2017 SPE / IADC Drilling Conference 2017

SPE-184702-MS

Advanced Modeling of Cement Displacement Complexities Saeid Enayatpour and Eric van Oort, The University of Texas at Austin

Copyright 2017, Society of Petroleum Engineers This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract Cement job success is largely determined by fluid displacement efficiency. Optimum displacement requires understanding of flow patterns, frictional pressure losses and mutual interactions of mud, spacers and cement in annular spaces. Modeling this complex behavior is very difficult, but understanding it is essential to guarantee displacement success. A state-of-the-art cement displacement study was carried out using the very latest in computational fluid dynamics (CFD) modeling techniques, to identify practical guidelines and solutions to cement displacement challenges.

A state-of-the-art 3D “3-phase” (i.e. mud-spacer-cement phases) CFD model was created and simulations were carried out, featuring tracking of fluid interfaces during displacement, calculation of frictional pressure drops, and characterization of complex flow profiles. These simulations accounted for the effects of such complexities as non-Newtonian rheological behavior of all fluids involved, eccentric / narrow annuli, and pipe movement / rotation. The integrated study clearly identifies the root cause(s) of cement displacement failures and highlights comprehensive practical solutions, which are proposed for implementation in field operations.

There are many causes for cement displacement problems and failures, including poor borehole conditioning, inappropriate displacement flow rates, insufficient casing centralization, viscosity contrast mismatches between mud-spacer-cement leading to interface instabilities, etc. Our high-resolution finite element study quantifies the effects of many of these causes and highlights parameters that can improve displacement, such as avoiding high shear strength in non-Newtonian mud and cement rheology, reducing pipe eccentricity and applying pipe rotation during displacement. The modeling approach is used to identify optimum parameters values, and studies interdependencies between factors, for instance determining optimum rheology, flow rate and pipe rotation speeds when pipe is placed eccentrically in the hole, in order to maximize the probability of displacement success in the field. Particularly revealing are the non-intuitive results obtained while modeling mud, spacer and cement as non-Newtonian yield power law (YPL) fluids, which has never been done before.

This paper presents: (1) a new, state-of-the-art 3D CFD model; (2) advanced numerical analysis of cement displacement, taking into account complexities such as non-Newtonian rheology, borehole enlargement, pipe eccentricity, and pipe movement during displacement; (3) practical guidelines derived from the modeling results that can be used for improved cement job pre-planning and field application.

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Introduction General Successfully displacing drilling fluid while placing cementitious material in casing annuli is crucial to establishing zonal isolation, which in turn is essential to the success of subsequent completion, stimulation and production operations. Displacement mistakes made during primary cementing operations can have profound safety and cost implications, including the necessity of costly secondary remediation, severe well control issues, compromised hydrocarbon production, and the loss of the well in its entirety. With ever-growing well complexity, associated with (ultra) deepwater drilling in narrow drilling-margin environments, extended reach drilling (ERD), high-pressure / high temperature (HPHT) drilling etc., the displacement challenge is continuously increasing in magnitude. This challenge is best met with an integrated approach that involves appropriate mud, spacer and cement material selection, laboratory testing, job simulation, executing the cement job as planned, and appropriate data-simulation to verify actual vs. planned results. This papers primary aim is to improve simulation capabilities.

Computer simulation to model mud displacement / cement placement is an important tool in both the planning of cement jobs as well real-time monitoring (see e.g. Creel et al., 2006). Its application and use has increased significantly in recent years, helping to facilitate complex cementing operations in variable environments. Simulation allows for many important displacement parameters to be studied and optimized prior - and increasingly during – cementing operations. Such parameters including:

• Pump/flow rates; • Fluid volumes and contact times; • Frictional annular pressure loss, determining equivalent circulating density (ECD) in relation to the

formation fracture gradient; • Optimum density contrasts, viscosity contrasts, polarity contrasts, and interface stability between

mud, spacer and cement; • Simulation of non-Newtonian rheologies; • The intricate role of wellbore caliper/quality, casing eccentricity, casing movement (rotation and

reciprocation) etc. on displacement efficiency. Software tools have become more sophisticated in recent years, being capable of modeling the above

parameters in fully three-dimensional (3D) models without making extensive simplifying assumptions. In 2006, Nelson and Guillot (2006) already stated: “Three-dimensional models allow a good understanding of the various phenomena but, owing to their complexity, they remain research tools today. As available computational power continues to increase, such tools will eventually enter the mainstream”. This prediction, made over a decade ago, is coming true. Although the work presented here is not (yet) mainstream, it does represent what is currently possible in fluid displacement modeling using state-of-the-art software and readily available computational power. The overall intent of the work is also to make sophisticated displacement modeling more accessible in order to improve planning and executing displacements in the field, with the overall goal to reduce cement failures (a prime cause of well blowouts) and to help guarantee zonal isolation.

Prior Work A large volume of relevant prior work, including modeling studies supported by extensive laboratory work and field validation, has revealed the intricacies of the displacement behavior of drilling, spacer and cementing fluids. Serving as an introduction to our own modeling studies, a brief summary is given below of some of the common knowledge and best practices regarding annular fluid displacement, while highlighting published work dedicated to its more complex aspects, such as the effects of casing eccentricity, pipe rotation, non-Newtonian rheology, etc.

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Effect of Wellbore Quality and Hole Caliper

At present, drilling practice seems primarily aimed at optimizing drilling performance, i.e. “fast drilling”. In principle, there is little wrong with this, unless the singular focus to drill as fast as possible jeopardizes wellbore quality, as it unfortunately often does. Highly tortuous wellbores with poor hole caliper may yield operational problems ranging from poor hole cleaning, a high pack-off and stuck pipe tendency, induced drillstring vibrations (see e.g. Zhou et al., 2016), etc., all the way to completion and production inefficiencies. Of particular importance here are problems associated with casing running, centralization and cementing in poor quality (e.g. tortuous, enlarged) hole. There are numerous studies (Sauer, 1987; Kettle et al., 1992; Cunningham, 2000; Chen et al., 2002; Mason and Chen, 2006; Barton et al., 2013) that show that a smooth, in-gauge wellbore highly benefits good mud displacement and cement placement. The key here is that drillers should be accountable for not only efficient hole-making (usually expressed using such metrics as rate-of-penetration (ROP), on-bottom drilling time, etc.), but also for a high-quality, borehole with a smooth, low-tortuosity wellbore that is in-gauge, stable, and free of obstructions such as cuttings/cavings and (prior to cement placement) filter cake. Creating a “cementable” borehole should clearly be a primary requirement, and this is also reflected by computer simulation results (see e.g. Savery et al., 2007).

