UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Experimental study of displacement of viscoplastic fluids in eccentric annulus Foolad, Yasaman 2020

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata


24-ubc_2021_may_foolad_yasaman.pdf [ 10.17MB ]
JSON: 24-1.0395477.json
JSON-LD: 24-1.0395477-ld.json
RDF/XML (Pretty): 24-1.0395477-rdf.xml
RDF/JSON: 24-1.0395477-rdf.json
Turtle: 24-1.0395477-turtle.txt
N-Triples: 24-1.0395477-rdf-ntriples.txt
Original Record: 24-1.0395477-source.json
Full Text

Full Text

Experimental Study of Displacement of Viscoplastic Fluidsin Eccentric AnnulusApplication in Primary Cementing of Oil and Gas WellsbyYasaman FooladB. A. Sc. Mechanical Engineering, The University of British Columbia, 2018A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Mechanical Engineering)The University of British Columbia(Vancouver)December 2020c© Yasaman Foolad, 2020The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Experimental Study of Displacement of Viscoplastic Fluids in Eccen-tric Annulussubmitted by Yasaman Foolad in partial fulfillment of the requirements for thedegree of Master of Applied Science in Mechanical Engineering.Examining Committee:Ian A. Frigaard, Mechanical EngineeringSupervisorSheldon Green, Mechanical EngineeringSupervisory Committee MemberAnthony Wachs, Chemical Engineering and MathematicsSupervisory Committee MemberiiAbstractThis thesis presents a series of targeted, practical experiments focused on the dis-placement of viscoplastic fluids with various Newtonian and non-Newtonian fluidsin a horizontal, eccentric annuli in laminar, turbulent and transitional flow regimes.The motivation of this study originates from primary cementing of horizontal oiland gas wells. During primary cementing, a sequence of fluids are pumped downthrough a metal casing and up through an annular region between the casing anda wellbore. Commonly, a low-viscosity, low-density preflush starts the sequence,followed by a denser and more viscous spacer fluid. Eventually, cement slurriesare pumped and placed in the annular region to provide hydraulic isolation andmechanical stability to the well. The eccentricity of the annular region, as well asthe viscoplastic nature of the fluids involved, might result in several fluid-relateddefects, such as residual mud channeling that allow the well to leak later.There are existing 2D and 3D models of primary cementing developed for var-ious flow regimes, including the laminar model of Bittleston et al. [9] and the tur-bulent and mixed model of Maleki & Frigaard [61]. These modelling approachesprovide us with valuable information. However, there is an undeniable demand forexperimental studies to validate the outcomes of such models. The main objectiveof our experiments was to experimentally gain insight into the role of flow regime,specifically turbulence, in fluid-fluid displacements that take place in primary ce-menting. The experiments performed in this study can be classified in three sets,including turbulent displacement flow of viscoplastic fluids in eccentric annulus, aswell as comparative studies of laminar-turbulent displacement in eccentric annulusunder imposed flow rate and imposed pressure drop conditions.The outcome of this experimental analysis allows us to understand the role ofiiiflow regime in the process of cementing in more depth. In particular, we show thatsome simple statements that are widely employed in industry do not necessarilyapply at all design scenarios. Instead, detailed study of the fluids involved andspecifying operating flow conditions in accordance to specific features of wellscan yield improved displacement quality and reduced cementing complications.ivLay SummaryPrimary cementing is one of the most critical steps in construction of oil and gaswells, during which cement slurries are placed between drilled out wellbore and ametal casing through which oil and gas are extracted. After cement is set, it willprovide the well with hydraulic seal and structural stability. Poor quality of annu-lar cement is likely to have severe economical and environmental consequences.In this study, we perform a series of experiments to examine several complexitiesof this process. For instance, complications may arise from the eccentric annulargeometry between the metal casing and the wellbore, which becomes more crucialin horizontal wells where proper placement of centralizers without damaging thecasing is quite complicated. Our aim is to study a wide range of practically inter-esting factors affecting the quality of cementing in a horizontal eccentric geometryin order to recognize limitations of current practice and make recommendations toalleviate the issues.vPrefaceThe research presented in this dissertation was conducted by the author, YasamanFoolad under the supervision of Prof. Ian A. Frigaard and with the advice of Dr.Majid Bizhani. The experimental set-up that is used in this work was originallydeveloped by Dr. M. Bizhani under the guidance of Prof. I. Frigaard to studyturbulent annular displacements.Some of the results of this thesis have been submitted for publication in thejournal of Physics of Fluids as:M. Bizhani, Y. Foolad, I.A. Frigaard, Turbulent Displacement Flow of ViscoplasticFluids in Eccentric Annulus: Experiments; submitted April 2020.The work has also been virtually presented at OMAE2020, the 39th Inter-national Conference on Ocean, Offshore and Arctic Engineering on August 3-8,2020: Y. Foolad, M. Bizhani, I.A. Frigaard, A Comparative Study of Laminar-Turbulent Displacement in Eccentric Annulus Under Imposed Flowrate Condi-tions, Paper ID: 18227.Both primary authors had equal contributions in above publications, both interms of performing the experiments, generating the contents and writing the drafts.Prof. I. Frigaard supervised the project, and assisted with writing the papers.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Why Horizontal Wells? . . . . . . . . . . . . . . . . . . . . . . . 21.2 Primary Cementing . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3.1 The Importance of Well Cement Integrity . . . . . . . . . 81.3.2 Primary Cementing in Numerical and Experimental Studies 101.4 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 17vii1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Experimental Setup and Methodology . . . . . . . . . . . . . . . . . 192.1 Horizontal Flow Loop . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Measurement Methodology . . . . . . . . . . . . . . . . . . . . . 232.3 Fluid Preparation and Rheological Properties . . . . . . . . . . . 253 Turbulent Displacement Flow of Viscoplastic Fluids in Eccentric An-nulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1 The Rheological Properties of Test Fluids . . . . . . . . . . . . . 293.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 313.3 Conclusions and Discussion . . . . . . . . . . . . . . . . . . . . 474 A Comparative Study of Laminar-Turbulent Displacement in Ec-centric Annulus Under Imposed Flow Rate Conditions . . . . . . . . 504.1 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . 514.1.1 Rheological Properties of Test Fluids . . . . . . . . . . . 514.1.2 Scope of Experiments . . . . . . . . . . . . . . . . . . . 534.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 554.2.1 Fully Eccentric (e = 1.0) . . . . . . . . . . . . . . . . . . 554.2.2 Partially Eccentric (e = 0.7) . . . . . . . . . . . . . . . . 634.3 Conclusions and Discussion . . . . . . . . . . . . . . . . . . . . 695 A Comparative Study of Laminar-Turbulent Displacement in Ec-centric Annulus Under Imposed Pressure Drop Conditions . . . . . 715.1 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . 725.1.1 Rheological Properties of Test Fluids . . . . . . . . . . . 735.1.2 Scope of Experiments . . . . . . . . . . . . . . . . . . . 765.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 765.3 Conclusions and Discussion . . . . . . . . . . . . . . . . . . . . 846 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856.1 Conclusions and Relevance of Results to Cementing Operation . . 856.2 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . 87viiiBibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89A Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 101ixList of TablesTable 2.1 Dimensions of the flow loop . . . . . . . . . . . . . . . . . . . 21Table 3.1 Herschel-Bulkley model parameters for the Carbopol solutions 30Table 3.2 Flow rates (liters/min) and pressure drops (kPa/m) associatedwith each set of experiments . . . . . . . . . . . . . . . . . . . 32Table 4.1 Rheological properties of test fluids . . . . . . . . . . . . . . . 54Table 4.2 Flow rates (liters/min) and pressure drops (kPa/m) associatedwith each experiment . . . . . . . . . . . . . . . . . . . . . . 57Table 5.1 Rheological properties of test fluids . . . . . . . . . . . . . . . 75Table 5.2 Flow rates (liters/min) and pressure drops (kPa/m) associatedwith each set of experiments . . . . . . . . . . . . . . . . . . . 76xList of FiguresFigure 1.1 Typical Austin Chalk well in South Texas, stacked drainholestarget multiple zones to increase production rate and recov-ery [13] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Figure 1.2 Schematic view of successive steps of primary cementing [64] 4Figure 1.3 A typical profile of standoff along an annulus (standoff is 1-e).The blue points show the position of centralizers. The pictureis taken from [40] . . . . . . . . . . . . . . . . . . . . . . . . 6Figure 1.4 Typical sequence of fluids pumped in primary cementing a ver-tical section of a wellbore . . . . . . . . . . . . . . . . . . . 7Figure 2.1 Schematic of the flow loop . . . . . . . . . . . . . . . . . . . 20Figure 2.2 Cross-sectional view of eccentric annulus . . . . . . . . . . . 22Figure 2.3 Configuration of cameras and UV lights with respect to theobservation window marked in Figure 2.1 . . . . . . . . . . . 23Figure 2.4 Example of an image showing both displacing and displacedfluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Figure 3.1 Shear stress vs. shear rate data of the Carbopol solutions . . . 30Figure 3.2 Amplitude sweep data for two Carbopol solutions with lowestand highest yield stresses . . . . . . . . . . . . . . . . . . . . 31Figure 3.3 Measured pressure drops reported also in Table 3.2 . . . . . . 33Figure 3.4 Time-evolution of the displacement corresponding to Series 1 34Figure 3.5 Time-evolution of the displacement corresponding to Series 5 35xiFigure 3.6 Schematic representation of the averaging technique for eval-uating h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 3.7 Profile of average thickness of the Carbopol gel vs. time afterswitching the fluids . . . . . . . . . . . . . . . . . . . . . . . 38Figure 3.8 Profiles of average wall shear stress vs. change with h/Do . . 39Figure 3.9 Profiles of average wall shear stress vs. change with time . . . 40Figure 3.10 Time-evolution of the displacement corresponding to: (a) Se-ries 2 (b) Series 3 . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 3.11 Time-evolution of the displacement corresponding to: (a) Se-ries 4 (b) Series 6 . . . . . . . . . . . . . . . . . . . . . . . . 42Figure 3.12 Time-evolution of the displacement corresponding to: (a) Se-ries 7 (b) Series 8 . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 3.13 Reynolds number profiles of the displacing fluids . . . . . . . 45Figure 3.14 Spatiotemporal profiles of the normalized pixel intensity for all8 experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 3.15 Spatiotemporal profiles of the normalized pixel intensity for all8 experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 4.1 Shear rheology data of Carbopol (fitted model coefficients arereported in Table 4.1) . . . . . . . . . . . . . . . . . . . . . 52Figure 4.2 Shear rheology data of Xanthan (fitted model coefficients arereported in Table 4.1) . . . . . . . . . . . . . . . . . . . . . 53Figure 4.3 Recorded pressure drop profiles for each experiment - ∆P/∆Lfor both Fluids 1 and 2 . . . . . . . . . . . . . . . . . . . . . 55Figure 4.4 Recorded pressure drop profiles for each experiment - ∆P/∆Lfor displacing fluids only . . . . . . . . . . . . . . . . . . . . 56Figure 4.5 Displacement of Carbopol with water in turbulent regime -Fully eccentric . . . . . . . . . . . . . . . . . . . . . . . . . 58Figure 4.6 Displacement of Carbopol with Xanthan solution in laminarregime - Fully eccentric . . . . . . . . . . . . . . . . . . . . 59Figure 4.7 Schematic representation of calculating Carbopol layer thick-ness and volumetric efficiency . . . . . . . . . . . . . . . . . 59xiiFigure 4.8 Displacement performance: Average measured thickness ofthe Carbopol layer in fully eccentric annulus . . . . . . . . . 60Figure 4.9 Displacement performance: Computed volumetric efficiencyin fully eccentric annulus . . . . . . . . . . . . . . . . . . . . 61Figure 4.10 Computed Reynolds number for displacing fluid in fully ec-centric annulus . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 4.11 Time evolution of non-dimensional ratio of displacing fluidshear stresses to displaced fluid yield stress through the dis-placement phase - Fully eccentric . . . . . . . . . . . . . . . 64Figure 4.12 Displacement of Carbopol with water in turbulent regime - Par-tially eccentric (e = 0.7) . . . . . . . . . . . . . . . . . . . . 65Figure 4.13 Displacement of Carbopol with Xanthan solution in laminarregime - Partially eccentric (e = 0.7) . . . . . . . . . . . . . . 65Figure 4.14 Displacement performance: Average measured thickness ofthe Carbopol layer in partially eccentric annulus (e = 0.7) . . 66Figure 4.15 Displacement performance: Computed volumetric efficiencyin partially eccentric annulus (e = 0.7) . . . . . . . . . . . . . 67Figure 4.16 Computed Reynolds number for displacing fluid in partiallyeccentric annulus (e = 0.7) . . . . . . . . . . . . . . . . . . . 68Figure 4.17 Time evolution of non-dimensional ratio of displacing fluidshear stresses to displaced fluid yield stress through the dis-placement phase - Partially eccentric (e = 0.7) . . . . . . . . 69Figure 5.1 Pressure plot for intermediate casing cement job [76] . . . . . 72Figure 5.2 Shear rheology data of Carbopol (fitted model coefficients arereported in Table 5.1) . . . . . . . . . . . . . . . . . . . . . 73Figure 5.3 Shear rheology data of Xanthan (fitted model coefficients arereported in Table 5.1) . . . . . . . . . . . . . . . . . . . . . 74Figure 5.4 Recorded pressure drop profiles for each experiment - ∆P/∆Lfor both Fluids 1 and 2 . . . . . . . . . . . . . . . . . . . . . 77Figure 5.5 Displacement of Carbopol with water in turbulent regime . . . 78Figure 5.6 Displacement of Carbopol with Xanthan solution in laminarregime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78xiiiFigure 5.7 Computed Reynolds number for displacing fluid . . . . . . . 79Figure 5.8 Displacement performance: Average measured thickness ofthe Carbopol layer in an imposed pressure drop condition . . . 81Figure 5.9 Displacement performance: Computed volumetric efficiencyin an imposed pressure drop condition . . . . . . . . . . . . . 82Figure 5.10 Time evolution of non-dimensional ratio of displacing fluidshear stresses to displaced fluid yield stress through the dis-placement phase . . . . . . . . . . . . . . . . . . . . . . . . 83Figure A.1 Schematic of the flow loop . . . . . . . . . . . . . . . . . . . 102Figure A.2 Experimental flow loop - View 1 . . . . . . . . . . . . . . . . 103Figure A.3 Experimental flow loop - View 2 . . . . . . . . . . . . . . . . 104Figure A.4 LabVIEW software user interface . . . . . . . . . . . . . . . 105Figure A.5 Configuration of cameras and UV lights with respect to theobservation window of interest . . . . . . . . . . . . . . . . . 106xivNomenclatureA: Cross-sectional area, [m2]D: Diameter, [m]Dh: Hydraulic diameter, [m]e: Annulus eccentricityh: Displaced fluid height, [m]l: Distance between the centers of two pipes, [m]L: Length, [m]n: Fluid behavior indexP: Pressure, [Pa]Pwet : Wetted perimeter, [m]Q: Flow rate, [m3/s]R: Radius, [m]t: Time, [s]u: Flow velocity, [m/s]Greek symbolsα: Radius ratioγ˙: Shear rate, [s−1]η : Displacement efficiencyκ: Consistency index, [Pa.sn]µ: Viscosity, [Pa.s]ρ: Fluid density, [kg/m3]τ: Shear stress, [Pa]τw: Wall or interfacial shear stress, [Pa]xvτy: Fluid yield stress, [Pa]ξ : Axial lengthSubscripts1: Displaced fluid2: Displacing fluidi: Inner pipeo: Outer pipexviGlossaryThe following technical terms are used throughout the thesis:• Casing: A metallic cylindrical pipe which gets inserted in, and cementedto, the wellbore. Wellbore equipments, such as blowout preventers and pro-duction packers are installed on the casing. The casing provides hydraulicisolation and mechanical stability to the well and controls pressure.• Cement slurry: A composition of cement powder, water and several addi-tives. The additives affect the rheological properties of the cement such asits yield stress, viscosity, thickening time, etc.• Centralizer: A device that gets fitted to the casing in order to keep it at thecenter of the wellbore. Centralizers typically have bowsprings to keep thecasing at the center.• Conditioning (Mud Conditioning): Mud conditioning is a process throughwhich mud properties are modified by adding additives and circulating themud around the flow path before cementing. For the sake of a better dis-placement, it is typically recommended to circulate the mud before and af-ter removal of drill pipe. Mud density and rheological properties are oftenchanged through addition of water or dispersants.• Drilling mud: Drilling mud is muddy liquid that is left after drilling. It isprimarily consisted of formation cuttings and drilling fluid. Drilling fluid isused during drilling to facilitate drilling. The drill cuttings are suspendedand carried by the drilling fluid. Drilling fluid also keeps the drill bit cooland stops the formation fluids from invading the wellbore.xvii• Drillpipe: Drillpipe is consisted of a series of tubular steel pipes that arefitted together. The drillpipe is connected to the rig surface from one endand to the drill bit at the other end. Drilling fluid is pumped through thedrillpipe during drilling.• Eccentricity: Considering the region between two parallel cylinders, eccen-tricity is a measure of offset of the two cylinders’ axes. The eccentricity iszero (stand off is 100%) if the two cylinders are co-axial. The eccentricity of1 or full-eccentric arrangement, the inner cylinder touches the outer cylinder.In this case stand off is 0%.• Liner: A liner is a casing that extends downwards from just above the previ-ous casing.• Preflush: Primary cementing typically starts with conditioning the mud andthen proceeds to pumping a sequence of the so called preflushes inside thecasing. Preflush can be a spacer or a wash. Preflushes are intended to breakthe static gelation in the mud, clean the wellbore from the cuttings and pro-vide a buffer layer between the mud and cement slurry.• Spacer: Spacers are heavier preflushes with viscosifying constituents. Be-cause of their larger density and viscosity, spacers are more often pumpedin laminar regime. Spacers are placed to separate cement slurry from thedrilling mud. Often cement slurries and the drilling mud are chemically in-compatible, meaning that their contact can damage highly tuned propertiesof cement slurry (such as thickening time) [76]. Furthermore, spacers rheo-logical parameters can be designed carefully to aid the displacement of thedrilling mud [102].• Wash: Washes may be water-based or oil-based. Rheologically, they aregenerally Newtonian fluid solutions (e.g. water). They are designed to washthe walls of the annulus free from residual fluids (and any remaining solids),to leave the annulus water-wet for the cement slurry. In addition, they shouldbreak any static gelation of the mud, mobilizing the mud in general. The lowviscosity of these fluids allows them to be pumped in turbulent flow regimes.Most common wash is water with a range of chemical additives.xviii• Wellbore: A hole that is drilled to extract natural resources such as oil andgas.• Yield stress fluid: Yield stress fluids, also call viscoplastic fluids, are a cat-egory of non-Newtonian fluid which exhibit yield stress behavior; i.e., theydo not flow, unless they are sufficiently stressed.xixAcknowledgmentsThesis acknowledgements is typically the last section that comes together, but hon-estly, I believe it is the most important one. Today, as I write this section, I feelquite fortunate and grateful to have been surrounded by many amazing individualswho have supported and encouraged me during the course of my master’s program.First of all, I would like to express my deepest gratitude for my supervisor,Professor Ian Frigaard for his knowledge and guidance for accomplishing this re-search work. He has patiently provided me with positive support and constructivefeedbacks throughout this research program. I feel truly privileged to have workedunder his supervision. ”Thank you Ian!”My second sincere appreciation goes to Dr. Majid Bizhani, to whom I will for-ever be grateful for his constant support, knowledge and kind friendship. Perform-ing the experiments and completion of my research work would not be possiblewithout your guidance and help. It was an absolute pleasure to work with you andlearn from you. ”Thank you Majid!”My biggest ”Thank you!” belongs to, of course, my family: Reza, Roya, Farzinand Simba, my father, mother, brother and lovely puppy. Without their uncondi-tional love and support, I could have never stand here. To Arman, thank you foryour love, encouragement and support, without which I could not make it throughthis journey. You have been there for me through all ups and downs. To Farnaz,thank you for being by my side at all times and supporting me every step of theway, more than a sister would have ever done for me.”Love you all!”Last but not least I would like to thank all my friends near and far, peers, office-mates in UBC Complex Fluids lab and colleagues at Fluor Canada. We have sharedmany moments of despair and laughter and I am looking forward to a lifetime ofxxfriendship with every single of you. ”Thank you all!”I also acknowledge the University of British Columbia, Natural Sciences andEngineering Research Council of Canada and Schlumberger for providing us withthe financial support for this research.xxiDedicationTo my beloved grandparents, Mamani Farangis, Baba Rasoul, Mamanjoon Zarin-taj, Amme Maryam, and Amoo Farhang, who have been never-ending source oflove, encouragement, support and inspiration. I am truly thankful for having youin my life. I hope that I have made you proud.xxiiChapter 1IntroductionIn this study, the displacement of one fluid by another is evaluated experimentallyin a narrow, horizontal annulus in an eccentric arrangement at a range of flowregimes, i.e., laminar, turbulent, and transitional. The work is motivated by theprocess of primary cementing or well cementing of oil and gas wells, where a seriesof preflushes and eventually cement slurry displaces the drilling mud, in the casingand then in the annulus between the casing and the wellbore. The main objectiveof this study is to experimentally investigate some aspects of the fluid mechanicsinvolved in this operation and verify the current industrial understandings of theeffects of flow regime on the efficiency of the process. In doing so, the main focusremains on whether turbulent displacement outperforms laminar displacement inprimary cementing of a horizontal, eccentric well.In the following section, we briefly review the different procedures involved inthe primary cementing and explain why this preparation process of the wells playsa critical role, not only economically (in terms of well lifetime and oil and gasproduction), but also environmentally. We continue the chapter by outlining theexisting literature on the fluid mechanics of primary cementing and displacementof yield stress fluids. In doing so, we briefly discuss displacement flows in bothpipe and annular geometries. We will then close the chapter by presenting theobjectives and the outline of the thesis.11.1 Why Horizontal Wells?Since the mid-1950s, oil has become the world’s most important source of energyand the essence of industrial development in all nations. Due to an endless demandfor oil and gas from energy point of view and a variety of other industries, the oiland gas industry has always faced a global competition to become more productive.The expedition to achieve higher productivity and access more remote oil andgas reservoirs in a harsh environment continually demands for more complex oiland gas wells. Therefore, the trajectory of wellbores are becoming increasinglycomplex and a number of techniques has enabled the industry to produce hydro-carbons from the reservoir in a more effective manner. In addition to conventionalvertical wells, use of horizontal, multilateral, and Extended Reach Wells (ERWs)is growing.Horizontal and ERWs play a critical role in maximizing recovery from oilfields. ERWs are long horizontal wells used to extend access to more remote reser-voirs from the drill site. In an offshore environment, these technologies are used toextend the production area of a reservoir from a single platform, and consequentlyreduce the cost of expensive offshore platforms and infrastructures by a significantamount. Multilateral wells, on the other hand, are essential for recovering fromheavy oil reservoirs and the offshore environments [1, 66, 73, 74, 91]. Figure 1.1presents a typical well drilled in Austin Chalk formation [13]. It can be illustratedhow multilateral wells are employed to increase production rate and recovery factorwhile decreasing drilling costs to minimum.As a result, the technical reasons for increasing use of directional wells are thehigher rate of return and recovery factor. Most oil and gas reservoirs are found to bemore extensive in their horizontal dimensions compared to their vertical (thickness)dimension. Therefore, compared to a conventional vertical well, a horizontal wellexposes significantly more reservoir rock to the wellbore through penetrating thereservoir parallel to its plane of more extensive dimension.Despite offering greater benefits, there are considerably more technical chal-lenges for successful drilling and cementing of inclined wells as compared to ver-tical wells. Also, the cost of drilling and preparation of a horizontal well for pro-duction can be up to 300% more than a vertical well [44]. Due its complexity and2Figure 1.1: Typical Austin Chalk well in South Texas, stacked drainholes tar-get multiple zones to increase production rate and recovery [13]higher cost, vertical drilling is still more viable in industry, unless vertical wellswould not be as financially successful.Regardless of the orientation of the well, oil wells are complex structures ofsteel and cement that can be compared to inverse skyscrapers that connect the sur-face to the subsurface. Each well undergoes the process of primary cementing atleast once during construction, and potentially many times according to the wellcomplexity.Primary cementing is an operation for placing cement in the annular spacebetween the wellbore and the casing. The cement hardens after placement andcreates a hydraulic seal in the borehole, which prevents the migration of formationfluids in the annulus, protects the casing string from corrosion and structurallysupports the casing. Primary cementing of eccentric horizontal wells is the subjectof interest in this study, which is described in more details in the following sections.3Figure 1.2: Schematic view of successive steps of primary cementing [64]1.2 Primary CementingPrimary cementing operations are performed during drilling and preparation ofoil and gas wells, to create a sealed production well during construction. Afterdrilling is carried out using a rotating drill bit cutting into the Earth and drillingmud1 transporting the drill cuttings (fragmented rock) to surface, the drilled bore-hole is often lined and isolated by placing cement slurry into the narrow annulargap formed between the outside of a steel casing (or liner) and the drilled well-bore, before any oil and gas can be extracted. At some point during drilling, whenthe pore pressure gradient at the bottom of the well exceeds the fracture gradient atthe higher sections of the well, the drillpipe is removed from the wellbore, leavingdrilling mud inside the wellbore. A steel pipe (casing or liner) is then placed downinto the well, typically creating an average annular gap of approximately 2-3 cm.The steel casing is inserted into the wellbore in sections of ∼ 10 m each and ce-mented in place, generating cemented sections that can extend 100 to 1000 meters.The process proceeds as shown in Figure 1.2.External casing attachments, such as centralizers, reduce the risk of failure in a1Throughout this section, several technical terms are highlighted with a bold font, which are fullydefined in the glossary provided on page xiv.4primary cementing job through preventing the heavy steel casing from slumping tothe lower side of the wellbore and improving mud removal and cement placementby positioning the casing more centrally in the hole. The eccentricity of the annulusis typically controlled via the use of centralizers, which are designed and fitted tothe outer wall of the casing. The centralizers are designed to exert normal forcesto the borehole wall at their contact points in order to align the casing with theborehole.There is a wide range of centralizers for various borehole geometry and me-chanical design. Centralizers for horizontal wells should have a low moving forceand present a high restoring capability, and ideally they should support both piperotation and reciprocation, such as bow-type centralizers. The effectiveness ofcentralizers is dependent of hole geometry and inclination, casing size, spacingand location, and all factors related to the side forces and drag. The recommendedspacing between centralizers varies substantially, typically from as far as 40 metersdown to as close as 9 meters, depending on the operator’s design preferences andstandards.The effectiveness of centralizers throughout the length of the well can be eval-uated by means of logging measurements taken after the cement job is finished.Positioning of centralizers is determined through the application of a range of mod-els: see Guillot et al. [40], Juvkan-Wold and Wu [50], Blanco et al. [12]. Figure1.3 presents a typical profile of eccentricity measurement by ultrasonic logs [40].The location of centralizers are indicated by the blue diamonds. It is interesting tohighlight that even in a vertical section of wellbore, the annulus has not achievedfully concentric. Therefore even after placing centralizers, it is common that theannulus is eccentric, especially in inclined and horizontal well. The maximumAPI standard recommendation for eccentricity is 33% [14].With steel casing in place and drilling mud on the outside and inside of thecasing, the primary cementing operation begins. During the primary cementingoperation itself, the drilling mud is first conditioned through circulating aroundthe flow path and then a sequence of various Newtonian and non-Newtonian fluidsis pumped down inside of the casing and returning up the outside of the annulusto displace the drilling mud and prepare the annulus for cement placement, as il-lustrated in Figures 1.2 and 1.4. Preflush fluids (i.e., spacers or washes) are5Figure 1.3: A typical profile of standoff along an annulus (standoff is 1-e).The blue points show the position of centralizers. The picture is takenfrom [40]followed by a series of cement slurries. In this stage, it is important to design fluidvolumes to ensure that the cement slurries fill the annular space between the casingand the wellbore. After the cement slurry has been placed in the wellbore annulus,cement hydrates (i.e., sets) becoming a hardened material filling up the annularspace between the steel casing and borehole walls.A fully completed well consist of a series of nested cemented casings pipes ofprogressively smaller diameter arranged telescopically down the well. In this tele-scopic structure, each casing overlaps the previous section’s casing pipe to create a6Figure 1.4: Typical sequence of fluids pumped in primary cementing a verti-cal section of a wellborefully isolated cement lining. Annulus inner diameters can start at as large as 50 cmand reduce to as small as 10 cm in the production zone.The main objective of the annular cement sheath is to mechanically stabilize thewellbore and isolate the wellbore by preventing pressurized formation fluids fromentering the well or flowing between subsurface zones from outside the casing.This can be achieved by securing an efficient cement displacement operation. Aperfect cementing process implies that all the drilling fluid and formation fluids arecompletely replaced by cement.71.3 Literature Review1.3.1 The Importance of Well Cement IntegrityThe life cycle of a well starts from the initial drilling and construction phase, whichtakes place over the span of 1 or 2 days and is of concern in this study, throughits operational phase which lasts for decades, and eventually terminates with itsabandonment phase. During the operational phase, remedial cementing is donefor the purpose of repairing the cement sheath, while in the abandonment phase,cement plugs are placed in the well to close it down, which is also referred to asplug cementing.The challenge in primary cementing is that the cemented well needs to retain itsintegrity for long time spans and protect the environment against leakage along thewell. Cement integrity is a critical component of well integrity, which essentiallymeans preventing flow of formation fluids along the well, throughout its lifetimeand even after abandonment. There are many examples of acute (of low probabil-ity) and chronic (of higher probability) leakage incidents that are caused by defec-tive or damaged annular cement sheaths or tubulars in wells. As the constructionmaterials degrade with age and due to exposure to high pressure and temperaturevariations in downhole fluids, the well becomes prone to failure and well integrityproblems tend to increase. In Canada, approximately 5-20% of wells leak to var-ious extent [27], due to failure of the primary cementing. Other countries havereported similar estimates as well [26]. This has both environmental and economi-cal consequences.In the context of this study, the sources of failure of primary cementing as afluid mechanics problem are considered only. The subsequent leakage of wells canbe narrowed down to three common fluid-related defects:• Contamination of the cement slurry: This is where the cement slurry ismixed and consequently contaminated in different scenarios, such as down-wards displacement within the casing [4, 101], fluid instabilities in laminarflows within the annulus [69, 70, 82] or in turbulent annular displacementflows [64]. Residual drilling fluid can be partially dispersed/eroded in a pass-ing slurry and contaminate long lengths of cement when the above scenarios8occur along with mud channels, micro-annuli or mud pockets left behind inirregular boreholes (e.g. washouts).• Residual mud channeling: This is a bulk flow feature, where the yield stressof the drilling mud prevents its displacement by preflushes and cement slur-ries, specifically on the narrow side of the eccentric annulus. This phenom-ena is extensively studied and predicted using both simple mechanical argu-ments [67] and more sophisticated models [9].• Wet micro-annulus: This is a local mechanical defect, where the displacingfluid does not accomplish sufficient shear stress to displace the mud at thewall of the wellbore. This feature can be predicted to some extent usingmodels of displacement flows [6, 35, 114, 117].Examples of the above failure modes in primary cementing jobs are illustratednicely in Watson [110].In addition to the above flow-related mechanisms, not all wellbore leakage isdue to a fluid-mechanical cause. Loss of well integrity can be caused by damageto rock formation in drilling phase, loss of cement adhesion to formation rocks orinner casing due to cement-to-formation or cement-to-casing bonding defects (i.e.,de-bonding) or cement volumetric shrinkage, development of cracks or fractures incement sheath due to downhole mechanical/hydraulic/thermal stresses, flow pathsthrough the cement due to enhanced porosity, or damage to downhole tubulars [76].Most of these issues can be traced back to defective cement placement [76]. Thesedeficiencies of a poorly executed well cementing operation can emerge as issueswith well control, casing failure, and eventually, the economic cost associated withmitigating them by means of remedial cementing. For more information regardingthe analysis of different leakage factors using significant data sets, the interestedreader is referred to Watson and Bachu [109, 111].There are also several types of cement mixture and additives available that aimto settle these issues, ensure a reliable solidification and good solid mechanicalproperties, but the quality of drilling mud displacement and cement placement op-erations also plays a crucial role in determining the reliability of well over its lifecycle. The goal of all primary cementing processes is the full displacement of the9drilling mud from the annular gap and maintaining a steady displacement frontwhich advances steadily up the well at a set pumping rate. From a fluid mechanicsperspective, one of the recurring major points of discussion is whether it is moreeffective to cement a well in turbulent or laminar flow regime.1.3.2 Primary Cementing in Numerical and Experimental StudiesThere is a considerable body of literature available on the subject of primary ce-menting, approaching the matter through study of displacement of one non-Newtonian,yield stress fluid with another Newtonian or non-Newtonian fluid. In the contextof displacement flows in primary cementing, the operation occurs in two distinctlydifferent categories: i) displacement in the casing (pipe) where the flow is down-ward and typically a heavier fluid displaces a lighter fluid, i.e., density unstable, ii)displacement in the annulus between the casing and the wellbore where the flowis upward and a heavier fluid displaces a lighter fluid, i.e., density stable. In bothscenarios, the main objective of any model or analysis is to predict the efficiencyof the displacement. Displacement flows in pipes in downward, near vertical andnear horizontal arrangements have been extensively studied by Frigaard and co-authors [3–6, 32, 98–101], as well as by Gabard and Hulin [36] and Hasnain etal. [42].The first thing to be noted is that the behavior of the flow in an annulus issignificantly different from the flow in a round tube. There is a coincidence ofradial locations of maximum velocity and zero shear stress in pipe flow due to itssymmetrical geometry [47, 84] and the total shear stress decays linearly with thedistance from the wall [30]. These features are not found in an annular geome-try, particularly in eccentric configurations. In annular geometry, the flow is notsymmetric and the shear stress does not vary linearly with the distance from thewalls. In the early studies of turbulent flow, it was assumed that the radius of zeroshear stress and maximum velocity coincide in the annular geometries as well [17],but the results of complementary studies, such as studies by Lawn et al. [57] andRehme [90], illustrated that the position of the maximum velocity occurred furtherfrom the inner wall of the annuli than that of the zero shear stress. This was con-firmed by the results of Direct Numerical Simulations (DNS) of Chung et Al. [20].10Besides the studies conducted to investigate the issue of coincidence of thesetwo mentioned radii, further studies were conducted on dependencies of these radiion the radius ratio as well as the resultant Reynolds number. In particular, somestudies suggest that the radius of maximum velocity depends on the Reynolds num-ber [105], while others propose that it depends on the radius ratio [89]. Results ofsome other investigations, however, suggest that in fully developed laminar or tur-bulent flow, the radius of maximum velocity is independent of both Reynolds num-ber and radius ratio [41]. Hanks et al. investigated the location of the maximumvelocity in transitional flow regime and reported a change in its radial location asthe flow transforms from laminar to turbulent flow [41]. On the other hand, there isa theoretical solution for the stress distribution in a laminar flow [34], and Maleki &Frigaard [60, 61] have developed analytical model to replicate the flow propertiesin transitional and turbulent flow regimes.In the matter of primary cementing, as previously discussed in Section 1.2, theindustry’s standard practice is to pump a number of preflushes ahead of the cementslurry (see Figure 1.4). Typically a low-viscosity low-density Newtonian pre-washstarts the sequence, followed by a denser and more viscous spacer fluid. Finally, thecement slurry is pumped, which may consist of a lead and tail slurry. The purposeof the Newtonian pre-wash is to promote turbulence, which is widely believed tobe an effective means of removing the gelled and dehydrated drilling mud [51, 56,93]. For instance, industry recommended practices developed by Energy SafetyCanada [18] state that turbulent flow displacement is the most effective techniquefor mud removal. The fluid should be designed in such a way that turbulence isachieved around the entire circumference of the annulus. A 10 minute contacttime is frequently recommended for sufficient removal of the drilling fluid [16] byturbulent flow. If turbulent displacement is not practical, a laminar displacementflow should follow certain design rules [58, 67].Guidelines to achieve a steady displacement front and avoid leaving behind amud channel can vary between companies but some commonalities also exist, e.g.typical would be:• The displacing fluid must be 10% denser than the displaced fluid [93],• The displacing fluid should generate at least 20% higher frictional pressure,11• The interface between the two fluids should advance at the same speed in thenarrow and wide side of the annulus,• The shear stress on the narrow side of the annulus should exceed the yieldstress of the mud, i.e., 1.1 is satisfied:∆P∆L>4τy(1− e)(Do−Di) (1.1)Here τy denotes the yield stress, e is the eccentricity, Do−Di is the hydraulicdiameter and ∆P∆L is the frictional pressure gradient of the displacing fluid.Eccentricity is the offset distance between the center of the pipes normalizedby the difference of radii.Some recent studies have questioned the validity of this widely accepted per-ception in the cementing community that turbulent displacement is necessarily su-perior to laminar displacement and warned that certain conditions must be metfor turbulent displacement to succeed [53, 76]. Subsequently, various aspects ofthis matter are examined in the work of Maleki and Frigaard [63], Kelessidis etal. [51], Enayatpour and van Oort [28] and Lavrov and Torsæter [56]. In the stud-ies performed by Smith and Ravi [96] and Howard and Clark [45], it was illustratedthat displacement efficiency has been improved in displacement experiments withhigher flow rates, but they did not compare laminar and turbulent regimes despitebeing often cited in this regard. Similarly, two papers by Haut and Crook [43] andSmith [95] suggest that “high flow rates, whether or not the cement is in turbulent,provide better displacement than plug flow rates” and “as the annular velocity isincreased there is no sharp increase in the displacement efficiency at the transitionfrom laminar to turbulent flow”.In laminar flow displacement, the importance of rheology and density differ-ence has been extensively studied [9, 65, 81–83], theoretically, numerically andexperimentally. These studies suggest that for the right parameters, a steady travel-ling wave solution is possible, meaning that the interface will advance at uniformspeed all around the annulus. The model of Bittleston et al. [9] is the basis for many2D simulations, in which variations across the annular gap are averaged. With thismodel Frigaard & Pelipenko have established rigorously that steady displacement12solutions are possible [83]. They have also examined rule-based guidelines, suchas those above, using this approach [82] showing that in general these rules giveconservative but physically sound design advice for vertical wells.The success of Bittleston et al.’s 2D model for laminar flows has prompted de-velopment of a similar approach for turbulent and mixed regime flows by Maleki &Frigaard [60]. The scaling and dimensional reduction are similar, in that the lead-ing order momentum balance used is locally a turbulent shear flow. However, themass transport between miscible fluids is now quite different, incorporating bothturbulent diffusion and anisotropic Taylor dispersion. The shear flow simplifica-tion allows computation in a similar way to the laminar flow models, but implicitlyeliminates the possibility of development of secondary flows of Prandtl’s secondkind in the annulus [15, 25, 37]. A number of different studies have however beenmade using the Maleki & Frigaard model [60].Maleki & Frigaard [61] studied turbulent cementing in detail, using both scal-ing arguments and model simulations. In the first place it was shown that rhe-ology becomes insignificant for a fully turbulent displacement flow. The authorsperformed a set of displacement simulations where the displacing fluid rheologyvaried, but the nominal effective viscosity was constant. The results showed nodiscernible difference. However, this only applied when both the displacing andthe displaced fluid are fully turbulent. If either fluid becomes laminar (even par-tially), then the rheology becomes relevant. On the contrary, when the flow ratewas adjusted to attain laminar displacement, rheology started affecting the process.From a practical point of view, mixed regime is a common scenario as typically atleast one of the fluids has high viscosity. Secondly, it was shown that even if turbu-lence aids displacement, further increases in flow rate can negate these benefits, i.e.,one can be too turbulent. In particular, in a vertical well a positive density differ-ence can be shown to help stabilize the interface [61], which counters the adverseimpact of casing eccentricity and promotes an even displacement all around theannulus. However, for high flow rates the turbulent stresses (−ρu′v′ ≈ 12 fρU2) be-come larger than that the buoyancy stresses (∆ρgD). Buoyancy becomes irrelevantto the displacement and only the underlying eccentricity of the annulus remains toinfluence the flow: the displacement front advances faster up the wide side of theannulus.13A second study [62] compared laminar and turbulent cementing under a fixedfrictional pressure drop constraint. Such a constraint is common in field applica-tion, i.e., due to constraints from the pore and fracture pressures of the surroundingrock. A new metric for quantifying displacement performance was introduced inwhich instead of using the volumetric efficiency of the whole annulus, only thevolumetric efficiency of the narrow side was used. The first criterion is commonlyused in the industry but is dominated by the wide side displacement and not sen-sitive to displacement defects which typically occur on the narrow side. The studyshowed that turbulence is not necessarily superior to laminar displacement, as longas the same operational constraints are applied.The other relevant study [62] looks at the merit of using low-viscosity washes,which are typically approximately water. Their usage is tied to the idea of a turbu-lent contact time [16], i.e., a time for which the low-viscous wash can be in contactwith the annular walls. Although the idea seems intuitive and straightforward, inpractice annular eccentricity coupled with adverse viscosity (and usually density)differences means that the wash travels preferentially in the wide side of the annu-lus and the problematic narrower parts of the annulus see little effect of the wash.This [62] and other model-based studies [39, 61] certainly make questionable theeffectiveness of turbulent washes and whether they should be part of industry rec-ommended practice.There are relatively few experimental studies focused on the matter of dis-placement flow in an annular geometry. Experimental research in the field of wellcementing and displacement flows began during the 1970’s with large scale labo-ratory based experiments to replicate and study primary cementing. A 10 ft perme-able sandstone tube was built by Clark and Carter to simulate formation rock [21].In these experiments, an inner pipe was inserted to simulate steel casing and drillingmud was injected into the annular gap. They even varied inner pipe diameter tosimulate a washout section. The pressures and temperatures were raised to re-produce field conditions and displacement experiments were repeated at variouseccentricities, inner pipe rotation, and reciprocation rates. They concluded thatvarious factors including reciprocation and rotation of the steel casing and con-ditioning the drilling mud immediately before cementing would produce a moreefficient displacement.14During the same decade, Zuiderwijk et al. [119] continued experimental re-search work on a vertical set-up similar to Clark and Carter [21], but using a fixedinner wall and using impermeable walls. In these experiments, a radioactive tracer(An198) was added to the drilling mud to discern the fraction of drilling mud leftbehind in the annulus after displacement, by measuring the residual radioactivity.They concluded that the displacement efficiency would increase by keeping thecasing centralized and producing turbulent flow at elevated flow rates. To generateturbulent flow regime, the viscosity of the working fluid was reduced and flow ratewas increased. They also repeated the experiments for slow flow velocities lessthan 0.5 ft/s, and reported that the displacing fluid’s density and viscosity shouldbe higher than that of the drilling mud.Experimental work on cementing was continued in the following decades, notonly proving and enhancing previous discoveries, but also investigating new ideasto optimize displacement flows through the use of spacer fluids [2] and conduct-ing drilling mud conditioning to reduce the amount of drilling mud constrained ina gelled state [49]. These early studies on well cementing generally stated thatthe turbulent displacement is more efficient in removing the mud during primarycementing than those displacement operations happening in laminar regime, e.g.[52, 75, 98].Here we re-examine the wash-mud system from an experimental perspective,using analogue fluids in a laboratory flow loop. One aspect of turbulent flow thatis not considered in the 2D model of Maleki & Frigaard [60] is the developmentof secondary flows and what influence they may have on removal of gelled fluid.Although the scaling arguments adopted in this model lead to valid leading orderapproximation of the (averaged) velocity, there are many instances involving vis-coplastic fluids where the stress field is not approximated to leading order by theshear flow terms, e.g. the eccentric annular flow of Walton & Bittleston [106]. Inthis and many similar flows with slow streamwise variation, the unyielded plug re-gions are strongly affected by neglected stresses. In place of an unyielded plug, wemay have pseudo-plug regions that exist (to leading order) at the yield stress, withnormal stresses exactly compensating for the deficit of the shear stresses below theyield stress.This type of effect also occurs in thin-film flows [7], which might be considered15a toy problem for the displacement. In the annular displacement context, this meansthat small contributions to the stress field may result in yielding of larger regionsof gelled mud than might be expected. Flow in a non-circular conduit gives rise toa secondary flow that has its origin in anisotropies of the turbulent stresses. Thesecondary flows are essentially time independent rotational flows, similar to re-circulation zones developed after a sudden expansion. Although secondary flowsare typically only 1− 2% of the streamwise velocity [79], they result in cross-stream momentum and mass transfer [77]. Results of DNS study by Nikitin etal. [78] in eccentric annuli revealed that two counter-rotating vortices appear oneach side of the plane of symmetry. The two vortices transfer high-velocity fluidfrom the wide gap to the narrow gap and return low-momentum fluid. As discussed,such motions may become relevant to displacement of gelled regions.The interaction of two flows with different turbulence intensities (e.g. a laminar-turbulent interface) is another aspect of the displacement flow in an eccentric an-nulus that falls below the resolution of the leading order gap-averaged model ofMaleki & Frigaard [60]. As shown, [77] flow in an eccentric annulus can effec-tively represents a turbulent-non-turbulent (T/NT) interface for sufficiently higheccentricity and low Reynolds number. It has long been recognized that such mixedregimes do routinely occur at fixed depth in cementing flows. The dynamics of aturbulent-non-turbulent interface is then relevant to the displacement mechanics.Narasimhamurthy et al. [72] studied such a case using DNS. One of the strikingfeatures of the interface was the development of large-scale Taylor-Go¨rtler like rollcells, which give rise to a wavy interface.Our study is targeted at exploration of displacement of viscoplastic fluids inhighly eccentric annuli by low-viscous fluids at various flow regimes.The high ec-centricity and design of the rheology both ensure that the viscoplastic fluid is hardto displace from the narrow side of the annulus. We consider iso-density fluids anduse a horizontal eccentric annulus. The objective is to understand the contributionof flow regime on the removal of the drilling mud and confirm whether the percep-tion of superiority of turbulent displacement over laminar displacement is corrector not. The displacing fluid in our study is either water or a low-viscous fluid.Thus, our experiments resemble the use of Newtonian pre-wash in the industry butallow us to vary the flow regime for otherwise similar fluids.161.4 Thesis ObjectivesDisplacement flow theory and industrial methods in various flow regimes have un-dergone many changes over the years, but the fundamentals underlying these dis-placement practices have not had a considerable change. Given normal cementingcircumstances, there is a series of established rules and methods that generally re-sult in satisfactory cementing operations. However accomplishing the same qualityof displacement in more abnormal and demanding circumstances is less plausible.The purpose of this study is to produce an experimental methodology and col-lect validation data that would be capable of replicating displacement flows in alllaminar, turbulent and transitional flow regimes that will extend the scientific un-derstanding of these flows and their resultant displacement efficiencies. Specifi-cally, we look to provide insight about the following queries:• There is a perception that turbulent displacement always outperforms lam-inar displacement. Does this generic statement apply at all design scenar-ios? This question is particularly suited to be investigated both numericallyand experimentally, as we can rarely find wells with comparable rheologicalspecifications and geometries that have been cemented with different dis-placement flow regimes. Accordingly, there is no systematic practical datathat can be used for analysis of effect of flow regime on displacement effi-ciency.• Where there is a set pump capacity available and where there is a definedpressure range due to risk of either fracturing the well or an influx, how doesa turbulent displacement compare with a laminar displacement? Does theintensity of turbulence (i.e., weak or strong turbulence) affect the outcome?1.5 Thesis OutlineSubsequent to Chapter 1, which outlines a brief overview of primary cementingand available literature relevant to this study, Chapter 2 presents the experimentalsetup and discusses the methodology and experimental procedure which have beenused in this experimental study. The content of this thesis, broadly speaking, canbe divided into three sections.17• In Chapter 3, we focus on fully turbulent displacement flows of viscoplasticfluids in a highly eccentric horizontal annulus. The principal question iswhether turbulent displacing flow will be effective at removing yield-stressfluid from the narrow side of the annulus and by what means.• In Chapter 4, we compare displacement flows at laminar, turbulent, and tran-sitional flow regimes under imposed flow rate condition (fixed pump capac-ity). In this section, we run all experiments at two degrees of eccentricity,fully eccentric and 70% eccentric. Therefore, in addition to investigatingwhether flow regime influences the outcome of displacement, we also lookinto the effect of eccentricity in a systematic way.• In Chapter 5, we turn our attention to imposed pressure drop displacementflows. In particular, we repeat the experiments performed in Chapter 4 ata constant pressure drop across the test section and study the effect of flowregime on the displacement quality from a different perspective.The main body of the thesis is then closed with Chapter 6, which presents theconclusions of this experimental study.18Chapter 2Experimental Setup andMethodologyGiven the difficulties of direct field observation and measurement, we study thedisplacement flows in a horizontal, eccentric annulus in a lab-scale experiment tovisualize the interface and investigate the effects of flow regime of the efficiencyof the displacement.In this chapter, details of the experimental facility and equipment, as well asrheological properties of test fluids, that have been used throughout this study areexplained. Proper procedures on how to utilize the instruments along with theirlimitations are discussed.2.1 Horizontal Flow LoopA schematic of the experimental set-up, identifying the individual equipment asso-ciated with it, is presented in Figure 2.1. The flow loop is designed to simulate thedisplacement of one fluid with another, analogous to pumping of a preflush/spacerto remove the drilling mud, during primary cementing. The system is built suchthat the displacing fluid and the displaced fluid are flowing simultaneously at thesame flow rate prior to the displacement, to minimize acceleration effects. Twopneumatic three-way valves are used to change the flow path. The course of anexperiment involves filling the tanks with the test fluids, pumping each fluid at the19Figure 2.1: Schematic of the flow loopdesired rate and switching the pneumatic valves once the flow is stabilized. Beforeactivating the valves, fluid 1 (displaced fluid) is flowing through the test sectionwhile fluid 2 (displacing fluid) is diverted to a bypass line. Upon activating thetwo valves simultaneously (with one switch), fluid 2 is diverted to the test sectionwhile fluid 1 changes direction to a bypass line. The inlet assembly is highlightedin Figure 2.1 where the two pneumatic valves control the direction of the flow foreach fluid.The horizontal annulus has a total length of 7.5 m, composed of five sectionsof high quality, optic grade Borosilicate glass pipes, each 1.5 m long with innerdiameter of 52 mm and wall thickness of 1 cm. The inner body is a stainless steelpipe with a length of 7.5 m and an outer diameter of 38 mm. The annulus has20Description Definition DimensionOuter pipe radius Ro 26 mmInner pipe radius Ri 19 mmAspect ratio δpi =1piRo−RiRo+Ri0.05Radius ratio α = RiRo 0.73Hydraulic diameter Dh = 2(Ro−Ri) 14 mmEccentricity e = lRo−Ri 0 to 1Axial length ξ = Lpi2 (Ro+Ri)106Table 2.1: Dimensions of the flow loopa radius ratio of 0.73 and a hydraulic diameter of 14 mm. To minimize saggingand vibration of the internal pipe, the pipe wall thickness was selected to be 1.25mm, satisfying near buoyancy condition in water-based solutions [29]. To ensurethat the internal pipe has a constant relative location compared to the outer bodyand also to control the eccentricity, a 3 mm rod is used every 1.5 m of the testsection that passes through the internal steel pipe and is fixed to it. Table 2.1summarizes the relevant dimensions of the flow loop. Figure 2.2 schematicallyshows a cross-sectional view of the eccentric annulus. Due to the small aspect ratioof the geometry, high fluid velocity and viscous fluids used in our experiments, theforce on the inner body is large. The pressure at the inlet can be as high as 80 psi(550 kPa), while the wall shear stress can reach as high as 150 Pa. To ensure thestructural integrity of the test section, the inner tubes are anchored to a uniquelydesigned flange at the inlet and the outlet of the test section.The working fluids are prepared and stored in two mixing tanks with capacityof 200 litres. The fluids are circulated through the loop using progressive cav-ity pumps (PCP) equipped with variable frequency drives (VFD). Each of thesepumps can deliver a flow rate up to 1000 l/min and differential pressures up to 100psi. They were specifically chosen to be suitable for handling viscous polymer flu-ids. Such fluids should be pumped with minimum damages to the integrity of thepolymer chains.Pulsation dampeners are installed along the piping system to reduce fluctua-21Figure 2.2: Cross-sectional view of eccentric annulustions in the flow and also absorb the pressure spike caused by sudden switchingin the flow direction. Furthermore, vibration-resistant hoses are utilized to furtherreduce the impact of switching from one fluid to the other.The flow rates are measured using a set of two magnetic flow meters (OMEGAFMG 606-R) with accuracy of±0.5%, each incorporated at the inlet of the test sec-tion and the bypass line. The temperature of each fluid is monitored and recordedthrough two thermocouples mounted in the tanks.The pressure drop along the an-nular test section is determined using a high accuracy, differential pressure trans-ducer (OMEGA DPG 409-050DWU) acting over a 3.0 m distance. The pressuretransducer has a measurement range of 0-50 psi and accuracy of 0.08% and itsprobes are located at an adequate distance downstream of the inlet (> 88DH). Thedevelopment distance of 88DH from the inlet is sufficient to attain fully developedlaminar flow [85], while a shorter distance would be necessary for turbulent flowto reach fully developed condition and eliminate the end effect [48]. Regulatingpump speeds, controlling pneumatic actuated valves and collecting all data suchas flow rates, pressure drop and temperatures are managed by a computerized dataacquisition system equipped with LabView software developed by National Instru-ments.For a step to step experimental procedure, please refer to Appendix A.22Figure 2.3: Configuration of cameras and UV lights with respect to the ob-servation window marked in Figure 2.12.2 Measurement MethodologyDirect visualization of the fluid-fluid interaction is the primary measurement tech-nique we use. This method requires a high degree of contrast between the twofluids. Uniform illumination is critical for obtaining reliable data. Using back-light illumination similar to displacement experiments conducted in pipes withinthe same research group [31] is not applicable in the annular configuration becausethe inner body is opaque. Moreover, the stainless-steel pipes reflect any visiblelight that is directly shone on the system. Light reflection is more generally anissue that affects the quality of the recorded images.To overcome the illumination problem, we use red fluorescent dye (excitationwavelength of 600 nm) in the displaced fluid and a minute amount of black inkin the displacing fluid. Two 50 W UV-light lamps (blue-light lamps with emit-ting wavelength of 385-400 nm) then stimulate the fluorescent dye. The excitedfluorescent dye emits red light with a wavelength in the visible range (635-700nm). During the experiments the ambient lights were turned-off, and only the UVlights were used for illuminating the flow. Two high-performance red-filters are23Figure 2.4: Example of an image showing both displacing and displaced flu-idsused on the cameras to block any other lights except the red light emitted by thedisplaced fluid. The displacing fluid is dyed using black ink; hence, it produces ahigh contrast with the displaced fluid. Using fluorescent dye and UV-light elimi-nates reflections off the shiny surface of the inner pipes. Figure 2.4 shows a typicalimage obtained in our experiment (note that this is after removing the backgroundimage). The interface between the two fluids is clear, and the illumination is rela-tively uniform.Due to the cylindrical shape of the glass pipes, perspective errors and lightrefraction are problematic for visualization purposes (i.e., magnification). To al-leviate visualization problems, the glass pipes are put inside rectangular plexiglasboxes filled with glycerol. The glycerol has a refractive index similar to that ofBorosilicate glass, hence, reduces the light refraction.For recording we use two different cameras (Oryx 10 Gig model from FLIRindustry with a 12 mm HP lens and f/1.8, and Prosilica GT 4096 camera fromAlliedVision combined with a 50 mm Zeiss planar lens and f/1.4). Measurementsare carried out from 4.5 m to 6.0 m from the inlet (see observation window Figure2.1). In a series of preliminary experiments, we determined there was no qualitativedifference between the data measured from 3.0-4.5 m and 4.5-6.0 meters awayfrom the inlet. Therefore, the data presented in this thesis are all recorded from4.5-6.0 m away from the inlet. Figure 2.3 shows the configuration of the camerasand the UV lights along with the respective field of view for each camera.Camera 1 with a resolution of 2448× 2048 and frame rate up to 162 fps(frames/s) combined with a 12 mm lens was used for recording the full lengthof one pipe (1.5 m). Camera 1 provides roughly 1.7 pixels per mm of data (i.e., ≈2485 pixels across pipe outer diameter and 2448 along the axial length of the pipe).The second camera with a resolution of 4896×3264 and a 50 mm lens is used forzooming in over approximately 40 cm length of the test section. Camera 2 pro-vides 12.5 pixels per mm (i.e., ≈ 650 pixels across pipe diameter and 4896 over40 cm axial length). The data from camera 1 shows how the displacement evolvesstream-wise while the data of camera 2 provides high-resolution images of the fluidinterface.2.3 Fluid Preparation and Rheological PropertiesThe dynamics of the fluid displacement in the annulus are affected by the rheolog-ical properties and relative densities of fluids involved. This influence is especiallycrucial for the local fluid dynamics at the interface of displaced and displacingfluids. Although there is some evidence demonstrating that the influence of fluidrheology becomes irrelevant in fully turbulent flows [82], many primary cement-ing jobs are carried out in either laminar or mixed regimes, due to pumping lim-itations, large eccentricities or varying fluid viscosities. For laminar and mixedregimes, fluid rheology is one of the most critical parameters affecting the qualityof primary cementing.Spacer fluids (preflushes) and cement slurries are non-Newtonian fluids typi-cally exhibiting shear-thinning behavior and a yield stress, τy (Pa), which impliesthat displacing these fluids is only possible if a deviatoric stress in excess of a cer-tain threshold