SPE 94623

Dynamics of Fluid Substitution While Drilling and Completing Long Horizontal-Section Wells E.S.S. Dutra, PUC-Rio; A.L. Martins, SPE, C. R. Miranda, A.F.L. Aragão, and G. Campos, Petrobras; P.R.S. Mendes and M.F. Naccache, PUC-Rio

Copyright 2005, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the Latin American and Caribbean Petroleum Engineering Conference held in Rio de Janeiro, Brazil, 20–23 June 2005. 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, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes 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 where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abstract Several fluid replacement operations take place during and after an oil well drilling operation, such as: the replacement of the drilling fluid by the completion fluid and the displacement of cleaning plugs or chemical treatment plugs. In such operations it is important to minimize the contamination of a fluid by the other to maintain the designed physical properties of the new fluid displaced.

This work presents a numerical simulation study of the operations related to the replacement of a fluid by another inside the well. The effects of density and rheology differences between the fluids are analyzed (Newtonian fluids displacing non-Newtonian fluids and vice-versa). The studies are based on the numerical solution of the governing equations for a two phase system and the subsequent evolution of the interface shape between the two fluids.

The present work details design criteria and fluid contamination predictions to some of the typical completion operations. Some displacement procedures are recommended to minimize contamination. Introduction In a well, replacement fluid operations during drilling and completion need a detailed design to assure its efficiency and the operational safety. Minimize the contamination, assure the correct position of the fluid in the well and define the dynamic pressures to guarantee that the operational window limits are respected are basic requirements to well succeeded operations.

The analysis of the replacement process of a fluid by another, with different physical properties, is characterized by the simulation of a two phase flow. The solution of the governing equations aims to represent the evolution of the interface shape between the two fluids during the displacement process. This is a complex problem, especially when one of

the fluids presents non-Newtonian rheological properties, which is common in several replacement operations.

The numerical simulation of flows is a powerful tool in the evaluation of different processes in the industry. Particularly in the oil industry, an experimental investigation in an oil well is an expensive task, and sometimes not operationally feasible.

Most previous studies about the subject aimed the representation of cementing operations, where complete fullfilment of the annular space with the cement slurry is a must for zonal isolation. Some works (Haut and Crook1,2; Sauer3; Lockyear and Hibbert4) show that the process of fluid displacement through vertical oil wells is mainly governed by the viscosity ratio between fluids, the eccentricity of annular space between the column and the casing, the flow rate and the density ratio. Jakobsen et al.5 analyzed experimentally the effects of viscosity ratio, buoyancy force and turbulence intensity in mud displacement through an eccentric annular tube.

The results obtained show that displacement is more efficient at the largest region, and that turbulence reduces the mud channeling at the narrowest region of the flow. Tehrani et al.6 performed a theoretical and experimental study of laminar flow of drilling fluids through eccentric annular spaces. They observed that as the eccentricity increases, the displacement becomes worse. For vertical displacements, it is also shown that the process is more efficient for higher densities differences between the displacer (higher density) and displaced fluids. Vefring et al.7 analyzed, numerically and experimentally, the influence of rheological and flow parameters in the displacement of a drilling mud followed by cement slurry. The results obtained indicate that numerical simulations provide good results in this kind of problems.

Frigaard et al.8, 9 present some theoretical results of cement displacement through eccentric annuli, considering a two dimensional situation. They show that the displacement front may reach permanent regime for some combinations of physical properties. For these cases, an analytical expression for the interface shape is obtained.

Guillot et al.10 performed a theoretical approximate analysis of the flow of a washer fluid pushing a drilling mud through eccentric annuli. All the results were obtained with the washing fluid density greater than the mud density, and they concluded that turbulent flows present smoother interface shapes than the laminar ones.

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Methodology The numerical solution of the flow was obtained via the finite volume technique and the volume of fluid method (VOF), using the Fluent Software (Fluent Inc.11). The VOF method solves a set of mass conservation equations and obtains the volume fraction of each phase αj through the domain, which should sum up unity inside each control volume according by Hirt12. Therefore, if

• αi=0, the volume does not contain the phase j; • αi=1, the volume contains only the phase j; • 0< αi <1, the volume contains the interface.