Effect of Fluid Density, Gel Strength, Viscosity, and Interface Stability It is well-known that solids-laden drilling fluids need conditioning prior to displacement, i.e. reducing elevated density (e.g. by circulating out drilled solids, including any cuttings beds left in the hole) and lowering gel strength, yield point and plastic viscosity without compromising well control or the integrity of the fluid itself (Howard and Clark, 1948). Excessive thinning of the fluid, on the other hand, may trigger fluid problems such as barite sag, particularly in deviated wellbores (see e.g. Keller et al, 1987; Crook et al., 1987), and should be avoided. From an operational standpoint, it is important that time spent on conditioning (typically at least one hole volume for vertical wells, more in deviated hole and preferably indicated by a tracer) before tripping out drillpipe, running logs and casing/liner is not seen as a waste of time, and may be essential for displacement success.

Drilling fluids are inherently designed to be thixotropic, i.e. they develop gel strength when not circulated in order to trap and suspend cuttings. Excessive gel strength can be a significant hindrance to good displacement and pressure management during cementing, providing a compelling reason for the aforementioned mud conditioning. Moreover, the negative effects of mud gelation can be further reduced by maintaining an appropriate displacement flow rate as well as casing movement, i.e. reciprocation and rotation (see below).

Chemical washes and spacers are typically pumped ahead of the cement to aid in mud and filter cake removal. The effect of density and rheology contrasts between displaced and displacing fluids have been studied extensively (Clark and Carter, 1973; Flumerfelt, 1975; Haut and Crook, 1979; Lockyear et al., 1990; Jakobsen et al., 1991; Tehrani et al., 1992; Miranda et al, 2007; Karbasforoushan et al., 2016) In general, upward displacement of dense mud by a lighter fluid typically leads to an unstable interface and a buoyant plume that leaves much of the drilling fluid behind (Nelson and Guillot, 2006). Displacement of a mud by a denser fluid typically leads to a more stable and flatter interface, a desirable characteristic with much better displacement efficiency. Viscous fingering is observed when attempting to displace a viscous mud by a less viscous one, with better displacement observed when displacing a less viscous mud by a viscous fluid. Although low density, low viscosity spacers can be used (Haut and Crook, 1982), particularly when pumped in the turbulent flow regime at larger volumes to offset channeling effects, the preference in more recent years for more challenging applications such as Deepwater and HPHT wells has been to use higher viscosity weighted spacers (see e.g. Parlar et al., 2002; Sarap et al., 2009).

Density hierarchy, viscosity hierarchy, and minimized pressure gradient are all integral part of design criteria for displacements (see Brady et al., 1992; Ryan et al., 1992; Kelessidis, 1996; Shadravan et al., 2015), leading to specific cleaning fluid sequences (see Nelson and Guillot, 2006).

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Effect of Flow Rate The mud displacement / cement placement problem shares many similarities with hole cleaning while

drilling (Moroni et al., 2009), particularly when it comes to the effects of flow rate, pipe eccentricity and pipe rotation discussed in the following. Factors that improve hole cleaning during drilling generally also improve fluid displacement. Displacement efficiency increases with increasing flow rate (Howard and Clark, 1948; Brice and Holmes, 1964), with marked improvement occurring for non-Newtonian fluids in the transition from laminar to turbulent flow. Calculating displacement efficiencies in turbulent flow, however, is significantly more complicated (see e.g. Schlichting, 1979). In environments with low drilling margins, particularly pertaining to deepwater wells in geopressured environments, ECD limitations may restrict flow rate, and good displacement may need to be guaranteed at sub-optimum flow rates (Ravi et al., 1999).

Effect of Casing Eccentricity The importance of casing centralization for displacement has been understood since the early days of

cementing, as shown by the cement channeling experiments by Jones and Berdine (1940). Under circumstances of elevated eccentricity, a channel of by-passed mud forms on the narrow part of the annulus with flow taking place predominantly in the wider annular space. The asymmetry presented an eccentrically placed casing in the wellbore may lead to situations where the Reynolds number varies azimuthally around the casing, such that the flow regime may be laminar on the narrow annular side and turbulent on the wider side. As indicated by Nelson and Guillot (2006), displacement in non-Newtonian shear-thinning fluids is much more affected than in Newtonian fluids due to the “breakthrough” behavior of these fluids. Noteworthy studies include the work of Luo and Peden (1987) on the eccentric annular flow of power-law and Bingham plastic fluids, and Siginer and Bakhtiyarov (1998) investigating the effect of pipe eccentricity on the flow of well bore fluids in annuli, both analytically and experimentally.

Effect of Pipe Movement The role of pipe rotation becomes more important when non-ideal conditions (such as high mud viscosity and gel strength, elevated casing eccentricity, etc.) exist. It is that regard very similar to hole cleaning in deviated / extended reach hole, where pipe rotation of an eccentrically placed drillstring return cuttings back from cuttings beds into the active flowstream. Bittleston and Hassenger (1992) studied the flow of viscoelastic fluids in a concentric annulus with casing rotation. Barton et al. (1994) simulated Heschel-Bulkley fluids in an eccentric annulus during casing rotation and reciprocation. Sanchez et al. (1999) showed the beneficial effect of drillstring rotation on hole cleaning and cuttings evacuation in deviated hole, with beneficial effect attributed to orbital motion of the drillstring and Taylor vortices. More recently, Moroni et al. (2009) indicated that the shear stress next to the casing on the narrow annular side should normally be sufficient to overcome the yield stress of the drilling fluid and cement, and allow flow to be initiated on this side. They also review the effects of rotation on annular frictional pressure drop (∆Pann), an important quantity which is also discussed in our simulations, as reported from different studies. The historical results are quite contradictory: Walker and Al-Rawi, Luo and Peden (1987), and Marken et al. (1996) report a reduction in annular friction pressure with increasing pipe rotation, whereas Moroni et al. (2009) themselves all report an increase in annular friction pressure with increasing pipe rotation. Wang et al. (2000) report a mixed case for rotation speeds up to 230 rev/min and annular eccentricities between 0.4 and 0.6, showing friction pressure to decrease for rotation speeds equal or less than 30 rev/min and to increase of rotation speeds greater than 70 rev/min.

