Presentation on theme: "Goal 1: Design a flash drum How big should the drum be? What height should the nozzle be? What T and P should the drum be? What T and P should the feed."— Presentation transcript:
Goal 1: Design a flash drum How big should the drum be? What height should the nozzle be? What T and P should the drum be? What T and P should the feed be?
Vapor-liquid equilibrium (VLE) Consider a binary (i.e., 2-component) system with 2-phases: T vap, P vap y A, y B T liq, P liq x A, x B What do we know? y A + y B = 1 x A + x B = 1 y A ≠ x A At equilibrium:T vap = T liq P vap = P liq Gibbs’ Phase Rule: degrees of freedom = # components (C) - # phases (P) + 2 For a binary, 2-phase system: 2 – = 2 We can specify only 2 intensive variables (all others are fixed, by VLE)
Useful definitions Boiling/bubble point T bp : temperature at which the average liquid molecule has just enough kinetic energy to escape from the surface of the liquid into the gas phase – Recall that kinetic energy follows a Boltzmann distribution, so molecules with higher than average kinetic energy can still escape from the surface at T < T bp, by evaporation Saturated liquid: a liquid at its boiling/bubble point Dew point T dp : temperature at which the average vapor molecule has just enough kinetic energy to condense Saturated vapor: a vapor at its dew point Vapor pressure: pressure at which the liquid and vapor phase are in equilibrium at a given temperature Azeotrope: a constant-boiling mixture, i.e., a mixture that behaves like a single component
How much liquid and vapor will the flash drum produce? mass balance method total mass balance (TMB): F = L + V component mass balance (CMB): F z A = L x A + V y A rearrange: OR inverse lever-arm method F, L and V are extensive variables L M V isotherm For a given F, we can now compute L and V.
Specify two of (P, T, volatility) total pressure temperature K = 1.0 DePriester Chart for a given P, find T bp (i.e., K = 1) for a given T, find P 0 (i.e., K = 1) for a given P, T, find K K > 1 prefers vapor phase K < 1 prefers liquid phase Don’t extrapolate beyond the range of the chart. T bp P0P0 pure compound Consider a pure compound: T´ P´ K > 1 T* P* K < 1
Using data from vapor pressure tables Raoult’s Law ideal liquid: non-ideal liquid: Dalton’s Law ideal gas: non-ideal gas: activity coefficient fugacity coefficient vapor pressure
Bubble point calculation for multi-component mixtures Trial-and-error method Given the composition of a subcooled liquid and P TOTAL, find T bp and (y i ) bp VLE: mole balance: Algorithm: 1.Pick a temperature T and find the corresponding K i (T) values for each component 2.Calculate the y i value for each K i (T) 3.Check to see if y i = 1 4.If not, pick a new temperature, repeat How to pick a temperature? How to pick the next temperature?
To achieve rapid convergence: Initial guess: (weighted average of boiling points of pure components) Next guess: pick a reference component (A) find T next using DePriester Chart
Dew point calculation for multi-component mixtures Trial-and-error method Given the composition of a superheated vapor and P TOTAL, find T dp and (x i ) dp VLE: mole balance: Algorithm: 1.Pick a temperature T and find the corresponding K i (T) values for each component 2.Calculate the x i value for each K i (T) 3.Check to see if x i = 1 4.If not, pick a new temperature and repeat
Relative volatility volatility strong function of temperature not a strong function of temperature; often assumed independent relative volatility for a binary system, substitute and rearrange:
Bubble point calculation using relative volatility definition of relative volatility: solve for y i : solve for K ref : sum: Algorithm: given a solution composition (x i values), find relative volatilities ( i values), then 1.guess T initial 2.calculate K ref 3. find T = T bp corresponding to K ref
Ex.: Finding T bp using relative volatilities Find the bubble point of a mixture of n-pentane (x P = 0.3), n-hexane (x X = 0.3) and n-heptane (x H = 0.4), at 1 atm total pressure. Find the composition of the first vapor bubble. Designate n-pentane as the reference. At 71 °C, K P = 2.8. Find T bp corresponding to K P = 2.0 (read from DePriester Chart): T bp = 58 °C Check: