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Advanced Mud Displacement Modeling for Slim Hole Cementing Operations

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Abstract

Successful design and execution of slim-hole cementing operations depend on reliable prediction of the annular pressure and the efficiency of mud displacement by cement. A 3D model of the flow inside the casing and in the annulus during mud displacement/cement placement operations was created. The yield-power-law fluid model was used for the rheological behavior of mud, spacers, and cement. Mud displacement was analyzed by splitting the well into multiple sections and analyzing the efficiency of mud removal by spacers and cement, as well as the associated pressure gradients in each section for applicable combinations of pump rate and casing rotation speed. The results from the various computational steps were then integrated to compute the overall pressure and cement placement efficiency during the cementing operation. Using the new 3D model, a field case study was performed for a slim hole casing cementation on an unconventional shale well. The simulated peak surface pressure was only 0.3% lower than the measured data, and the trend of the pressure matched the measured data. This work provides a new tool for the well construction industry to predict and analyze the pressure during complicated cementing operations, thereby enabling safer and more cost-effective operations.
Citation: Wang, N.; Lamb, C.; Ashok,
P.; van Oort, E.; Granier, G.; Gobert, T.
Advanced Mud Displacement
Modeling for Slim Hole Cementing
Operations. Energies 2024,17, 1226.
https://doi.org/10.3390/en17051226
Academic Editors: Mofazzal Hossain
and S.M. Farouq Ali
Received: 13 December 2023
Revised: 16 February 2024
Accepted: 26 February 2024
Published: 4 March 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
energies
Article
Advanced Mud Displacement Modeling for Slim Hole
Cementing Operations
Ningyu Wang 1,* , Christopher Lamb 1, Pradeepkumar Ashok 1, Eric van Oort 1, * , Garrett Granier 2
and Tatiana Gobert 2
1Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin,
Austin, TX 78712, USA
2Occidental, Houston, TX 77046, USA
*Correspondence: wny001@sina.com (N.W.); vanoort@austin.utexas.edu (E.v.O.)
Abstract: Successful design and execution of slim-hole cementing operations depend on reliable
prediction of the annular pressure and the efficiency of mud displacement by cement. A 3D model
of the flow inside the casing and in the annulus during mud displacement/cement placement
operations was created. The yield-power-law fluid model was used for the rheological behavior
of mud, spacers, and cement. Mud displacement was analyzed by splitting the well into multiple
sections and analyzing the efficiency of mud removal by spacers and cement, as well as the associated
pressure gradients in each section for applicable combinations of pump rate and casing rotation
speed. The results from the various computational steps were then integrated to compute the overall
pressure and cement placement efficiency during the cementing operation. Using the new 3D model,
a field case study was performed for a slim hole casing cementation on an unconventional shale well.
The simulated peak surface pressure was only 0.3% lower than the measured data, and the trend of
the pressure matched the measured data. This work provides a new tool for the well construction
industry to predict and analyze the pressure during complicated cementing operations, thereby
enabling safer and more cost-effective operations.
Keywords: mud displacement; 3D modeling; pressure analysis; surface pressure; pump rate
1. Introduction
Cementing is a pivotal step in well construction [
1
4
]. Cement acts as a barrier
that seals the gap between casing strings and wellbore sections, thereby isolating zones
of varying subsurface pressure and mechanically securing and supporting the casing.
Improper cement placement may compromise well integrity, in turn potentially leading to
safety incidents and environmental upsets (such as fluid leaks to the surface, gas emissions
to air, etc.).
During cement placement, the annular drilling fluid (mud) is replaced by cement. The
quality of the cement displacement can be quantified by the cement displacement efficiency
(CDE) and is defined by the volume fraction of cement in a cross-section in the annulus [
2
].
If non-displaced drilling fluid is left in the annulus, it may contaminate the cement and
prevent it from setting and sealing properly, leading to safety, economic, and environmental
issues (associated with a lack of zonal isolation and poor well integrity). The non-displaced
drilling fluid also decreases the equivalent flow path cross-section area for the cement and
thus increases the pressure gradient.
In slim hole cementing operations, improper pressure estimation has become a major
concern, even in the absence of CDE problems. Underestimating pressure can lead to
significant delays and increased expenses, as peak surface pressure is an important design
parameter for determining the required surface pumping equipment. If the peak surface
pressure is underestimated during the design phase, the equipment used may lack the
Energies 2024,17, 1226. https://doi.org/10.3390/en17051226 https://www.mdpi.com/journal/energies
Energies 2024,17, 1226 2 of 27
capability to perform the cement job as planned. Failure to properly estimate peak pressure
has caused significant operation delays and economic losses in the field. At the same
time, maintaining pressure within set limits, similar to drilling operations, is essential to
prevent wellbore damage. Excessive pressure in the annulus, particularly at the bottom
hole location, can fracture the formation. This can, in turn, result in circulation loss and
formation damage.
Cement displacement is impacted by a variety of factors, such as the properties of
the drilling fluid, the flow regime, the flow rate, the annulus geometry [
1
,
3
], etc. Early
numerical studies, such as those reported by McLean et al. [
5
] and Beirute and Flumerfelt [
6
],
focused on modeling the flow pattern in a cross-section in the annulus. Even today, interface
stability is still actively investigated to improve the CDE [7,8].
In more recent years, 3D models have been established to investigate more complicated
cases, as shown in Table 1. Savery et al. [
9
] proposed a 3D finite difference model of two-
phase flow in the annulus as a tool for studying the cement front. They ignored the axial and
azimuthal velocities as well as the azimuthal pressure gradient in the tangential momentum
equation. This model was later adopted to study the intermixing at the cement front [
10
]
and the free fall of the cement in the casing while the flow in the annulus is single-phase [
11
].
Chen et al. [
12
] reported a 3D finite difference model without details of the model to study
the intermixing. Enayatpour and van Oort [
2
] developed a 3D finite volume model based
on the volume of fluid (VOF) method to study the frictional pressure and CDE and found
that pipe rotation and higher eccentricity decrease the frictional pressure while pipe rotation
and lower eccentricity improve the CDE, with pipe rotation being able to partially offset
the negative effects of higher eccentricity on CDE. Gao et al. [
13
] applied this model and
found that the wellbore size has a significant impact on the pressure gradient. Bu et al. [
14
]
subsequently deployed this model on a different software platform and found that a higher
density difference between the mud and the cement first increases and then decreases the
CDE. Tardy and Bittleston [
15
] created a (2+1)D finite volume method with a narrow gap
assumption and averaging the fluid volume fraction and velocity along the radial direction
to study the mud displacement in the annulus. Based on this model, Tardy et al. [
16
]
presented a simplified 3D model of the entire wellbore by segmenting the wellbore into
many sections and analyzing the cement displacement in each section. This model was
later used to analyze a few wells in the Gulf of Mexico [
17
]. To improve the accuracy of
this model, Tardy [
18
] kept the narrow gap assumption but introduced a radial variation of
the averaged parameters and proposed that the model may still be less computationally
expensive than a full-scale 3D model. However, Tardy’s model underestimates the pressure
gradient, especially at high eccentricity (>0.3). By further assuming the flow pattern at the
widest and narrowest parts of the annulus, Foroushan et al. [
19
] created a semi-analytical 3D
model with a sequential solution of the single-phase flow plus a partial differential equation
for the two-phase interface. Maleki and Frigaard [
20
] also built a 3D model based on the
narrow gap assumption and used it to study primary cementing [
21
]. Zhang et al. [
22
]
developed a 3D model to study the flow around the centralizer during cementing to
compare the nonspiral and spiral flow displacement.