The results show that casing movement, in particular pipe rotation, can partially offset the negative effect of pipe eccentricity on displacement efficiency and erosion/removal of mud filter cake (the latter when used in combination with scratchers/scrapers/wiper). Casing rotation appears to be the preferred pipe movement to aid displacement, as reciprocation often presents drawbacks such as surge and swab pressures, stuck pipe risks and movement amplitude being reduced by pipe stretch or buckling (see e.g. Nelson & Guillot, 2006).

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Prior Modeling Work

As indicated by Nelson and Guillot (2006), the best models for planning field operations are currently based on a 2D displacement representation. High computational requirements have limited the use of more complex 3D models. Moreover, computational models usually make simplifying and limiting assumptions, either by simplifying the governing Navier-Stokes equation and/or assuming simplified behaviors, such as fluid separation by sharp interfaces. One of the most sophisticated models introduced in the last decade is a 3D finite difference displacement simulator by Savery et al. (2007), which was used by Edwards et al. (2013) to predict residual cement after balanced plug cementing. Chen et al. (2014) used a CFD model with 2D and 3D visualization capability recently to study intermixing of cementing fluids for several field cases.

It appears fair to state that displacement modeling has been almost exclusively the playground of major service providers using proprietary, confidential simulators that are not generally available. It is the intent of this work to make advanced displacement simulation more widely available.

Theoretical Governing Equations We concentrate on 3D flow modeling of Newtonian and Yield Power Law (YPL) fluids through concentric and eccentric annuli, where the inner pipe/casing can be either stationary or rotating about its axis. Use is made of the finite volume method (a cell-centered numerical method) of the computational fluid dynamics (CFD) model ANSYS Fluent 17.0 for numerically solving the Navier-Stokes equations. To perform CFD simulations, both the mass conservation (or continuity) equation and the momentum conservation equation need to be solved. The general form of the mass conservation/continuity equation is given in Eq. 1, which is valid for both incompressible and compressible fluids:

𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕

+ ∇. (𝜌𝜌�⃗�𝑣) = 𝑆𝑆𝑚𝑚 (1)

where 𝜌𝜌 is density, �⃗�𝑣 is the fluid velocity vector, and 𝑆𝑆𝑚𝑚 is the source term added to the continuous phase from the element boundaries or from any dispersed phase inside the continuous phase. For incompressible fluids, Eq.1 reduces to:

∇. (�⃗�𝑣) = 0 (2)

i.e. zero divergence of fluid velocity. Eq.3 describes the conservation of momentum:

𝜕𝜕𝜕𝜕𝑣𝑣�⃗𝜕𝜕𝜕𝜕

+ ∇. (𝜌𝜌�⃗�𝑣�⃗�𝑣) = −∇𝑝𝑝 + ∇. (𝜏𝜏̿) + 𝜌𝜌�⃗�𝑔 + �⃗�𝐹 (3)

where 𝑝𝑝 is fluid pressure, 𝜏𝜏̿ is the stress tensor given below in Eq.4, �⃗�𝑔 is the acceleration of gravity (i.e. gravitational body load), and �⃗�𝐹 represents any other external body load (e.g. created by an external magnetic field). The second term on the left hand side of Eq.3 is the convection term, and the second term on the right hand side is the diffusion term. The stress tensor 𝜏𝜏̿ in this diffusion term is given by:

𝜏𝜏̿ = 𝜇𝜇 �(∇�⃗�𝑣 + ∇�⃗�𝑣𝑇𝑇) − 23∇�⃗�𝑣𝐼𝐼� (4)

where 𝜇𝜇 is the fluid molecular viscosity and 𝐼𝐼 is the identity tensor.

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In the following, we will mainly concentrate on laminar flow of incompressible fluids in a first set of

results that serves the purpose of demonstrating the capabilities of our modeling approach. Note that these conditions are used for convenience only, and are not inherent limitations of the modeling approach itself (i.e. the approach can also be used to model turbulent flow behavior, compressible fluids, etc.).

Multi-Phase Flow (MPF) Modeling Our simulations generally deal with three discrete fluid “phases” in displacement, namely drilling mud,

spacer, and cement (the term “phase” here should not be confused with the usual thermodynamical phases of gas, liquid and solid). We will use this definition of “phase” throughout the remainder of the document. In a first approach, focus will be primarily on only two such “phases”, with one displacing the other.

In the modeling, the phases are allowed to mix, e.g. because of unstable interfaces between them. We define volume fractions for any dispersed phase 𝛼𝛼𝑝𝑝 and for the continuous phase 𝛼𝛼𝑞𝑞 within a total volume 𝜕𝜕𝜕𝜕 containing the phases at fractional volumes 𝜕𝜕𝜕𝜕𝑝𝑝 and 𝜕𝜕𝜕𝜕𝑞𝑞 respectively as:

𝛼𝛼𝑝𝑝 = 𝜕𝜕𝜕𝜕𝑝𝑝𝜕𝜕𝜕𝜕 (5A)

𝛼𝛼𝑞𝑞 = 𝜕𝜕𝜕𝜕𝑞𝑞𝜕𝜕𝜕𝜕 (5B)

With the sum of these volume fractions adding up to 1:

𝛼𝛼𝑝𝑝 + 𝛼𝛼𝑞𝑞 = 1 (6)

Volume of Fluid (VOF) Model The Volume of Fluid (VOF) Model, a free-surface modelling technique (see e.g. Hirt and Nichols, 1981), was used to solve the CFD model numerically. Using this method, the phase volume fractions are calculated using either explicit or implicit solution schemes, with a separate scheme employed for tracking the interface between the fluid phases. The effects of fluid surface tension and wall adhesion are considered, while the (secondary) effects of mass and heat transfer are ignored for the time being. Information about imposed boundary conditions and solver settings vary for the various simulations, and will be given when discussing individual results below.