value is applied to them. As the deviatoric stress in the fluid exceedsthe yield stress, the fluid should behave as a viscous fluid. The most common rhe-ological model that is used to describe their behavior is the Hershel-Bulkley modelgiven byτ = τy+κγ˙n (2.1)where τ is deviatoric stress (Pa), τy is yield stress (Pa), γ˙ is shear rate (s−1), κ is theconsistency (Pa.sn), and n is the flow behavior index. The consistency determinesthe magnitude of the viscous stresses at a given shear rate, while the flow behaviorindex determines the degree of shear-thinning behavior. Here we expect n < 1(shear-thinning) for both spacer and cement slurry.25In vertical wells the density difference between fluids is often used to im-prove displacement efficiency, but it has proved to be less effective in a horizontalwell [83]. In consequence, in this study, working fluids have neutral density differ-ence (ρ1 = ρ2).Although the rheology of our fluids does exhibit Hershel-Bulkley behavior, inpractice the rheology of the wellbore fluid is considerably more complex. Drillingfluids can have strong thixotropic properties and accordingly, the properties of thefluid vary with time. It becomes particularly significant when the yield stress buildsup a gel strength due to colloidal particles developing a structure as the slurryrests. This phenomenon is a reversible process and the structures can be broken asthe fluid is sheared. On the other hand, the fluid can also experience irreversiblestrength build up due to chemical reactions.In our study, we aimed to simulate the viscoplastic properties of drilling fluidby using a model laboratory fluid. In such experiments, aqueous Carbopol polymersolutions are frequently preferred over other viscoplastic fluids to be employed inflow visualization experiments [15, 25, 37, 60], because they are highly transparentand are relatively easy to prepare [61–63]. However, these solutions also have somedrawbacks, including difficulties to find a good rheological model to describe lowshear behavior.Carbopol EZ-2 polymer from Lubrizol Inc. is used in our study. The mixingprocedure for the Carbopol was to mix a concentrated un-neutralized solution in40 liters of water overnight. The mixture was then neutralized in the tank usingNaOH at a ratio of 1.0 gram of NaOH to 3.5 grams of Carbopol. The ratio of 1/3.5NaOH to Carbopol was determined to give a pH in the range of 6.5 to 7.5 and buildhigh yield stresses. The neutralized solution is then circulated through the systemfor 45 minutes to ensure homogeneity. Both the displacing and the displaced fluidshave a density of 999 kg/m3.Note that in a cementing job, freedom in design of displacement process isusually with the spacer. With regard to selection of right displacing fluid relative tothe mud in horizontal drilling, the drag reducing additives are commonly used tominimize the frictional pressure losses within the well, and therefore increase thelength of horizontal reach of the well. In the research work that is included in thisthesis, it is aimed to study a range of displacing flow regimes. In addition to wa-26ter, 3 solutions (100, 300 and 600 ppm) of polyethylene oxide polymer (PEO, withmolecular weight of over 100,000 g/mol) and 3 solutions of Xanthan gum (0.125%,0.25% and 0.5%) have been considered to be used in these experiments becauseof their distinct rheological properties in water-based solutions. The intention ofusing the polyethylene oxide polymer at low concentration is to suppress the pro-duction of turbulence while maintaining a similar viscosity to that of water. Thesolutions of Xanthan gum, on the other hand, are power law fluids which presenthigh viscosity, shear thinning, and turbulent drag reduction [39]. These displacingfluids were also mixed in concentrated batches overnight and diluted 45 minutesbefore experimenting.A high-resolution Malvern Kinexus rheometer was used for the rheologicalcharacterization of the test fluids, which was done immediately after displacementexperiments. Fluid samples were collected just before switching the pneumaticvalves. Because of the mixing procedure we used and also temperature variationswithin the lab, it was imperative to characterize the fluids after each experiment.Furthermore, for measuring rheology of the Carbopol solutions, a roughened par-allel plates geometry was used to eliminate wall slip effects.The rheological properties of both displaced and displacing fluids specificallyused in each set of experiments shall be discussed at the beginning of each subse-quent chapter.27Chapter 3Turbulent Displacement Flow ofViscoplastic Fluids in EccentricAnnulusFully turbulent displacement flows (meaning that all fluids are fully turbulent) arerelatively infrequent in practice. Indeed, if all fluids are fully turbulent then theyare mobile and do displace. The only questions then are regarding dispersion andmixing of two turbulent fluids, which is partly addressed in the modelling work ofMaleki & Frigaard [60, 61].Therefore, the interesting relevant questions address mixed regime and situa-tions in which displacement is difficult. The examples studied here address thequestion of whether a turbulent flow of the displacing fluid will be effective atremoving the static narrow side channel and by what means.Our study is targeted at exploration of displacement of viscoplastic fluids inhighly eccentric annuli by turbulent low-viscous fluids. The high eccentricity andchoice of the rheology both ensure that the viscoplastic fluid is hard to displacefrom the narrow side of the annulus. This mimics the situation found in the ce-menting of horizontal oil and gas wells. In this configuration it is common thatthe yield stress of the displaced fluid prevents displacement from the lower narrowside of the annulus, where it remains static. We consider iso-density fluids and usea horizontal eccentric annulus. The displacing fluid in our study is either water or28a low concentration (drag reducing) polymer. Thus, our experiments resemble theuse of a Newtonian pre-wash in the industry but allow us to vary the turbulencefor otherwise similar fluids. The displaced fluid is a Carbopol solution, of differentselected concentrations.The flows proceed with rapid displacement along the wide side of the annu-lus leaving behind a gelled channel of fluid on the narrow side. The narrow sideis displaced either slowly or not at all. This depends on both the yield stress ofthe displaced fluid and the turbulence characteristics of the displacing fluid. Weinfluence the latter through the use of drag-reducing polymers. We show that sec-ondary flows in the turbulent displacing fluid are essential to the displacement andnot only the increased pressure drop of the turbulent flow. We hypothesize thatthe displacement is enhanced by the transmission of normal stresses into the gelledlayer.The focus on turbulent displacement in this chapter paves the way to understandlaminar and more sophisticated mixed regime displacement that will be studiedlater in following chapters of this thesis.A version of this chapter is published in Physics of Fluids [11].3.1 The Rheological Properties of Test FluidsFigure 3.1 shows the shear rheology data of all the Carbopol solutions used in thisstudy. The fitted parameters of the model are reported in Table 3.1. The aqueoussolutions of PEO exhibit Newtonian viscosity profiles. The 100 ppm has a shearviscosity similar to water. The 300 ppm solution has a shear viscosity of 1.221 cpand the 600 ppm solution a shear viscosity of 1.971 cp.To characterize the elastic properties of the Carbopol fluids, we conducted aseries of stress amplitude sweep tests. The results for series 1 and 3 (i.e., fluidswith the highest and lowest yield stress (see Table 3.1) are reported in Figure3.2. For low shear stresses (i.e., below yield stress), both moduli are constant,indicative of the linear viscoelastic region. For stresses below the yield stress,the microstructures of the gel remain intact. Therefore, the elasticity of the gel issignificant in the linear viscoelastic region. The results presented later show thatin most of the experiments the gel is subjected to stresses below the yield-stress,29Figure 3.1: Shear stress vs. shear rate data of the Carbopol solutionsEccentricity (e) Series Displacing Fluid Displaced Fluid τy (Pa) κ (Pa.sn) n0.65−0.75 1 Water Carbopol 5.22 2.33 0.480.65−0.75 2 Water Carbopol 8.7 3.75 0.470.65−0.75 3 Water Carbopol 12.74 4.27 0.470.65−0.75 4 100 ppm PEO Carbopol 6.6 2.66 0.490.65−0.75 5 300 ppm PEO Carbopol 7.5 3.14 0.480.65−0.75 6 600 ppm PEO Carbopol 7.94 3.73 0.461.0 7 Water Carbopol 11.81 4.7 0.461.0 8 Water Carbopol 5.4 2.46 0.49Table 3.1: Herschel-Bulkley model parameters for the Carbopol solutionstherefore, elasticity becomes dominant.Before presenting the results of the displacement experiments, it is worthwhileto explain the test matrix briefly. Experiments series 1-3 represents three caseswhere the displacing fluid is kept constant (rheology and flow condition) while the30Figure 3.2: Amplitude sweep data for two Carbopol solutions with lowestand highest yield stressesdisplaced Carbopol solution becomes progressively more difficult to remove. Se-ries 4-6 are tests where the displaced Carbopol is kept similar. At the same time,the flow turbulence of the displacing fluid is manipulated by using minute amountsof PEO polymer in the displacing fluid. A comparison of the displacement perfor-mance of series 1-3 with those of 4-6 allows us to draw a conclusion on the impactand extent of flow turbulence on displacement performance. Tests 7 and 8 are per-formed in a fully eccentric annulus (extreme case) with water as displacing fluidand two different Carbopol solutions. Comparison of displacement performance ofseries 7-8 with series 1-3 shows the impact of change in eccentricity (and implicitlyalso flow turbulence, as the latter depends upon eccentricity).3.2 Experimental ResultsTable 3.2 summarizes the details of the experiments discussed here. Subscript 1refers to the displaced fluid, and subscript 2 denotes the attributes of displacing31Eccentricity (e) Series (∆P∆L )1(kPa/m) (∆P∆L )2(kPa/m) Q1(litre/min) Q2(litre/min)0.7 1 20.48 1.52 70.8 70.10.7 2 26.34 1.64 71.3 73.30.7 3 34.82 1.62 69.4 69.70.7 4 22.5 1.16 70.0 71.80.7 5 24.13 0.96 72.8 71.20.7 6 24.27 0.96 72.8 71.31.0 7 26.9 2.64 70.1 69.71.0 8 17.23 2.28 69.4 70.7Table 3.2: Flow rates (liters/min) and pressure drops (kPa/m) associated witheach set of experimentsfluid (see Table 3.1).For each pair of fluids (the displaced fluid is always a Car-bopol solution with rheology reported in Table 3.1), the respective pressure dropand flow rates are reported in Table 3.2. The flow rates of each fluid are controlledto within 2 litres/min of each other. Note that the superficial velocity is in the range1.1 - 1.2 m/s. The ratio of frictional pressure drops (i.e., (∆P)2/(∆P)1) is small,reflecting the significant rheological differences. For the experiments in the fullyeccentric annulus (series 7 & 8), we observe a reduction in the pressure drop forthe Carbopol solution, which is in line with that reported in the literature [79].Figure 3.3 shows the recorded pressure drop data during the experiments. Thesharp change in the pressure drop is a clear transition from one fluid to the other.Additionally, the transition is almost instantaneous, indicating a large portion ofthe annulus is displaced very quickly, which will be discussed in more detail later.Note that the reported pressure drop data in Figure 3.3 starts long before switchingthe fluids. The sudden change in the recorded pressure drops indicate the momentwhen the valve is actuated and the displacement begins.Figure 3.4 shows the time-evolution of the displacement flow for series 1. Theblack fluid is the Carbopol solution and t = 0 corresponds here to the first imagein the sequence. The color-bar indicates normalized image intensity (IN). The ini-tial few seconds of the experiment is very fast and dominated by advection. Inabout 2 seconds, almost half of the annular area is displaced as the highly turbulent32Figure 3.3: Measured pressure drops reported also in Table 3.2displacing fluid advances along the wide side. In terms of the displacement frontdynamics the displacement is characterized as unsteady. The displacement on thenarrow side of the annulus is much slower, as illustrated, but eventually the Car-bopol is removed. Figure 3.5 shows the displacement corresponding to series 5.The first few seconds of the test is similar to the previous case: rapid bulk displace-ment on the wide side, development of an elongated interface between the twofluids with the Carbopol solution remaining in the narrow gap. As the displace-ment continues, unlike the previous case, the test reaches an equilibrium where thedisplacing fluid fails to displace the Carbopol gel completely. The reasons why thepolymer solution fails to completely remove the gel will be discussed later.These two examples show that the initial displacement in the wide gap is mostlyunaffected by the choice of the displacing fluids. The eccentric configuration pro-motes a higher fluid velocity in the wider side of the annulus; therefore, higher flowturbulence compared to the narrow side. The result is an inertially dominated flowthat eventually results in a fast-displacement of the Carbopol. After the first few33Figure 3.4: Time-evolution of the displacement corresponding to Series 1seconds of the test, the Carbopol gel in the narrow gap comes to a full stop. In con-trast, in the pre-circulation stage and in the first few seconds of the displacement(before the front reaches) the Carbopol moves on the narrow side. This can beseen via the motion of small bubbles trapped in the fluid. The change from mobileviscoplastic fluid in a cross-section of the annulus to a two-layer flow in which theviscoplastic fluid becomes slow/static on the narrow side is a feature predicted by2D gap-averaged models [60–62]. It intuitively makes sense to presume that if theshear stress generated by the displacing fluid at the interface is higher than the yieldstress of the Carbopol layer, the Carbopol yields at the interface and hence moveswith the displacing fluid. The displacement test of Figure 3.5 is a case where shearstress is not sufficient to yield and remove the Carbopol gel.The knowledge gap is in understanding the behaviour of the elongated in-terface. The interface between the two fluids is analogous to a turbulent/non-34Figure 3.5: Time-evolution of the displacement corresponding to Series 5turbulent (T/NT) mixing layer [72], which brings some interesting complexitiesinto the problem. The shape of the interface in such cases is convoluted and duneshaped [24], similar to the profiles shown in Figure 3.4. The interface here repre-sents a shear layer, as opposed to a free shear layer, because there is a significantchange in the velocity gradients across the interface. However, it is not exactly asolid wall. Theoretically, the sheared interface can induce normal stress fluctua-tions in the Carbopol gel, if other conditions are met [24]. In simple terms, if theeddies have a significant velocity difference with the mean flow, pressure fluctua-tion becomes significant. In such a case, the interface act similarly to a shear-freeinterface and large fluctuations can be induced at the interface. This mechanismcould potentially be in effect in our experiments, responsible for the waves/dunesobserved. Other relevant characteristics of a T/NT layer is that it is a boundarywith maximum vorticity [112] (as is likely here), and with elongated micro-scale35vortices [23]. The vortices move at a micro-scale speed relative to the large-scaleflow [24]. Such structures also appear in turbulent flows at high Reynolds number.In other words, the significant difference in turbulence intensity on the oppositesides of the interface may contribute to further production of turbulent energy atthe interface.The dynamics of T/NT layers has been studied extensively in the literature.However, we must be careful when extrapolating the findings to the problem wehave here because the static fluid is a yield-stress fluid whereas most T/NT inves-tigations are directed at boundary layer or jet flows. The gelled fluid acts as asolid interface with respect to the velocity when unyielded. However, stresses thatare transmitted can either yield the fluid or can be absorbed when below the yieldstress, and potentially released back due the elastic nature of the gel. Thereforealthough we feel the T/NT analogy to be valuable, it is simplistic to assume the dy-namics of the interaction between the two fluids would be the same as other T/NTcases.An unusual aspect of the interfaces (especially those shown in Figure 3.5)is the lack of any small-scale instabilities (e.g. fingering or Kelvin-Helmholtz).The large viscosity ratio of the two fluids could induce instabilities. Lack of suchinstabilities could be due to the shear-sheltering mechanism of the interface [24],or to effects of the Carbopol yield stress and viscosity in damping the growth ofinstabilities. In the laminar multi-layer flow context, when the visco-plastic fluid isunyielded at the interface, interfacial instabilities are suppressed [46, 71], and thereis little evidence of them when static wall layers are found [6, 116]. However, whenyielded at the interface the usual linear interfacial instabilities can develop [92].Estimation of the Reynolds number of the displacing fluid and the averageshear stress at the interface requires knowledge of the geometry in which each fluidis moving. As discussed earlier, after a few seconds, a clear interface developedbetween the two fluids. We use image processing techniques to calculate how muchof the annular cross-section is occupied by each fluid at a given time. Figure 3.6schematically illustrates the concept of evaluating the geometrical parameters. Theheight h refers to the average height of the Carbopol gel in the annulus. Once h isknown, we then calculate the hydraulic diameter (Dh) and the average flow velocitybased on the flow rate. Equations (3.1)− (3.4) are used to calculate the Reynolds36Figure 3.6: Schematic representation of the averaging technique for evaluat-ing hnumber and average wall/interfacial shear stress.Dh =4A1Pwet(3.1)u =QA1(3.2)Re =ρuDhµ(3.3)τw(h) =Dh4× ∆P∆L(3.4)In Equations (3.1)−(3.4), A1 refers to the flow area occupied by the displacingfluid, Pwet is the wetted perimeter, Q is the flow rate, u is the mean flow velocity,µ is the viscosity, and τw is the wall or interfacial shear stress (assumed the samewhen the Carbopol layer is static).Figure 3.7 shows a comparison of h for the eight experiments. Note that h isalso a measure of the volumetric efficiency of the displacement that can be usedto quantify the performance of the displacement process. In the first few seconds,37Figure 3.7: Profile of average thickness of the Carbopol gel vs. time afterswitching the fluidsmore than half of the annulus displaces. Four of the tests in the partially eccentricannulus (3 water and the 100 ppm PEO), eventually lead to complete displacement(h→ 0). The 300 and 600 ppm PEO displacements fail to reduce h to zero, andmore importantly, h reaches a plateau (h→ h∞ 6= 0), which indicates residual fluidin the annulus. Despite having similar yield stress to series 3 and 1 respectively,tests 7 and 8 in the fully eccentric annulus have incomplete displacement. Thisobservation reiterates the main point of Maleki and Frigaard [63], where the au-thors emphasize that the adverse impact of eccentricity dominates any other factor.The three experiments with water in the partially eccentric annulus are interestingin a sense that h goes to zero despite increasing the displaced fluid’s yield stress,from 5.22 to 12.74 Pa. The process becomes significantly slower in the case of thethicker fluid; nonetheless, it results in a complete displacement.The computed wall shear stress per Equation (3.4) divided by the yield stressof the Carbopol solutions for each test is shown in Figures 3.8 and 3.9. The38Figure 3.8: Profiles of average wall shear stress vs. change with h/Dologic of normalizing the wall shear stress with the yield stress is rather obvious. Inour experimental procedure the Carbopol gel becomes static after a few seconds ofthe test. The ratio τw/τy infers whether the remaining layer of the Carbopol willbehave as a fluid (i.e., yield) or if the shear stress is insufficient to overcome theyield stress. In the latter case, one expects the Carbopol gel to remain un-yielded,and hence, an incomplete displacement to result. Figure 3.8 shows the change inthe wall shear stress versus that of h, and Figure 3.9 shows the time-evolution ofwall shear stress during displacement. We see that there is in general a reductionin τw/τy due to the drop in h. Indeed this can amount to a nearly 30% reduction inthe shear stress at the interface during the displacement.We observe in 3 of the experiments (series 2-4) complete displacement isachieved despite having τw/τy < 1. Both tests in the fully eccentric annulus haveincomplete displacement. Series 8 has τw/τy ≥ 1 while a layer of Carbopol gelremained in the annulus. This suggests that the average shear stress determined us-ing Equation (3.4) overestimates the shear stress in the narrow side of the annulus.This is entirely possible since Equation (3.4) gives only the interfacial stress. Un-39Figure 3.9: Profiles of average wall shear stress vs. change with timeder constant pressure drop in a narrow annulus, motion of the narrow side can takeplace if the shear stress on the narrow side of the annulus exceeds that of the yieldstress of the mud, i.e., Equation (3.5) is satisfied. Thus, τw/τy > 1 is possible witha static layer and the implication of series 8 is simply that lower shear stresses existin the narrower lower section. We could also estimate the mean wall shear stressin the Carbopol layer, but in any case we expect variations in this layer. Certainly,a non-uniform distribution of flow and Reynolds stresses in an eccentric annulus iswell-known [78].