In this study, only two phases are present. The properties appearing in the transport equations Φ, are given by:

( ) 1222 1 φα−+φα=φ (1)

The interface between phases is obtained by the solution of continuity equation for αj:

0=∂α∂

+∂α∂

j

ii

i

xu

t (2)

The volume fraction of the other phase is obtained with

the following constraint equation:

121 =α+α (3) The momentum equation is given by:

( ) ( ) ( ) ( )k

i

i

k

i

iki

kii gxu

xu

uxp

xuu

tu

ρ+⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂+

∂∂

η∂∂

+∂∂

−=∂

ρ∂+

∂ρ∂

(4) In the above equation, xi are the coordinates, ui are the

velocity components, P is the pressure, ρ is the density and η is the viscosity function.

A tri-dimensional mesh was created to simulate the transient flow. The tube length is 5m, and the diameters are shown in Tables 1 and 2. Motivation Well conscruction in offshore environments are related to high cost and risk. Exploratory trends advance to deep and ultra deep waters while the search for new reserves consider heavy oils. In this scenario, long horizontal wells constitue economical drives for such field development. The main focus of this work is to optimize the relevant fluid displacement processes which take place during drilling and completion phases.

Development horizontal wells in the Brazilian coast are normally drilled with synthetic based fluids till the reservoir phase where a drill-in fluid is used. In most situations, the well is cased till the reservoir entrance. Normally, in the horizontal section, a premium production screen is installed and the annular space gravel packed. Among the several replacement situations, two critical ones are highlighted in this paper.

Case Studies Fluids Physical Properties. The rheology plays a fundamental role on the displacement efficiency. The relation between fluid viscosities must be considered. As synthetic fluid and Drill-in fluids usually present non-Newtonian behavior, it is necessary to adopt one rheological model that describes their behavior depending on the shear rate.

The Herschel-Bulkley model was adopted to describe the fluids behavior (Equation 5). This model takes into account the viscoplastic characteristics of the fluids and the yield stress.

⎪⎩

⎪⎨

⎧

τ<τ∞=η

τ>τγ+γ

τ=η −

0

0n

if ,

,K 10

(5)

Table 1 describes the fluid rheological properties for the

fluids considered for the case studies in this paper. Figure 1 presents the flow curves for each fluid.

Table 1 - Rheological parameters of the fluids:

Synthetic Fluid Drill-in Spacer1 Spacer2

το 4.543 5.605 13.16 2.220K 0.118 0.214 1.130 0.173n 0.800 0.701 0.620 0.630

Figure 1 – Flow Curve – Fluids Rheology

Figure 1 shows that the viscosity is strongly dependent on the shear rate. For the same geometry and the same fluid increasing the shear rate (or the flow velocity), a relevant decrease in viscosity occurs. It is known that the relation between viscosities is essencial on the liquids displacement efficiency, and that more viscous fluids better displace low viscosity fluids. Therefore, it is expected that a non-Newtonian fluid, presenting the same characteristics of a synthetic fluid or of the Drill-in, displaced by water, present better displacement results at higher flow rates.

A simple way to define the average viscosity is to evaluate it at a characteristic shear rate, which for tubes is given by:

SPE 94623 3

Rv

c =γ (6)

and for an annuli:

( )RiRov

c −=γ (7)

Where v is the average velocity at the entrance surface, R

is the tube radius, Ro is the inner radius of the outer tube and Ri is the outer radius of the inner tube.

The relation between densities also has a significant effect on the displacement performance. Depending on the density difference between the fluids and on the pumping rate, the buoyancy forces may be significative.

The fluids densities were kept constant, as shown:

Water = 998.2 Kg/m3 (8.33 pd/gal); Synthetic Fluid = 1174 Kg/m3 (9.80 pd/gal); Drill-in Fluid = 1150 Kg/m3 (9.60 pd/gal). Spacer1 = 998.2 Kg/m3 (8.33 pd/gal); Spacer2 = 998.2 Kg/m3 (8.33 pd/gal); Case 1 – Removing the synthetic fluid from the well.

This case shows an operation performed after drilling 12 ¼” phase. Similar situation happens before setting the 13 3/8” casing. At this point, the annulus will be cemented and the synthetic fluid should be displaced by a water based chemical wash. In this case, it is important to minimize the contamination of the synthetic fluid by the new fluid and to assure complete fullfilment of the annular space with the cement slurry. The focus of the present analysis is to minimize fluid contamination and fluid discharge treatment which will directly affect costs. Cementing issues will not be addressed. The expected critical region for contamination problems is the riser annulus, where fluid velocities are lower.