In addition to the above ‘traditional’ models based on Navier–Stokes equations, Li
and Novotny [
23
] and Grasinger et al. [
24
] each proposed a 2D Lattice–Boltzmann model
for pipe flow and suggested possible application in the annulus.
This paper introduces a 3D finite volume model for the entire cement displacement
process. It builds upon the submodel developed by Enayatpour and van Oort [
2
], which
modeled flow in a well section without assuming a narrow gap. We have integrated this
submodel to analyze the full cement displacement operation in a well. Our model’s capabil-
ity to simulate CDE assists high-precision pressure analysis during cement placement and
mud/spacer displacement because the CDE impacts the pressure gradient by impacting
the cross-sectional area of the cement flow. We demonstrate the model’s enhanced preci-
sion through a field case study. Here, we compare our pressure prediction results with
those from a commercial model, whose output had significant discrepancies with actual
Energies 2024,17, 1226 3 of 27
cementing field data. Additionally, the developed model allows us to explore the impact of
wellbore diameter distribution on pressure estimation.
Table 1. Recent numerical models for cement displacement analysis.
Paper Model Simplification of Conservation Equations Application
[911] 3D finite difference.
Ignored the axial and azimuthal velocities as
well as the azimuthal pressure gradient in
the tangential momentum equation.
Velocity profile of the annular
two-phase flow. Free fall of cement in
the pipe.
[12] Not reported. Not reported. Intermixing of mud and cement.
[2,13,14] 3D finite volume. None.
Pressure gradient and cement
displacement efficiency in a section in
the annulus.
[1517,20,21] (2+1)D finite volume.
Narrow gap assumption. Averaged the fluid
volume fraction and velocity along the radial
direction.
Pressure gradient and cement
displacement efficiency in a section in
the annulus. Pressure in the annulus
during cement placement.
[18] 3D finite volume.
Narrow gap assumption with radial
variation of averaged fluid volume fraction
and velocity.
Pressure gradient and cement
displacement efficiency in a section in
the annulus.
[19]3D semi-analytical.
Sequential solution.
Narrow gap assumption. Assumed flow
pattern at the widest and narrowest parts of
the annulus.
Pressure gradient and cement
displacement efficiency in a section in
the annulus.
[22] 3D finite volume. None.
Pressure field and cement displacement
near the centralizer.
[23,24]
2D Lattice–Boltzmann.
Fluids are treated as particles moving and
colliding.
Velocity profile of the annular
two-phase flow.
2. Cement Displacement Analysis under the Uniform Wellbore Assumption
The process of mud displacement and cement placement involves both single- and
two-phase flows in the casing, as well as in the annulus. Here, ‘phase’ refers to a distinct
type of fluid, such as mud spacer or cement, rather than a thermodynamic phase like solids,
liquids, or gases. To calculate the pressure profile and CDE, it is necessary to model the flow
in each well section separately. The results from each section are then combined to form
a comprehensive analysis. With increasing wellbore length, the well may comprise more
geometrically varied sections. We address this complexity by discussing the application of
statistical methods that aim to simplify the model and expedite the analysis.
2.1. Problem Statement and Model Partitioning
During the mud displacement process, the casing interior and the annulus together act
like a U-tube for fluids. Initially, fluids flow through the casing before entering the annulus.
The pressure at the top of the annulus is either atmospheric or regulated by the surface
back pressure (SBP) in managed pressure cementing (MPC). To determine the pressure
profile and standpipe pressure, we calculate the pressure gradient in both the casing and
the annulus. We then integrate these gradients along the casing and annulus to obtain a
complete pressure profile.
The flow in the annulus is influenced by the flow rate, fluid rheology, and the geometry
of the annulus. In deviated or horizontal wellbores, the casing tends to be displaced towards
the lower side of the hole due to gravity, buoyancy, and elasticity/stiffness, even when
centralizers are used. As a result, the annulus usually has an eccentric shape. Eccentricity
in the annulus, denoted as
ϵ
, is defined by the distance between the casing’s axis and the
wellbore’s axis, divided by the gap between them. The annular eccentricity is given by:
ϵ=Dwellbore Dcentralizer
Dwellbore Dcasing
(1)
Energies 2024,17, 1226 4 of 27
where
Dwellbore
is the wellbore diameter,
Dcasing <Dwellbore
is the casing outer diam-
eter, and
Dcentralizer Dwellbore
is the outer diameter of the centralizer.
ϵ=
0 when
Dcentralizer >Dwellbore.
The wellbore diameter is variable, and the casing’s relative position changes due
to complex loads. Therefore, the annulus’ eccentricity varies along the wellbore and its
measured depth.
To analyze flow in a wellbore with varying eccentricity, a clear strategy is to first
divide the wellbore into multiple segments. We then model and simulate each segment
individually. During each operational period, characterized by specific flow rates and
casing rotations, we determine the flow model. In segments where cement displaces
another fluid, such as mud or spacer, we use a two-phase flow model. In other segments,
we apply a single-phase model to simplify and accelerate the simulation. The methodology
for modeling annular flow in each segment is detailed in the following section.
With this strategy, the total modeling simulation time is approximately proportional
to the total number of sections. The computation of such a detailed model that consists
of hundreds or thousands of segments may take weeks or months, which is practically
undesirable. Procedures need to be taken to decrease the number of simulations while
minimizing the loss of precision. Enayatpour and van Oort [
2
] showed that, as the ec-
centricity increases, the pressure gradient in the annulus decreases, and the CDE changes
monotonically. In this work, we assume that the casing in each segment is parallel to the
wellbore and the eccentricity
ϵ
is as defined in Equation (1). We also assume the eccentricity
in the vertical section to be zero. By proper placement of the section boundary, we can seg-
ment the eccentricity while keeping the average pressure gradient the same, and the CDE
analysis will tend to be conservative (i.e., biased towards lower values) after segmentation.
To use this segmenting method, another underlying assumption is that the frictional
pressure is only a function of the well geometry, the fluid rheology, and the flow rate.
When the pump rate changes during the operation, the pressure and flow rate in the
well go through a transient process before the steady-state flow is restored in the well,
and the flow rate is constant along the wellbore. Thus, the flow in a well segment is
dependent on the transient flow in the upstream well segment. In this model, we neglect
this transient pressure change when the flow rate changes and assume the steady-state state
is immediately achieved. Thus, in all well segments, the mass flow rates at the segment
entrances are the same during the same operation step. The flow in adjacent well segments
is decoupled, and the flow in each well segment can be modeled separately based on
the local geometry and the global flow rate. Further, this strategy enables parallelized
simulation of the flow in all well segments. With enough computational resources, the
analysis of the entire cement placement operation in the well can be performed within
approximately the same time as simulating the flow in one well segment.
The flow in the casing is much simpler than the flow in the annulus. Since the
intermixing of the fluids is less of a concern in the casing, a single-phase model would be
sufficient to estimate the pressure gradient in the casing for pressure analysis. In current
cementing practice, the fluids are often treated as Bingham plastic whenever a Newtonian
model is determined to be insufficient. Assuming steady-state laminar flow, the velocity
profile of a Bingham plastic in the cross-section of a circular casing in the cylindrical
coordinate system is given by Dixon [25]:
u(r,z)=1
4k
dp
dz ·(R2r2) + τ0
k(rR),r>2τ/dp
dz (2)
where the pressure
p
is a function of the radial coordinate
r
and the measured depth
z
,
R
is
the casing inner diameter, τ0is the yield point, and kis the plastic viscosity.
2.2. 3D Modeling of Yield-Power-Law Fluid in Casing and Annulus
Although the rheological behavior of cementing fluids can often be approximated as
following the Bingham plastic model in drilling practice, the yield power law or Herschel–
Energies 2024,17, 1226 5 of 27
Bulkley model is commonly used when developing cement displacement models and
solvers. We have the following:
τ=τ0+k.
γn(3)
where
τ
is the shear stress,
.
γ
is the shear rate,
τ0
is the yield stress,
k
is the consistency
index, and nis the flow index. When n=1, the fluid behaves as a Bingham plastic.
The cement slurry is usually protected by the top and bottom plugs from contami-
nation of the mud while flowing down the casing. Thus, the casing flow is essentially a
single-phase flow. The pressure gradient of a yield-power-law fluid in a circular pipe of
diameter
D
flow, at an average velocity
V
, can be numerically solved using the method
described by Chilton and Stainsby [26]:
P
L=4k
D8V
Dn3n+1
4nn1
1X 1
1aX bX2cX3n
(4)
where
X=4τ0
DP
L(5)
a=1
2n+1;b=2n
(n+1)(2n+1);c=2n2
(n+1)(2n+1)(6)
In this paper, we apply the 3D submodel for single- and two-phase annular flow as
described by Enayatpour and van Oort [
2
]. This submodel was programmed using the
Ansys Fluent 2021R2 software. For more comprehensive details on the model, readers are
referred to Enayatpour and van Oort [
2
], with a concise summary provided in Appendix A.
2.3. Casing Connections Modeling
Casing connections link casing sections, creating a continuous barrier against forma-
tion fluids. The casing connection can vary in type (threaded coupling, integral, weld-on)
and dimensions to enhance its mechanical strength and sealing ability. Different vendors
offer casing connections of various inner and outer diameters with different lengths.
The effect of casing connections on mud displacement modeling is not negligible and
needs to be considered explicitly to arrive at accurate pressure predictions. Each casing
connection is treated as a short section in the casing, assuming the impact of the edges
of the casing connection to be negligible. The flow inside the casing connection can be
analytically determined, and the annulus flow can be modeled using the methods described
in the previous section.
After computing the pressure gradient inside and outside the casing connections, the
length-weighted average of the frictional pressure gradient in the pipe and annulus can
be calculated. The average frictional pressure gradient is used in the final integration of
the results.
2.4. Model Validation
Detailed validations of the submodel can be found in Enayatpour and van Oort [
2
].
This validated submodel is used to establish a model of the flow in the entire well to arrive
at a holistic estimate of cement placement. A quick validation of the single-phase flow
model against the analytical solution (Bingham plastic) in a circular pipe (Equation (2))
is shown in Figure 1. The inlet mass flow rate is 3.0891
×
10
5
kg/s and the average
axial velocity is 0.3933 m/s. The pipe radius is 0.005 m, the fluid yield point is 15 Pa,
the consistency index is 0.05 Pa
·
s, and the fluid density is 1000 kg/m
3
. The analytically
calculated pressure gradient is 1.414 ×104Pa/m.
Energies 2024,17, 1226 6 of 27
Energies 2024, 17, x FOR PEER REVIEW 6 of 29
shown in Figure 1. The inlet mass ow rate is 3.0891 ×10 kg/s and the average axial
velocity is 0.3933 m/s. The pipe radius is 0.005 m, the uid yield point is 15 Pa, the con-
sistency index is 0.05 Pas., and the uid density is 1000 kg/m3. The analytically calculated
pressure gradient is 1.414×10 Pa/m.
Figure 1. Validation of the single-phase ow in a circular pipe. The simulated axial velocity matches
the analytical solution.
2.5. Result Integration and Entire Displacement Analysis Process
The entire analysis process is elucidated in Figure 2. Firstly, data from the well, the
casing, the uids, and the cement placement operation are loaded as inputs. The well ge-
ometry can be from measured or designed directional surveys or from simulation results
from a drilling model [27]. Secondly, the location of each uid in the well is determined
by the geometry information and the operation seings, especially the pump rate. The
uid interfaces during the displacement operation are tracked to nd the critical time
frames when any uid interface reaches any well section boundary and when the ow
rate changes. In estimating the front of the cement, we assume a negligible impact from
an un-displaced spacer, valid mainly when the CDE is close to 100%. At lower CDEs, the
cement–spacer interface propagates faster, altering the critical time frames. The wellbore
is then segmented as outlined in the model partitioning section. Thirdly, a 3D transient
nite volume model of single- or two-phase ow is established and simulated for each
annular well segment. This step is based on the previous work [2], and no modication
was made to the modeling in each section. The frictional pressure in each casing section is
either simulated in the same way as in the annulus or, if it is single-phase Bingham plastic,
is analytically calculated. Finally, the CDE is determined at the cement front position in
the annulus, and the pressure is calculated by summing up pressure drop across all down-
stream pipe and annular well segments, using Bernoulli’s equation.
Figure 1. Validation of the single-phase flow in a circular pipe. The simulated axial velocity matches
the analytical solution.
2.5. Result Integration and Entire Displacement Analysis Process
The entire analysis process is elucidated in Figure 2. Firstly, data from the well, the
casing, the fluids, and the cement placement operation are loaded as inputs. The well
geometry can be from measured or designed directional surveys or from simulation results
from a drilling model [
27
]. Secondly, the location of each fluid in the well is determined by
the geometry information and the operation settings, especially the pump rate. The fluid
interfaces during the displacement operation are tracked to find the critical time frames
when any fluid interface reaches any well section boundary and when the flow rate changes.
In estimating the front of the cement, we assume a negligible impact from an un-displaced
spacer, valid mainly when the CDE is close to 100%. At lower CDEs, the cement–spacer
interface propagates faster, altering the critical time frames. The wellbore is then segmented
as outlined in the model partitioning section. Thirdly, a 3D transient finite volume model of
single- or two-phase flow is established and simulated for each annular well segment. This
step is based on the previous work [
2
], and no modification was made to the modeling in
each section. The frictional pressure in each casing section is either simulated in the same
way as in the annulus or, if it is single-phase Bingham plastic, is analytically calculated.
Finally, the CDE is determined at the cement front position in the annulus, and the pressure
is calculated by summing up pressure drop across all downstream pipe and annular well
segments, using Bernoulli’s equation.
All the input variables involved in the proposed model are listed in Figure 3. Although
not marked separately, the system may have several wellbore sections, several casing
sections, and several fluids. Associated with each of these elements will be a separate
input data set with variables, as shown in Figure 3. The well trajectory can be the designed
trajectory, the measured survey, or the simulation results from a numerical model [
27
].
When a wellbore caliper log is available, or the distribution of the wellbore diameter can
be inferred from historical data (e.g., acoustic pseudo-caliper obtained during drilling), it
is possible to break the wellbore into hundreds or thousands of segments for very precise
analysis. However, performing such a detailed level of analysis within a reasonable time
will require more advanced and optimized modeling following, e.g., a data-based approach,
a topic that is beyond the scope of this paper. To decrease the computational expense, a
straightforward idea is to average the wellbore diameter in a relatively long well segment
and assume the flow in the segment can be approximated by the flow in the well of the
averaged geometry. To justify this practice of averaging the wellbore diameter, Appendix B
examines the wellbore diameter distribution of a well segment, and Appendix Canalyzes
the impact of the wellbore diameter distribution on the pressure gradient analysis using the
Energies 2024,17, 1226 7 of 27
model in this work. In this paper, we break down the well into a few long well segments,
assume the wellbore diameter in each well segment follows its own distributions, and use
the average wellbore diameter in each well segment for the flow analysis.
Energies 2024, 17, x FOR PEER REVIEW 7 of 29
Figure 2. Workow of cement placement/mud displacement analysis. The chronological and spatial
sequence of the uids is established based on the geometry and operation parameters. The ow in
each section in the casing and annulus is modeled and simulated before being integrated into the
nal results of CDE and pressure.
All the input variables involved in the proposed model are listed in Figure 3. Alt-
hough not marked separately, the system may have several wellbore sections, several cas-
ing sections, and several uids. Associated with each of these elements will be a separate
input data set with variables, as shown in Figure 3. The well trajectory can be the designed
trajectory, the measured survey, or the simulation results from a numerical model [27].
When a wellbore caliper log is available, or the distribution of the wellbore diameter can
be inferred from historical data (e.g., acoustic pseudo-caliper obtained during drilling), it
is possible to break the wellbore into hundreds or thousands of segments for very precise
analysis. However, performing such a detailed level of analysis within a reasonable time
will require more advanced and optimized modeling following, e.g., a data-based ap-
proach, a topic that is beyond the scope of this paper. To decrease the computational ex-
pense, a straightforward idea is to average the wellbore diameter in a relatively long well
segment and assume the ow in the segment can be approximated by the ow in the well
of the averaged geometry. To justify this practice of averaging the wellbore diameter, Ap-
pendix B examines the wellbore diameter distribution of a well segment, and Appendix C
analyzes the impact of the wellbore diameter distribution on the pressure gradient analy-
sis using the model in this work. In this paper, we break down the well into a few long
well segments, assume the wellbore diameter in each well segment follows its own distri-
butions, and use the average wellbore diameter in each well segment for the ow analysis.
Figure 2. Workflow of cement placement/mud displacement analysis. The chronological and spatial
sequence of the fluids is established based on the geometry and operation parameters. The flow in
each section in the casing and annulus is modeled and simulated before being integrated into the
final results of CDE and pressure.
Energies 2024, 17, x FOR PEER REVIEW 8 of 29
Figure 3. Data inputs involved in modeling the mud displacement/cement placement operation.
The modeling of the single- and two-phase ow in a wellbore segment was discussed
in the previous section. Although the model is transient, steady-state pressure and CDE
are used for the analysis. After modeling and simulating the ow in each wellbore seg-
ment, the pressure and the CDE are post-processed separately.
The pressure gradient in each wellbore segment indicates the associated frictional
pressure loss in that segment. We integrate this pressure gradient along the casing and the
annulus to obtain the total frictional pressure loss in the well. Combining the frictional
pressure loss and the total gravity yields the surface pressure. This assumes no MPC sur-
face back pressure management (if MPC is used, that back pressure can be straightfor-
wardly added to the surface pressure). The pressure is analyzed at every critical time
frame, as dened at the beginning of this section. The pressure between these critical time
frames is linearly interpolated.
The CDE in each wellbore segment is correlated with the position of the cement front.
As the mud displacement operation continues, the cement front advances in the annulus.
In each segment in the annulus, the geometry is constant or averaged, as discussed in
Appendixes B and C; thus, the CDE is constant at a constant ow rate.
3. Field Case Study
We applied our proposed modeling method to a horizontal well’s cementing opera-
tions, which faced unexpectedly high surface pressure during a slim-hole cement job.
Firstly, the impact of several factors on the surface pressure was evaluated. Then, the sur-
face pressure and CDE were analyzed based on pre-job and post-job data with a constant
wellbore diameter assumption for the well (referred to in the following as Well X). Finally,
we incorporate the wellbore diameter obtained from ultrasonic borehole diameter meas-
urement and the impact of the mud viscosity to demonstrate the impact of these parame-
ters and the accuracy of our modeling method.
3.1. Case Introduction
Well X was an actual horizontal well of typical L-shape geometry and approximately
22,000 ft measured depth. The kick-o point (KOP) was at approximately 11,000 ft TVD,
and the lateral section started at approximately 12,000 ft TVD. The schematic and trajec-
tory in accordance with the well survey of Well X are shown in Figure 4. Based on the
concept of segmentation, the entire annulus was broken into three segments, and the pres-
sure uctuation caused by non-constant wellbore diameter was assumed to average out.
The vertical section was drilled in the previous operation steps, and the inner diameter of
Figure 3. Data inputs involved in modeling the mud displacement/cement placement operation.
The modeling of the single- and two-phase flow in a wellbore segment was discussed
in the previous section. Although the model is transient, steady-state pressure and CDE are
used for the analysis. After modeling and simulating the flow in each wellbore segment,
the pressure and the CDE are post-processed separately.
The pressure gradient in each wellbore segment indicates the associated frictional pres-
sure loss in that segment. We integrate this pressure gradient along the casing and the annulus
to obtain the total frictional pressure loss in the well. Combining the frictional pressure loss
and the total gravity yields the surface pressure. This assumes no MPC surface back pressure
management (if MPC is used, that back pressure can be straightforwardly added to the surface
pressure). The pressure is analyzed at every critical time frame, as defined at the beginning of
this section. The pressure between these critical time frames is linearly interpolated.
Energies 2024,17, 1226 8 of 27
The CDE in each wellbore segment is correlated with the position of the cement front.
As the mud displacement operation continues, the cement front advances in the annulus.
In each segment in the annulus, the geometry is constant or averaged, as discussed in
Appendices Band C; thus, the CDE is constant at a constant flow rate.
3. Field Case Study
We applied our proposed modeling method to a horizontal well’s cementing oper-
ations, which faced unexpectedly high surface pressure during a slim-hole cement job.