∆P∆L>4τy(1− e)(Do−Di) (3.5)Our interest is anyway with those cases of Figures 3.8 and 3.9 where τw/τy <1, but the fluids were removed. If only a shear stress balance is relevant this shouldnot happen, so what is happening? To explain, at least partly, we must consider theimpact of flow turbulence. The use of the PEO polymer solutions is intended forthis purpose.40(a) Series 2 (b) Series 3Figure 3.10: Time-evolution of the displacement corresponding to:(a) Series 2 (b) Series 3The displacement process (as shown in Figures 3.4 and 3.5) and in more detailin Figures 3.10 to 3.12 undergoes two different mechanisms of removal. In theearly stages (i.e., the wide gap), the displacement is dominated by a high degreeof mixing and advective displacement of Carbopol along the wide gap. Once thedisplacement front passes and the interface elongates, both shear stress and inertialeffects reduce. Effective displacement then becomes dependent upon other factorsnot dominant in the initial stages. Time-dependent large-scale turbulence-inducedstructures (e.g. coherent structures), secondary flows and other mechanisms be-come significant contributors to the removal process. This can be seen in Figures3.10 and 3.11a where the trapped gel in the narrow side of the annulus is removedin a non-uniform manner. Chaotic time-dependent motions control the process,and the gel breaks at different points. In the experiments, often, we observed that41(a) Series 4 (b) Series 6Figure 3.11: Time-evolution of the displacement corresponding to:(a) Series 4 (b) Series 6pieces of the Carbopol gel are detached from the residual layer and transported bythe high-velocity core of the flow. The chunks often remained intact until reachingthe fast stream on the wide side, where the highly turbulent flow broke them apartand mixed them with the carrier fluid. Certainly this is neither a steady/wavy filmflow (as in many laminar displacements), nor is it a gradually eroded layer (as ine.g. a granular gel or solids bed).Comparison of displacement performance of water as displacing fluid (series1-3) and the drag-reducing polymers (series 4-6) illustrates the importance of tur-bulence and the secondary flows (e.g. series 1 and 2 versus series 5 and 6). Thesecondary flows have their roots in inhomogeneous turbulence caused by the eccen-tricity [78]. The inhomogeneity causes the development of secondary flows of thesecond kind. DNS results [78] have shown that in such a case two vortices emerge42(a) Series 7 (b) Series 8Figure 3.12: Time-evolution of the displacement corresponding to:(a) Series 7 (b) Series 8on each side of the symmetry plane, moving low-speed low-momentum fluid fromthe narrow gap to the wide gap and vice versa. Narasimhamurthy et al. [72] stud-ied the T/NT layer in a Couette flow geometry using DNS. They showed that theinterface exhibits a large-scale meandering motion, which does not appear in thelaminar case. The cause of such a phenomenon was attributed to rolling cell Taylor-Go¨rtler vortices. Therefore, in addition to the secondary flows induced by the ge-ometrical variations and flow turbulence, we can hypothesize enhanced vorticalactivities at the interface due to changes in flow regime.A comparison of the results of series 5 or 6 with that of series 3 illustrates thedifference that turbulence and the associated phenomena can make in the displace-ment process. All of the three cases have similar τw/τy ratio, yet series 5 and 6have an unsuccessful displacement. We attribute this to the mechanism of drag43reduction. The polymer solutions of series 5 and 6 result in some 30− 40% re-duction of the frictional drag (see Table 3.2), while the shear viscosity remainsrelatively low. Effectiveness of PEO as a drag reducing agent is well studied anddocumented [19, 54]. Elastic polymers such as PEO produce drag reduction bysuppressing the production of turbulence [88, 107, 108]. The spanwise fluctuationcomponent reduces significantly due to an elastic shielding effect, which results ina severe decrease of the turbulent stresses [87, 94]. Ultimately, this ends in reducedturbulent shear stress and intensity. The polymer chains orient themselves with thedirection of the shear; hence, it suppresses development of secondary flows.Sureshkumar et al. [97] showed drag-reducing fluid inhibits the production ofturbulence generating events in the buffer layer and also a reduced vorticity fluctu-ation, which has its root in enhanced extensional viscosity [94]. Stretching of theelastic polymer chains is linked to drag reduction [113, 115]: the stretching causesa reduction of momentum flux from the bulk flow to the wall [86, 118]. Compar-ing the results of the PEO polymers with those of water, we might argue that thesecondary flows and the large-scale turbulent structures (coherent structures, andvortical activities), which are progressively suppressed by increased PEO concen-tration, have a non-negligible effect on mass and momentum transfer between thefluids at the interface.Series 7 and 8 were both in the fully eccentric annulus and both gave incom-plete displacement. This is interesting in that series 8 has τw/τy ≈ 1, but stillincomplete displacement. The only significant difference between series 7 and 8with series 1 and 3 is the change in eccentricity from 0.7 to 1. Such a seeminglysmall change results in significantly different outcomes. One possible cause is thereduced flow velocity and turbulence in the very narrow gap where the Carbopolgel is trapped. From a practical point of view, an eccentricity ≈ 1 presents signif-icant challenges for cementing operations. The use of centralizers in the field isless common for horizontal sections due to the risk of the casing sticking. With nocentralizers, an eccentricity of 1 is very likely and the results suggest that even infully turbulent flow mud removal in horizontal sections will be very difficult.The Reynolds number of the displacing fluid varies significantly in one ex-periment. In Equation (3.3) the Reynolds number varies with Dh and u, both ofwhich decrease as the displacement continues. Figure 3.13 shows the profile of44Figure 3.13: Reynolds number profiles of the displacing fluidsReynolds number versus h for each experiment. The decrease is notable: nearly a50% reduction for a change of h/Do from 0.5 down to zero. Except for series 5 and6 (polymer solutions of higher concentration), the Reynolds number for the othercases are all in the same range. These are clearly in the fully turbulent regime. Se-ries 5 and 6 have a significant difference in terms of Reynolds number. However,they both have similar displacement performance. We note that both fluids haveregistered the same pressure loss (see Table 3.2). Defining the Reynolds numberbased on a global variable, e.g. as in Equation (3.3), may not be the best wayto represent the complexity of flow in an eccentric annulus, where mixed regimeflows are possible [63, 78].Spatiotemporal plots of the average pixel intensities are given in Figure 3.14.As we discussed in previous sections, only series 1 has τw/τy > 1 and achievescomplete displacement. The spatiotemporal profiles reveal a notable change interms of the characteristics of the final stage of the displacement (i.e., the narrowgap). For the case where τw/τy > 1 the Carbopol gel yields throughout the exper-45iment and the displacement is seen to be more or less continuous in the directionof the flow. When τw/τy < 1, the average stress at the interface is not sufficientto keep the Carbopol layer yielded and moving, in this case, there is no longer asteady movement of the Carbopol in the narrow side. The gel breaks at differentpositions along the axis of the annulus. We see that the final dark fronts in series2-4 have a jagged profile reflecting this method of removal. Before this we observeintermittent but coherent waves in the spatiotemporal plots.Spatiotemporal plots for the 3 series with PEO (series 4, 5 and 6) are alsoshown in Figure 3.14. The last two show an incomplete displacement while thefirst case displaces completely. For the data of series 4, similar attributes to those ofdisplacement with water are observed. In this case, the degree of drag reduction islow, and hence, large-scale turbulent structures are still dominant. An irregular in-terface also marks the final stage of the displacement. The spatiotemporal of series5 and 6 (and also series 7 and 8 in the full eccentric annulus) show unsuccessfuldisplacements. Similar to the data of Figure 3.6, the tests reach a steady-statewhere the colormaps become approximately invariant in time. A notable differ-ence in the spatiotemporal plots of series 4 and 5 compared to the other cases isthe absence of ripple-like bands. A plausible explanation for that could be that theaddition of drag-reducing polymer suppresses the production of turbulent kineticenergy, and as a result, inhibits large turbulent structures in the flow: the wave-likebehaviour vanishes.The spatiotemporal profile across the height of the pipe (i.e., we average alongthe pipe), is reported in Figure 3.15. The profiles in the vertical direction, asopposed to the axial direction, show the shape of the interface from an Eulerianperspective, although this does not correspond precisely with the measurement onewould obtain from a gap-averaged 2D simulations [63], similar qualitative infor-mation is gained. The key feature of all the displacements is that the narrow gapis displaced after the wide gap. Alternatively, spatiotemporal profiles of Figure3.15 are analogous to the data of Figure 3.7 where h is the binarized form spa-tiotemporal of Figure 3.15 The lag (i.e., the time difference between the front inthe narrow gap and the wide gap) varies from 20 seconds up to infinity in the caseof incomplete displacement. If we multiply the time lag by the wide gap veloc-ity, an estimate of the interface elongation is obtained. Figure 3.15 also confirms46Figure 3.14: Spatiotemporal profiles of the normalized pixel intensity for all8 experimentsthat wide gap displacement is fast and not very dependent on the choice of thedisplacing fluid.3.3 Conclusions and DiscussionThe results of eight displacement experiments in an eccentric horizontal annuluswere presented. In the experiments, water or low concentrations of polyethyleneoxide polymer (PEO) was the displacing fluid, while the displaced fluid was al-ways a Carbopol solution of varying yield-stress (concentration). The PEO so-lutions showed significant reduced pressure drops compared to the water, whenpumped at similar flow rates, giving evidence that they are affecting the turbulencesignificantly at these flow rates.In terms of displacement performance, all the tests were unsteady (i.e., wide47Figure 3.15: Spatiotemporal profiles of the normalized pixel intensity for all8 experimentsgap front velocity was higher than that of the narrow gap). Indeed, the wide sidedisplacement was rapid and advective, over in 1-3 seconds, while the narrow sidedisplacement took 20 seconds or more (incomplete displacement). In the config-uration with an eccentricity of 1, it was almost impossible to displace the gelledfluid completely. On the other hand, in a partially eccentric annulus, full displace-ment was achieved, albeit only using water and not the higher concentrations ofpolymer.In terms of the importance of flow turbulence, it was shown to be an essentialfactor in removal of the gelled liquid. A comparison of the displacement perfor-mance of the polymer solutions with that of water at the same flow rate showeda significant difference. We have argued that the development of the secondaryflows of the second type as well as suppression of flow turbulence by the polymer48additives were the two major contributing factors for the observed differences. Es-timates of the interfacial stresses generally lie below the yield stress following theinitial front passing on the wide side. Thus, yielding of the gelled layer appears torely on transmission of normal stresses across the interface. This feature and thedunelike structures observed resemble variations along T/NT layers that have beenobserved elsewhere [72].The eventual removal of the narrow side fluid is not continuous and smooth inthe cases where water is used. Instead chunks break from the layer, are lifted intothe wide side stream and advected downstream/broken further by turbulent eddies.Similar breaking mechanisms are found in the ripped-type displacements of Albaet al. [4], also using Carbopol and water in a pipe geometry, although there is noturbulent free stream to wash away the chunks. There are also numerous studies ofindustrial cleaning (of e.g. biofilms, healthcare or food products), using turbulentwater flow in pipes/ducts [22, 38] that show similar phenomenology.49Chapter 4A Comparative Study ofLaminar-Turbulent Displacementin Eccentric Annulus UnderImposed Flow Rate ConditionsThe previous chapter was explicitly focused on fully turbulent displacing fluids.However, in practice, it is more likely that primary cementing displacement flowsin horizontal wells fall into mixed or laminar flow regimes. In this chapter, welook into two degrees of eccentricity in a horizontal casing (i.e., fully eccentric and70% eccentric) and experimentally investigate whether flow regime influences theoutcome of mud displacement at a constant imposed flow rate in the absence ofany stabilizing buoyancy effect (i.e., isodensity fluids).As mentioned in Chapter 1, it is normally expected that turbulent flow of pre-flushes (spacers or washes) improves the displacement efficiency in mud removaland cement placement through producing a flatter fluid velocity profile, turbulenteddies and pressure fluctuations, as well as the faster increase in the pressure gra-dient with the flow rate in turbulent flow compared to laminar flow [52, 56, 75, 93].While some recent studies have questioned the validity of this preference and sug-gested that certain flow conditions should be satisfied for turbulent displacement to50outperform laminar displacement [53, 63, 76].On the other hand, it was discussed that the eccentricity of the annulus is oneof the most critical parameters affecting the effectiveness of displacement flowsduring primary cementing [76]. It is important to realize that the extent of annuluseccentricity can dominate any other effects. The extent of eccentricity is rarelyreported in well cementing jobs in the literature and site reports. There is no rou-tinely applied post-placement test that monitors eccentricity throughout the lengthof the annulus, nor is there any persistent regulation on mechanical design and doc-umentation of the centralization program, particularly external to the operator orservice company. This lack of documentation makes it hard to assess the actualannulus eccentricities in primary cementing jobs. As suggested in Chapter 2, ourexperimental setup is capable of simulating wells with a full range of eccentricityvalues. Therefore, for the sake of studying the effect of eccentricity, we chose toset the extent of annulus eccentricity in this series of experiments to e = 1 (i.e.,fully eccentric) and e = 0.7 (i.e., strongly eccentric annulus, standoff 30%).Another important set of parameters affecting the displacement in the primarycementing procedure is the pumping rates, as well as fluid density and rheology.As previously mentioned, these experiments are performed using isodensity fluids.The results of fluid rheology and pumping rate measurements at both eccentricitiesare presented in more details in sections 4.1.1 and 4.1.2, respectively.A version of this chapter is presented in OMAE2020 conference [33].4.1 Experimental MethodsThe experimental setup is as described in Chapter Rheological Properties of Test FluidsThe dynamics of the fluid displacement flow in the annulus are affected by therheological properties and relative densities of fluids involved. This influence isespecially crucial for the local fluid dynamics at the interface of displaced anddisplacing fluids. In primary cementing, the drilling mud is usually highly viscous,and therefore, considering pumping limitations, is commonly pumped in laminarregime. Thus, there is more focus on identifying the ”right” spacer fluid relative to51Figure 4.1: Shear rheology data of Carbopol (fitted model coefficients arereported in Table 4.1)the mud. For laminar and mixed regimes, fluid rheology is one of the most criticalparameters affecting the quality of primary cementing.In the experiments of this chapter, Carbopol solution (a viscoplastic fluid) withconstant composition is displaced by water (a Newtonian fluid) and different com-positions of Xanthan solutions (power law fluids). The rheological properties ofthe fluids involved are measured using a Malvern Kinexus rheometer and are listedin Table 4.1. As shown in Figures 4.1 and 4.2, the rheological parameters of Car-bopol and Xanthan were determined by analyzing the flowcurve data and fittingthem to Herschel-Bulkley and power law models, respectively. All samples werepre-sheared in the rheometer before data acquisition.52Figure 4.2: Shear rheology data of Xanthan (fitted model coefficients are re-ported in Table 4.1)4.1.2 Scope of ExperimentsThe ranges of flow conditions and measured average pressure drops for both dis-placed and displacing flows are summarized in Table 4.2. We study fluid-fluiddisplacement flows under a constant nominal flow velocity (i.e., an imposed flowrate of ≈ 70l/min). Note that Q1 is the flow rate of displaced fluid (fluid 1, Car-bopol) before switching the pneumatic valves and displacing fluid entering the testsection. The set flow rate was the lowest attainable flow rate by the pumps.As listed in Table 4.1 and discussed in the previous section, a constant compo-sition of Carbopol solution was used as the displaced fluid, while four fluids withdifferent compositions and properties were investigated as the displacing medium.At a constant imposed flow rate, these combinations of fluids represent a wide53Experiment e Fluid Description Fluid τy (Pa) κ (Pa.sn) n1 1.0 Displacing Water − 1.002x10−3 1Displaced Carbopol (0.125%) 5.41 2.46 0.492 1.0 Displacing Xanthan (0.5%) − 1.18 0.36Displaced Carbopol (0.125%) 5.73 2.54 0.493 1.0 Displacing Xanthan (0.25%) − 0.3 0.5Displaced Carbopol (0.125%) 6.56 4.54 0.444 1.0 Displacing Xanthan (0.125%) − 0.11 0.56Displaced Carbopol (0.125%) 6.85 3.54 0.465 0.7 Displacing Water − 1.002x10−3 1Displaced Carbopol (0.125%) 5.2 2.34 0.496 0.7 Displacing Xanthan (0.5%) − 1.16 0.36Displaced Carbopol (0.125%) 5.23 3.42 0.417 0.7 Displacing Xanthan (0.25%) − 0.32 0.49Displaced Carbopol (0.125%) 5.04 3.59 0.408 0.7 Displacing Xanthan (0.125%) − 0.07 0.67Displaced Carbopol (0.125%) 4.98 4.78 0.38Table 4.1: Rheological properties of test fluidsrange of flow parameters, covering from a highly turbulent high Reynolds numberdisplacement to transitional and high Reynolds laminar displacements.The significant drop in the recorded pressure drops in the test section, which isalso shown in Figure 4.3, is associated with the difference in the rheology of bothfluids in each of the experiments. The abrupt change in ∆P/∆L implies that a largeportion of the displaced fluid in the annulus is removed quickly by the displacingfluid, resulting in fast transition of the pressure drop from fluid 1 (displaced fluid)to approximately that of fluid 2 (displacing fluid).Figure 4.4, on the other hand, focuses on the variations of the pressure dropassociated with the displacing fluid during the displacement process. It can be seenthat the fluctuations in the registered pressure drops are more significant during theslower part of the displacement. Also note that decreasing the eccentricity from 1.0to 0.7 results in an increase of frictional pressure drop (see Table 4.2), an aspectalso documented in the previous experiments in Chapter 3.54Figure 4.3: Recorded pressure drop profiles for each experiment - ∆P/∆L forboth Fluids 1 and 24.2 Experimental ResultsIn this section, the experimental results of fully eccentric geometry (e = 1.0) arereported and then they are compared to the outcomes of the partially eccentricarrangement (approximately 70% eccentric).4.2.1 Fully Eccentric (e = 1.0)Figure 4.5 and 4.6 show the illustrations of turbulent and laminar displacementsfrom t = 1s to t = 30s after the displacing fluid is introduced into the flow loopthrough experiments 1 and 2, respectively. Beyond t = 30s, the displacement in-terface does not change appreciably with time. In the first four experiments, theannulus is fully eccentric with inner pipe resting on the bottom of the annulus.55Figure 4.4: Recorded pressure drop profiles for each experiment - ∆P/∆L fordisplacing fluids onlyNote that only half of the annulus is shown in these figures, the narrow side is onthe bottom of the annulus. The displaced and displacing fluids are coloured blackand white, respectively.At each instant through the experiment, the bulk velocity of fluid i (i.e., eitherdisplaced or displacing fluid) is computed using the following equation:ui =QAi(4.1)where Q is the flow rate that is reported by the flowmeters and Ai denotes thecross-section that is occupied by the fluid. Here the flow cross-sectional areas areestimated using the average displaced fluid’s height estimated from analysis of thesnapshots of the displacement.56Experiment e Q1(litre/min) Q2(litre/min) (∆P∆L )1(kPa/m) (∆P∆L )2(kPa/m)1 1.0 69.3 74.4 17.3 1.42 1.0 71.1 72.1 18.5 3.83 1.0 68.7 71.0 23.4 2.54 1.0 72.2 73.5 22.3 1.95 0.7 70.9 70.8 20.5 1.66 0.7 72.8 73.4 18.2 4.37 0.7 71.4 70.1 27.3 2.48 0.7 72.0 75.5 23.3 2.1Table 4.2: Flow rates (liters/min) and pressure drops (kPa/m) associated witheach experimentTo quantitatively compare the effectiveness of various displacing fluid can-didates in Table 4.1, Figure 4.8 demonstrate changes in the non-dimensionaldisplaced fluid heights (i.e., h/Do) and Figure 4.9 compares estimated volumet-ric efficiency (η) over the displacement phase, respectively. The trends of non-dimensional displaced fluid heights can be translated to represent the efficiency ofdisplacement in a concentric annulus (i.e., 1−h/Do); but considering the eccentricarrangement of the annulus in this series of experiments, they cannot be interpretedsimilarly. Considering h/Do ratio in an eccentric annulus, the volumetric efficiencyshall be underestimated, as the narrow gap volume is much smaller than the widegap and the narrow side of the annulus is where the displaced fluid becomes static.Figure 4.7 schematically shows the method of measuring the cross-sectional areaof the annulus which is occupied by each fluid. The volumetric efficiency is thencalculated using Equation (4.2).