There are multiple techniques for tracking fluid interfaces, such as Marker Particles, Moving Grid and, in our case, VOF, which was found to be most suitable for the problem at hand. Note that the VOF model is valid for finding the shape of fluid interfaces as long as the interface length is large compared to the computational grid mesh size, as shown in Figure 1. As the mesh size increases to get closer to the size of the interface, the accuracy of the VOF method will decrease. It is therefore important to select domain discretization in such a way for the VOF method to remain valid.

Figure 1 – The VOF method yields reliable results when the computational grid size remains smaller than the interface length.

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Simulation Results & Discussion Validation To ensure the quality of simulation results, steps were taken to verify the solutions as complexities were added to the simulation cases. Pressure gradients and velocity profiles were verified wherever analytical solutions existed, and the model set-up of confirmed models was used to create more advanced, high-resolution finite element models. Intermediate results were inspected upon approaching final solutions to make sure results (e.g. incorporating the effects of pipe rotation and eccentricity) were realistic. Meshing requirements were adjusted, particularly in cases of higher eccentricity: when eccentricity e increases (e = 0 represents fully concentric pipe, e = 1 is eccentric pipe), meshing requirements call for a great number of elements at the narrow section of the pipe, with an associated increase in computational time (a number of higher eccentricity case, e.g. e = 0.75 and 0.95, will be discussed below). Verification was achieved using several simple validation models (“toy models”), which are briefly described in the following.

Validation Model 1 – Newtonian Fluid Flow To outline the general procedure for solving displacement problems, including how mesh evaluation

and refinement was accomplished, we start out with simple Newtonian pipe flow of water at 20 deg. C in a concentric pipe situation, and compare the numerical results against analytical solutions. Figure 2 shows meshing and boundary layer elements to capture the velocity gradient at the boundary. The number of nodes generated for this mesh is 378,000. Numerical parameters for this model are shown in Table 1. Figure 3 shows the convergence plot of inlet pressure over time (which is not known or given a value at the start of the simulation) and is calculated as part of the simulation. The numerical value of 587 Pa/m pressure drop is within 1.2% of the analytical value of 578 Pa/m. This small error is generally considered to be acceptable, but can be further reduced with mesh refinement.

Property Value Inlet Velocity 0.05 (m/s) Reynolds Number 95 (laminar flow) Dynamic Viscosity 0.001 (Pa.s) Fluid Mass Density 1000 (kg/m3) – 1.0 SG Outlet Pressure 0 Pa Pipe OD / ID 0.375 / 0.3 (in)

Table 1 – Boundary conditions and fluid properties for validation model 1.

Figure 2 – Meshing and boundary layer elements to capture velocity gradients at the boundary.

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Figure 3 – Pressure convergence plot for a Newtonian fluid flowing in a concentric annulus.

The shear stress at the wall was also calculated and compared with the analytical value given by Eq. 7:

𝜏𝜏𝑦𝑦𝜋𝜋(𝑂𝑂𝑂𝑂 + 𝐼𝐼𝑂𝑂)𝐿𝐿 = 𝑝𝑝𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝜕𝜕𝐴𝐴𝑓𝑓𝑖𝑖𝑓𝑓𝑓𝑓 = 𝑝𝑝𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝜕𝜕𝜋𝜋(𝑂𝑂𝑂𝑂2−𝐼𝐼𝑂𝑂2)

4 (7)

where 𝜏𝜏𝑦𝑦 is the shear stress at the wall, 𝑝𝑝𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝜕𝜕 is the inlet pressure, and OD, ID and L are the outer diameter, inner diameter and length of the pipe section respectively. With a maximum shear stress of 0.325 Pa developed at the boundary, the left hand side of Eq. 7 gives a shear force of 0.0159 N and the right hand side amounts to 0.0149 N. The error between the numerical and the closed form analytical force balance is therefore 6.3% when using the aforementioned 378K nodes. This result shows that a finer mesh is required to study wall shear force. With a finer mesh count of 850K elements, the error reduces to 0.5%.

Validation Model 2 – YPL Fluid Flow In the second validation model, single phase flow of a YPL fluid is studied. The data for this problem

is given in Table 2. Note that for YPL fluids, the relationship between shear stress 𝜏𝜏 and shear rate �̇�𝛾 is given by:

𝜏𝜏 = 𝜏𝜏0 + 𝐾𝐾(�̇�𝛾)𝑖𝑖 (8)

where 𝜏𝜏0 is the yield strength, n is the flow behavior index (note that for n = 1, the fluid behavior is that of a Bingham Plastic) , and 𝐾𝐾 is the consistency index. Figure 4 shows the comparison of the velocity profile between the analytical and numerical solution for this case. The difference in the velocity profile calculation is only 0.4%

Property Value Inlet Pressure 1.414 x 104 (Pa) Outlet Pressure 0 (Pa) Pipe Section Length 1 (m) Pipe Radius 0.005 (m) Flow Behavior Index n 1 Yield Strength 𝜏𝜏0 15 (Pa) Consistency index 𝐾𝐾 0.05 (Pa.s) Fluid Mass Density 1000 (kg/m3)

Table 2 – YPL fluid properties, boundary conditions, and pipe geometry data for validation model 2.

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Figure 4 – Comparison of analytical and numerical ANSYS fluent solutions for validation model 2.

Validation Model 3 – Two-Phase Immiscible Newtonian Fluid Flow This model was developed to look into the fluid displacement pattern, and particularly the phase

separation and interface between two immiscible fluids having the same density but different viscosities. The fluid properties and simulation data for displacement in a concentric annulus are listed in Table 3. Figure 5 shows the pressure profile, velocity vector plot and phase separation contour with an interface between the two fluids that remains stable throughout the displacement.

Property Value Density of Fluid 1 / 2 1000 / 1000 (kg/m3) Viscosity of Fluid 1 / 2 0.001 / 0.002 (Pa.s) Simulation Time 6 hours Time Steps / number 0.0005 (s) / 4000 Maximum iterations 20 / timestep Pipe OD / ID 2 / 1 (in)

Table 3 – Fluid properties for two-phase immiscible Newtonian fluid displacement in validation model 3. Note that fluid 1 is displaced by fluid 2.

Figure 5 – (a) Stable fluid pressure profile; (b) velocity vector plot; (c) phase separation contour of displaced fluid 1 (blue) by displacing fluid 2 (red).