Firstly, the impact of several factors on the surface pressure was evaluated. Then, the
surface pressure and CDE were analyzed based on pre-job and post-job data with a con-
stant wellbore diameter assumption for the well (referred to in the following as Well X).
Finally, we incorporate the wellbore diameter obtained from ultrasonic borehole diameter
measurement and the impact of the mud viscosity to demonstrate the impact of these
parameters and the accuracy of our modeling method.
3.1. Case Introduction
Well X was an actual horizontal well of typical L-shape geometry and approximately
22,000 ft measured depth. The kick-off point (KOP) was at approximately 11,000 ft TVD,
and the lateral section started at approximately 12,000 ft TVD. The schematic and trajectory
in accordance with the well survey of Well X are shown in Figure 4. Based on the concept
of segmentation, the entire annulus was broken into three segments, and the pressure
fluctuation caused by non-constant wellbore diameter was assumed to average out. The
vertical section was drilled in the previous operation steps, and the inner diameter of the
previous intermediate casing string was 6.969 in. The planned average borehole diameter
was 6.75 in. below 11,000 ft TVD. The wellbore diameter distribution of a section of the
wellbore acquired from the ultrasonic measurement data is shown in Appendix B. However,
in this paper, we base the analysis on the average wellbore diameter because the analysis
in Appendix Cshows that the relative error between using the average wellbore diameter
and the real wellbore diameter is <1%. The production casing had a 5.5 in. outer diameter
and a 4.778 in. inner diameter with 6.252 in. centralizers placed at every 44 ft along the
casing. Based on the wellbore and casing properties, the typical annulus eccentricity was
0.3–0.4. The measured bottom hole static temperature (BHST) was 168.2 F.
Energies 2024, 17, x FOR PEER REVIEW 9 of 29
the previous intermediate casing string was 6.969 in. The planned average borehole diam-
eter was 6.75 in. below 11,000 ft TVD. The wellbore diameter distribution of a section of
the wellbore acquired from the ultrasonic measurement data is shown in Appendix B.
However, in this paper, we base the analysis on the average wellbore diameter because
the analysis in Appendix C shows that the relative error between using the average well-
bore diameter and the real wellbore diameter is <1%. The production casing had a 5.5 in.
outer diameter and a 4.778 in. inner diameter with 6.252 in. centralizers placed at every 44
ft along the casing. Based on the wellbore and casing properties, the typical annulus ec-
centricity was 0.3–0.4. The measured boom hole static temperature (BHST) was 168.2 °F.
Figure 4. (a) Schematic of Well X, with a snapshot of a moment during the displacement. Colors:
light blue—brine; grey—cement; yellow—spacer; dark blue—mud. The uid densities are marked
in the gure, and additional uid properties are included in Table 2. (b) 2D trajectory of Well X (side
view), true vertical depth (TVD) vs. horizontal displacement (HD).
Before the cement operation started, both casing and annular spaces were lled with
oil-based mud (OBM). Then, the uids were pumped into the casing in the order of spacer,
cement, and brine. The properties of the uids (mud, spacer, cement, brine) used in the
case study analysis are from the cementing job report and are listed in Table 2. Although
the model is designed for a more generalized yield-power-law uid, the Bingham plastic
uid is easily modeled by seing the ow index to 𝑛=1, as mentioned in Section 2.2.
Note that the reported OBM viscosity was measured at 150 °F, not 168 °F.
Table 2. Fluid properties.
Fluid Density,
ppg
Density,
kg/m
3
Consistency Index 𝒌 (Plas-
tic Viscosity, PV), cP
Yield Pressure (YP) 𝝉𝟎,
Pa
Measurement Temperature,
°F
OBM 12.1 1450 17 5.27 150
Spacer 12.0 1438 16.3 7.56 168
Cement 13.2 1582 60.7 4.42 168
Brine 10.1 1213 1.0 0.96 120
Figure 5 shows the planned (dash lines) and actual (solid lines) pump rate and sur-
face pressure during the entire cement displacing operation. The entire cement displace-
ment operation consisted of the following steps.
Step 1: from 0 bbl to 375 bbl displacement, the spacer and the cement were pumped.
Although a constant ow rate of 4.0 bpm was planned, the actual pump rate uctuated
between 1.4 bpm and 4.3 bpm. From 25 bbl to 160 bbl displacement, the actual pump rate
Figure 4. (a) Schematic of Well X, with a snapshot of a moment during the displacement. Colors:
light blue—brine; grey—cement; yellow—spacer; dark blue—mud. The fluid densities are marked in
the figure, and additional fluid properties are included in Table 2. (b) 2D trajectory of Well X (side
view), true vertical depth (TVD) vs. horizontal displacement (HD).
Energies 2024,17, 1226 9 of 27
Table 2. Fluid properties.
Fluid Density,
ppg
Density,
kg/m3
Consistency Index k(Plastic
Viscosity, PV), cP
Yield Pressure (YP) τ0,
Pa
Measurement Temperature,
F
OBM 12.1 1450 17 5.27 150
Spacer 12.0 1438 16.3 7.56 168
Cement 13.2 1582 60.7 4.42 168
Brine 10.1 1213 1.0 0.96 120
Before the cement operation started, both casing and annular spaces were filled with
oil-based mud (OBM). Then, the fluids were pumped into the casing in the order of spacer,
cement, and brine. The properties of the fluids (mud, spacer, cement, brine) used in the
case study analysis are from the cementing job report and are listed in Table 2. Although
the model is designed for a more generalized yield-power-law fluid, the Bingham plastic
fluid is easily modeled by setting the flow index to
n=
1, as mentioned in Section 2.2. Note
that the reported OBM viscosity was measured at 150 F, not 168 F.
Figure 5shows the planned (dash lines) and actual (solid lines) pump rate and surface
pressure during the entire cement displacing operation. The entire cement displacement
operation consisted of the following steps.
Energies 2024, 17, x FOR PEER REVIEW 10 of 29
was 1765% lower than the planned pump rate. The actual surface pressure was only 0–
32% lower than the planned pump pressure. However, from 160 bbl to 310 bbl, when the
actual pump rate was only 5% higher than the planned pump rate, the actual surface pres-
sure was 33% higher than the planned surface pressure. Multiple pauses (0–20 min) were
made for various operations after 310 bbl displacement. At 375 bbl displacement, the
pump was stopped, and the top plug was dropped. Operations in this step lasted for less
than half an hour.
Step 2: from 375 bbl to 700 bbl displacement, the displacement brine was pumped.
Because of the higher-than-expected pressure during 0–425 bbl displacement, the ow
rate was decreased by 0.2 bpm from 3.5 bpm to 3.3 bpm after 425 bbl displacement. The
spacer front reached the boom hole at 500 bbl displacement volume. The estimated bot-
tom hole circulating temperature (BHCT) during this time was 167.8 °F in the plan, and
the surface pressure estimation used the OBM viscosity at 167.8 °F, which was not pro-
vided in the design report. At 650 bbl displacement, the actual surface pressure sharply
increased while the planned surface pressure gradually decreased. The surface pressure
peaked (4277 psi) at 700 bbl displacement and was 22% higher than the planned maximum
surface pressure of 3500 psi, leading to a pause in the operation.
