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10. Notations 92 10. Notations 10. Notations Latin Symbols A Pre-exponential factor in the Arrhenius equation L/(mol s) A Debye-Hückel parameter kg1/2mol-1/2 2 Afilm Surface area of the liquid film on the tubes m 2 Ajets Surface area of the water jets between the tubes m 2 APh Phase interface area m ai Activity of the component i - b Sum of the ion and gas specific parameters m3/kmol 3 b+ Ion specific parameter for cations m /kmol 3 b- Ion specific parameter for anions m /kmol 3 bG Gas specific parameter m /kmol 3 Ci Concentration of the component i mol/m C2 Constant in equation (5.46) - CF Concentration Factor - Cl Chlorinity g/kg 2 DiL Diffusion coefficient of the component i in the solution L m /s di Inside tube diameter m do Outside tube diameter m djets diameter of the jets m E Enhancement factor - EA Activation energy kJ/mol g Gravitational acceleration m/s2 3 Hij Henry’s law coefficient of the gas i in the solution j mol/(m bar) h Heat transfer coefficient W/(m2 K) h Sum of the ion and gas specific parameters kg/mol, L/mol h+ Ion specific parameter for cations kg/mol, L/mol h- Ion specific parameter for anions kg/mol, L/mol hG Gas specific parameter kg/mol, L/mol I Ionic strength mol/kg [i] Concentration of the component i mol/kg solution [i]SW Concentration of the component i that is free and involved in ion-pairs in seawater mol/kg solution 10. Notations 93 K Constant in equation (5.46) - K Thermodynamic equilibrium constant of the reaction on molal scale - KSW Stoichiometric equilibrium constant of the reaction referring to the seawater scale on the basis mol/kg solution - SW K1 First dissociation constant of carbonic acid in seawater on the basis mol/kg solution - SW K2 Second dissociation constant of carbonic acid in seawater on the basis mol/kg solution - SW KSP Solubility product constant of calcium carbonate in seawater on the basis mol2/kg2 solution - SW KW Dissociation constant of water in seawater on the basis mol2/kg2 solution - k Boltzmann constant J/K k Rate constant of the reaction 1/s, L/(mol s) k Thermal conductivity W/(m K) ko Rate constant of the reaction in ideal solution 1/s, L/(mol s) k1 Rate constant of forward reaction 1/s k-1 Rate constant of backward reaction 1/s k2 Rate constant of second order reaction L/(mol s) o kL Mass transfer coefficient in liquid phase without chemical reaction m/s kL Mass transfer coefficient in liquid phase with chemical reaction m/s KL Overall mass transfer coefficient in the liquid phase m/s L Length of tube m LSI Langelier Saturation Index - mi Molality of the component i mol/kg solvent m! Mass flow rate kg/s NTA Normalized total alkalinity mol/kg NTC Normalized total carbon dioxide content mol/kg N! i Molar desorption rate of the component i mol/s 2 n! i Molar desorption flux of the component i mol/(m s) njets Number of water jets between adjacent tubes - nrow Number of tubes in a horizontal tube row - ntubes Number of tubes in the tube bundle - pH pH value - 2 pi Partial pressure of the component i N/m , bar 94 10. Notations R Universal gas constant J/(mol K) RSI Ryznar Stability Index - r Reaction rate mol/(m3 s) ro Outside tube radius m S Salinity g/kg S Vertical tube spacing m s Rate of surface renewal 1/s T Temperature K T0 Top brine temperature °C t The age of the element in the penetration theory s TA Total alkalinity mol/kg TC Total carbon dioxide content mol/kg tD Diffusion time s tP Residence time s tR Average reaction time s u Velocity m/s V Liquid volume m3 V! Volume flow rate m3/s z Distance from the tube bottom line m Greek Letters 3 βA Contribution of the neutral molecule A in eq. (4.49) m /kmol 3 βion Contribution of the ion in eq. (4.48) m /kmol γ Activity coefficient of the component i - δ Film thickness m δf Thickness of liquid film flowing over horizontal tubes m m Γ Mass flow rate per unit tube length (Γ = ! )kg/(m s) 2 L λ Distance between the water jets (wavelength) m λd Taylor wavelength m µ Dynamic viscosity kg/(m s) ν Kinematic viscosity m2/s ρ Density kg/m3 σ Surface tension N/m ϑ Temperature °C 10. Notations 95 Indices A Component A BBulk BD Blow-down bbrine CO2 Carbon dioxide 2- CO3 Carbonate ion D Distillate eq Chemical equilibrium F Feed water FC Final condenser GGas g Gas phase H+ Hydrogen ion - HCO3 Bicarbonate ion H2CO3 Carbonic acid i Component L Liquid side OH- Hydroxide ion Ph Phase interface s Solid s Saturation SW Seawater v Vapour WWater * Physical equilibrium Dimensionless Numbers 3 π d g Ga Galilei number Ga = o 2 ν 2 k D Ha Hatta number Ha = 1 A o kL σ3 ρ Ka Kapitza number Ka = g µ 4 96 10. Notations 1 h ν 2 3 Nu Nusselt number Nu = k g c µ Pr Prandtl number Pr = p k 4 Γ Re Film Reynolds number Re = µ ν Sc Schmidt number Sc = D 1 k 0 ν 2 3 Sh Sherwood number Sh = L D g .
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