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The relative computational ease of this model makes it well-suited for evaluating the effects of pipe

eccentricity and pipe rotation. The pipe geometry is shown in Fig. 6 for an eccentricity of 0.75. The same fluids as given in Table 3 are used, with an inlet velocity of 0.1 m/s, outlet pressure of 0 Pa, simulated pipe length of 0.5 m, and 350K total simulation elements. Fig. 7 shows the displacement pattern 2.76 sec. into the simulation: a clear mud channel is forming on the narrow side of the annulus where displaced fluid 1 (shown in red) is clearly lagging behind the advancing fluid front of displacing fluid 2 (shown in blue) on the wider side of the annulus. When pipe rotation is introduced (here simulated at the high rotation rate of 100 RPM), it is seen that the mud channel disappears and that fluid displacement becomes homogenous around the entire pipe.

Figure 6 – Pipe geometry, meshing, and boundary elements for the eccentric two-phase immiscible Newtonian fluids model with pipe rotation.

Figure 7 – Fluid contour plots: (a) at the start of the simulation, and (b) at time t = 2.76; notice the immediate occurrence of a mud channel at the narrower end of the annulus.

Figure 8 – Volume of fluid contour plots: (a) at the start of the simulation, and (b) at time t = 3.02 in the presence of pipe rotation; notice that the mud channel is avoided in this case.

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Validation Model 4 – Two-Phase YPL / Newtonian Fluid Flow This validation case involves a YPL fluid that is being displaced by a Newtonian fluid, for instance in

case of a YPL drilling fluid is being displaced by a Newtonian spacer, in a concentric annulus. The fluid properties and simulation parameters are given in Table 4. Graphical results of the simulation are shown in Fig. 9, indicating that the fluid interface between the two fluids is not stable and leads to viscous fingering and intermixing / contamination, a well-known result, as discussed in the section “prior work”.

Property Value Density of Fluid 1 / 2 1000 / 1000 (kg/m3) Viscosity of Fluid 1 0.001 (Pa.s) Consistency index 𝐾𝐾 – Fluid 2 0.2145 (Pa.s) Flow Behavior Index n - Fluid 2 0.5748 Yield Strength 𝜏𝜏0 - Fluid 2 2.383 (Pa) Outlet Pressure 0 (Pa) Simulation Time 11 hours Time Steps / number 0.0001 (s) / 200,000 Maximum iterations 20 / timestep Pipe OD / ID 2 / 1 (in)

Table 4 – Fluid properties, boundary conditions, and pipe geometry data for validation model 4, involving a YPL fluid (displaced fluid) and a Newtonian fluid (displacing fluid).

Figure 9 – Unstable YPL / Newtonian two-phase displacement at a velocity of 0.5 m/s, with (a) cross-section plot; (b) view on the pipe wall, and (c) pressure gradient (in Pa). The YPL fluid (in blue) is being displaced by a Newtonian fluid (in red) at a fluid velocity of 0.5 m/s.

Contamination effects can be minimized / avoided either by pumping the Newtonian fluid at a faster

rate (e.g. in turbulence) and/or increasing the volume and contact time of this fluid. Another way is to reduce the yield strength of the YPL fluid. This is shown in Fig. 10 below, where the yield strength was reduced from 2.383 Pa to 1 Pa; moreover, the displacement velocity was reduced from 0.5 m/s to 0.1 m/s for this simulation. Fig.10 shows the stable time evolution of the two phase interface tracking contour plot and the onset of local interface instability. The latter, however, only occurs at the leading edge of the displacement and immediately disappears, leading to a relatively stable interface with limited intermixing / contamination. Clearly, thinning a YPL drilling fluid aids in the displacement, as expected.

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(a) Figure 10 – Time evolution of the two-phase YPL / Newtonian fluid interface, with (a) contour plot; (b) enlargement showing (limited) interface instability at the leading edge of the displacement, which disappears quickly.

Validation Model 5 – Two-Phase Immiscible YPL Fluid Flow Fig. 11 shows the geometry of an eccentrically placed pipe used to study the effect of two-phase YPL

fluid displacement (either a YPL drilling mud displaced by a YPL spacer, a YPL spacer displaced by YPL cement, or YPL drilling mud directly displaced by YPL cement). YPL fluid properties are as shown in Table 4. The cross sections of the pipe shown in Fig. 11a&b help to explain the pipe contour plot shown in Fig.12, which clearly shows that the fluid-fluid interface lags behind on the narrower end of the annulus as time progresses, leading to the usual follow-up problems with cement contamination, formation of a channel, potential hydrocarbon migration, etc. Note that the CFD simulation is fully able to handle realistic fluid displacement scenarios such as this.

Figure 11 – (a) Pipe geometry with eccentricity; (b) pipe cross section

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Figure 12 – Three instances at sequential times of interface locations and conditions in a two-phase immiscible YPL fluid displacement.

Deepwater Intermediate Casing String Simulations After completing an extensive number of validation cases, of which the previous ones are representative examples, a first set of simulations was completed for the scenario of cementing a 13 5/8” intermediate string in 16 ½” hole (see Fig.13), as is done frequently in deepwater tight clearance casing schemes. The cementing of this (usually very heavy) casing string poses particular challenges in deepwater from a cementing displacement perspective, particularly when trying to manage annular pressures within the available narrow drilling margin to avoid lost circulation of drilling fluid and cement.

Table 5 gives an overview of the various variables that were considered in the simulations, including fluid rheology, flow rate, casing eccentricity and rotation. Table 6 gives an overview of the various cases that have been run to date. Note that it is not our intent here to show an overview of intermediate casing cementing that is exhaustive and complete: the limited work presented here simply serves to illustrate what the capabilities of the new CFD model are, and what could be achieved in the very near-future in better simulating– and thereby planning for – complex displacement scenarios.

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Figure 13 – Graphical display of problem description for a 13 5/8” deepwater casing string in 16.5” hole: (a) two immiscible YPL fluid phases (mud + spacer, spacer + cement, mud + cement) at t = 0 sec; (b) problem geometry and meshing; (c) simulation of fluid displacement in pipe; (d) cross-sections to study cement displacement efficiency; (e) evaluation of cement displacement through cross sections of the pipe; (f) improved displacement using the effects of pipe rotation.

