Heat Transfer in a Drilling Fluid with Geothermal Applications

The effects of various conditions on the fluid flow, particle migration and heat transfer in non-linear fluids encountered in drilling and geothermal applications are studied. We assume that the drilling fluid is a suspension composed of various substances, behaving as a non-linear complex fluid, where the effects of particle volume fraction, shear rate, and temperature on the viscosity and thermal diffusivity are considered. The motion of the particles is described using a concentration flux equation. Two problems are studied: flow in a vertical pipe and flow between two (eccentric) cylinders where the inner cylinder is rotating. We consider effects of earth temperature, the rotational speed of the inner cylinder, and the bulk volume fraction on the flow and heat transfer.

[1]  J. Antaki,et al.  Study of blood flow in several benchmark micro-channels using a two-fluid approach. , 2015, International journal of engineering science.

[2]  M. Kaviany.  Principles of heat transfer in porous media , 1991 .

[3]  Thomas F. Irvine,et al.  Shear rate dependent thermal conductivity measurements of non-Newtonian fluids , 1997 .

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

[5]  Nadine Aubry,et al.  Heat transfer and flow of a dense suspension between two cylinders , 2017 .

[6]  A. Mujumdar,et al.  Heat transfer characteristics of nanofluids: a review , 2007 .

[7]  Teuku Meurah Indra Mahlia,et al.  Potential of geothermal energy for electricity generation in Indonesia: A review , 2016 .

[8]  W. Jones,et al.  The prediction of laminarization with a two-equation model of turbulence , 1972 .

[9]  Kumbakonam R. Rajagopal,et al.  Mechanics of Mixtures , 1995 .

[10]  A. J. Reynolds.  The prediction of turbulent Prandtl and Schmidt numbers , 1975 .

[11]  Ladislaus Rybach,et al.  Geothermal Power Growth 1995-2013-A Comparison with Other Renewables , 2014 .

[12]  H. Rusche.  Computational fluid dynamics of dispersed two-phase flows at high phase fractions , 2003 .

[13]  Tian-Jian Hsu,et al.  Schmidt number and near-bed boundary condition effects on a two-phase dilute sediment transport model , 2005 .

[14]  Tian-Jian Hsu,et al.  On modeling boundary layer and gravity‐driven fluid mud transport , 2007 .

[15]  Dennis A. Siginer,et al.  Flow of drilling fluids in eccentric annuli , 1998 .

[16]  Mehrdad Massoudi,et al.  Remarks on Constitutive Modeling of Nanofluids , 2012 .

[17]  Winslow H. Herschel,et al.  Konsistenzmessungen von Gummi-Benzollösungen , 1926 .

[18]  Joe D. Goddard,et al.  Experiments on the conductivity of suspensions of ionically‐conductive spheres , 1990 .

[19]  Tatjana Kaluđerović Radoičić,et al.  Hydrodynamic modeling of downward gas–solids flow. Part I: Counter-current flow , 2014 .

[20]  Goodarz Ahmadi,et al.  Brownian diffusion of submicrometer particles in the viscous sublayer , 1991 .

[21]  Nadine Aubry,et al.  Heat transfer in granular materials: effects of nonlinear heat conduction and viscous dissipation , 2013 .

[22]  Saeed Salehi,et al.  Characterization of drilling fluids filtration through integrated laboratory experiments and CFD modeling , 2016 .

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

[24]  Nadine Aubry,et al.  A numerical study of blood flow using mixture theory. , 2014, International journal of engineering science.

[25]  Josef Weber,et al.  Deep Geothermal Energy Production in Germany , 2014 .

[26]  Roland May,et al.  A generalized mathematical model to predict transient bottomhole temperature during drilling operation , 2016 .

[27]  Van Rijn,et al.  Sediment transport; Part I, Bed load transport , 1984 .

[28]  Ingo Müller,et al.  On the entropy inequality , 1967 .

[29]  Vikas Mahto,et al.  Rheological study of a water based oil well drilling fluid , 2004 .

[30]  D. Jeffrey,et al.  Conduction through a random suspension of spheres , 1973, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[31]  B. C. Meikap,et al.  Hydrodynamics of a multi-stage counter-current fluidized bed reactor with down-comer for amine impregnated activated carbon particle system , 2017 .

[32]  H. Rabia,et al.  Oilwell Drilling Engineering : Principles and Practice , 1986 .

[33]  G. Batchelor,et al.  Thermal or electrical conduction through a granular material , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[34]  Samuel R. Subia,et al.  Modelling of concentrated suspensions using a continuum constitutive equation , 1998, Journal of Fluid Mechanics.

[35]  John W. Lund,et al.  Direct utilization of geothermal energy. , 2010 .

[36]  D. Wilcox.  Formulation of the k-w Turbulence Model Revisited , 2008 .

