## 3D Simulator Predicts Realistic Mud Displacement in Deviated and Horizontal Wells

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Over the past several decades, the industry has dedicated considerable attention to the topic of mud displacement. For deeper wells with complex trajectories, such as highly deviated or horizontal wells, conventional 2D annular-displacement simulator models face limitations. The complete paper discusses the advancements in mud-displacement simulation that overcome the limitations of the previous-generation simulator and provide a more-realistic simulation in highly deviated and horizontal wells.

## Introduction

The 2D mud-displacement simulator is now a standard in the industry. Nonetheless, because of the growing complexity of well geometries, some of its limitations have become apparent.

First, the simulation work flow considers fluid displacement in the annulus only and neglects what happens as fluids travel down the pipe. The assumption is that different fluids are perfectly separated inside the casing, even after hundreds or thousands of meters. In reality, without a mechanical separator, such separation is physically impossible.

Second, as a matter of performance optimization, the simulator was implemented to simulate only half the annulus, assuming symmetrical flow in the other half. This assumption prevents the determination of azimuthal flow, or flow around the casing, which is of great importance in deviated and horizontal wells with high-density-contrast fluids.

A third limitation is related to the determination of the annulus geometry. The widespread soft-string centralization model used to determine casing eccentricity assumes that standoff is always oriented in the direction of gravity. When a 3D wellbore is considered, it becomes necessary to consider 3D displacements and not just those in the vertical plane. Otherwise, unrealistic mud-displacement results can be obtained.

## Simulation Work Flow

A complex simulation work flow must be followed to obtain cement-slurry placement in the annulus at the end of the operation.

The first step consists of running a hydraulics simulation of the operation together with a temperature simulator. This step accounts for the U-tubing effect and provides the position of the free surface in the pipe and the resulting flow rate in the annulus. In addition, the temperature simulation also allows accounting for the downhole properties of fluids, which are often temperature- and pressure-dependent. All these results are needed as input for the displacement simulators.

As a second step, the centralization of the string that will be cemented is determined. Because the centralization results depend on the positions of the fluids within the flow path, the choice is usually made to consider the moment when cement slurry first enters the annulus. This situation also usually corresponds to the most critical in terms of standoff, because the apparent weight of the casing string is the highest. It is, however, possible to determine centralization at any time during cement placement and to use these results instead.

All the inputs needed for the two displacement simulators are now available: flow rates in pipe and annulus, free surface position, and 3D annulus geometry.

## Stiff-String Centralization Simulator

The position of the casing inside the well determines the annular geometry used in the fluid-displacement simulator. Owing to its extreme length/diameter ratio, the tubular string is modeled as an assembly of 1D elastic beams. Each beam is characterized by a uniform cross-section geometry and Hooke elastic constants (Young’s modulus and Poisson’s ratio). Beam elements are individually bounded by two nodes, such that a string of *N* discrete elements defines *N*+1 nodal points. Local deformations occur under the action of distributed and nodal forces, as well as bending and torsion moments. Thus, each node has six degrees of freedom—namely, displacement and rotation vectors in three dimensions. String beams are coupled by displacement and rotation continuity at nodes. This implies in particular that bending moments are transmitted from one element to the next along the string. Hence, the model is referred to as “stiff string,” as opposed to the simpler model widely used in the industry, usually referred to as “soft string.”

Transverse displacement is constrained by the annular clearance between the casing outer radius and wellbore radius. Hard contact, when it occurs, is handled by a penalty method, through a return force normal to the wellbore wall imposed onto the casing string at contacting nodes. Contact mechanics makes the calculation of displacements nonlinear, because contact points are not known beforehand. The possible presence of bow-spring centralizers is modeled by an additional spring force proportional to the local absolute transverse displacement.

Finally, the obtained solution provides the nodal displacement and rotation angles satisfying the balance between internal elastic stresses, buoyancy/gravity forces, and contact forces. The relative eccentricity of the string at a given depth is computed as the ratio of the absolute transverse displacement to the local annular clearance. This quantity is located between zero (centered casing) and unity (contact). Standoff orientation is not inferred, as in the soft-string model, but computed from the displacement components in each cross-sectional plane. Axial resolution for typical field cases varies from 1 to 5 m. Full resolution results are submitted as input to the annular-displacement simulator.

**Fluid Displacement in Pipe or Casing. **The pipe/casing interior is modeled as a series of cylindrical tubes of varying diameters. The pipe/casing trajectory is defined by the centralization simulator for a given hole survey and casing string. Pipe/casing deviation angles and pipe/casing azimuths are calculated and simulated during flow simulations because they may affect fluid distribution along the pipe/casing.

The model assumes that the flow may be locally laminar or turbulent. Where laminar, the fluid/fluid displacement pattern may be concentric or segregated depending on the effect of buoyancy forces. Concentric displacement patterns occur when buoyancy forces are not sufficient to segregate the fluids and prevent viscous forces from forcing the displacing fluid to flow preferentially in the region of the pipe center. With sufficiently large buoyancy forces, the lighter (denser) fluid tends to occupy the upper (lower) part of the pipe, leading to a stratified displacement pattern. The model also detects the onset of laminar-flow instability such as the Kelvin-Helmholtz and roll-wave instabilities that may occur at the fluid/fluid interfaces, as shown in **Fig. 1.** When these instabilities occur, the fluids mix and a homogeneous mixture is generated, similar to that observed in turbulent flow in which the fluids mix because of flow-velocity fluctuations. Once mixed, fluids do not segregate back to concentric or stratified flow, even under laminar-flow conditions. One pipe/casing-model output is the volume fraction of each fluid at the shoe at all times. This information is transferred to the annular-displacement model that considers the fluids during their upward flow.

**Fluid Displacement in the Annulus.** The annular-gap width varies significantly along the wellbore, both axially and azimuthally. Such variations give rise to preferential flow paths and must be captured as accurately as possible. Before running the displacement calculation, the simulator analyzes the geometrical variations of the annulus along the wellbore: standoff magnitude, standoff orientation, inner and outer diameters, wellbore-deviation angle, and azimuth. The axial grid spacing is automatically adjusted to capture all the details of the actual annular geometry for maximum accuracy.

The simulator assumes that fluid rheology follows the Herschel-Bulkley model. Fluids flow and displace each other depending on the balance of buoyancy forces, viscous forces, and the actual annular geometry. Casing rotation and reciprocation are also accounted for. This latter feature has proved very useful in showing enhanced mud removal while rotating the casing during cement pumping. Flow symmetry is not assumed, standoff orientation may take any value, and the model lets azimuthal buoyancy effects develop fully without unphysical symmetry. Simulations have shown that allowing full development of azimuthal flow may lead to less-pessimistic mud-displacement predictions.

The annular-flow model assumes that the annular-gap width is small compared with the wellbore radius. This assumption allows significant simplifications to take place during the resolution of the Navier-Stokes equations in the 2D azimuthal/axial plan, as opposed to the actual 3D axial/azimuthal/radial flow, without significant loss of accuracy. Indeed, the gap-width radial dimension is not neglected but is averaged only. Doing so allows determining only the mean axial and azimuthal velocity components while still providing accurate friction pressures. The main benefit of using this assumption is that the central-processing-unit time is reduced significantly, allowing simulation results to be obtained in a reasonable time while using a high-definition description of the annular geometry, both axially and azimuthally (e.g., variations of the standoff magnitude and orientation).

## Coupling the New Annular and the Stiff-String Simulators

Unlike the traditional soft-string model, the stiff-string centralization model couples all simulation points through the transmission of forces and bending moments along the entire casing/pipe string. This structural mechanics approach provides a more-realistic prediction of standoff, and alleviates all a priori assumptions on standoff orientation. For example, the centralization engine is able to predict helicoidal buckling when the casing string is subjected to sufficiently large compressive axial forces. Therefore, stiff-string centralization results provide a fully 3D annular-flow-path geometry in actual 3D well trajectories.

The association of these two simulators thus presents a powerful modeling tool to assess the efficiency of mud removal and the quality of cement placement in a target zone. Additionally, the pipe-flow simulator evaluates the severity of undesired mixing as the various cementing fluids are pumped into the well.

The ability of this novel simulator suite to predict real-life cementing fluid placement is demonstrated with a case study presented in the complete paper.

*JPT*Technology Editor Chris Carpenter, contains highlights of paper SPE 184677, “New-Generation 3D Simulator Predicts Realistic Mud Displacement in Highly Deviated and Horizontal Wells,” by

**P.M.J. Tardy, N.C. Flamant, E. Lac, A. Parry, C. Sri Sutama,**and

**S.P. Baggini Almagro,**Schlumberger, prepared for the 2017 SPE/IADC Drilling Conference and Exhibition, The Hague, The Netherlands, 14–16 March. The paper has not been peer reviewed.

3D Simulator Predicts Realistic Mud Displacement in Deviated and Horizontal Wells

01 November 2017

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