η(t) =A2(t)A(4.2)where A2 is the area that is occupied by the displacing fluid (fluid 2) and A is thetotal area of the annulus.In terms of h, about 25−55% of Carbopol is un-displaced. However, the esti-mated volumetric efficiency is in the range of 70−95%. Note that the above defi-nition of displacement efficiency might be deceptive, in that 95% efficiency gives57Figure 4.5: Displacement of Carbopol with water in turbulent regime - Fullyeccentrica biased impression of how effective a displacement has been, despite of havingsignificant displaced fluid left behind on the narrow side of the annulus. In prac-tice, a residual mud channel allows for severe well leakage through gas invasionand leakage pathways that can also develop in residual well layers [104, 117].In general, the characteristics of the flow depend on the Reynolds number.Here, the Reynolds number (Re) is calculated using the generalized Reynolds num-ber equation (Equation (4.3)) valid for power-law fluids [59] and is defined basedon the fluid’s mean bulk velocity (ui) and its calculated hydraulic diameter (Dh,i),both changing as the displacement proceeds. These are defined by:Re =ρui2−nDnh,iκ((3n+1)/(4n))n8n−1(4.3)Dh,i =4AiPwet,i(4.4)where Ai is the area occupied by the fluid and Pwet,i is the wetted perimeter of thefluid, including the interface.The results of the determination of the Reynolds number are shown in Figure4.10. The range of resultant Reynolds number experienced in each case varies due58Figure 4.6: Displacement of Carbopol with Xanthan solution in laminarregime - Fully eccentricFigure 4.7: Schematic representation of calculating Carbopol layer thicknessand volumetric efficiencyto changes in flow velocity and hydraulic diameter. It can be observed that theflow regime is laminar for displacement of Carbopol with 0.5% Xanthan solution(experiment 2), while displacements of Carbopol with 0.25% and 0.125% Xanthansolutions (experiments 3 and 4) are transitional and low Reynolds turbulent, respec-tively. In the case of displacement of Carbopol with water (experiment 1) however,59Figure 4.8: Displacement performance: Average measured thickness of theCarbopol layer in fully eccentric annulusthe displacing flow is turbulent. Despite the change in flow regime from laminarand transitional in the case of experiments 2 and 3 to turbulent in the case of experi-ments 1 and 4, the displacement does not appear to be effective, as the Carbopol onthe narrow side barely moves. Although the displacement is of course improvedin case of experiment 1, which appears to be due to achieving highly turbulentregime, the displacement has deteriorated in case of experiment 4 in comparisonto experiments 2 and 3, despite its turbulent nature. Before analyzing the displace-ment efficiency in more detail, we note that none of the displacement outcomescould be considered successful. The common understanding that a turbulent flowspreads around the annulus and delivers a more effective displacement is not foundto be true in such fully eccentric annuli.Also, as shown in Figures 4.5 and 4.6, the distinction between the displace-60Figure 4.9: Displacement performance: Computed volumetric efficiency infully eccentric annulusment mechanisms involved in laminar and turbulent displacements can be observedat the interface between the two fluids. The interface is relatively smooth at lowerReynolds numbers (Figure 4.6) compared to that at higher Reynolds numbers (Fig-ure 4.5). In turbulent displacement, as shown in Figure 4.5, the instantaneousstreamwise shear-layer exhibits a wavy pattern between the non-turbulent and tur-bulent parts of the flow, contrary to the case in Figure 4.6. This flow pattern mightbe caused by the large scale flow structures that are typically found in turbulentplane Couette flow experiments [55] and simulations [8, 103].Regardless of the interfacial differences in laminar and turbulent shear-layers,all displacement scenarios investigated in this analysis are unsteady in the sensethat the interface proceeds faster on the wide side and slower on the narrow side.This leads to accumulation of highly viscous high yield stress Carbopol solutions61Figure 4.10: Computed Reynolds number for displacing fluid in fully eccen-tric annuluson the narrow side. In an ideal displacement, it is aimed to avoid leaving mudbehind through reducing the viscosity of the displaced fluid and enhancing turbu-lence, or increasing the viscoplastic stresses of the displacing fluid.As previously discussed, the other key parameter in achieving adequate ce-menting job is having sufficient stresses generated by the displacing fluid. Theaverage wall shear stress generated by the displacing fluid flow at the inner andouter walls of the annulus, as well as the interface of two fluids was calculatedfrom pressure drop measurements using the following equation:τw,2 =Dh,24∆P∆L(4.5)obtained from the equilibrium of forces over the duct, assuming that the displaced62fluid layer at the bottom of the annulus can be considered stationary at each instantthrough the experiment. The calculated average shear stress of displacing fluid(w,2)for each experiment was then normalized with the measured displaced fluid’syield stress (y,1). Figure 4.11 is of particular interest. It indicates that τw,2/τy,1 > 1does not ensure an effective displacement in highly eccentric annular configura-tion. Note that the value of shear stress on the inner and outer walls of the annulusdepend on the radius ratio and eccentricity, and its absolute value increases in theregion of small cross-sectional area. This increase is known to be more significantcloser to the inner wall [80]. In the current configuration of the experimental appa-ratus and measurement devices, it is not possible to characterize these variations inthe local shear stresses and frictional factors. Regardless, these experiments sug-gest that the resultant viscoplastic stresses of displacing fluid is of great importancein understanding the displacement. As shown in Figure 4.11, 0.5% Xanthan so-lution, used in experiment 2, generated higher wall shear stress in comparison tomore dilute Xanthan solutions in experiments 3 and 4. Under this circumstances,comparing experiments 2 to 4, 0.5% Xanthan solution despite of its laminar natureperformed better in removal of Carbopol in the course of displacement (see Figure4.8).4.2.2 Partially Eccentric (e = 0.7)In this series of experiments, the previous four experiments in fully eccentric ar-rangement are repeated in a partially eccentric geometry with eccentricity of 0.7.Figures 4.12 and 4.13 present snapshots of the displacements of Carbopol by water(turbulent flow) and 0.5% Xanthan solution (laminar flow), respectively, at varioustimes during the first 30 seconds immediately after switching the pneumatic valves.As shown in Figures 4.14 and 4.15, in regards to the non-dimensional dis-placed fluid heights (i.e., h/Do) and volumetric efficiencies (η), we observed sim-ilar relative trends as the first four experiments with an overall improvement in theefficiency of displacement and a reduction in average height of the residual layerin partially eccentric experiments compared to fully eccentric cases.We also see that similar to the displacements in fully eccentric arrangement, alarge portion of the Carbopol inside the annulus is displaced within the first few63Figure 4.11: Time evolution of non-dimensional ratio of displacing fluidshear stresses to displaced fluid yield stress through the displacementphase - Fully eccentricseconds. Through this initial displacement phase, the volumetric efficiencies ofall experiments are within the same range regardless of the extent of eccentricity.However, as mentioned, the volumetric efficiency of the partially eccentric exper-iments eventually increases past those of fully eccentric, indicating facilitation ofremoval of static fluid from the narrow side of the annulus with a decrease in thedegree of eccentricity.As shown in Figure 4.16, these experiments, similar to fully eccentric ones,represent a wide range of flow parameters. As a result of having a less eccentric an-nulus, the velocity profile should be slightly more uniform in annular cross-section,but still similar flow regimes are found for the different displacing fluid candidates.We observe that the flow regime for the displacing fluid is turbulent in experiment64Figure 4.12: Displacement of Carbopol with water in turbulent regime - Par-tially eccentric (e = 0.7)Figure 4.13: Displacement of Carbopol with Xanthan solution in laminarregime - Partially eccentric (e = 0.7)5 transitioning to partially turbulent in experiments 6 and 7 and high Reynoldslaminar in experiment 8. The details on how to calculate the Reynolds number forpower law fluids were explained in section 4.2.1. Comparing experiments 5-8 to1-4, the displacement regimes remain relatively unchanged and almost the samebehavior is seen with respect to the effect of flow regime on the displacement effi-65Figure 4.14: Displacement performance: Average measured thickness of theCarbopol layer in partially eccentric annulus (e = 0.7)ciencies. Turbulent displacement in the case of experiment 5 is the most effectivedisplacement scenario; however, comparing experiments 6-8, the displacement hasdeteriorated despite transitioning from laminar displacement in experiment 6 tohigher Reynolds displacements in experiments 7 and 8. As a result, it can be seenthat even at eccentric arrangement (e = 0.7), the highly viscous displacing fluidat laminar (or even high Reynolds laminar) displacement outperforms other lessviscous transitional or low Reynolds turbulent displacements. Overall, despite thechanges in the flow regime from turbulent to laminar and transitional, it appearsthat the displacement outcome is only marginally influenced by the displacementregime.Similar to the previous section, the average shear stress induced by the dis-placing fluid on the walls and fluid-fluid interface is presented in Figure 4.17, in66Figure 4.15: Displacement performance: Computed volumetric efficiency inpartially eccentric annulus (e = 0.7)which it has become non-dimensional through being divided by the yield stress ofthe displaced fluid. Considering the displacement efficiencies presented in Figure4.15 and comparative study of average shear stresses of displacing fluids in Figure4.17, it appears that increasing the viscosity of the displacing fluid, while keepingthe viscosity and yield stress of the displaced fluid unchanged, brings about an im-provement in the efficiency of displacement (compare experiments 6-8 for variousXanthan solutions). On the other hand, a lower flow rate leads to a flatter velocityprofile for the displacing fluid across the annular gap. Such velocity profiles mightbe more productive for removing the displaced fluid from the narrow gap and thewalls of the annulus. However, the distinct effect of each of these factors cannot bedistinguished through this set of experiments.In addition to affecting the displacement efficiency, the extent of eccentric po-67Figure 4.16: Computed Reynolds number for displacing fluid in partially ec-centric annulus (e = 0.7)sitioning of the casing pipe affects the annular pressure drop. The annular pressuredrops for both fluids are lower in the experiments at partially eccentric annulus ascompared to those in fully eccentric arrangement. As per the reported pressuredrops in Table 4.2, the increase in the annular frictional pressure drop caused bythe decrease in eccentricity from 1.0 to 0.7 is more pronounced for a yield-stressdisplaced fluid than they are for Newtonian or power law displacing fluids.In summary, the displacement efficiency is improved by reduction in the eccen-tricity of the casing. However, according to some industrial guidelines, a minimumeccentricity of 25% to 33% (20% for cementing liners) should be maintained inorder to achieve good quality of cementing [68, 76]. Maintaining sufficient ec-centricity is technically more challenging in horizontal and deviated wells than invertical wells.68Figure 4.17: Time evolution of non-dimensional ratio of displacing fluidshear stresses to displaced fluid yield stress through the displacementphase - Partially eccentric (e = 0.7)4.3 Conclusions and DiscussionThis chapter presented an experimental investigation of the effect of flow regime ondisplacement efficiency of a variety of spacer-mud displacement flows in a horizon-tal annular duct, covering the range from laminar to fully turbulent in an imposedflow rate condition. The outcomes of experiments suggest that turbulent displace-ment does not necessarily outperform laminar displacement, when pumped at thesame flow rate. This widely accepted understanding needs reconsiderations andfurther clarification.As we have shown in our experiments, there is no definite indication that higherReynolds number displacement yields improved results in a cementing process. Inthe experiments with various compositions of Xanthan solutions displacing the69same Carbopol composition, the highly viscous displacing fluid in lower Reynoldsnumber flow (i.e., displacement with 0.5% Xanthan solution) delivered more ef-ficient displacement compared to its higher Reynolds number displacements withother concentrations of Xanthan solutions. This improvement of the cementing jobis due to increasing the resultant stresses exerted by displacing fluid. On the otherhand, the highly turbulent displacement flow, achieved using water as the displac-ing fluid, rather outperformed all the other case scenarios. It is believed that com-parisons should be made within the context of operational constraints in respectto frictional pressure regardless of displacement flow regime. Accordingly, theseexperiments are to be repeated at imposed total frictional pressure drop condition.The displacement scenarios discussed above are all considered as unsteady,meaning that the fluid-fluid displacement interface is faster on the wide side ofthe annular geometry compared to its narrow side. This difference in interfacialvelocity leads to elongation of the interface and accumulation of displaced fluid(fluid 1) that is left behind on the narrow side of the annulus. Three different direc-tions may be pursued to enhance the efficiency of the displacement process in animposed flow rate condition: i) reduce the viscosity of the displacing fluid and en-hance turbulence, ii) reduce the extent of eccentricity in the annular geometry andiii) increase the shear stresses of the displacing flow through increasing viscosityand yield stress of the displacing fluid in laminar and transitional flow conditions.However, in regards to reducing the viscosity of displacing fluid to achieve turbu-lence rather than by increasing the flow rate, there is a risk of channeling and thusreducing the displacement efficiency, as we saw earlier in this chapter.In addition, on examining the 2D snapshots of the interface between the dis-placed and displacing fluids, differences are observed in displacement patternsin various flow regimes. This subject can be further investigated using more so-phisticated optical techniques, such as Particle Image Velocimetry (PIV) or LaserDoppler Anemometry (LDA).70Chapter 5A Comparative Study ofLaminar-Turbulent Displacementin Eccentric Annulus UnderImposed Pressure DropConditionsAs previously discussed in Chapter 1, it is important to consider that the design ofthe displacement process (including both displaced and displacing fluids) is gov-erned by the pore pressure and the formation fracture pressure, also known as thepore-frac envelope. This means that if the frictional pressure drop falls beyond thebounds of the pore-frac envelope (e.g. pumping a highly viscous spacer at a largeflow rate), the fluid can fracture the wellbore formation or alternately allow an in-flux resulting in fluid contamination. Which of these is more likely depends onthe operation, but in either case an accurate examination of bottomhole pressure isnecessary for well control and achieving successful well cementing through estab-lishment of the constraints for frictional pressure drop through the annulus. Thismeans that a minimum fluid density is required for well control during and afterplacement, and fluid rheology dictates the frictional pressure drop during place-71Figure 5.1: Pressure plot for intermediate casing cement job [76]ment. A typical cementing of an intermediate casing string, with its maximum andminimum hydrostatic pressures, is illustrated in Figure 5.1 [76].Therefore, in order to conduct a more realistic analysis in comparing flowregimes and fluid designs, we keep the pumping capacity constant. More specifi-cally, in this chapter, following up on the work presented in Chapter 4, we imposethat the total frictional pressure drop generated by the displacing fluid over thelength of the experimental setup should be about 4.3− 4.5kPa/m. Four experi-ments are discussed which were conducted to investigate the role of flow regimeunder a constant imposed pressure drop in the absence of any stabilizing buoyancyeffect (i.e., isodensity fluids). Different flow regimes (laminar to fully turbulentflow regimes) are investigated by changing the physical properties and flow ratesof testing fluids.5.1 Experimental MethodsThe experimental setup is as described in Chapter 2.72Figure 5.2: Shear rheology data of Carbopol (fitted model coefficients arereported in Table 5.1)5.1.1 Rheological Properties of Test FluidsThe capacity of the system in each experiment is about 200 liters for each fluid. Forthe experiments presented in this chapter, similar to the previous chapters, the dis-placed fluid (or fluid 1) is always a Carbopol solution of 0.125% concentration. Asmentioned in Chapter 2.3, Carbopol EZ-2 polymer from Lubrizol Inc. is first mixedwith water in a concentrated un-neutralized batch of ≈ 40 liters overnight and thenthis mixture is neutralized using NaOH at a ratio of 1/3.5 grams of NaOH to thatof Carbopol. This neutralization ratio is determined to achieve a pH between 6.5to 7.5 and build rather high yield stresses. The mixture is then diluted in the con-73Figure 5.3: Shear rheology data of Xanthan (fitted model coefficients are re-ported in Table 5.1)tainment tank to 200 liters and then circulated through the experimental flow loopfor minimum 45 minutes to have a homogeneous solution. The main advantage ofusing Carbopol as the displaced fluid is that its shear rheology is representative ofdrilling muds in primary cementing operations.Four low-viscosity fluids with different rheological properties are listed in Ta-ble 5.1, which are either water or different concentrations of Xanthan-water so-lutions. Table 5.1 summarizes the displaced and displacing fluid pairs used inthis set of experiments, as well as their fitted rheological parameters. These fourdisplacing fluids represent a wide range of displacement flow parameters, rangingfrom laminar displacement to highly-turbulent high-Reynolds displacement.74Experiment e Fluid Description Fluid τy (Pa) κ (Pa.sn) n1 0.7 Displacing Water − 1.002x10−3 1Displaced Carbopol (0.125%) 5.21 3.46 0.402 0.7 Displacing Xanthan (0.5%) − 1.16 0.36Displaced Carbopol (0.125%) 5.23 3.42 0.413 0.7 Displacing Xanthan (0.25%) − 0.28 0.49Displaced Carbopol (0.125%) 5.25 3.77 0.394 0.7 Displacing Xanthan (0.125%) − 0.08 0.61Displaced Carbopol (0.125%) 5.2 4.46 0.35Table 5.1: Rheological properties of test fluidsRheological characteristics of the test fluids were determined using a high-resolution Malvern Kinexus rheometer, further discussed in Section 2.3. Fluidsamples of both displaced and displacing fluids were collected just before switch-ing the pneumatic valves. The properties of fluids were measured immediatelyafter each experiment. In order to eliminate wall slip effects, a roughened parallelplate geometry was used for measuring the rheological properties of the Carbopolmixtures. While, a cone and plate geometry was used for studying the rheologyof the Xanthan-water solutions considering the low-viscosity nature of these non-Newtonian solutions. For the range of shear rates encountered in this experimentalstudy, the power law model (per Equation (5.1)) was fitted to the apparent viscos-ity data of displacing fluid (Xanthan), while the displaced fluid (Carbopol) adheresto Herschel-Bulkley rheological model (per Equation (5.2)).τ = κγ˙n (5.1)τ = τy+κγ˙n (5.2)In these equations, τ is the shear stress (Pa), τy is the yield stress (Pa) (if appli-cable), κ is the consistency index (Pa.sn) and n is the flow behavior index. Figures5.2 and 5.3 illustrate the rheograms of Carbopol and Xanthan solutions used inthis study, respectively.75Experiment Q1(litre/min) Q2(litre/min) (∆p∆l )1(kPa/m) (∆P∆L )2(kPa/m)1 124.6 126.4 28.8 4.42 72.8 73.4 18.2 4.33 91.5 89.9 27.7 4.44 122.5 125.1 18.9 4.5Table 5.2: Flow rates (liters/min) and pressure drops (kPa/m) associated witheach set of experiments5.1.2 Scope of ExperimentsIn this set of experiments, the flow rates are established for different displacingfluids to achieve almost the same frictional pressure drops of 32− 34 kPa acrossthe 7.5 m length of the experimental flow loop (equivalent to 4.3−4.5kPa/m).Table 5.2 summarizes the flow conditions under which the displacement ex-periments were taken place. The flow rate of displaced fluid (fluid 1) is presentedas Q1 which is measured just before switching the pneumatic valves and displac-ing fluid entering the test section in the flow loop. The measured average pressuredrops for both fluids are also reported in the Table 5.2. Figure 5.4 presents therecorded pressures before and through the experiment. Note that the significantchange in the pressure drops upon switching to the displacing fluid reflects thedifference in the rheological properties of the fluids involved.5.2 Experimental ResultsBefore analyzing various displacement scenarios and their associated efficiencies,we begin by presenting the displacement snapshots for experiments 1 and 2 inFigures 5.5 and 5.6, respectively. Experiments 1 and 2 represent turbulent andhigh Reynolds laminar displacements in constant pressure drop conditions alongthe annulus from t = 1s to t = 30s after the displacing fluid is introduced into theflow loop. The details on how to interpret the snapshots, together with the errorsassociated with our method of analysis were explained in sections 3.2 and 4.2.1 inthe previous chapters.In the interest of discussions on flow regimes, it should be noted that Reynolds76Figure 5.4: Recorded pressure drop profiles for each experiment - ∆P/∆L forboth Fluids 1 and 2number is the primary factor in analyzing the flow regime and behavior in any typeof flow when there is considerable velocity gradient (i.e., shear) involved, which isthe case in such displacement scenarios. Considering that Xanthan solution exhibitpower-law fluid behavior, Reynolds number (Re) is calculated using the general-ized Reynolds number equation (Equation (5.3)) [59]. Note that the fluid’s meanbulk velocity (ui) and its hydraulic diameter (Dh,i from equation (5.4)) vary duringthe displacement phase. Calculated Reynolds number for displacing fluid in allexperiments is shown in Figure 5.7, in which the Reynolds number can be usedto approximately classify the displacement flow regime as laminar below 2000 andturbulent above 4000. Despite the changes in the flow regime from turbulent dis-77Figure 5.5: Displacement of Carbopol with water in turbulent regimeFigure 5.6: Displacement of Carbopol with Xanthan solution in laminarregimeplacement in experiment 1 (Figure 5.5) to high Reynolds laminar displacementin experiment 2 (Figure 5.6), the displacement outcome does not appear to havesignificant improvement and there is a residual Carbopol layer left behind.Re =ρui2−nDnh,iκ((3n+1)/(4n))n8n−1(5.3)78Figure 5.7: Computed Reynolds number for displacing fluidDh,i =4AiPw,i(5.4)where Ai is the area occupied by the fluid and Pw,i is the wetted perimeter of thefluid, including the interface.To compare the displacing candidates in Table 5.1 more precisely, it is custom-ary in literature to study the displacement quality using non-dimensional displacedfluid height (i.e., h/Do) and volumetric efficiency η(t), which is the percentage ofmud (i.e., displaced fluid or fluid 1) that is displaced. Mathematically, it is equiva-lent to Equation (5.5).