Table 2 describes the simulation geometries for case 1. These include the flow through the pipe and casing, besides several annular geometries in different inclination and eccentricity values. The eccentricity is defined by the variable stand–off (STO) which assumes the value one for the concentric annulus and zero for the fully eccentric annulus. A typical operational value for flow rate is 700 GPM which can be increased in the riser annulus by additional flow through the kill and choke lines.

Table 2 – Geometries for Case 1

GeometryInclination

[º]STO

Pump Rate

[GPM] 5'' pipe 0 - 700

9 5/8" casing 45 - 700 9 5/8" casing 80 - 700

Annulus 20" x 5'' 0 1 700 to 1200Annulus 12 1/4" x 9 5/8" 45 0.5 700Annulus 12 1/4" x 9 5/8" 45 0.3 700Annulus 12 1/4" x 9 5/8" 80 0.5 700Annulus 12 1/4" x 9 5/8" 80 0.3 700

The results are shown graphically, where the efficiency of displacement is evaluated plotting the percentual of displaced liquid remaining inside the annular volume versus a dimensionless time, which is given by the following expression:

Lt.v

VolumeInsidePumped Volumest * ==

where t is the pumping time and L is the annuli or tube length.

In order to see and understand the displacement process efficiency, it is also shown images of the volume fraction of each liquid, in a particular section of the length. It is possible to depict how the eccentricity affects the process, since it is difficult for the displacing liquid to flow through the annular narrow region.

Initially, the simulations reproduce the displacement of the synthetic fluid by a chemical wash with physical properties similar to the water. Figure 2 shows the displacement behavior in pipe flow geometry while Figure 3 shows the same simulations in annular flow. Figure 4 shows cross sections of some of the annular flow simulations.

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Figure 2 – Chemical Wash displacing synthetic fluid inside a vertical pipe of 5’’ and inside a 9 5/8” casing with 45º and 80º inclination. Pump rate 700 GPM.

Figure 3 – Chemical wash displacing synthetic fluid in a 12 ¼” x 9 5/8” annulus with 45º and 80º inclination and STO 0.3 and 0.5. Pump Rate 700GPM.

(a) (b)

(c) (d)

Figure 4– Chemical wash (red) displacing synthetic fluid (yellow). Cross section in the middle of the geometry, 12 ¼” x 9 5/8”, pump rate 700GPM. (a) STO 0.3 - 45º (b) STO 0.3 - 80º; (c) STO 0.5 - 45º (d) STO 0.5 - 80º .

Figure 2 indicates that after about 1.5 volumes pumped, the displacement process has reached reasonable efficiency for the pipe flow. Note that efficiency is larger for the 5 in pipe geometry. Figure 3 shows results for the annular flow. Efficiency is lower and decreases with the increasing eccentricity. Stabilization values occur at larger pumped volumes. Figure 4 highlights the major role of eccentricity in the substitution process: at the higher eccentricities (STO 0.3) the synthetic fluid occupies the lower portion of the annulus at the end of the simulation time. For the less eccentric case, substitution is satisfactory.

Figure 5 represents the substitution process in the riser annulus. The replacement efficiency was evaluated for different flow rates. Additionally a different fluid displacement strategy was also simulated: 10 bbl of a viscosified spacer fluid is pumped between the two fluids in order to minimize contamination. Two different spacers were tried.

Figure 5 –– Chemical wash displacing synthetic fluid in a Riser 20’’ x 5’’ – STO 1 (fully concentric), with and without spacer.

SPE 94623 5

Figure 6 highlights the ammount of synthetific fluid at the riser outlet for the several simulations previously discussed. The unsteady behavior in all the curves where direct contact between chemical wash and synthetic fluid occures denotes high degree of contamination. In the simulations where a spacer fluid is added there is an abrupt decay in the amount of synthetic fluid leaving the riser annulus. This behavior denotes a piston type displacement, minimizing contamination.

Figure 6 – Chemical wash displacing a syntethetic fluid in a riser.

Results indicate the poor displacement efficiency in the riser annulus when direct contact of wash and synthetic fluids occur. The increase of flow rate enhances but seems not to solve the undesired contamination problems. The introduction of a viscosified spacer seems to be a nice alternative to optimize the process. Both spacer rheological properties lead to good results.

Case 2 - Completion fluid replacing drill-in fluid.

The most critical replacement operation occurs after drilling a horizontal well. In this case, it is necessary to eliminate the contamination and to assure the absence of solids in the completion fluid, in order to avoid permeability reduction due to screen and formation plugging. Normally the reservoir is drilled horizontally with 8 ½” bits. In the heavy oil scenario, a possible alternative to enhance productivity is to drill larger holes. The displacement process will consider the drill-in fluid properties detailed in Table 1 while the completion fluid presents properties similar to water.

Table 3 describes the simulation geometries for case 2. These include the flow through the pipe, besides several annular geometries in different eccentricity values.

Table 3 -– Geometries for Case 2

GeometryInclination [º]

STOPump Rate

[GPM]Tube 5'' 90 - 420

Tube 6'' 5/8 90 - 420Annulus 8'' 1/2 x 5'' 90 0 420, 500, 600Annulus 8'' 1/2 x 5'' 90 0.1 420Annulus 8'' 1/2 x 5'' 90 0.3 420Annulus 8'' 1/2 x 5'' 90 0.5 420Annulus 9'' 1/2 x 5'' 90 0 420Annulus 9'' 1/2 x 5'' 90 0.5 420Annulus 12'' 1/4 x 5'' 90 0 420Annulus 12'' 1/4 x 5'' 90 0.5 420

Figure 7 shows the displacement behavior in pipe flow

geometry while Figure 8 shows the same simulations in annular flow for the 8 ½” hole and different flow rates. Figure 9 shows cross sections for the three annular flow simulations of Figure 8.

Figure 7 – Completion fluid displacing drill-in fluid in horizontal 5’’ and 6 5/8” pipes. Pump rate of 420 GPM.

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Figure 8 – Completion fluid displacing drill-in fluid in horizontal 8 ½” x 5’’ annulus, fully eccentric (STO0), for different pump rates.

(a) (b)

(c)

Figure 9 – Completion fluid (red) displacing Drill-in (yellow). Cross Section in the middle of the geometry 8 ½” x 5’’. Annular positioned horizontally and fully eccentric (STO0). Pump rates – (a) 420 GPM, (b) 500 GPM and (c) 600 GPM.

Results indicate that displacement in pipe flow is efficient while in the fully eccentric annulus is poor, with drill-in fluids remaining in its lower portion. The assumption of fully eccentric annular flow is pessimistic and conservative, since pipe movement always occur in rotary drilling. This fact motivated new simulations highlighted in figures 10 and 11. Figure 10 shows the annular flow displacement for STO 0 and

0.5 for different wellbore and pipe diameters. Figure 11 shows the strategy of using a spacer fluid between the drill in and the completion fluids for the 8 ½” well at different eccentricities. In this case, 0.82 bbl of spacer was used.Figure 12 shows cross sections for the four annular flow simulations of Figure 11.

Figure 10 – Completion fluid displacing drill-in in different horizontal geometries and eccentricities. Pump Rate of 420 GPM.

Figure 11 – Completion fluid displacing drill-in in a horizontal 8 ½” x 5’’ geometry with spacers as intermediate liquid. Different eccentricities. Pump Rate of 420 GPM.

SPE 94623 7

(a) (b)

(c) (d)

Figures 12 – Completion fluid and Spacer (red) displacing Drill-in (yellow). Cross section in the middle of a horizontal 8 ½” x 5’’ geometry – (a) STO 0.1 and Spacer1; (b) STO 0.1 and Spacer2; (c) STO 0.3 and Spacer 1; (d) STO 0.3 and Spacer2. Pump rate of 420 GPM.

Figure 10 highlights replacing fluids difficulties in large annular spaces. Figure 11 shows the increase in efficiency when the spacer is pumped in the middle of both fluids. Figure 12 (c) shows that total replacement was obtained with the more viscous spacer, emphasizing the role of rheolgy in the process.

