Nomenclature

a0, a1, S0 parameters of yield distribution function Equation (5.58) A1, B1 Riazi's correlation parameters A2 Goto and Smith's correlation parameter A fitting parameter of Equation (5.13) Arrhenius preexponential factor for catalytic kinetic constants (h-1) Arrhenius preexponential factor for deactivation constants (h-1) van't Hoff preexponential factor for hydrogen sulfide adsorption constant (cm3/mol) aL gas-liquid interfacial area (cm-1) aMOC unit conversion factor of Equation (5.17) AS sectional area of the reactor (cm-2) aS liquid-solid interfacial area (cm-1) Arrhenius preexponential factor for thermal kinetic constants (h-1) B matrix for orthogonal collocation, fitting parameter of Equation (5.13) C reactant or species concentration CA reactant concentration of A species asphaltene content (wt%) reactant concentration at entrance of reactor system basic nitrogen content (ppm) hydrogen concentration (mol/cm3) Ci molar concentration of compound i (cm3/mol), content of the compound i at the reactor outlet content of the compound i at the reactor inlet c(k,t) concentration of the species with reactivity k at residence time t c(k, 0) concentration of the species with reactivity k in the feed hydrogen sulfide concentration (mol/cm3) nonbasic nitrogen content (ppm) nickel content (ppm) Cp molar concentration of compound i (cm3/mol) sulfur content (wt%) vanadium content (ppm) cwt cumulative weight fraction D bulk diffusion effective diffusivity of A in the pores of catalyst D(k) species-type distribution function for hydrocracking reaction Dr restrictive diffusion coefficient dp catalyst particle diameter dt reactor diameter D0 initial diffusion coefficient within pore catalyst Dt diffusion coefficient within pore catalyst activation energy for the catalytic reactions (kcal/mol) activation energy for the thermal reactions (kcal/mol) deactivation energy for the reaction i (kcal/mol) EOR end-of-run e exponential function basis g gas mass rate (g/s) GL superficial liquid mass velocity (kg/m2 s) Hi Henry's law constant for compound i (MPa cm3/mol) H2/oil hydrogen-to-oil ratio (std m3/m3) I degree of polynomial I0 Bessel function of the first kind, zero order I1 Bessel function of the first kind, first order K reaction rate constant per unit of surface area k hydrocracking reactivity of any species (h-1) k0 global rate constant for hydrocracking of residue k1 second-order rate constant for hydrocracking of residue to VGO k2 second-order rate constant for hydrocracking of residue to distillates k3 second-order rate constant for hydrocracking of residue to naphtha k4 second-order rate constant for hydrocracking of residue to gas k5 first-order rate constant for hydrocracking of VGO to distillates k6 first-order rate constant for hydrocracking of VGO to naphtha k7 first-order rate constant for hydrocracking of VGO to gases k8 first-order rate constant for hydrocracking of distillates to naphtha k9 first-order rate constant for hydrocracking of distillates to gases k10 first-order rate constant for hydrocracking of naphtha to gases kapp apparent rate coefficient kinetic constants for the three and four kinetic models catalytic kinetic constant for the HDAsph reaction (wt%-0.503/h) catalytic kinetic constant for the HDNBN reaction (ppm-0.792/h) catalytic kinetic constant for the reaction i catalytic kinetic constant for the HDNNBN reaction (wt%-1.154/h) catalytic kinetic constant for the HDNi reaction (ppm-1.406/h) catalytic kinetic constant for the HDS reaction (wt%-0.503/h) catalytic kinetic constant for the HDV reaction (ppm0.290/h) kd deactivation rate constant deactivation constant for the reaction i (h-1) adsorption-equilibrium constant for the hydrogen sulfide (cm3/mol) kint reaction rate constant gas-liquid mass transfer coefficient for compound i (cm/s) liquid-solid mass transfer coefficient for compound i (cm/s) ki intrinsic rate coefficient kmax hydrocracking reactivity of the species with the highest TBP in the mixture (h-1) kp particle rate coefficient thermal kinetic constant for the HDAsph reaction (wt%0.795/h) thermal kinetic constant for the HDNBN reaction (ppm0.137/h) thermal kinetic constant for the reaction i thermal kinetic constant for the HDNNBN reaction (ppm0.137/h) thermal kinetic constant for the HDNi reaction (ppm0.350/h) thermal kinetic constant for the HDV reaction (ppm0.487/h) thermal kinetic constant for the HDS reaction (wt%0.062/h) L characteristic catalyst particle size LHSV, l liquid hourly space velocity (h-1) Mms molecular weight of metal sulfide compounds MOC concentration of metals-on-catalyst (wt%) MOR middle-of-run m deactivation rate order mi deactivation order for the reaction i total mass flow N reaction order, total number of species in the mixture, total concentration of sites available for any particular reaction n reaction order of the hydrocracking of residue reaction order of the catalytic...