Chemical Process Design / Diseño de Procesos Químicos Topic 4.7. Flash Javier R. Viguri Fuente Eva Cifrian Bemposta Department of Chemistry and Process & Resource Engineering GER Green Engineering and Resources Research Group This wor is published under a License: Crea>ve Commons BY- NC- SA 4.
4.3. Flash: Module used to build other separation modules, such as distillation or adsorption V, y µ F1 F, z f = F z P, T v = V y Representation the flash as a Splitter. µ ij F Flash Define: L, x Q l = L x a) "Split fraction component in vapor" b) Key component (or the reference) c) Fraction of F as Vapor (Vaporization) Variables that are usually specified ξ = v f = n ϕ = V F,ϕ,P,T,Q µ F2 What s important is to obtain the split fraction, but fulfilling the liquid-vapor equilibrium at flash operation conditions of T and P. Flash unit with feed stream defined has 2 degrees of freedom Thermodynamic subject. We exclude the choice of Q as variable to maintain the linear mass balance Decoupled Mass and Energy balances.
Consider the following cases: Case 1. Specification of and P or T. Fixed Recovery Flash. More used case ). ϕ Case 2. specified and T or P. Fixed Vaporization Flash. Case 3. T and P specified. Isothermal Flash. Important Phase Equilibrium Vapor/liquid phase equilibrium f v = f l for all components. φ y P = γ x f (Eq. 1) Where: φ γ f Vapor fugacity coefficient. Liquid activity coefficient. Pure component fugacity. To simplify: ideal behavior which leads to the following assumptions: φ =1 γ =1 f = P Antoine equation for vapor pressure LnP = A T + C From Eq. 1 y P = x P Raoult Law We define the equilibrium constant K = y = P x P (Eq. 2) B Coefficients can be found in Reid (et al.), 1987.
Define a relative volatility: = K = P K n P n If is non volatile: If is non condensable: If you now T, you now P with Antoine, and then you now: Now, we redefine relative volatility as: Reintroduce the split fraction and define: (Eq. 4) Substitutes in Eq. 3: = ξ /(1 ξ ) /(1 ) = K K n = y / x y n / x n V / L V / L = v /l v n /l n (Eq. 3) v = ξ f l = (1 ξ ) f α We can express in function of, obtaining: ξ = /n ξ 1+ ( 1) (Eq. 5) For all n. For limiting cases: If is non volatile (heavy component, lie Toluene): ξ If is non condensable (Volatile component, lie H 2 ): ξ 1
How can you calculate P (or T) from the solved mass balance? or How can you chec if the T (or P) guess is correct? We consider equilibrium using the Bubble Point Equation or Dew Point Equation. - At bubble point (for the saturated liquid effluent stream): y i = K i x i =1 K = y = P as, (P i / P)x i P = P i (T )x i x P Bubble Point Equation, where we need all expression of P (T) for each component i. For this reason we obtain the Bubble Point Equation in terms of relative volatility : α α = α i/n x i = (K i / K n )x i =1/ K n Substituting in Eq. 2: P P = K = α 1. For T fixed and P unnown 2. For P fixed and T unnown P = α P (T ) P (T ) = α P Using the Bubble Point Equation, to reduce approximation errors, choose to be the most abundant component in liquid phase.
Algorithms for the three cases: Case 1. and P (or T) Fixed. Fixed Recovery Flash. More used case. 1. Choose ey component n, specified and P (or T), guess T (or P). 2. Calculate K, at specified T. α ξ = /n 1+ ( 1) 3. Evaluate for each component. 4. Solve equations mass balances for all : v = ξ f y = v / l = (1 ξ ) f x = l / l i v i 5. For T specified, calculate: For P specified, calculate: P = α P (T ) P (T ) = α P Compare this P from the mass balance with initial P from my guess is Step 1. Compare this T from the mass balance with initial T from my guess in Step 1. If T (or P) calculated is different to T (or P) guesses, return to Step 2 with new T (or P) guess.
Algorithms for the three cases: ϕ Case 2. and P (or T) Fixed. Fixed Vaporization Flash. ϕ = V / F 1. Choose ey component n, specified and P or T. 2. Guess, calculate K, and α ξ = /n 1+ ( 1) 3. Evaluate for each component. 4. Solve equations mass balances for all : v = ξ f l = (1 ξ ) f x = l / l i 5. If V/F ϕ go to Step 6, otherwise go to Step 2 and re-guess y = v / v i 6. Calculate P (or T) from the bubble point equation to calculate P or T. P = α P (T ) P (T ) = α P
Algorithms for the three cases: Case 3. P and T Fixed. Isothermal Flash. Typically in the reactor downstream. 1. Choose ey component n, and guess. Follow Step 2 ( ) and Step 4 (v, l, ) of algorithm Case 1. α α = P / P 5. If the bubble point equation is satisfied Stop. Otherwise re-guess and start again.