Chemical equation balancer with hydrates

Y=contact angle of liquid/liquid interface on hydrate measured through water-rich liquid phase Zu=z at an arbitrary level far above reference level, z = 0ДЄ=order of reaction for hydrate formationДЄD,gw=mass transfer coeВЃcient for CO2 on water-rich-liquid-phase side based on conventional deВ®nitionД«=order of reaction for hydrate decompositionД«D,gw=mass transfer coeВЃcient for CO2 on water-rich-liquid-phase side deВ®ned in equation (23)Д®=porosity of hydrate В®lm or volume fraction of liquid phase in hydrate/liquid mixtureД®c=volume fraction of liquid phase in space closely packed with spherical hydrate particles XГ„$w=overall mole fraction of water (including host water molecules in hydrate) in multi- or single-phase space Д®qual to xГ„w in single-liquid-phase space XГ„ws=solubility of water in CO2 expressed in mole fraction XГ„w=mole fraction of water in liquid phase XГ„$g=overall mole fraction of CO2 (including guest CO2 molecules in hydrate) in multi- or single-phase space Д®qual to xГ„g in single-liquid-phase space X~ hg =mole fraction of guest CO2 molecules in hydrate (=1/(1 + n) XГ„g,1=xГ„g in bulk of water-rich liquid phase XГ„gs(0)=xГ„gs in metastable absence of hydrate (used only when distinction from xГ„gs(h) is necessary) XГ„gs(h)=xГ„gs in equilibrium with hydrate (used only when distinction from xГ„gs(0) is necessary)

XГ„gs=solubility of CO2 in water expressed in mole fraction Nh=z-directional velocity of hydrate particles regarded as virtual ВЇuid

Th=hydrate/water-rich-liquid/CO2-rich-ВЇuid equilibrium temperature as function of p Г‡rh=speciВ®c molar rate of hydrate formation Rh=radius of spherical region, around CO2 drop, in which cg exceeds cgs(h) Rc=radius of microperforations distributed in hydrate В®lm R=radial distance measured from center of CO2 drop Ph=hydrate/water-rich-liquid/CO2-rich-ВЇuid equilibrium pressure as function of T NГ‡ wh=molar ВЇux of water through hydrate В®lm NГ‡ wg=molar ВЇux of water diВЂusing into CO2-rich liquid phase NГ‡ gw=molar ВЇux of CO2 diВЂusing into water-rich liquid phase NГ‡ gh=molar ВЇux of CO2 through hydrate В®lm Mh=eВЂective molar mass of hydrate given by Mg+nMw Kfg, kfw=kf in CO2-rich liquid phase and that in water-rich liquid phase, respectively Kf=reaction rate constant for hydrate formation

Kdg, kdw=kd in CO2-rich liquid phase and that in water-rich liquid phase, respectively Kd=reaction rate constant for hydrate decomposition *Address correspondence to: Fax: +81-4, e-mail: : CLATHRATE HYDRATE FORMATION G,1=fugacity of CO2 in bulk of water-rich liquid phase All rights reservedДЄg=activity of CO2 dissolved in water-rich liquid phaseДЄh=speciВ®c hydrate/liquid interfacial areaД¬g=mass concentration of CO2 in water-rich liquid phaseД¬gs=solubility of CO2 in water expressed in mass concentrationД¬gs(h)=cgs in equilibrium with hydrate (used only when distinction from cgs(0) is necessary)Д¬gs(0)=cgs in metastable absence of hydrate (used only when distinction from cgs(h) is necessary)Д¬g,d=cg at z = d (hydrate/water-rich-liquid interface)Д¬g,1=cg in bulk of water-rich liquid phaseД¬Г„g=molar concentration of CO2 in liquid phaseД¬Г„g,1=cГ„g in bulk of water-rich liquid phaseД¬~*g =overall molar concentration of CO2 (excluding guest CO2 molecules in hydrate) in multi- or singlephase space equal to cГ„g and cГ„ $g when cГ„h=0Д¬Г„ $g=overall molar concentration of CO2 (including guest CO2 molecules in hydrate) in multi- or singlephase space equal to c~*g and cГ„g when cГ„h=0Д¬Г„h=molar concentration of hydrate regarded as compound with molar mass MhД¬Г„L=molar density of liquid phase (=cГ„g+cГ„w)Д¬Г„w=molar concentration of water in liquid phaseД¬~*w =overall molar concentration of water (excluding host water molecules in hydrate) in multi- or singlephase space equal to cГ„w when cГ„h=0Дgh=mass diВЂusivity for CO2 in hydrate phaseДgw=mass diВЂusivity for CO2 in water-rich liquid phaseДh=eВЂective diВЂusivity for hydrate particles in liquid phaseДwg=mass diВЂusivity for water in CO2-rich liquid phase Revealed suggests the necessity of more careful consulting of pertinent experimental observations toД®stablish our physical view about hydrate В®lms, which should serve as the base of any further work on The state of the art of hydrate-В®lm modeling thus Reality or mathematical formulation is pointed out. Each model is critically examined, and if any, its weakness in physical This paper reviews those rival models one by one and illustrates how they are discrepant. On the formation and metabolic self-preservation of a hydrate В®lm at the interface and also the mass Eight diВЂerent models have been proposed so far To mitigate the emission of CO2 into the atmosphere. Liquid water is one of the key processes in the course of direct CO2 disposal into deep seasГђan option All rights reservedДepartment of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 2238522, JapanДЄbstractГђThe clathrate hydrate formation at the interface between liqueВ®ed carbon dioxide (CO2) and

Chemical equation balancer with hydrates