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Variables Fluid Properties Newtonian 𝜌𝜌 = 1900 kg/m3; 𝜇𝜇 = 0.05 Pa/s; YPL (thin) 𝜌𝜌 = 1850 kg/m3; 𝐾𝐾 = 0.6 Pa/s; n = 0.54; 𝜏𝜏0 = 1.2 Pa; critical shear rate = 10-5 (s-1-)

YPL (thick) 𝜌𝜌 = 1800 kg/m3; 𝐾𝐾 = 0.55 Pa/s; n = 0.57; 𝜏𝜏0 = 1.5 Pa; critical shear rate = 10-5 (s-1-) Displacement Cases I Newtonian rheology used exclusively II YPL (thin) is displacing YPL (thick) III YPL (thick) is displacing YPL (thin) Pipe Eccentricity Case 1 / 2 / 3 e = 1 / 0.5 / 0.95 Pipe Rotation Case A / B / C 0 / 10 / 20 RPM Flow Rate Case a / b / c Q = 1 / 3 / 6 bpm Casing Section Length Simulated Case i / ii / iii L = 1 / 2 / 5 m

Table 5 – Variables used for 13 5/8” casing displacement simulation.

Table 6 – Detail of 15 simulation cases with variable indicators as specified in Table 5.

Simulations were run for all 15 cases shown in Table 6. Pressure gradients were calculated for each case, and the displacement efficiency at the end of the simulation was captured using a Cement Displacement Efficiency (CDE) as follows:

𝐶𝐶𝑂𝑂𝐶𝐶 (%) = (1 − 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑝𝑝𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑓𝑓𝑛𝑛𝑓𝑓𝑛𝑛𝑛𝑛 𝑣𝑣𝑛𝑛𝑛𝑛𝑓𝑓𝑣𝑣𝑛𝑛 𝑓𝑓𝑓𝑓𝑛𝑛𝑛𝑛𝑓𝑓𝑛𝑛𝑛𝑛𝑛𝑛) × 100 (9)

where the non-displaced volume fraction is the volume fraction (in the range 0 -1) of any non-displaced fluid left behind the casing. The results are compiled in Table 7. The following observations are made: • Casing section length has a large effect on simulation time (which, for the more involved cases, can

take up to 2-4 days on an Intel i-7 processor with 4 cores). From the results obtained from Newtonian displacement cases 1, 2 and 3 and YPL displacement cases 5 and 6, it is concluded that simulating a casing length of 2 m gives an acceptable error on the order of only 1-5%.

• Eccentricity without pipe rotation strongly reduces the displacement efficiency, as shown by comparable displacement cases 6 (no rotation) with only 88.6% efficiency and 7 (20 RPM rotation) with 99.2% efficiency for an eccentricity e = 0.5 for both cases.

Model # Displacement Case

Eccentricity Case

Rotation Case

Flow Rate Case

Length Case

1 I 3 A c i 2 I 3 A c ii 3 I 3 A c iii 4 I 3 C c iii 5 III 3 A c iii 6 III 3 A c ii 7 III 3 C c ii 8 III 2 A c ii 9 III 2 C c ii 10 II 2 A c ii 11 II 2 C c ii 12 III 1 A c ii 13 III 1 C c ii 14 II 1 A c ii 15 II 1 C c ii

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• Eccentricity by itself leads to a lower frictional pressure drop in the annulus, as shown by comparing

case 12 (no eccentricity, e = 0) with 492 Pa/m pressure drop, case 8 (e = 0.5) with 474 Pa/m pressure drop and case 6 (e = 0.95) with 329 Pa/m pressure drop. Note that associated with this drop in pressure there is, of course, also a noticeable deterioration in displacement efficiency.

• Pipe rotation at relatively low rotation speeds (several tens of RPM) leads to a modest reduction in frictional pressure drop in the annulus for both concentric and eccentric casing strings, as shown by comparing concentric case 14 (no pipe rotation) with 456 Pa/m pressure drop with case 15 (20 RPM rotation) with 450 Pa/m, comparing eccentric (e = 0.5) case 10 (no rotation) with 446 Pa/m pressure drop with case 11 (20 RPM rotation) with 443 Pa/m pressure drop, and comparing eccentric (e = 0.95) case 6 (no rotation) with 329 Pa/m pressure drop with case 7 (20 RPM rotation) with 322 Pa/m pressure drop. This effect is also visualized in Fig. 14. Note that this results shed light on the long-standing issue of the effect of rotation on pressure drop noted in the “Prior Work” section above: our simulations show that frictional pressures are reduced at low rotational speeds (e.g. < 30 RPM used for most casing rotations), but will increase at higher rotational speeds.

• All cases, with the exception of case 6 for a highly eccentric casing scenario, show relatively high displacement efficiencies, which is a direct consequence of using relatively high displacement rates (6 bpm for all cases) for the simulations. However, only case 15 achieves 100% efficiency for the case of a thin YPL fluid displaced by a thick YPL fluid when casing is perfectly centralized and the pipe is rotated. Note that without pipe rotation (case 14), however, it is already possible to get a near-perfect displacement (99.7%) in this case, i.e. pipe rotation is less essential when pipe is centralized.

• How important pipe rotation is for cement displacement when casing is placed eccentrically in the hole is emphasized in Fig. 15. Pipe rotation has the ability to drag fluid/cement around the pipe to the narrow side of the annulus, thereby contributing strongly to better displacement efficiency. As shown by Fig 16, our simulations indicate that the effect works more efficiently at higher eccentricity values.

• Note that all of these observations are in very good qualitative agreement with field experience and the studies mentioned in the section on “Prior Work”.

Model # Pressure Drop (Pa/m) CDE (%) 1 1,139 - 2 1,046 - 3 988 - 4 777 - 5 321 - 6 329 88.6 7 322 99.2 8 474 95.3 9 461 98.8 10 446 98.6 11 443 99.0 12 492 96.3 13 478 96.8 14 456 99.7 15 450 100

Table 7 – Results of simulation cases specified in Table 6 expressed in terms of a calculated frictional pressure drop and CDE (see Eq.9).

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Figure 14 – Frictional pressure drop (pressure gradient in Pa/m) shown as a function of eccentricity in the absence of pipe rotation and presence of pipe rotation (20 RPM), for cases specified in Tables 6 and 7.

