5Useful definitionsBoiling/bubble point Tbp: temperature at which the average liquid molecule has just enough kinetic energy to escape from the surface of the liquid into the gas phaseRecall that kinetic energy follows a Boltzmann distribution, so molecules with higher than average kinetic energy can still escape from the surface at T < Tbp, by evaporationSaturated liquid: a liquid at its boiling/bubble pointDew point Tdp: temperature at which the average vapor molecule has just enough kinetic energy to condenseSaturated vapor: a vapor at its dew pointVapor pressure: pressure at which the liquid and vapor phase are in equilibrium at a given temperatureAzeotrope: a constant-boiling mixture, i.e., a mixture that behaves like a single component
6How much liquid and vapor will the flash drum produce? F, L and V are extensive variablesmass balance method total mass balance (TMB): F = L + V component mass balance (CMB): F zA = L xA + V yA rearrange:OR inverse lever-arm method•LMVisothermFor a given F, we can now compute L and V.
8Specify two of (P, T, volatility) pure compoundT´P´K > 1Consider a pure compound:• for a given P, find Tbp (i.e., K = 1)• for a given T, find P0 (i.e., K = 1)• for a given P, T, find KK > 1 prefers vapor phaseK < 1 prefers liquid phaseTbpP0pressuretotalK = 1.0temperatureT*P*K < 1DePriester ChartDon’t extrapolate beyond the range of the chart.
10Using data from vapor pressure tables Raoult’s Law ideal liquid: non-ideal liquid:activity coefficientDalton’s Lawideal gas:non-ideal gas:fugacity coefficient
11Bubble point calculation for multi-component mixtures Trial-and-error method Given the composition of a subcooled liquid and PTOTAL, find Tbp and (yi)bp VLE: mole balance:Algorithm:Pick a temperature T and find the corresponding Ki(T) values for each componentCalculate the yi value for each Ki(T)Check to see if Syi = 1If not, pick a new temperature, repeatHow to pick a temperature? How to pick the next temperature?
12To achieve rapid convergence: Initial guess: (weighted average of boiling points of pure components)Next guess:pick a reference component (A)find Tnext using DePriester Chart
13Dew point calculation for multi-component mixtures Trial-and-error method Given the composition of a superheated vapor and PTOTAL, find Tdp and (xi)dp VLE: mole balance:Algorithm:Pick a temperature T and find the corresponding Ki(T) values for each componentCalculate the xi value for each Ki(T)Check to see if Sxi = 1If not, pick a new temperature and repeatLecture 3 ends here
14Relative volatility volatility relative volatility strong function of temperaturevolatilitynot a strong function of temperature; often assumed independentrelative volatilityfor a binary system, substitute and rearrange:
15Bubble point calculation using relative volatility definition of relative volatility:solve for yi:sum:solve for Kref:Algorithm:given a solution composition (xi values), find relative volatilities (ai values), then1. guess Tinitial2. calculate Kref3. find T = Tbp corresponding to Kref
16Ex.: Finding Tbp using relative volatilities Find the bubble point of a mixture of n-pentane (xP = 0.3), n-hexane (xX = 0.3) and n-heptane (xH = 0.4), at 1 atm total pressure. Find the composition of the first vapor bubble.Designate n-pentane as the reference. At 71 °C, KP = 2.8.Find Tbp corresponding to KP = 2.0 (read from DePriester Chart): Tbp = 58 °CCheck: