace a Point on the WIDE side 7

This is not a velocity ratio; rather it is a unique displacement

ratio for any given location in the well. It is the key parameter
of Fig. 7, a hierarchy contour plot specific to a 70% standoff
situation in a 6.5-in. hole with 5-in. casing. Trends for this
eccentric case follow the same general trends observed in the
concentric case, but the uniqueness of this contour plot is that
it shows a relative comparison between what is happening on
the narrow side vs. the wide side.
Say a preliminary design suggests using a displacing fluid
with the same properties as the mud. This situation refers to
point [1,1] on Fig. 7. The plot indicates that a narrow-side
interval would take approximately 12x as long to reach 99%
displacement as compared to the adjacent wide-side interval.
So what can be done to lower this ratio? Fig. 7 indicates that
changing the apparent viscosity ratio will have a greater
impact than changing the density ratio because the nearest
contour line is >45. Moving to an apparent viscosity ratio to
0.2, for instance, would cut the displacement ratio in half to
approximately 6x, a better proposition than adjusting the
density ratio. Another practical way to lower the displacement
time ratio would be to use centralizers. Fig. 8 shows a similar
situation with a standoff of 85%. Applying an apparent
viscosity ratio of 0.2 as before would cut the ratio down to
approximately 2x!
A job designer choosing a spacer or flush would want to
move toward the upper left red region of these types of
contour plots. The trend generally favors displacement.
Alternatively, moving toward the bottom right blue/black
region would make displacement progressively less efficient.
In simplistic terms, a thin spacer is trying to displace a thick
mud, which intuitively is destined to fail. To overcome this
problem, the designer must place his current selection on the
contour plot and look at the angle of the contour lines
surrounding this location. If the absolute angle of the nearest
contour line is >45, changing the apparent viscosity would
have a greater impact on displacement efficiency. If the
absolute angle of the nearest contour line is <45, changing

the density would have a greater impact on displacement

efficiency. Finally, if the absolute angle is 45, he should be
indifferent as to which ratio to change first; logically it should
be the most cost-effective change or, perhaps, both
Theoretically, this method can be applied to any fluid
property, any well geometry, any standoff value, or any
designated displacement percentage (e.g. 95%, 90%, or the
percent at which cement integrity will remain immune to mud
contamination). Also, the 2-D contour plot method may also
be extended to a 3-D contour plot including a third
dimensionless variable. Variables may include standoff
percent, pump rate, RPM of casing rotation, casing
reciprocation parameters such as cycles per minute and stroke,
and wettability numbers. Even the top-of-cement (TOC)
locations in wells with offset casing may be predicted using
this method. In fact, numerous possibilities of 2-D or 3-D
contour plots could be created. For example, if an engineer
wanted to determine how casing rotation would affect
displacement efficiency, he could use input RPM, density, and
apparent viscosity to build the 3-D contour plot. A generalized
version of this idea incorporates dimensionless terms 1,
2N plotted with respect to each other with a toggle
feature. Using dimensionless terms would enable the user to
easily analyze any pertinent relationship(s) between variables.
Thus, this method gives flexibility to the cement job designer
to plot, at a given point in the well, the critical variables they
need to make the best decision.
The authors thank the management of Halliburton for
permission to publish this paper.
2-D = Two dimensional
3-D = Three dimensional
ID = Inner diameter
OD = Outer diameter
PV = Plastic viscosity
RPM = Rotations per minute
VASR = Volume average shear rate
YP = Yield point
= Dimensionless term
Q = Volumetric flow rate
h = Annular gap
w = Average circumference
= Apparent viscosity
= Density
1. Savery, M. and Darbe, R.: Capability of CFD to Simulate NonNewtonian Fluid Displacement in Annular Gaps, International
Oil & Gas CFD Conference, London, Nov 31 - Dec 1, 2006.
2. Fredrickson, A.G. and Bird, R.B.: Non-Newtonian Flow in
Annuli, Ind. Eng. Chem., 50, 347-52 (1958).


Fig. 1Five-foot concentric model.

Fig. 2Variances in displacement efficiency for the concentric model as a f(, YP, PV).


Predicting Mud Removal During Cementing A New and Simple Approach

Fig. 3Times to 99% displacement efficiency for the concentric model.

Fig. 4Hierarchy contour plot for the concentric model showing time (sec) to 99% displacement.


Fig. 5Supporting chart for geometric proof.

Fig. 6Five-foot eccentric model.



Predicting Mud Removal During Cementing A New and Simple Approach

Fig. 7Hierarchy contour plot for a 70% standoff model showing the displacement time ratio.

Fig. 8Hierarchy contour plot for an 85% standoff model showing the displacement time ratio.