η(t) =A2(t)A(5.5)where A2 is the area that is occupied by the displacing fluid (fluid 2) and A is the79total area of the annulus.Note that the above definition of displacement efficiency might be deceptive,due to the fact that the volume of annulus is smaller on the narrow side. Thereforewhen fluid 1 on the wide side of annulus is displaced, the magnitude of displace-ment volumetric efficiency grows rapidly. In which case, the displaced fluid mightbe left behind in the narrow gap, but that will not be detected, because the volumeof narrow gap is small and does not affect displacement volumetric efficiency con-siderably. Nevertheless, it is important to note that a residual mud channel is one ofthe most influential sources of prospective well leakage problems. For instance, ina partially eccentric annulus with e = 0.7, the narrowest quartile of annulus has avolume about 5 times smaller than that of the widest quartile. This number furtherdecreases to more than 10 times smaller, if the annulus is fully eccentric. This isparticularly of concern in highly eccentric arrangements, because in such geome-try, the volumetric efficiency can reach as high as 80−90%, even if a residual mudlayer is still left on the narrow side. In fact, this is the case for the displacementexamples shown in Figures 5.8 and 5.9.Figure 5.8 plots the non-dimensional displaced fluid height (i.e., h/Do) as afunction of time (t), while Figure 5.9 presents the volumetric efficiency η duringthe displacement phase for all four displacing fluids. Despite the fact that the vol-umetric efficiency values are as high as 80−90%, none of the experiments can beconsidered successful.Comparing volumetric efficiency values, we observe that the best score is forwater in experiment 1, then the other three experiments with various concentra-tions of Xanthan solutions as displacing fluid yield almost the same displacementresults in the case of constant pressure drop conditions in the annulus. This is inter-esting, because it appears that the laminar displacement (experiment 2) performedalmost equally good as the low Reynolds turbulent displacements (experiments 3and 4). More critically, water (displacing fluid) in experiment 1 which is flowingin turbulent regime did not displace Carbopol (i.e., displaced fluid or drilling mud)on the narrow side during the recorded displacement phase of the experiment andthe efficiency grows only as high as 92% (see Figure 5.9). The above observationsillustrate that the notion that ”turbulent flow cementing yields improved results andreduces the amount of remedial work required” [16] needs some modifications.80Figure 5.8: Displacement performance: Average measured thickness of theCarbopol layer in an imposed pressure drop conditionAlso, still missing in this study is presentation of viscous shear stress generatedby various displacing fluid candidates. Figure 5.10 shows the calculated averageshear stress for displacing fluid which is normalized with the measured displacedfluid’s yield stress. In all the four experiments, the average viscous shear stressexceeds the recorded yield stress of the displaced fluid (τw/τy > 1); however, aresidual Carbopol layer is left behind at the narrow side of the annulus. Studiessuch as Zare et al. [117] and Allouche et al. [6] show that wherever the local vis-cous shear stress of the displacing fluid does not overcome the yield stress of thedisplaced fluid, a residual mud layer is left behind. It is important to understandthat, in a highly eccentric annular geometry similar to this set of experiments, thelocal displacement flow regime and viscous shear stresses vary on a single sectionof the annulus. For example, the flow can be laminar or even static on the nar-81Figure 5.9: Displacement performance: Computed volumetric efficiency inan imposed pressure drop conditionrow side and turbulent on the wide side, and local shear stress is a function of thelocal flow velocity which is lower on the narrow side of the annulus compared toits wide side. Accordingly, in order to achieve an effective displacement flow, theshear stress on the narrow side of the annulus, rather than the average shear stress,should exceed the yield stress of the displaced fluid.Despite the lower viscosity of 0.125% Xanthan solution in experiment 4, com-pared to higher concentrations of Xanthan solutions in experiments 2 and 3, thedisplacement with 0.125% Xanthan solution has resulted in slightly higher mea-sured ∆P/∆L and calculated τw/τy. This is due to its higher flow rate which hasalso increased the average Reynolds number of the displacing fluid and resultedin low Reynolds turbulent flow regime in experiment 4. One effect of turbulencein comparison to a laminar flow is that the velocity profile, and hence wall shear82Figure 5.10: Time evolution of non-dimensional ratio of displacing fluidshear stresses to displaced fluid yield stress through the displacementphasestress, vary less along the boundary. However, note that the outcomes of thesethree experiments (experiments 2 to 4) are pretty much the same in terms of theirdisplacement efficiencies. This may seem intuitive, but bear in mind that one ofthe strategies for enhancing mud displacement quality in an annular geometry thatis often cited in literature is to use a low viscous preflush in order to achieve tur-bulent displacement in the annulus. Comparison of experiments 2− 4 disprovesthis idea to be applicable at all times. In Chapter 4, we presented more examplescontradicting this generic statement.835.3 Conclusions and DiscussionThis chapter presented four experiments at 70% eccentric annular geometry un-der imposed pressure drop conditions, in a range of flow regimes. We exploreddisplacement scenarios to determine whether the displacing flow regime has anyimpact on the quality of displacement. In particular, we investigated if the notionof turbulent displacement is always preferred than laminar is always applicable.Our analysis shows that the effect of annulus eccentricity dominates the out-come of displacement, regardless of displacement flow regime. All the experimentsconsistently confirmed that in a strongly eccentric annulus (0.7 for the case of theseexperiments), displacement of a yield stress displaced fluid is generally unsuccess-ful, regardless of displacing flow regime. Further study of other eccentricity valuesis recommended in future.Comparing experiments 2-4 with various concentrations of Xanthan solutionsas displacing fluids, there is no clear indication that turbulent displacement outper-forms laminar displacement in imposed pressure drop conditions. On the contrary,we showcased that in these three experiments that highly viscous laminar displace-ment flow (experiment 2) achieved almost the same displacement efficiency com-pared to other two experiments with lower viscous displacing fluids, flowing athigher Reynolds, partially turbulent flow regimes.We feel the value of the experiments presented in this chapter, as well as theprevious chapters, is not particularly in the experiments performed, as arguablyslightly different experimental conditions might favour particular fluid and dis-placement flow design strategies. We see the contribution in convincing other re-searchers and field engineers, that although industrial practice prefers simple andgeneric rules/statements, aiming for turbulent flow regime as being the ”better”strategy does not always benefit the displacement. This is an area where designengineers need to spend more effort on each specific well to consider all the designparameters involved, before making a design decision.84Chapter 6Conclusions6.1 Conclusions and Relevance of Results to CementingOperationIn this thesis, we performed a series of experiments that were aimed at simulatingthe performance of both Newtonian and non-Newtonian preflushes. Our objec-tive was to gain insight into the mechanism of mud removal and study the role offlow regime in regards to displacement flows of yield stress fluids in an eccentrichorizontal annuli. The results revealed several exciting features of relevance towellbore cementing.First, in a fully eccentric annulus, displacement becomes significantly chal-lenging, this is no surprise as previous studies all have indicated eccentricity is thenumber one factor leading to poor fluid displacement. The industry’s practice isto use centralizers, which are cylindrical springs fitted to the outside of the casingto help reduce the eccentricity. However, there is often reluctance to use central-izers in the horizontal section of a well: running centralizers into the horizontalsection is technically challenging due to high friction with the borehole wall andthe potential for the casing to stick or even buckle. In the horizontal section, it isnot far from reality to assume a fully eccentric annulus. Even if a centralizer isused every 50-100 meters, the chances that the casing sags in between and resultsin an eccentricity of 1 are high. As we have seen, such high eccentricities presentchallenges for cement placement around the full circumference of the casing.85Second, considering the outcome of experiments presented in Chapter 3, turbu-lence contributes to fluid removal and can potentially provide better displacementof a mud layer. The mechanism by which turbulence helps fluid removal is a com-bination of secondary flows and large-scale turbulent structures interacting withthe narrow side layer. Our comparisons with the ineffective PEO washes illustrateclearly the role played by turbulence. However, in Chapter 4, we compared theeffectiveness of different preflushes (i.e., water and various concentrations of Xan-than solutions) at displacing the mud (i.e., Carbopol). A series of experiments wereperformed at a constant imposed flow rate (or pump capacity), achieving a range offlow regimes by application of various displacing fluids. Our analysis showed thatthe effect of flow regime becomes very minimal in the range of weak turbulent andhigh Reynolds laminar flow regimes, with laminar displacement flow marginallyoutperforming weak turbulent and transitional displacement flows. Similarly, inChapter 5, we repeated the experiments in Chapter 4, but under a constraint totalfrictional pressure drop, i.e., mimicking the real constraints in a cementing job byremaining within a required pressure range of avoiding influx as well as formationfracture. These experiments also highlighted that the effect of flow regime becomesinsignificant in comparing laminar versus weak turbulent displacement flows.On the other hand, a key message for cementing operations from this study isthat the use of a Newtonian pre-wash for a ”difficult displacement” will result in anunsteady displacement, i.e., the rapid advance along the wide side. The unsteadynature of the process reduces the operator’s control over the process and makesthe mud interface detection much harder. The industry typically confirms displace-ment using visual methods (i.e., observing fluid returns at the surface). The use ofturbulent flow, as shown in this study, results in a very rapid displacement in thewide gap, which volumetric-wise constitutes a significant portion of the well. Butthere is always the danger of leaving behind a mud channel on the narrow side atthe time at which returns are observed at surface. These features and the dangers ofusing a wash have been highlighted before [39, 62], as well as the ineffectivenessof designs based on contact time requirements.The above makes it hard to say whether turbulent washes are advisable or not.The cement slurry itself is typically not in fully turbulent regime, so the questionis really whether a turbulent prewash or laminar viscous spacer produces better86effects? The modelling perspective is inconclusive [63], but ignores the secondaryflow effects observed in our experiments. On the other hand, if the Newtonian washitself creates the wide-side channel and narrow side static mud, perhaps a viscousspacer would remove it? In our experiments here we note that the Carbopol flowingalone (at eccentricity 0.7) was mobile on the narrow side, but only became staticas the wash by-passed and reduced the pressure gradients locally. In other words,the contrast in frictional pressure gradients leads to formation of the narrow sidechannel.We did not investigate the impact of buoyancy forces in this study. As shown byMaleki & Frigaard [61], buoyancy may be exploited to achieve steady displacementwhile turbulent, countering the effects of eccentricity. This is effective in verticalsections where buoyancy contributes to flow along the annulus. However, in ahorizontal section this effect is absent. Indeed since washes are typically also lessdense than the mud, buoyancy pushes washes towards the top of the annulus. Thishas been recently studied by Bizhani & Frigaard [10].To summarize, if the goal is to achieve steady displacement, then the use ofturbulent flow in eccentric annulus in the absence of buoyancy stresses is not ad-vised. We did not find any consistent indication that turbulent displacement flowresults in better displacement quality compared to laminar displacement flow. Onthe contrary, we identified cases where displacing fluid with higher viscosity thatflows in laminar flow regime performs better than its turbulent low-viscous coun-terpart. If removal of the gelled and possibly dehydrated mud on the narrow sideof the annulus is concerned, then sustained turbulence could help in that regard.However, the use of lightweight low viscous washes may themselves contribute toformation of the gelled narrow side mud.6.2 Future DirectionsSome possible future directions, following the work done in this thesis, are asfollows.• While 3D computations of regularized viscoplastic fluid flows are viable,some care would be needed to consider the rheological closure most appro-priate for describing the sub-yield stress behaviour. Also these have only87been used (so far) for laminar flow computations.• In terms of future direction, the turbulent-non-turbulent (T/NT) layer anal-ogy would be interesting to explore further, both from an analytical/compu-tational perspective and experimentally.• Experimentally, our setup and the experiments reported were all focused atvisualization. To delve deeper we would need to establish permanent flowsand quantify the turbulent structures in the flowing part of the annulus. In-vestigation of this subject requires implementation of more sophisticated op-tical techniques, such as Particle Image Velocimetry (PIV) or Laser DopplerAnemometry (LDA). These are longer term perspectives and would be non-trivial experiments.88Bibliography[1] B. S. Aadnøy. Technology focus: Multilateral/extended-reach wells.Journal of Petroleum Technology, 67(5):114, 2015. → page 2[2] S. W. Ahn and K. C. Kim. Characteristics of turbulent flow in the annuliwith smooth and rough surfaces. Korean Society of Mechanical Engineers(KSME) International Journal, 13(2):183–190, 1999. → page 15[3] K. Alba, S. M. Taghavi, and I. A. Frigaard. Miscible density-stabledisplacement flows in inclined tube. Physics of Fluids, 24(12), 2012. →page 10[4] K. Alba, S. M. Taghavi, J. R. de Bruyn, and I. A. Frigaard. Incompletefluid–fluid displacement of yield-stress fluids. part 2: Highly inclinedpipes. Journal of Non-Newtonian Fluid Mechanics, 201:80–93, 2013. →pages 8, 49[5] K. Alba, S. M. Taghavi, and I. A. Frigaard. Miscible density-unstabledisplacement flows in inclined tube. Physics of Fluids, 25(6), 2013.[6] M. Allouche, I. A. Frigaard, and G. Sona. Static wall layers in thedisplacement of two visco-plastic fluids in a plane channel. Journal ofFluid Mechanics, 424:243–277, 2000. → pages 9, 10, 36, 81[7] N. J. Balmforth and R. V. Craster. A consistent thin-layer theory forbingham plastics. Journal of Non-Newtonian Fluid Mechanics, 84(1):65–81, 1999. → page 15[8] K. H. Bech, N. Tillmark, P. H. Alfredsson, and H. I. Andersson. Aninvestigation of turbulent plane couette flow at low reynolds numbers.Journal of Fluid Mechanics, 286:291–325, 1995.doi:10.1017/S0022112095000747. → page 6189[9] S. H. Bittleston, J. Ferguson, and I. A. Frigaard. Mud removal and cementplacement during primary cementing of an oil well – laminarnon-newtonian displacements in an eccentric annular hele-shaw cell.Journal of Engineering Mathematics, 43(2):229–253, 2002. → pagesiii, 9, 12[10] M. Bizhani and I. A. Frigaard. Buoyancy effects on turbulent displacementof viscoplastic fluids from strongly eccentric horizontal annuli. Physics ofFluids, October 2020. → page 87[11] M. Bizhani, Y. Foolad, and I. A. Frigaard. Turbulent displacement flow ofviscoplastic fluids in eccentric annulus: Experiments. Physics of Fluids, 32(4), 2020. doi:10.1063/5.0003518. → page 29[12] A. Blanco, V. Ciccola, and E. Limongi. Casing centralization in horizontaland highly inclined wellbores. 02 2000. doi:10.2523/59138-MS. → page 5[13] S. Bosworth, H. S. ElSayed, and G. Ismail. Key issues in multilateraltechnology. Oilfield Review, 1998. → pages xi, 2, 3[14] A. Bottiglieri, A. Brandl, R. Martin, and R. Prieto. Successful single-stagecementing in a weak formation: A case history in spain. 06 2014.doi:10.2118/169936-MS. → page 5[15] P. Bradshaw. Turbulent secondary flows. Annual Review of FluidMechanics, 19(1):53–74, 1987. doi:10.1146/annurev.fl.19.010187.000413.→ pages 13, 26[16] J. W. Brice and B. C. Holmes. Engineered casing cementing programsusing turbulent flow techniques. 1964. doi:10.2118/742-PA. → pages11, 14, 80[17] J. A. Brighton and J. B. Jones. fully developed turbulent flow in annuli.ASME Journal of Basic Engineering, 86(4):835–842, 1964.doi:10.1115/1.3655966. → page 10[18] E. S. Canada. Primary cementing: An industry recommended practice (irp)for the canadian oil and gas industry. 2017. → page 11[19] H. J. Choi and M. S. Jhon. Polymer-induced turbulent drag reduction.Industrial & Engineering Chemistry Research, 35(9):2993–2998, Jan 1996.doi:10.1021/ie9507484. → page 4490[20] S. Y. Chung, G. H. Rhee, and H. J. Sung. Direct numerical simulation ofturbulent concentric annular pipe flow. part 1: Flow field. InternationalJournal of Heat and Fluid Flow, 23(4):426–440, 2002. → page 10[21] C. R. Clark and G. L. Carter. Mud displacement with cement slurries.Journal of Petroleum Technology, 25(7):775–783, 2013;1973;. → pages14, 15[22] G. L. Cuckston, Z. Alam, J. Goodwin, G. Ward, and D. I. Wilson.Quantifying the effect of solution formulation on the removal of soft solidfood deposits from stainless steel substrates. Journal of Food Engineering,243:22–32, 2019. doi:10.1016/j.jfoodeng.2018.08.018. → page 49[23] C. B. da Silva and R. J. N. dos Reis. The role of coherent vortices near theturbulent/non-turbulent interface in a planar jet. PhilosophicalTransactions of The Royal Society of London. Series A: Mathematical,Physical, and Engineering Sciences, 369(1937):738–753, 2011. → page 36[24] C. B. da Silva, J. C. R. Hunt, I. Eames, and J. Westerweel. Interfacial layersbetween regions of different turbulence intensity. Annual Review of FluidMechanics, 46(1):567–590, 2014.doi:10.1146/annurev-fluid-010313-141357. → pages 35, 36[25] Y. J. Dai and C. X. Xu. Wall pressure and secondary-flow origination in asquare duct. Physics of Fluids, 31(8), 2019. → pages 13, 26[26] R. J. Davies, S. Almond, R. S. Ward, R. B. Jackson, C. Adams, F. Worrall,L. G. Herringshaw, J. G. Gluyas, and M. A. Whitehead. Oil and gas wellsand their integrity: Implications for shale and unconventional resourceexploitation. Marine and Petroleum Geology, 56:239–254, 2014. → page 8[27] M. B. Dusseault, R. E. Jackson, and D. Macdonald. Towards a road mapfor mitigating the rates and occurrences of long-term wellbore leakage.University of Waterloo, 2014. → page 8[28] S. Enayatpour and E. Van Oort. Advanced modelling of cementdisplacement complexities. 01 2017. doi:10.2118/184702-MS. → page 12[29] M. P. Escudier, I. W. Gouldson, and D. M. Jones. Flow of shear-thinningfluids in a concentric annulus. Experiments in Fluids, 18(4):225–238,1995. → page 2191[30] M. P. Escudier, S. Rosa, and R. J. Poole. Asymmetry in transitional pipeflow of drag-reducing polymer solutions. Journal of Non-Newtonian FluidMechanics, 161(1-3):19–29, 2009. → page 10[31] A. Etrati and I. A. Frigaard. Viscosity effects in density-stable miscibledisplacement flows: Experiments and simulations. Physics of Fluids, 30(12), 2018. doi:10.1063/1.5065388. → page 23[32] A. Etrati, K. Alba, and I. A. Frigaard. Two-layer displacement flow ofmiscible fluids with viscosity ratio: Experiments. Physics of Fluids, 30(5),2018. → page 10[33] Y. Foolad, M. Bizhani, and I. A. Frigaard. A comparative study oflaminar-turbulent displacement in eccentric annulus under imposed flowrate conditions. Fort Lauderdale, FL, USA., 2020. ISBNOMAE2020-18227. → page 51[34] A. Fredrickson and R. B. Bird. Non-newtonian flow in annuli. Industrialand Engineering Chemistry, 50(3):347–352, 1958. → page 11[35] I. A. Frigaard, S. Leimgruber, and O. Scherzer. Variational methods andmaximal residual wall layers. Journal of Fluid Mechanics, 483:37–65,2003. → page 9[36] C. Gabard and J. Hulin. Miscible displacement of non-newtonian fluids ina vertical tube. The European Physical Journal, Soft Matter and BiologicalPhysics, 11(3):231–241, 2003. → page 10[37] F. B. Gessner. The origin of secondary flow in turbulent flow along acorner. Journal of Fluid Mechanics, 58(1):1–25, 2006;1973;. → pages13, 26[38] K. Goode, G. Christian, and P. Fryer. Chapter 32: Improving the cleaningof heat exchangers. In H. Lelieveld, J. Holah, and D. Gabric´, editors,Handbook of Hygiene Control in the Food Industry, pages 465–489.Woodhead Publishing, San Diego, second edition edition, 2016. ISBN978-0-08-100155-4. doi:10.1016/B978-0-08-100155-4.00032-7. → page49[39] D. Guillot, J. Desroches, and I. A. Frigaard. Are preflushes reallycontributing to mud displacement during primary cementing? 