Figure 15 – Impact of pipe rotation on cement displacement efficiency for two-phase YPL displacement (eccentricity = 0.95, models 6 (0 RPM) and 7 (20 RPM)). Shown is the change of the non-displaced fluid volume fraction (e.g. bypassed mud) as a function of time for the two models. Insert shows the principle of pipe rotation dragging the displacing fluid around the casing.

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Figure 16 – Impact of casing rotation on CDE as a function of eccentricity, for cases as specified in Tables 6 & 7.

Conclusions

This paper documents the development of an advanced CFD model for cement displacement, which has been used to simulate 3D laminar flow and displacement of Newtonian and YPL fluids in concentric annuli without making limiting simplifying assumptions to numerically solve the Navier-Stokes equations. The model was verified using various simple validation cases and applied in a preliminary study on the displacement of a 13 5/8” deepwater intermediate casing string. Its results emphasize the highly beneficial effect of casing rotation in improving cement displacement efficiency and slightly lowering displacement pressures. The beneficial effect of rotation extends to the point where it can almost completely compensate for the negative effects of casing eccentricity, of evident importance for field cementing in deepwater tight clearance casing schemes (but also for other displacement operations, such as cementing long horizontal casing string in unconventional shale wells). The key behind the CFD model development is that cement displacement complexities such as non-Newtonian rheologies, casing eccentricity and rotation, etc., can now be quantitatively modeled and readily be studied to aid in cement displacement planning using software that is more readily available. It thereby will help improve cementing success, which is expected to result in turn in better zonal isolation, longer productive well life, and improved rig safety.

Acknowledgment This work was carried with financial assistance from the Offshore Energy Safety Institute (OESI), which is committed to improving safety in offshore well construction. The support by OESI is gratefully acknowledged.

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Nomenclature 𝐴𝐴 = area 𝛼𝛼𝑝𝑝 = volume fraction of the dispersed phase 𝛼𝛼𝑞𝑞 = volume fraction of the continuous phase 𝜕𝜕𝜕𝜕 = total volume of in a mixture containing different phases 𝜕𝜕𝜕𝜕𝑝𝑝 = volume of the dispersed phase in a mixture 𝜕𝜕𝜕𝜕𝑞𝑞 = volume of the continuous phase in a mixture e = pipe/casing eccentricity �⃗�𝐹 = external body load vector �⃗�𝑔 = gravitational acceleration ID/OD = pipe/casing inner / outer diameter 𝐼𝐼 = identity tensor 𝐾𝐾 = consistency index 𝐿𝐿 = pipe/casing length 𝜇𝜇 = fluid molecular viscosity n = flow behavior index 𝑝𝑝 = fluid pressure 𝜌𝜌 = fluid constant density 𝑆𝑆𝑚𝑚 = source term added to the continuous phase �̿�𝜏 = shear stress tensor 𝜏𝜏0 = yield strength 𝜏𝜏𝑦𝑦 = shear stress at the wall �⃗�𝑣 = fluid velocity vector Glossary 2D/3D = 2-dimensional/3-dimensional CDE = cement displacement efficiency CFD = computational fluid dynamics ECD = equivalent circulating density ERD = extended reach drilling HPHT = high pressure / high temperature ROP = rate of penetration RPM = rotation per minute VOF = volume of fluid YPL = yield power law References Aranha, P. E., Miranda, C., Cardoso, W., Campos, G., Martins, A., Gomes, F. C., Carvalho, M. (2012, December 1). A Comprehensive

Theoretical and Experimental Study on Fluid Displacement for Oilwell-Cementing Operations. Society of Petroleum Engineers. doi:10.2118/150276-PA

Barton, S., Herrington, D., Gaines, M., Morrison, R., Stroud, D., & Lines, L. (2013, March 5). New Technology Enhances Rotary Steerable System performance and Provides Superior Borehole Quality and Reduces Vibration in Rotary Steerable Applications. Society of Petroleum Engineers. doi:10.2118/163562-MS

Bittleston, S., and Hassenger, O. Flow of Viscoplastic Fluids in a Rotating Concentric Annulus, Journal of Non-Newtonian Fluid Mechanics (March 1992) 42, No.1-2, p. 19-36

Brady, S. D., Drecq, P. P., Baker, K. C., & Guillot, D. J. (1992, January 1). Recent Technological Advances Help Solve Cement Placement Problems in the Gulf of Mexico. Society of Petroleum Engineers. doi:10.2118/23927-MS

Chen, D. C.-K., Gaynor, T., & Comeaux, B. (2002, January 1). Hole Quality: Why It Matters. Society of Petroleum Engineers. doi:10.2118/74403-MS

Chen, Z., Chaudhary, S., & Shine, J. (2014, March 4). Intermixing of Cementing Fluids: Understanding Mud Displacement and Cement Placement. Society of Petroleum Engineers. doi:10.2118/167922-MS

Clark, C. R., & Carter, G. L. (1973, July 1). Mud Displacement with Cement Slurries. Society of Petroleum Engineers. doi:10.2118/4090-PA

20 SPE-184702-MS

Creel, P. G., McKenzie, D. D., Briney, M. R., & Pipes, H. (2006, January 1). Real-Time Cementing Designs vs. Actual Jobs in Progress.

Society of Petroleum Engineers. doi:10.2118/98079-MS Crook, R. J., Keller, S. R., & Wilson, M. A. (1987, August 1). Deviated Wellbore Cementing: Part 2 Solutions. Society of Petroleum

Engineers. doi:10.2118/14198-PA Cunningham, E. B. (2000, January 1). Applications for RAB Large Borehole Caliper in Deepwater Cementing. Offshore Technology

Conference. doi:10.4043/11883-MS Flumerfelt, R. W. (1975, April 1). Laminar Displacement of Non-Newtonian Fluids in Parallel Plate and Narrow Gap Annular Geometries.

Society of Petroleum Engineers. doi:10.2118/4486-PA Haut, R. C., & Crook, R. J. (1979, January 1). Primary Cementing: The Mud Displacement Process. Society of Petroleum Engineers.

doi:10.2118/8253-MS Haut, R. C., & Crook, R. J. (1982, August 1). Laboratory Investigation of Lightweight, Low-Viscosity Cementing Spacer Fluids. Society of

Petroleum Engineers. doi:10.2118/10305-PA Hirt, C.W.; Nichols, B.D. (1981). "Volume of fluid (VOF) method for the dynamics of free boundaries". Journal of Computational Physics.

