Comprehensive Modeling of Precipitation and Fouling in Turbulent Pipe Flow

Supersaturation with respect to an active compound triggers several precipitation-related processes that may proceed (essentially concurrently) along the flow path. The interaction between fluid dynamics and physicochemical processes (i.e., nucleation, particle growth, and coagulation) leads to an axial variation of bulk properties (species concentration and particle size distribution) and of ionic and particulate deposition rates at the pipe wall. To simulate this complicated system, very simple hydrodynamics (plug flow) is combined with rather comprehensive modeling of physicochemical phenomena. Considerable effort is devoted to the optimization of computational requirements, thus developing a numerical algorithm efficient and flexible enough to cope with even more demanding future tasks such as the inclusion of mixing. The performance of the model is examined using, as a test case, the precipitation of a sparingly soluble salt under conditions typical for geothermal installations. An extensive study of the effects of the initial saturation ratio and of the tendency for particle coagulation on the deposition rate and on the particle size distribution along the pipe is carried out.

[1]  R. Thompson,et al.  Analysis of the formation of monodisperse populations by homogeneous nucleation , 1991 .

[2]  R. Phillips.  Calculation of multisphere linearized Poisson-Boltzmann interactions near cylindrical fibers and planar surfaces , 1995 .

[3]  E. Giannetti.  Nucleation mechanisms and particle size distributions of polymer colloids , 1993 .

[4]  Michael J. Hounslow,et al.  Aggregation during precipitation from solution. Kinetics for calcium oxalate monohydrate , 1997 .

[5]  Narayan S. Tavare,et al.  Mixing in continuous crystallizers , 1986 .

[6]  Thomas L. Theis,et al.  A Unified Kinetic Model for Particle Aggregation , 1996 .

[7]  John Garside,et al.  The concept of effectiveness factors in crystal growth , 1971 .

[8]  D. Saville,et al.  Electrostatic Interactions between a Nonuniformly Charged Sphere and a Charged Surface , 1995 .

[9]  P. Saffman,et al.  On the collision of drops in turbulent clouds , 1956, Journal of Fluid Mechanics.

[10]  On the modified gamma distribution for representing the size spectra of coagulating aerosol particles , 1985 .

[11]  S. Pratsinis,et al.  Gas phase production of particles in reactive turbulent flows , 1991 .

[12]  Michael A. Delichatsios,et al.  Particle coagulation in steady turbulent flows: Application to smoke aging , 1980 .

[13]  J. Seinfeld,et al.  Aerosol formation by rapid nucleation during the preparation of SiO2 thin films from SiCl4 and O2 gases by CVD process , 1991 .

[14]  René David,et al.  Crystallization and precipitation engineering—V. Simulation of the precipitation of silver bromide octahedral crystals in a double-jet semi-batch reactor , 1995 .

[15]  A. E. Nielsen,et al.  Electrolyte crystal growth kinetics , 1984 .

[16]  William H. Press,et al.  Numerical recipes , 1990 .

[17]  L. Spielman.  Viscous interactions in Brownian coagulation , 1970 .

[18]  Terry A. Ring,et al.  Fundamentals of crystallization: Kinetic effects on particle size distributions and morphology , 1991 .

[19]  J. Nývlt,et al.  The Kinetics of industrial crystallization , 1984 .

[20]  J. Villadsen,et al.  Solution of differential equation models by polynomial approximation , 1978 .

[21]  Menachem Elimelech,et al.  Particle Deposition and Aggregation: Measurement, Modelling and Simulation , 1995 .

[22]  S. Friedlander,et al.  Role of the electrical double layer in particle deposition by convective diffusion , 1974 .

[23]  A. Karabelas,et al.  Procedures for rapid calculation of the stability ratio of colloidal dispersions , 1991 .

[24]  S. Pratsinis.  Simultaneous nucleation, condensation, and coagulation in aerosol reactors , 1988 .

[25]  T. Dąbroś,et al.  On the convective diffusion of fine particles in turbulent flow , 1983 .

[26]  A. Karabelas,et al.  Crystallization and Deposit Formation of Lead Sulfide from Aqueous Solutions I. Deposition Rates , 1991 .

[27]  J. A. V. BUTLER,et al.  Theory of the Stability of Lyophobic Colloids , 1948, Nature.

[28]  A. Karabelas,et al.  SULFIDE SCALE FORMATION AND CONTROL: THE CASE OF LEAD SULFIDE , 1991 .

[29]  L. Scriven,et al.  Non-local free-energy density-functional theory applied to the electrical double layer , 1990 .

[30]  P. Wiersema,et al.  Effect of hydrodynamic interaction on the coagulation rate of hydrophobic colloids , 1971 .

[31]  A. B. Hedley,et al.  particle deposition behaviour from turbulent flows , 1984 .

[32]  Sotiris E. Pratsinis,et al.  Gas-phase manufacture of particulates: interplay of chemical reaction and aerosol coagulation in the free-molecular regime , 1989 .

[33]  René David,et al.  Modelling of agglomeration in industrial crystallization from solution , 1995 .

[34]  J. Israelachvili.  Intermolecular and surface forces , 1985 .

[35]  S. Pratsinis,et al.  The effect of ionic additives on aerosol coagulation , 1992 .

[36]  Piero M. Armenante,et al.  MASS TRANSFER TO MICROPARTICLES IN AGITATED SYSTEMS , 1989 .

[37]  W. Koch,et al.  The effect of particle coalescence on the surface area of a coagulating aerosol , 1990 .

[38]  S. Yuu.  Collision rate of small particles in a homogeneous and isotropic turbulence , 1984 .

[39]  W. Russel,et al.  The electrostatic repulsion between charged spheres from exact solutions to the linearized poisson-boltzmann equation , 1983 .

[40]  J. C. Barrett,et al.  Improving the accuracy of the moments method for solving the aerosol general dynamic equation , 1996 .

[41]  S. K. Friedlander,et al.  Behavior of suspended particles in a turbulent fluid , 1957 .

[42]  K. W. Lee,et al.  Conservation of particle size distribution parameters during Brownian coagulation , 1985 .

[43]  D. E. Rosner,et al.  Deposition rates from polydispersed particle populations of arbitrary spread , 1989 .

[44]  C. Megaridis,et al.  A Bimodal Integral Solution of the Dynamic Equation for an Aerosol Undergoing Simultaneous Particle Inception and Coagulation , 1990 .

[45]  Alan Jones,et al.  Mass transfer with chemical reaction and precipitation , 1991 .

[46]  A. Karabelas,et al.  Crystallization and deposit formation of lead sulfide from aqueous solutions: II. Morphology of the deposits , 1991 .

[47]  B. Dahneke.  Diffusional deposition of particles , 1974 .

[48]  R. Flagan,et al.  Simultaneous homogeneous nucleation and aerosol growth , 1984 .

[49]  M. Hounslow,et al.  Adjustable discretized population balance for growth and aggregation , 1995 .

[50]  J. Brock.  Simulation of Aerosol Dynamics , 1983 .

[51]  D. E. Rosner,et al.  Boundary layer coagulation effects on the size distribution of thermophoretically deposited particles , 1989 .

[52]  M. Seckler,et al.  INFLUENCE OF HYDRODYNAMICS ON PRECIPITATION: A COMPUTATIONAL STUDY , 1995 .

[53]  D. Prieve,et al.  The effect of a distribution in surface properties on colloid stability , 1982 .

[54]  Gruy,et al.  Turbulent Coagulation Efficiency , 1997, Journal of colloid and interface science.

[55]  J. Garside,et al.  Mixing, reaction and precipitation: Limits of micromixing in an MSMPR crystallizer , 1985 .

[56]  Michael J. Hounslow,et al.  Aggregation during Precipitation from Solution: A Method for Extracting Rates from Experimental Data , 1996 .

[57]  C. Zukoski,et al.  Uniform Silica Particle Precipitation : An Aggregative Growth Model , 1991 .

[58]  H. Brenner.  The slow motion of a sphere through a viscous fluid towards a plane surface , 1961 .

[59]  John Garside,et al.  Industrial crystallization from solution , 1985 .

[60]  Margaritis Kostoglou,et al.  Evaluation of Zero Order Methods for Simulating Particle Coagulation , 1994 .

[61]  Timothy C. Scott,et al.  Flocculation of paramagnetic particles in a magnetic field , 1995 .

[62]  O. Söhnel,et al.  Precipitation: Basic Principles and Industrial Applications , 1992 .

[63]  Margaritis Kostoglou,et al.  EVALUATION OF NUMERICAL METHODS FOR SIMULATING AN EVOLVING PARTICLE SIZE DISTRIBUTION IN GROWTH PROCESSES , 1995 .

[64]  F. Crundwell.  MICRO-MIXING IN CONTINUOUS PARTICULATE REACTORS , 1994 .

[65]  A. E. Nielsen.  DIFFUSION CONTROLLED GROWTH OF A MOVING SPHERE. THE KINETICS OF CRYSTAL GROWTH IN POTASSIUM PERCHLORATE PRECIPITATION , 1961 .

[66]  B. D. Bowen,et al.  Fine particle deposition in laminar and turbulent flows , 1995 .

[67]  Rodney O. Fox,et al.  PDF modeling of turbulent‐mixing effects on initiator efficiency in a tubular LDPE reactor , 1996 .

[68]  M. K. Alam,et al.  The Effect of van der Waals and Viscous Forces on Aerosol Coagulation , 1987 .

[69]  H. S. Fogler,et al.  Emulsion stability—theoretical studies on simultaneous flocculation and creaming , 1981 .

[70]  T. Tsang,et al.  Comparison of Different Numerical Schemes for Condensational Growth of Aerosols , 1988 .

[71]  Douglas W. Fuerstenau,et al.  Mutual coagulation of colloidal dispersions , 1966 .

[72]  David R. Williams,et al.  A stochastic computer simulation of emulsion coalescence , 1991 .

[73]  E. R. Cohen,et al.  Approximate solution of the equations for aerosol agglomeration , 1971 .

[74]  M. Donohue,et al.  A kinetic approach to crystallization from ionic solution: I. Crystal Growth , 1988 .

[75]  A. Karabelas,et al.  FLOW OF SUPERSATURATED SOLUTIONS IN PIPES. MODELING BULK PRECIPITATION AND SCALE FORMATION , 1995 .

[76]  J. Katz,et al.  A kinetic approach to crystallization from ionic solution: II. Crystal Nucleation , 1988 .

[77]  E. Ruckenstein,et al.  Rate of deposition of Brownian particles under the action of London and double-layer forces , 1973 .

[78]  John E. Sader,et al.  Accurate Analytic Formulas for the Double-Layer Interaction between Spheres , 1995 .