Step 3: after 700 bbl displacement, the pump rate was decreased (initially by 0.3 bpm
and then more) from the planned value to keep the pressure within the limits of the sur-
face system. However, higher surface pressure, even at the lowered pump rates, was seen.
In the absence of sucient data to directly reveal the cause, one possible hypothesis is that
the cement gelled during the longer pumping time due to the lower pump rate and the
pause. At 840 bbl displacement, the pressure exceeded 4000 psi again. The operation was
paused, and a pressure test was performed. The operation continued after the pause at
progressively lowered pump rates and even higher surface pressure.
Figure 5. Planned (dash line) and actual (solid line) pump rate and surface pressure at dierent
pumped volumes during the displacement. Note the discrepancy between actual pressure (green
solid line) and planned pressure (blue dashed line).
During Step 1, the actual surface pressure was considerably higher than anticipated.
In Step 2, the peak surface pressure reached 4277 psi at 700 bbl, nearing the upper limit
(4500 psi) of the pressure test, jeopardizing safety and system integrity, leading to
Figure 5. Planned (dash line) and actual (solid line) pump rate and surface pressure at different
pumped volumes during the displacement. Note the discrepancy between actual pressure (green
solid line) and planned pressure (blue dashed line).
Step 1: from 0 bbl to 375 bbl displacement, the spacer and the cement were pumped.
Although a constant flow rate of 4.0 bpm was planned, the actual pump rate fluctuated
between 1.4 bpm and 4.3 bpm. From 25 bbl to 160 bbl displacement, the actual pump rate
was 17–65% lower than the planned pump rate. The actual surface pressure was only 0–32%
lower than the planned pump pressure. However, from 160 bbl to 310 bbl, when the actual
pump rate was only 5% higher than the planned pump rate, the actual surface pressure
was 33% higher than the planned surface pressure. Multiple pauses (0–20 min) were made
for various operations after 310 bbl displacement. At 375 bbl displacement, the pump was
stopped, and the top plug was dropped. Operations in this step lasted for less than half
an hour.
Energies 2024,17, 1226 10 of 27
Step 2: from 375 bbl to 700 bbl displacement, the displacement brine was pumped.
Because of the higher-than-expected pressure during 0–425 bbl displacement, the flow rate
was decreased by 0.2 bpm from 3.5 bpm to 3.3 bpm after 425 bbl displacement. The spacer
front reached the bottom hole at 500 bbl displacement volume. The estimated bottom hole
circulating temperature (BHCT) during this time was 167.8
F in the plan, and the surface
pressure estimation used the OBM viscosity at 167.8
F, which was not provided in the
design report. At 650 bbl displacement, the actual surface pressure sharply increased while
the planned surface pressure gradually decreased. The surface pressure peaked (4277 psi)
at 700 bbl displacement and was 22% higher than the planned maximum surface pressure
of 3500 psi, leading to a pause in the operation.
Step 3: after 700 bbl displacement, the pump rate was decreased (initially by 0.3 bpm
and then more) from the planned value to keep the pressure within the limits of the surface
system. However, higher surface pressure, even at the lowered pump rates, was seen. In
the absence of sufficient data to directly reveal the cause, one possible hypothesis is that
the cement gelled during the longer pumping time due to the lower pump rate and the
pause. At 840 bbl displacement, the pressure exceeded 4000 psi again. The operation was
paused, and a pressure test was performed. The operation continued after the pause at
progressively lowered pump rates and even higher surface pressure.
During Step 1, the actual surface pressure was considerably higher than anticipated.
In Step 2, the peak surface pressure reached 4277 psi at 700 bbl, nearing the upper limit
(4500 psi) of the pressure test, jeopardizing safety and system integrity, leading to oper-
ational pauses and non-productive time (NPT). Notably, at 650 bbl displacement, there
was a sharp increase in surface pressure, contrary to the expected gradual decrease. This
study is independent of that of the service company, and it is unknown what modeling
approach was used or what assumptions were made that led to the evident discrepancy in
peak surface pressure. The differences between planned and actual pressures, as shown
in Figure 5, highlight the need for improved analysis methods. Precise pressure analysis
for slim-hole cement placement operations is crucial to avoid future incidents of excessive
surface pressure, associated risks, and NPT.
3.2. Factors Influencing Surface Pressure
To understand the displacement process, we first study the influence of several factors
on the frictional pressure.
During mud and spacer displacement, the pump rate is reduced to prevent turbulent
flow in the annulus and to improve the stability of the cement–spacer interface. This
minimizes cement contamination and improves CDE. Thus, the flow is assumed to be
laminar. The influence of the pump rate on the laminar flow frictional pressure in the
annulus is shown in Figure 6. The fluid properties of the spacer, OBM, and cement are
listed in Table 2. The dots are simulation results, and the straight lines are linear fits to
the data points. The annular frictional pressure gradient appears to increase linearly with
the pump rate for both OBM and spacer. In mud displacement operations, fluid may pass
through an annulus section at varying pump rates during different operational stages. This
study leverages the linear relationship between the annular frictional pressure gradient
and flow rate to streamline and expedite analysis. For single-phase flow cases, we simulate
only the case with the smallest and largest flow rates. Other scenarios are interpolated
based on this linear relationship for each fluid in every well section. The reduction in the
simulation cases varies with the number of operation steps.
The frictional pressure gradient in the annulus increases nonlinearly when the well-
bore diameter decreases, as shown in Figure 7. The trend lines are polynomial, and the
preliminary result of fitting the pressure gradient data is included in Appendix C. The
flow rate, in this case, is 2.2 bpm. The pressure gradient increases rapidly as the wellbore
diameter decreases and approaches the casing diameter, closing the already narrow gap.
The difference in the frictional pressure gradient between different fluids also increases
rapidly when the wellbore diameter decreases. The wellbore diameter is never constant and
Energies 2024,17, 1226 11 of 27
may decrease in some well sections because of elevated reservoir pressure and wellbore
instability, non-optimum directional drilling practices, etc. When the cement front enters a
narrow zone in the annulus, the pressure gradient in the annulus section rapidly increases,
leading to a sharp increase in the surface pressure. The pressure–wellbore diameter relation-
ship also impacts the frictional pressure of casings with a casing connection of larger outer
diameter. For example, a 5.5 in. casing with a 6.05 in. outer diameter casing connection
covering 2% of the length of the casing could give rise to a 3% higher frictional pressure in
the annulus than a 5.5 in. casing with a flush connection.
Energies 2024, 17, x FOR PEER REVIEW 11 of 29
operational pauses and non-productive time (NPT). Notably, at 650 bbl displacement,
there was a sharp increase in surface pressure, contrary to the expected gradual decrease.
This study is independent of that of the service company, and it is unknown what model-
ing approach was used or what assumptions were made that led to the evident discrep-
ancy in peak surface pressure. The dierences between planned and actual pressures, as
shown in Figure 5, highlight the need for improved analysis methods. Precise pressure
analysis for slim-hole cement placement operations is crucial to avoid future incidents of
excessive surface pressure, associated risks, and NPT.
