Steady Flow of a Cement Slurry

Understanding the rheological behavior of cement slurries is important in cement and petroleum industries. In this paper, we study the fully developed flow of a cement slurry inside a wellbore. The slurry is modeled as a non-linear fluid, where a constitutive relation for the viscous stress tensor based on a modified form of the second grade (Rivlin–Ericksen) fluid is used;we also propose a diffusion flux vector for the concentration of particles. The one-dimensional forms of the governing equations and the boundary conditions are made dimensionless and solved numerically. A parametric study is performed to present the effect of various dimensionless numbers on the velocity and the volume fraction profiles.

[1]  Quanhua Sun,et al.  On the Significance of Normal Stress Effects in the Flow of Glaciers , 1987, Journal of Glaciology.

[2]  Kazuo Yamada,et al.  Interaction between cement and chemical admixture from the point of cement hydration, absorption behaviour of admixture, and paste rheology , 1999 .

[3]  Yiqiu Tan,et al.  Rheology of fresh cement asphalt emulsion pastes , 2015 .

[4]  Bjørnar Lund,et al.  Annular displacement in a highly inclined irregular wellbore: Experimental and three-dimensional numerical simulations , 2019, Journal of Petroleum Science and Engineering.

[5]  Mehrdad Massoudi,et al.  A note on the meaning of mixture viscosity using the classical continuum theories of mixtures , 2008 .

[6]  Nathan Tregger,et al.  Influence of clays on the rheology of cement pastes , 2010 .

[7]  J. E. Dunn,et al.  Fluids of differential type: Critical review and thermodynamic analysis , 1995 .

[8]  V. Vand.  Viscosity of solutions and suspensions; theory. , 1948, The Journal of physical and colloid chemistry.

[9]  Ronald S. Rivlin,et al.  Further Remarks on the Stress-Deformation Relations for Isotropic Materials , 1955 .

[10]  Steven Wang,et al.  Acoustic Method for Determining the Static Gel Strength of Slurries , 1999 .

[11]  H. Van Damme,et al.  Gelation, Shear-Thinning and Shear-Thickening in Cement Slurries , 2004 .

[12]  Mehrdad Massoudi,et al.  Boundary conditions in mixture theory and in CFD applications of higher order models , 2007, Comput. Math. Appl..

[13]  Mehrdad Massoudi,et al.  Heat transfer analysis and flow of a slag-type fluid: Effects of variable thermal conductivity and viscosity , 2015 .

[14]  Mehrdad Massoudi,et al.  A Mixture Theory formulation for hydraulic or pneumatic transport of solid particles , 2010 .

[15]  Forrest J. Masters,et al.  A Multivariate Computational Framework to Characterize and Rate Virtual Portland Cements , 2018, Comput. Aided Civ. Infrastructure Eng..

[16]  R. Roscoe.  The viscosity of suspensions of rigid spheres , 1952 .

[17]  K. R. Rajagopal,et al.  Pulsatile Flow of a Chemically-Reacting Nonlinear Fluid , 2006, Comput. Math. Appl..

[18]  R. Probstein.  Physicochemical Hydrodynamics: An Introduction , 1989 .

[19]  Forrest J. Masters,et al.  Proficiency analysis of VCCTL results for heat of hydration and mortar cube strength , 2018 .

[20]  Pierre J. Carreau,et al.  Rheology of Polymeric Systems: Principles and Applications , 1997, Engineering Plastics.

[21]  J. M. Piau,et al.  Physicochemical study of the hydration process of an oil well cement slurry before setting , 1999 .

[22]  D. A. Stiles,et al.  Successful Cementing in Areas Prone to Shallow Saltwater Flows in Deep-Water Gulf of Mexico , 1997 .

[23]  Thierry Palermo,et al.  Rheological behaviour of cement and silica suspensions: Particle aggregation modelling , 2008 .

[24]  E. Worrell,et al.  Energy Efficiency Improvement and Cost Saving Opportunities for Cement Making. An ENERGY STAR Guide for Energy and Plant Managers , 2008 .

[25]  Stefan Z. Miska,et al.  On the Instability of the Cement/Fluid Interface and Fluid Mixing (includes associated erratum) , 2017 .

[26]  Jennifer A. Rice,et al.  Structural displacement measurements using DC coupled radar with active transponder , 2017 .

[27]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[28]  Mehrdad Massoudi,et al.  Flow of a generalized second grade fluid between heated plates , 1993 .

[29]  Bo Zhang,et al.  Numerical study on the pipe flow characteristics of the cemented paste backfill slurry considering hydration effects , 2019, Powder Technology.

[30]  Getting to the Root of Gas Migration , 1996 .

[31]  Nickolas J. Themelis,et al.  Management of Environmental Quality : An International Journal Use of waste derived fuels in cement industry : a review , 2016 .

[32]  Eric Murphy,et al.  The rheology of slurries of athermal cohesive micro-particles immersed in fluid: A computational and experimental comparison , 2019, Chemical Engineering Science.

[33]  Phillip Frank Gower Banfill,et al.  THE RHEOLOGY OF FRESH CEMENT AND CONCRETE - A REVIEW , 2003 .

[34]  Howard A. Barnes,et al.  The yield stress—a review or ‘παντα ρει’—everything flows? , 1999 .

[35]  Alireza Bahadori,et al.  Global strategies and potentials to curb CO2 emissions in cement industry , 2013 .

[36]  J. E. Dunn,et al.  Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade , 1974 .

[37]  Pierre J. Carreau,et al.  Review of some useful rheological equations , 1979 .

[38]  Jan Mewis,et al.  Colloidal Suspension Rheology: Preface , 2011 .

[39]  Andre Leibsohn Martins,et al.  On the Rheological Parameters Governing Oilwell Cement Slurry Stability , 2004 .

[40]  D. Bentz.  Three-Dimensional Computer Simulation of Portland Cement Hydration and Microstructure Development , 1997 .

[41]  J. R. Abbott,et al.  A constitutive equation for concentrated suspensions that accounts for shear‐induced particle migration , 1992 .

[42]  E. Garboczi,et al.  Computer simulation of the diffusivity of cement-based materials , 1992 .

[43]  Harald Justnes,et al.  Viscosity of Cement Slurries as a Function of Solids Content , 2005 .

[44]  X. Fenga,et al.  Prediction of Cement Physical Properties by Virtual Testing , 2003 .

[45]  Mehrdad Massoudi,et al.  Heat Transfer and Dissipation Effects in the Flow of a Drilling Fluid , 2016 .

[46]  John C. Slattery,et al.  Advanced transport phenomena , 1999 .

[47]  Michael J. Economides,et al.  Determining Wellbore Pressures in Cement Slurry Columns , 1993 .

[48]  Yubai Li,et al.  The effects of particle concentration and various fluxes on the flow of a fluid-solid suspension , 2019, Appl. Math. Comput..

[49]  Leslie J. Struble,et al.  Viscosity of Portland cement paste as a function of concentration , 1995 .

[50]  Michael A. Galler,et al.  Influence of particle size distributions on yield stress and viscosity of cement–fly ash pastes , 2012 .

[51]  Yulong Ding,et al.  Constitutive modelling of flowing granular materials: A continuum approach , 2004 .

[52]  Della M. Roy,et al.  Rheological properties of cement mixes: IV. Effects of superplasticizers on viscosity and yield stress , 1980 .

[53]  Jeffrey W. Bullard,et al.  Modeling and simulation of cement hydration kinetics and microstructure development , 2011 .

[54]  Phillip Frank Gower Banfill,et al.  USE OF A CONTROLLED STRESS RHEOMETER TO STUDY THE YIELD STRESS OF OILWELL CEMENT SLURRIES , 1991 .

[55]  Jon Elvar Wallevik,et al.  Thixotropic investigation on cement paste: Experimental and numerical approach , 2005 .

[56]  V. Marinkovič,et al.  Effect of Storage Time on the Rheological Behavior of Oil Well Cement Slurries , 1991 .

[57]  H. Barnes.  Thixotropy—a review , 1997 .

[58]  Phillip Frank Gower Banfill,et al.  The rheology of fresh concrete , 1983 .

[59]  M. Bellotto,et al.  Cement paste prior to setting: A rheological approach , 2013 .

[60]  Mehrdad Massoudi,et al.  A continuum model for granular materials: Considering dilatancy and the Mohr-Coulomb criterion , 2001 .

[61]  Nadine Aubry,et al.  Heat Transfer in a Drilling Fluid with Geothermal Applications , 2017 .

[62]  Chi-Sing Man,et al.  Nonsteady channel flow of ice as a modified second-order fluid with power-law viscosity , 1992 .

[63]  Liang Jin,et al.  Model for Predicting Wellbore Pressures in Cement Columns , 1989 .

[64]  Surendra P. Shah,et al.  Fresh and hardened properties of self-consolidating concrete , 2005 .

[65]  D. Wilson,et al.  Critical review: Injectability of calcium phosphate pastes and cements. , 2017, Acta biomaterialia.

[66]  Kenneth A. Snyder,et al.  Suspended hydration and loss of freezable water in cement pastes exposed to 90% relative humidity , 2004 .

[67]  Mehrdad Massoudi,et al.  On some generalizations of the second grade fluid model , 2008 .