Final Remarks

• Rheology has a major influence in the displacement process. Since the viscosity ratio has an effect in the process, shear thinning behavior of the liquids must be very well known, in order to predict their viscosity at a particular pump rate. Little variation in pump rates may lead to different efficiencies. If the non-Newtonian fluid is being displaced by water, the process will be more efficient at higher pump rates, due to the decrease in the first liquid viscosity. A good picture of that can be seen at all cases with different geometries. For the same pump rate, different geometries imply in different velocities and, therefore different viscosities. Higher velocities cause lower viscosities, which leads to a better displacement process for the low viscosity fluid.

• In general, eccentricity contributes to a poor displacement, especially in horizontal geometries where a layer of the displaced liquid remains practically stationary at the inner tube wall.

• The use of high viscosity spacer pills may be a good strategy to enhance displacement efficiency in critical situations.

• The proposed methodology is a powerful tool for displacement operations design. Volumes, rheological properties, densities and flow rates can be optimized for a number of different operations.

Nomenclature k =consistency Index, Pasn

L =geometry length, m n =power-law Index g =gravity vector, m/s2

p =Pressure, Pa R =radius, m Ri =inner radius of the outer tube, m Ro =outer radius of the inner tube, m STO =stand-off t =time, s t* =dimensionless time u =velocity, m/s ui =velocity vector components, m/s v =average velocity, m/s α =volume fraction γ =shear rate, 1/s

cγ =characteristic shear rate, 1/s ϕ =property of transport equation η =viscosity Function, Pa.s ηc =caracteristic Viscosity, Pa.s ρ =specific Mass, Kg/m3

τ =shear Stress, Pa τ0 =yield Shear Stress, Pa

References 1. Haut, R. C., Crook, R. J.: “Primary Cementing: The Mud

Displacement Process”, paper SPE 8253 presented at SPE Annual Technical Conference and Exhibition, 23-26 September, Las Vegas, Nevada, 1979.

2. Haut, R. C., Crook, R. J.: “Laboratory Investigation of Lightweight, Low-Viscosity Cementing Spacer Fluids”, Journal of Petroleum Technology, August . 1982, pg. 1828-1834.

3. Sauer, C. W.: “Mud Displacement During Cementing: A State of the Art”, Journal of Petroleum Technology, September 1987, pg. 1091-1101.

4. Lockyear, C. F., Hibbert, A. P.: “Integrated Primary Cementing Study Defines Key Factors for Field Success”, Journal of Petroleum Technology, Vol. 41, Number 12, December 1989, pg. 1320-1325.

5. Jakobsen J., Sterri N., Saasen A., Aas B., Kjosnes I., Vigen A.: “Displacement in Eccentric Annuli During Primary Cementing in Deviated Wells”, paper SPE 21686 presented at SPE Production Operations Symposium, 7-9 April, Oklahoma City, OK. 1991.

6. Tehrani A., Ferguson J., Bittleston S.H.: “Laminar Displacement in Annuli: A Combined Experimental and Theoretical Study”, paper SPE 24569 presented at SPE Annual Technical Conference and Exhibition, 4-7 October, Washington, D.C, 1992.

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7. Vefring E. H., Bjorkevoll K. S., Hansen S. A., Sterri N., Saevareid O., Aas B., Merlo A.: “Optimization of Displacement Efficiency During Primary Cementing”, paper SPE 39009 presented at Latin American and Caribbean Petroleum Engineering Conference, 30 August – 03 September, Rio de Janeiro, Brazil, 1997.

8. Frigaard I. A., Bittleston S. H., Ferguson J.: “Mud Removal and Cement Placement During Primary Cementing of an Oil Well”, Society of Petroleum Engineers – Kluwer Academic Publishers. 2002.

9. Frigaard I. A., Pelipenko S.: “Effective and Ineffective Strategies for Mud Removal and Cement Slurry Desing”. Paper SPE 80999 presented at Latin American and Caribbean Petroleum Engineering Conference, Port-of-Spain, Trinidad and Tobago, 2003.

10. Guillot D., Couturier M., Hendriks H., Callet F.: “Design Rules and Associated Spacer Properties for Optimal Mud Removal in Eccentric Anulli”. Paper SPE 21594 presented at CIM/SPE International Technical Meeting, 10-13 June, Calgary, Alberta, Canada, 1990.

11. Fluent User’s Guide, version 6.1, Fluent Inc., 2003.

12. Hirt, C. W., Nichols B. D.: “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries”, Journal of Computational Physics – 39, 204-225. 1981