02 2007.doi:10.2523/105903-MS. → pages 14, 27, 8692[40] D. Guillot, B. Froelich, E. Caceres, and R. Verbakel. Are current casingcentralization calculations really conservative? 2, Jan 2008.doi:10.2118/112725-MS. → pages xi, 5, 6[41] R. W. Hanks and W. F. Bonner. Transitional flow phenomena in concentricannuli. Industrial & Engineering Chemistry Fundamentals, 10(1):105–113, 1971. → page 11[42] A. Hasnain, E. Segura, and K. Alba. Buoyant displacement flow ofimmiscible fluids in inclined pipes. Journal of Fluid Mechanics, 824:661–687, 2017. → page 10[43] R. C. Haut and R. J. Crook. Primary cementing: the mud displacementprocess. Society of Petroleum Engineers, 1979. doi:10.2118/8253-MS. →page 12[44] L. Helms. Horizontal drilling. Department of Mineral Resources (DMR)Newsletter, 35(1). → page 2[45] G. Howard and J. Clark. Factors to be considered in obtaining propercementing of casing. Drilling and Production Practice API, page 257–272,1948. → page 12[46] C. K. Huen, I. A. Frigaard, and D. M. Martinez. Experimental studies ofmulti-layer flows using a visco-plastic lubricant. Journal ofNon-Newtonian Fluid Mechanics, 142(1-3):150–161, 2007. → page 36[47] A. Japper-Jaafar, M. Escudier, and R. Poole. Turbulent pipe flow of adrag-reducing rigid “rod-like” polymer solution. Journal ofNon-Newtonian Fluid Mechanics, 161(1):86–93, 2009. ISSN 0377-0257.doi:10.1016/j.jnnfm.2009.04.008. → page 10[48] A. Japper-Jaafar, M. P. Escudier, and R. J. Poole. Laminar, transitional andturbulent annular flow of drag-reducing polymer solutions. Journal ofNon-Newtonian Fluid Mechanics, 165(19-20):1357–1372, 2010. → page22[49] O. C. Jones and J. C. M. Leung. An improvement in the calculation ofturbulent friction in smooth concentric annuli. Journal of FluidsEngineering, 103(4):615–623, 1981. → page 15[50] H. C. Juvkan-Wold and J. Wu. Casing deflection and centralizer spacingcalculations. Society of Petroleum Engineers: Drilling Engineering, 121992. ISSN 0885-9744. doi:10.2118/21282-PA. → page 593[51] V. C. Kelessidis, A. Merlo, R. Rafferty, G. Borriello, and D. J. Guillot.Field data demonstrate improved mud removal techniques lead tosuccessful cement jobs. Society of Petroleum Engineers: AdvancedTechnology Series, 4(1):53–58, 1996. → pages 11, 12[52] F. C. Kettl, M. G. Edwards, and R. L. Covington. Practical horizontalcementing today. Society of Petroleum Engineers: Middle East Oil Show,(25546), 1993. → pages 15, 50[53] P. Khalilova, B. Koons, D. Lawrence, and A. Elhancha. Newtonian fluid incementing operations in deepwater wells: friend or foe? 09 2013.doi:10.2118/166456-MS. → pages 12, 51[54] C. A. Kim, J. H. Sung, H. J. Choi, C. B. Kim, W. Chun, and M. S. Jhon.Drag reduction and mechanical degradation of poly(ethylene oxide) inseawater. Journal of Chemical Engineering of Japan, 32(6):803–811, 1999.doi:10.1252/jcej.32.803. → page 44[55] O. Kitoh, K. Nakabyashi, and F. Nishimura. Experimental study on meanvelocity and turbulence characteristics of plane couette flow:low-reynolds-number effects and large longitudinal vortical structure.Journal of Fluid Mechanics, 539:199–227, 2005.doi:10.1017/S0022112005005641. → page 61[56] A. Lavrov, M. Torsæter, S. O. service), and S. ebooks Energy. Physics andmechanics of primary well cementing. Springer International Publishing,2016. ISBN 9783319431659. → pages 11, 12, 50[57] C. J. Lawn and C. J. Elliott. Fully developed turbulent flow throughconcentric annuli. Journal of Mechanical Engineering Science, 14(3):195–204, 1972. doi:10.1243/JMES JOUR 1972 014 027 02. → page 10[58] C. F. Lockyear and A. P. Hibbert. Integrated primary cementing studydefines key factors for field success. Journal of Petroleum Technology, 121989. ISSN 0022-3522. doi:10.2118/18376-PA. → page 11[59] K. Madlener, B. Frey, and H. Ciezki. Generalized Reynolds Number forNon-Newtonian Fluids, volume 1, pages 237–250. 09 2009. ISBN978-2-7598-0411-5. doi:10.1051/eucass/200901237. → pages 58, 77[60] A. Maleki and I. A. Frigaard. Primary cementing of oil and gas wells inturbulent and mixed regimes. Journal of Engineering Mathematics, 107(1):201–230, 2017. → pages 11, 13, 15, 16, 26, 28, 3494[61] A. Maleki and I. A. Frigaard. Turbulent displacement flows in primarycementing of oil and gas wells. Physics of Fluids, 30(12), 2018. → pagesiii, 11, 13, 14, 26, 28, 87[62] A. Maleki and I. A. Frigaard. Using lightweight or low viscosity preflushesfor primary cementing of surface casing. 37th International Conference onOcean, Offshore & Arctic Engineering., 2018. → pages 14, 34, 86[63] A. Maleki and I. A. Frigaard. Comparing laminar and turbulent primarycementing flows. Journal of Petroleum Science & Engineering, 177:808–821, 2019. → pages 12, 26, 38, 45, 46, 51, 87[64] A. Maleki Zamenjani. Annular displacement flows in turbulent and mixedflow regimes. PhD thesis, University of British Columbia, 2019. URLhttps://open.library.ubc.ca/collections/ubctheses/24/items/1.0374286. →pages xi, 4, 8[65] S. Malekmohammadi, M. Carrasco-Teja, S. Storey, I. A. Frigaard, andD. M. Martinez. An experimental study of laminar displacement flows innarrow vertical eccentric annuli. Journal of Fluid Mechanics, 649:371–398, 2010. doi:10.1017/S0022112009993508. → page 12[66] C. Mason. Technology focus. Journal of Petroleum Technology, 60(5):74,2008. → page 2[67] R. H. McLean, C. W. Manry, and W. W. Whitaker. Displacementmechanics in primary cementing. Journal of Petroleum Technology, 19(2):251–260, 2013;1967;. → pages 9, 11[68] S. A. McPherson. Cementation of horizontal wellbores. Society ofPetroleum Engineers: Drilling Engineering, January 1 2000.doi:10.2118/62893-MS. → page 68[69] M. A. Moyers-Gonzalez and I. A. Frigaard. Kinematic instabilities intwo-layer eccentric annular flows. part 1: Newtonian fluids. Journal ofEngineering Mathematics, 62(2):103–131, 2008. → page 8[70] M. A. Moyers-Gonzalez and I. A. Frigaard. Kinematic instabilities intwo-layer eccentric annular flows. part 2: shear-thinning and yield-stresseffects. Journal of Engineering Mathematics, 65(1):25–52, 2009. → page 8[71] M. A. Moyers-Gonzalez, I. A. Frigaard, and C. Nouar. Nonlinear stabilityof a visco-plastically lubricated viscous shear flow. Journal of FluidMechanics, 506:117–146, 2004. → page 3695[72] V. D. Narasimhamurthy, H. I. Andersson, and B. Pettersen. Novel featuresof a fully developed mixing-layer between co-flowing laminar and turbulentcouette flows. Physics of Fluids, 26(3), 2014. → pages 16, 35, 43, 49[73] A. Negrao. Technology focus. Journal of Petroleum Technology, 65(5):66,2009. → page 2[74] A. Negrao. Technology focus. Journal of Petroleum Technology, 66(5):130, 2014. → page 2[75] E. B. Nelson. Well cementing, volume 28. Elsevier, New York, NY, USA,1990. ISBN 0444887512. → pages 15, 50[76] E. B. Nelson and D. Guillot. Well cementing. Schlumberger, Sugar Land,Tex, 2nd edition, 2006. ISBN 0978853008. → pagesxiii, xviii, 9, 12, 51, 68, 72[77] N. Nikitin and A. Yakhot. Direct numerical simulation of turbulent flow inelliptical ducts. Journal of Fluid Mechanics, 532:141–164, 2005. → page16[78] N. Nikitin, H. Wang, and S. Chernyshenko. Turbulent flow and heattransfer in eccentric annulus. Journal of Fluid Mechanics, 638:95–116,2009. → pages 16, 40, 42, 45[79] J. M. Nouri, H. Umur, and J. H. Whitelaw. Flow of newtonian andnon-newtonian fluids in concentric and eccentric annuli. Journal of FluidMechanics, 253:617–641, 1993. doi:10.1017/S0022112093001922. →pages 16, 32[80] F. Ogino, T. Sakano, and T. Mizushina. Momentum and heat transfers fromfully developed turbulent flow in an eccentric annulus to inner and outertube walls. Wa¨rme- und Stoffu¨bertragung (Zeitschrift. 1968), 21(2-3):87–93, 1987. → page 63[81] S. Pelipenko. Two-dimensional computational simulation of eccentricannular cementing displacements. IMA Journal of Applied Mathematics,69(6):557–583, 2004. → page 12[82] S. Pelipenko and I. A. Frigaard. Visco-plastic fluid displacements innear-vertical narrow eccentric annuli: prediction of travelling-wavesolutions and interfacial instability. Journal of Fluid Mechanics, 520:343–377, 2004. → pages 8, 13, 2596[83] S. Pelipenko and I. A. Frigaard. Mud removal and cement placementduring primary cementing of an oil well. part 2; steady state displacements.Journal of Engineering Mathematics, 48(1):1–26, 2004.doi:10.1023/B:ENGI.0000009499.63859.f0. → pages 12, 13, 26[84] F. T. Pinho and J. H. Whitelaw. Flow of non-newtonian fluids in a pipe.Journal of Non-Newtonian Fluid Mechanics, 34(2):129–144, 1990. →page 10[85] R. J. Poole. Development-length requirements for fully developed laminarflow in concentric annuli. Journal of Fluids Engineering, 132(6), 2010. →page 22[86] I. Procaccia, V. S. L’vov, and R. Benzi. Colloquium: Theory of dragreduction by polymers in wall-bounded turbulence. Reviews of ModernPhysics, 80(1):225–247, 2008;2007;. → page 44[87] P. K. Ptasinski, F. T. M. Nieuwstadt, B. H. A. A. Van Den Brule, and M. A.Hulsen. Experiments in turbulent pipe flow with polymer additives atmaximum drag reduction. Flow, Turbulence and Combustion, 66(2):159–182, 2001. doi:10.1023/A:1017985826227. → page 44[88] P. K. Ptasniski, B. J. Boersma, F. T. M. Nieuwstadt, M. A. Hulsen, B. H.A. A. Van Den Brule, and J. C. R. Hunt. Turbulent channel flow nearmaximum drag reduction: simulations, experiments and mechanisms.Journal of Fluid Mechanics, 490:251–291, 2003. → page 44[89] A. Quarmby. An experimental study of turbulent flow through concentricannuli. International Journal of Mechanical Sciences, 9(4):205–221, 1967.→ page 11[90] K. Rehme. Turbulent flow in smooth concentric annuli with small radiusratios. Journal of Fluid Mechanics, 64(2):263–288, 1974.doi:10.1017/S0022112074002394. → page 10[91] J. Ruszka. Technology focus. Journal of Petroleum Technology, 66(11):110, 2014. → page 2[92] K. C. Sahu, P. Valluri, P. D. M. Spelt, and O. K. Matar. Linear instability ofpressure-driven channel flow of a newtonian and a herschel-bulkley fluid.Physics of Fluids, 19(12), 2007. → page 36[93] C. W. Sauer. Mud displacement during cementing state of the art. Journalof Petroleum Technology, 39(9):1091–1101, 1987. → pages 11, 5097[94] S. Sibilla and A. Baron. Polymer stress statistics in the near-wall turbulentflow of a drag-reducing solution. Physics of Fluids, 14(3):1123–1136,2002. doi:10.1063/1.1448497. → page 44[95] T. R. Smith. Cementing displacement practices field applications. Journalof Petroleum Technology, 42(5):564–629, 1990. → page 12[96] T. R. Smith and K. M. Ravi. Investigation of drilling fluid properties tomaximize cement displacement efficiency. Society of Petroleum Engineers,1991. doi:10.2118/22775-MS. → page 12[97] R. Sureshkumar, A. N. Beris, and R. A. Handler. Direct numericalsimulation of the turbulent channel flow of a polymer solution. Physics ofFluids, 9(3):743–755, Mar 1997. doi:10.1063/1.869229. → page 44[98] S. M. Taghavi and I. A. Frigaard. Estimation of mixing volumes in buoyantmiscible displacement flows along near-horizontal pipes. CanadianJournal of Chemical Engineering, 91(3):399–412, 2013. → pages 10, 15[99] S. M. Taghavi, K. Alba, and I. A. Frigaard. Buoyant miscible displacementflows at moderate viscosity ratios and low atwood numbers innear-horizontal ducts. Chemical Engineering Science, 69(1):404–418,2012.[100] S. M. Taghavi, K. Alba, M. Moyers-Gonzalez, and I. A. Frigaard.Incomplete fluid–fluid displacement of yield stress fluids in near-horizontalpipes: Experiments and theory. Journal of Non-Newtonian FluidMechanics, 167:59–74, 2012.[101] S. M. Taghavi, K. Alba, T. Seon, K. Wielage-Burchard, D. M. Martinez,and I. A. Frigaard. Miscible displacement flows in near-horizontal ducts atlow atwood number. Journal of Fluid Mechanics, 696:175–214, 2012. →pages 8, 10[102] B. Theron, D. Bodin, and J. Fleming. Optimization of spacer rheologyusing neural network technology. 02 2002. doi:10.2118/74498-MS. →page xviii[103] T. Tsukahara, H. Kawamura, and K. Shingai. Dns of turbulent couette flowwith emphasis on the large-scale structure in the core region. Journal ofTurbulence, 7:1–16, 01 2006. doi:10.1080/14685240600609866. → page6198[104] T. Vra˚lstad and R. Skorpa. Digital cement integrity: A methodology for 3dvisualization of cracks and microannuli in well cement. Sustainability, 12,05 2020. doi:10.3390/su12104128. → page 58[105] J. E. Walker and R. R. Rothfus. Transitional velocity patterns in a smoothconcentric annulus. AIChE Journal, 5(1):51–54, 1959.doi:10.1002/aic.690050112. → page 11[106] I. C. Walton and S. H. Bittleston. The axial flow of a bingham plastic in anarrow eccentric annulus. Journal of Fluid Mechanics, 222(1):39–60,1991;2006;. → page 15[107] M. D. Warholic, H. Massah, and T. J. Hanratty. Influence of drag-reducingpolymers on turbulence: effects of reynolds number, concentration andmixing. Experiments in Fluids, 27(5):461–472, 1999. → page 44[108] M. D. Warholic, D. K. Heist, M. Katcher, and T. J. Hanratty. A study withparticle-image velocimetry of the influence of drag-reducing polymers onthe structure of turbulence. Experiments in Fluids, 31(5):474–483, 2001.→ page 44[109] T. Watson and S. Bachu. Identification of wells with high co2 leakagepotential in mature oil fields developed for co2-enhanced oil recovery.Society of Petroleum Engineers, (112924), Apr 2008.doi:10.2118/112924-MS. → page 9[110] T. L. Watson. Surface casing vent flow repair: a process, Jul 2004. → page9[111] T. L. Watson and S. Bachu. Evaluation of the potential for gas and co2leakage along wellbores. Society of Petroleum Engineers, 24(1):115–126,2013;2009;. → page 9[112] J. Westerweel, C. Fukushima, J. M. Pedersen, and J. C. R. Hunt.Mechanics of the turbulent-nonturbulent interface of a jet. Physical ReviewLetters, 95(17), 2005. → page 35[113] C. M. White and M. G. Mungal. Mechanics and prediction of turbulentdrag reduction with polymer additives. Annual Review of Fluid Mechanics,40(1):235–256, 2008. → page 44[114] K. Wielage-Burchard and I. A. Frigaard. Static wall layers in plane channeldisplacement flows. Journal of Non-Newtonian Fluid Mechanics, 166(5):245–261, 2011. → page 999[115] L. Xi. Turbulent drag reduction by polymer additives: Fundamentals andrecent advances. Physics of Fluids, 31(12), 2019. → page 44[116] M. Zare and I. A. Frigaard. Buoyancy effects on micro-annulus formation:Density unstable newtonian–bingham fluid displacements in verticalchannels. Journal of Non-Newtonian Fluid Mechanics, 260:145–162,2018. → page 36[117] M. Zare, A. Roustaei, and I. A. Frigaard. Buoyancy effects onmicro-annulus formation: Density stable displacement ofnewtonian–bingham fluids. Journal of Non-Newtonian Fluid Mechanics,247:22–40, 2017. → pages 9, 58, 81[118] L. Zhu and L. Xi. Vortex dynamics in low- and high-extent polymer dragreduction regimes revealed by vortex tracking and conformation analysis.Physics of Fluids, 31(9), 2019. doi:10.1063/1.5118251. → page 44[119] J. Zuiderwijk. Mud displacement in primary cementation. Society ofPetroleum Engineers: European Spring Meeting, 29-30 May, Amsterdam,Netherlands, 1974. doi:10.2118/4830-MS. → page 15100Appendix AExperimental ProcedureA schematic view of the large-scale flow loop facility used in this study is shownin Figure A.1, while Figure A.2 and A.3 are actual images captured from theexperimental set-up.In this appendix, we present the experimental procedure step-to-step. It is rec-ommended that future operators of the set-up, read the entire experimental proce-dure in details before proceeding.Step 1: Experiments started by closing the drain valves of the positive dis-placement pumps and filling the 200 L capacity tanks with experimental fluids ofinterest and the required amount of water should be added to each tank to achievethe desired fluid dilutions, as follow:• Tank No. 1 (connected to Pump No. 1) to be filled out with the displacingfluid colored with a suitable amount of black dye for better contrast• Tank No. 2 (connected to Pump No. 2) to be filled out with the displacedfluid colored with a suitable amount of fluorescent dyeIn this experimental set-up, Pump No. 2 and Tank No. 2 are the ones closer tothe wall.Step 2: In this step, Pump No. 2 should be turned on by switching up thepower lever on the corresponding power handling box and starting the pump us-ing LabVIEW software. The user interface specifically arranged for these set of101Figure A.1: Schematic of the flow loopexperiments is shown in Figure A.4. The user should make sure that the com-puter is connected to the internet and then run the LabVIEW software using the”Run” switch on top left of the interface. The water and concentrated fluids arethen mixed in the set-up while the mixtures are circulated through the flow loopat high flow rates. The mixtures should be circulated for 45 minutes to achieve auniform concentration for both displaced and displacing fluids along the flow loop(which would eventually allow us to obtain constant fluid rheological propertiesfor both fluids).Step 3: In order to ensure proper function of the pressure transducer, it is im-portant to have no air bubbles stuck in its measurement lines. Therefore, uponturning on Pump No. 2, it is important to detach and reattach the pressure trans-102Figure A.2: Experimental flow loop - View 1ducer lines and have them filled out with water. Note that the first volume of fluidthat enters the annulus is water that has remained in the setup from the previousexperiment. That is why it is required to fill up the pressure transducer’s capillarieswith water at this point, specially for experiments involving yield stress fluids (i.e.,Carbopol).Step 4: The next critical task is to set-up the cameras and UV lights. Thedetails of cameras and UV lights that are used in our experiments are presented inCh. 2.• Camera No. 1 is FLIR Oryx 10Gig camera and Camera No. 2 is ProsilicaGT 4096 camera from AlliedVision in the following explanations.• Create separate folders for saving the images from each of the cameras.• Camera No. 1 is controlled using SpinView software installed from FLIRindustry platform (https://www.flir.ca/support-center), in which we should103Figure A.3: Experimental flow loop - View 2follow below steps:– Find and select Camera No. 1 on the top left menu.– Use camera live view switch for getting feedback while you are makingchanges to the settings of the camera. Note that the live view should beoff, while you are applying changes to the settings.– Adjust the focus quality of the camera using the quality of live viewimage near the edges of the outer pipe rather than focusing on the innerpipe.– Settings are assigned per experimental conditions and desired outcomes,but here is an example of set conditions for this camera:∗ Acquisition Control· Exposure Auto: Off104Figure A.4: LabVIEW software user interface· Exposure Time: about 20,000 µs (one of the factors affectingthe resultant maximum frame rate available)∗ Analog Control· Gain: about 20 dB· Gamma: 0.7 to 0.8∗ Image Format Control· Width· Height· OffsetX105Figure A.5: Configuration of cameras and UV lights with respect to the ob-servation window of interest· OffsetY· Pixel Format: Mono16 or Mono12p (affecting the frame rate)– Click on the “Recording” switch (red circle) on the top right toolbar.∗ Assign Filename: folder name + file name (i.e., “\Image”)∗ Either assign the number of frames to be captured, or set it as zerofor manual control over the number of frames to be captured.∗ Choose the desired image format (i.e., ”.tiff”)– Ready to start recording.• Camera No. 2 is controlled using Allied Vision software (https://www.alliedvision.com/en/support), in which we should follow below steps:– Find and select Camera No. 2 on the top left menu.– Use camera live view switch for getting feedback while you are makingchanges to the settings of the camera. Note that the live view should beoff, while you are applying changes to the settings.106– Adjust the focus quality of the camera using the quality of live viewimage near the edges of the outer pipe rather than focusing on the innerpipe.– Settings are assigned per experimental conditions and desired outcomes,but here is an example of set conditions for this camera:∗ Exposure Time: about 30,000 µs∗ Gain: about 20 dB∗ Gamma: about 0.6 to 0.7∗ Pixel Format: Mono12∗ Adjust location and size of frame– Assign the folder to save the images:∗ File→Allow 16-Bit Tiff Saving∗ File→Image Series Options (image format of “.tif”)– Ready to start recording.Step 5: After setting up the cameras and having them ready for recording,turn Pump No. 1 on by switching up the power lever on the correspondingpower handling box and starting the pump using LabVIEW software. Notethat Pump No. 1 is turned on with a delay compared to Pump No. 2, as thedisplacing fluids in these experiments were Newtonian fluids with no need tofurther pumping it through the bypass loop for mixing purposes (pre-mixed).Step 6: As previously mentioned in Ch.2, two pneumatic three-way valvesare incorporated in the set-up to change the flow path (i.e., switching fluidthat enters the test section). Pressurized air line is required for actuation ofair-controlled pneumatic valves. Accordingly, in this step, it is important toopen the pressurized air lines of the lab.Step 7: Before proceeding with the experiment, it is required to take samplesfrom test fluids at this stage.Step 8: After everything is set-up and sample fluids are taken, start recordingon both cameras and then switch two pneumatic control valves using switchbottom in LabVIEW software.107Step 9: When you are done with the experiment, stop recording images onboth cameras and wait for all images to get saved.Step 10: Turn off the cameras (Camera No. 2 is turned off by disconnectingits data acquisition cable), UV lights and pumps (using LabVIEW software)Step 11: Close the pressurized air line valve.Step 12: Open drain valves on the pumps and let the test fluids to drain asmuch as possible.Step 13: Fill up both tanks with water and rinse the set-up using the pumpsas much as required (the number of rinsing sequences depend on the fluidsinvolved).Step 14: Stop operating the pumps and then turn them off using their powerlever.Note that it is recommended to study the rheological properties of the fluidsinvolved as soon as possible, preferably on the same day as the experiment.108


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items