[37]  S. Report,et al.  Handbook of Best Practices for Geothermal Drilling , 2010 .

[38]  Goodarz Ahmadi,et al.  Dispersion and deposition of Brownian particles from point sources in a simulated turbulent channel flow , 1991 .

[39]  J. C. Jaeger,et al.  Application of the Theory Of Heat Conduction to Geothermal Measurements , 2013 .

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

[41]  Maria Grazia De Giorgi,et al.  Horizontal Air-Ground Heat Exchanger Performance and Humidity Simulation by Computational Fluid Dynamic Analysis , 2016 .

[42]  Ravi Prasher,et al.  Dependence of Thermal Conductivity and Mechanical Rigidity of Particle-Laden Polymeric Thermal Interface Material on Particle Volume Fraction , 2003 .

[43]  Li Shao,et al.  Simulation of a domestic ground source heat pump system using a three-dimensional numerical borehole heat exchanger model , 2011 .

[44]  Yoshihide Tominaga,et al.  Turbulent Schmidt numbers for CFD analysis with various types of flowfield , 2007 .

[45]  G. Marrucci Allen.  Rheology of polymeric systems, principles and applications. By P. J. Carreau, D. C. R. De Kee, and R. P. Chhabra, Hanser/Gardner Publications, Cincinnati, OH, 1997, 520 pp., $197.50 , 1999 .

[46]  Mehdi Behzad,et al.  CFD–DEM approach to investigate the effect of drill pipe rotation on cuttings transport behavior , 2015 .

[47]  Mehrdad Massoudi,et al.  Viscosity and thermal conductivity of nanofluids containing multi-walled carbon nanotubes stabilized by chitosan , 2011 .

[48]  Simon J. Rees,et al.  A transient two-dimensional finite volume model for the simulation of vertical U-tube ground heat exchangers , 1999 .

[49]  Kuppalapalle Vajravelu,et al.  Peristaltic transport of a Herschel–Bulkley fluid in an inclined tube , 2005 .

[50]  Mehrdad Massoudi,et al.  Heat Transfer and Flow of Nanofluids in a Y-Type Intersection Channel with Multiple Pulsations: A Numerical Study , 2017 .

[51]  T. Papanastasiou.  Flows of Materials with Yield , 1987 .

[52]  O. K. Crosser,et al.  Thermal Conductivity of Heterogeneous Two-Component Systems , 1962 .

[53]  Wei-Tao Wu,et al.  Fully developed flow of a drilling fluid between two rotating cylinders , 2016, Appl. Math. Comput..

[54]  Li Wang,et al.  High temperature and high pressure rheological properties of high-density water-based drilling fluids for deep wells , 2012, Petroleum Science.

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

[56]  Diego González-Aguilera,et al.  Efficiency Analysis of the Main Components of a Vertical Closed-Loop System in a Borehole Heat Exchanger , 2017 .

[57]  Avinoam Nir,et al.  Viscous dissipation rate in concentrated suspensions , 1994 .

[58]  Y. S. Touloukian,et al.  Thermophysical properties of matter - the TPRC data series. Volume 10. Thermal diffusivity. (Reannouncement). Data book , 1974 .

[59]  Brian J. Briscoe,et al.  The properties of drilling muds at high pressures and high temperatures , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

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

[61]  Yuuml,et al.  Investigation of some physical and mechanical properties of concrete produced with barite aggregate , 2010 .

[62]  Ali Karimi Vajargah,et al.  Determination of drilling fluid rheology under downhole conditions by using real-time distributed pressure data , 2015 .

[63]  R. Winterton,et al.  Heat in History , 2001 .

[64]  James F. Antaki,et al.  An Anisotropic Constitutive Equation for the Stress Tensor of Blood Based on Mixture Theory , 2008 .

[65]  I. Krieger,et al.  Rheology of monodisperse latices , 1972 .

[66]  Arild Saasen,et al.  The Effect of Drilling Fluid Rheological Properties on Hole Cleaning , 2002 .

[67]  Samuel R. Subia,et al.  Particle migration in a Couette apparatus: Experiment and modeling , 1998 .

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

[69]  O. Ubbink.  Numerical prediction of two fluid systems with sharp interfaces , 1997 .

[70]  Andreas Jupke,et al.  Development of a CFD model for the simulation of a novel multiphase counter-current loop reactor , 2017 .

[71]  S. L. Soo,et al.  Fluid dynamics of multiphase systems , 1967 .

[72]  Mehrdad Massoudi,et al.  Modeling and numerical simulation of blood flow using the Theory of Interacting Continua. , 2012, International journal of non-linear mechanics.

[73]  Andreas N. Alexandrou,et al.  Steady Herschel–Bulkley fluid flow in three-dimensional expansions , 2001 .

[74]  Paul L. Younger,et al.  Geothermal Energy: Delivering on the Global Potential , 2015 .