39 (1): 201–225. doi:10.1016/0021-9991(81)90145-5. Howard, G.C., and Clark, J.B. Factors to be Considered in Obtaining Proper Cementing of Casing. DPP API 1948 (1948), p.257-272 Jakobsen, J., Sterri, N., Saasen, A., Aas, B., Kjosnes, I., & Vigen, A. (1991, January 1). Displacements in Eccentric Annuli during Primary

Cementing in Deviated Wells. Society of Petroleum Engineers. doi:10.2118/21686-MS Jones, P.H., and Berdine, D. Oil Well Cementing: Factors Influencing Bond between Cement and Formation, API Drilling and Production

Practices, Washington, DC, USA, American Petroleum Institute (March 1940), 45-63 Karbasforoushan, H., Ozbayoglu, E. M., Miska, S. Z., Yu, M., & Takach, N. (2016, September 14). On the Instability of Cement-Fluid

Interface and Fluid Mixing. Society of Petroleum Engineers. doi:10.2118/180322-MS Keller, S. R., Crook, R. J., Haut, R. C., & Kulakofaky, D. S. (1987, August 1). Deviated-Wellbore Cementing: Part 1 - Problems. Society of

Petroleum Engineers. doi:10.2118/11979-PA Kelessidis, V. C., Guillot, D. J., Rafferty, R., Borriello, G., & Merlo, A. (1996, May 1). Field Data Demonstrate Improved Mud Removal

Techniques Lead to Successful Cement Jobs. Society of Petroleum Engineers. doi:10.2118/26982-PA Kettl, F. C., Edwards, M. G., & Covington, R. L. (1993, January 1). Practical Horizontal Cementing Today. Society of Petroleum Engineers.

doi:10.2118/25546-MS Lockyear, C. F., Ryan, D. F., & Gunningham, M. M. (1990, September 1). Cement Channeling: How To Predict and Prevent. Society of

Petroleum Engineers. doi:10.2118/19865-PA Luo, Y., & Peden, J. M. (1990, February 1). Flow of Non-Newtonian Fluids Through Eccentric Annuli. Society of Petroleum Engineers.

doi:10.2118/16692-PA Marken, C. D., He, X., & Saasen, A. (1992, January 1). The Influence of Drilling Conditions on Annular Pressure Losses. Society of

Petroleum Engineers. doi:10.2118/24598-MS Mason, C. J., & Chen, D. C.-K. (2006, January 1). The Wellbore Quality Scorecard (WQS). Society of Petroleum Engineers.

doi:10.2118/98893-MS Miranda, C. R., Carvalho, K. T., Vargas, A. A., Rodrigues, L. F., & Marchesini, F. H. (2007, January 1). Minimizing Fluid Contamination

During Oilwell Cementing Operations. Offshore Mediterranean Conference. Paper 2007-111. Moroni, N., Ravi, K., Hemphill, T., & Sairam, P. (2009, January 1). Pipe Rotation Improves Hole Cleaning and Cement-Slurry Placement:

Mathematical Modeling and Field Validation. Society of Petroleum Engineers. doi:10.2118/124726-MS Nelson, E.B., Guillot, D. Well Cementing, second edition. Schlumberger, 2006 Parlar, M., Brady, M. E., Morris, L., Ali, S. A., Twynam, A., Newberry, P., Foxenberg, W. E. (2002, January 1). Filtercake Cleanup

Techniques for Openhole Water Injectors with Sand Control: Lessons From Laboratory Experiments and Recommendations for Field Practices. Society of Petroleum Engineers. doi:10.2118/77449-MS

Ravi, K., Biezen, E. N., Lightford, S. C., Hibbert, A., & Greaves, C. (1999, January 1). Deepwater Cementing Challenges. Society of Petroleum Engineers. doi:10.2118/56534-MS

Ryan, D. F., Kellingray, D. S., & Lockyear, C. F. (1992, January 1). Improved Cement Placement on North Sea Wells Using a Cement Placement Simulator. Society of Petroleum Engineers. doi:10.2118/24977-MS

Sauer, C. W. (1987, September 1). Mud Displacement During Cementing State of the Art. Society of Petroleum Engineers. doi:10.2118/14197-PA

Sarap, G. D., Sivanandan, M., Patil, S. P., & Deshpande, A. (2009, January 1). The Use of High-Performance Spacers for Zonal Isolation in High-Temperature High-Pressure Wells. Society of Petroleum Engineers. doi:10.2118/124275-MS

Savery, M., Darbe, R., & Chin, W. (2007, January 1). Modeling Fluid Interfaces During Cementing Using a 3D Mud Displacement Simulator. Offshore Technology Conference. doi:10.4043/18513-MS

Schlichting, H. Boundary Layer Theory. New York, USA, McGraw-Hill Book Company, Inc. (1979) Shadravan, A., Narvaez, G., Alegria, A., Carman, P., Perez, C., & Erger, R. (2015, March 16). Engineering the Mud-Spacer-Cement

Rheological Hierarchy Improves Wellbore Integrity. Society of Petroleum Engineers. doi:10.2118/173534-MS Siginer, D.A, Bakhtiyarov, S.A. Flow of drilling fluids in eccentric annuli. Journal of Non-Newtonian Fluid Mechanics, 78, 119-132. (1998) Tehrani, A., Ferguson, J., & Bittleston, S. H. (1992, January 1). Laminar Displacement in Annuli: A Combined Experimental and Theoretical

Study. Society of Petroleum Engineers. doi:10.2118/24569-MS Walker, R. E., & Al-Rawi, O. (1970, January 1). Helical Flow of Bentonite Slurries. Society of Petroleum Engineers. doi:10.2118/3108-MS Wang, H., Su, Y., Bai, Y., Gao, Z., & Zhang, F. (2000, January 1). Experimental Study of Slimhole Annular Pressure Loss and Its Field

Applications. Society of Petroleum Engineers. doi:10.2118/59265-MS Zhou, Y., Zheng, D., Ashok, P., & van Oort, E. (2016, March 1). Improved Wellbore Quality Using a Novel Real-Time Tortuosity Index.

Society of Petroleum Engineers. doi:10.2118/178869-MS