3.2. Factors Inuencing Surface Pressure
To understand the displacement process, we rst study the inuence of several fac-
tors on the frictional pressure.
During mud and spacer displacement, the pump rate is reduced to prevent turbulent
ow in the annulus and to improve the stability of the cement–spacer interface. This min-
imizes cement contamination and improves CDE. Thus, the ow is assumed to be laminar.
The inuence of the pump rate on the laminar ow frictional pressure in the annulus is
shown in Figure 6. The uid properties of the spacer, OBM, and cement are listed in Table
2. The dots are simulation results, and the straight lines are linear ts to the data points.
The annular frictional pressure gradient appears to increase linearly with the pump rate
for both OBM and spacer. In mud displacement operations, uid may pass through an
annulus section at varying pump rates during dierent operational stages. This study lev-
erages the linear relationship between the annular frictional pressure gradient and ow
rate to streamline and expedite analysis. For single-phase ow cases, we simulate only the
case with the smallest and largest ow rates. Other scenarios are interpolated based on
this linear relationship for each uid in every well section. The reduction in the simulation
cases varies with the number of operation steps.
Figure 6. Linear relationship between the frictional pressure gradient and the pump rate in the an-
nulus for dierent uids at dierent wellbore diameters and dierent eccentricities, 𝝐. The casing
outer diameter is 5.5 in. with 6.252 in. outer diameter centralizers with laminar ow in the annulus.
The frictional pressure gradient in the annulus increases nonlinearly when the well-
bore diameter decreases, as shown in Figure 7. The trend lines are polynomial, and the
preliminary result of ing the pressure gradient data is included in Appendix C. The
ow rate, in this case, is 2.2 bpm. The pressure gradient increases rapidly as the wellbore
diameter decreases and approaches the casing diameter, closing the already narrow gap.
The dierence in the frictional pressure gradient between dierent uids also increases
Figure 6. Linear relationship between the frictional pressure gradient and the pump rate in the
annulus for different fluids at different wellbore diameters and different eccentricities,
ϵ
. The casing
outer diameter is 5.5 in. with 6.252 in. outer diameter centralizers with laminar flow in the annulus.
Energies 2024, 17, x FOR PEER REVIEW 12 of 29
rapidly when the wellbore diameter decreases. The wellbore diameter is never constant
and may decrease in some well sections because of elevated reservoir pressure and well-
bore instability, non-optimum directional drilling practices, etc. When the cement front
enters a narrow zone in the annulus, the pressure gradient in the annulus section rapidly
increases, leading to a sharp increase in the surface pressure. The pressure–wellbore di-
ameter relationship also impacts the frictional pressure of casings with a casing connec-
tion of larger outer diameter. For example, a 5.5 in. casing with a 6.05 in. outer diameter
casing connection covering 2% of the length of the casing could give rise to a 3% higher
frictional pressure in the annulus than a 5.5 in. casing with a ush connection.
Figure 7. Impact of wellbore diameter on the frictional pressure gradient in the annulus. The casing
diameter is 5.5 in. with 6.252 in. centralizers. The ow rate is 2.2 bpm.
The frictional pressure gradient in the annulus increases when the plastic viscosity
and yield point increase, and vice versa. The frictional pressures of the OBM as a function
of plastic viscosity and yield point are shown in Figure 8. When the temperature increases,
the plastic viscosity and the yield point of an OBM may decrease sharply [28,29]. Accurate
measurement of plastic viscosity and yield point at the correct temperature is crucial for
precise pressure analysis during cement displacement. Therefore, accurately predicting
downhole temperature behavior during the cementing job is vital for proper uid viscos-
ity characterization.
Figure 7. Impact of wellbore diameter on the frictional pressure gradient in the annulus. The casing
diameter is 5.5 in. with 6.252 in. centralizers. The flow rate is 2.2 bpm.
The frictional pressure gradient in the annulus increases when the plastic viscosity
and yield point increase, and vice versa. The frictional pressures of the OBM as a func-
tion of plastic viscosity and yield point are shown in Figure 8. When the temperature
increases, the plastic viscosity and the yield point of an OBM may decrease sharply [
28
,
29
].
Accurate measurement of plastic viscosity and yield point at the correct temperature is
crucial for precise pressure analysis during cement displacement. Therefore, accurately
Energies 2024,17, 1226 12 of 27
predicting downhole temperature behavior during the cementing job is vital for proper
fluid viscosity characterization.
Figure 8. Impact of (a) plastic viscosity (with yield point = 5.27 Pa) and (b) yield point (with plastic
viscosity = 17 cP) on the frictional pressure gradient in the annulus. The constant yield point is chosen
to be 5.27 Pa. The casing diameter is 5.5 in. with 6.252 in. centralizers.
3.3. Simulation Results
In this section, we first show the simulated surface pressure based on the planned
pump rate, the planned wellbore diameter, the OBM viscosity measured at 150
F, and
the reported cement viscosity, assuming it did not gel during the placement. Then, we
successively adjust the pump rate, the OBM viscosity, the wellbore diameter, and the cement
viscosity in the model based on data from the post-job report and lab measurements. The
surface pressure is simulated based on the adjusted inputs to show the particular influence
of the various factors.
Well X had 19 operation steps according to the actual pump rate data. To assess the
frictional pressure gradient in each well segment for every operation step, we initially
required 140 simulation cases. However, leveraging the linear relationship between pump
rate and annular pressure gradient, we reduced the number of simulations to 42. The
skipped simulations were effectively estimated using linear interpolation. The simulations
were performed on a laptop computer with an Intel i7-4940MX CPU (8 cores at 3.10 GHz).
The simulation time for an analysis was less than seven days. The simulation of the flow in
each well segment took 0.5–2 h.
The simulated surface pressure based on the planned data is shown in Figure 9. From
0 bbl to 375 bbl displacement, the simulated pressure is within the 200 psi range from the
planned pressure when the actual pump rate is slightly higher than the planned pump
rate. From 375 bbl to 715 bbl displacement, the simulated pressure is higher than the actual
pressure because the input OBM viscosity was measured at 150
F, a factor that will be
discussed later in this paper. The planned pressure showed a maximum surface pressure
of 4264 psi at 715 bbl displacement, which is only 0.3% lower than the measured data of
4277 psi at 700 bbl. The trend of the simulated surface pressure always follows the trend of
the actual surface pressure.
Energies 2024,17, 1226 13 of 27
Energies 2024, 17, x FOR PEER REVIEW 14 of 29
Figure 9. Planned (dashed line) and actual (solid line) pump rate, 𝑞, and surface pressure, 𝑝, at
dierent pumped volumes during the displacement. The planned pressure is based on the proposed
model and the planned pump rate, 𝑞.
Figure 10 shows the simulated surface pressure based on the actual pump rate. From
0 bbl to 160 bbl displacement, the simulated surface pressure tracked the actual surface
pressure with minor errors. The error is mostly caused by the transient pressure uctua-
tion, which is not considered in this model. The simulated peak surface pressure (3992
psi) at 700 bbl displacement is 6.6% lower than the actual peak surface pressure (4277 psi).
The surface pressure decreases when the pump rate increases, meaning that if the actual
pump rate had been provided, the results from the commercial software would have fur-
ther deviated from the actual pressure.
Figure 9. Planned (dashed line) and actual (solid line) pump rate,
q
, and surface pressure,
p
, at
different pumped volumes during the displacement. The planned pressure is based on the proposed
model and the planned pump rate, q.
Figure 10 shows the simulated surface pressure based on the actual pump rate. From
0 bbl to 160 bbl displacement, the simulated surface pressure tracked the actual surface
pressure with minor errors. The error is mostly caused by the transient pressure fluctuation,
which is not considered in this model. The simulated peak surface pressure (3992 psi) at
700 bbl displacement is 6.6% lower than the actual peak surface pressure (4277 psi). The
surface pressure decreases when the pump rate increases, meaning that if the actual pump
rate had been provided, the results from the commercial software would have further
deviated from the actual pressure.
The design report listed the BHCT during cement placement as 167.8
F. We used
a thermal-hydraulics model, as described by Khaled et al. [
30
,
31
], to analyze the mud
temperature distribution, with the result shown in Figure 11. At a BHCT of 168
F, the OBM
temperature in the lateral section is at least 166
F, decreasing upon leaving this section.
According to Fakoya and Ahmed [
32
], the OBM viscosity decreases as the temperature
increases. Hence, the OBM viscosity measured at 150
F exceeds that at 168
F. To estimate
the actual OBM viscosity at 168
F, not provided in the report, we measured the viscosity of
a similar OBM at 150–168
F using a rheometer, as detailed in Table 3. The plastic viscosity
of the similar OBM decreased from 29.9 cP to 22.2 cP, while the yield pressure decreased
from 12.9 Pa to 11.9 Pa. Based on these measurements, we hypothesize that, in the field
case, the OBM plastic viscosity decreased from 17 cP by 7 cP to 10 cP during the cement
placement and then increased back to 17 cP, with an assumption of a constant yield point
of 5.27 Pa for simplicity. This approximation seems reasonable, considering the similar
impacts of the yield point and the plastic viscosity on the frictional pressure, as illustrated
in Figure 8. Figure 12 shows the surface pressure with the adjusted OBM viscosity. With
the OBM viscosity corrected, the simulated surface pressure matches the actual surface
pressure in most parts in the 0 bbl to 700 bbl displacement interval. The surface pressure at
370 bbl displacement is lowered by 400 psi by the correction of the viscosity. The results
from the commercial software are already based on the OBM viscosity measured at 168
F;
therefore, it could not be further improved by the correction of viscosity.
Energies 2024,17, 1226 14 of 27
Energies 2024, 17, x FOR PEER REVIEW 15 of 29
Figure 10. Simulated and actual pump rate, 𝑞, and surface pressure, 𝑝, at dierent pumped vol-
umes during the displacement. The simulated pressure is based on the proposed model and the
actual pump rate, 𝑞.
The design report listed the BHCT during cement placement as 167.8 °F. We used a
thermal-hydraulics model, as described by Khaled et al. [30,31], to analyze the mud tem-
perature distribution, with the result shown in Figure 11. At a BHCT of 168 °F, the OBM
temperature in the lateral section is at least 166 °F, decreasing upon leaving this section.
According to Fakoya and Ahmed [32], the OBM viscosity decreases as the temperature
increases. Hence, the OBM viscosity measured at 150 °F exceeds that at 168 °F. To estimate
the actual OBM viscosity at 168 °F, not provided in the report, we measured the viscosity
of a similar OBM at 150168 °F using a rheometer, as detailed in Table 3. The plastic vis-
cosity of the similar OBM decreased from 29.9 cP to 22.2 cP, while the yield pressure de-
creased from 12.9 Pa to 11.9 Pa. Based on these measurements, we hypothesize that, in the
eld case, the OBM plastic viscosity decreased from 17 cP by 7 cP to 10 cP during the
cement placement and then increased back to 17 cP, with an assumption of a constant
yield point of 5.27 Pa for simplicity. This approximation seems reasonable, considering
the similar impacts of the yield point and the plastic viscosity on the frictional pressure,
as illustrated in Figure 8. Figure 12 shows the surface pressure with the adjusted OBM
viscosity. With the OBM viscosity corrected, the simulated surface pressure matches the
actual surface pressure in most parts in the 0 bbl to 700 bbl displacement interval. The
surface pressure at 370 bbl displacement is lowered by 400 psi by the correction of the
viscosity. The results from the commercial software are already based on the OBM viscos-
ity measured at 168 F
; therefore, it could not be further improved by the correction of
viscosity.
Figures 11 and 12 highlight the importance of considering the impact of temperature
in the model. We introduce a one-way coupling strategy, as described at the end of Ap-
pendix C, to incorporate the impact of temperature on the viscosity.
Figure 10. Simulated and actual pump rate,
q
, and surface pressure,
p
, at different pumped volumes
during the displacement. The simulated pressure is based on the proposed model and the actual
pump rate, q.
Energies 2024, 17, x FOR PEER REVIEW 16 of 29
Figure 11. Mud temperature in the well during the cement placement after 380 bbl displacement.
The BHCT is 168 °F.
Table 3. OBM viscosity.
Temperature, °F Plastic Viscosity, cP Yield Point, Pa
150 29.9 12.9
160 25.7 12.3
168 22.2 11.9
Figure 12. Simulated and actual pump rate, 𝑞, and surface pressure, 𝑝, at dierent pumped vol-
umes during the displacement. The simulated pressure is based on the proposed model, the actual
pump rate, 𝑞, and the corrected OBM viscosity, 𝜇.
Contrary to the initial assumption of a uniform 6.75 in. wellbore, ultrasonic borehole
diameter measurements revealed an average wellbore diameter of only 6.58 in. between
Figure 11. Mud temperature in the well during the cement placement after 380 bbl displacement.
The BHCT is 168 F.
Table 3. OBM viscosity.
Temperature, F Plastic Viscosity, cP Yield Point, Pa
150 29.9 12.9
160 25.7 12.3
168 22.2 11.9
Energies 2024,17, 1226 15 of 27
Energies 2024, 17, x FOR PEER REVIEW 16 of 29
Figure 11. Mud temperature in the well during the cement placement after 380 bbl displacement.
The BHCT is 168 °F.
Table 3. OBM viscosity.
Temperature, °F Plastic Viscosity, cP Yield Point, Pa
150 29.9 12.9
160 25.7 12.3
168 22.2 11.9
Figure 12. Simulated and actual pump rate, 𝑞, and surface pressure, 𝑝, at dierent pumped vol-
umes during the displacement. The simulated pressure is based on the proposed model, the actual
pump rate, 𝑞, and the corrected OBM viscosity, 𝜇.
Contrary to the initial assumption of a uniform 6.75 in. wellbore, ultrasonic borehole
diameter measurements revealed an average wellbore diameter of only 6.58 in. between
Figure 12. Simulated and actual pump rate,
q
, and surface pressure,
p
, at different pumped volumes