Flash Distillation Notes PDF

2. Flash Distillation Explain and sketch the basic flash distillation process Binary flash vapourization or distillation Derive and plot the operating equation for binary flash distillation on a y-x diagram. Solve sequential and simultaneous binary flash distillation problems u...

2. Flash Distillation Explain and sketch the basic flash distillation process Binary flash vapourization or distillation Derive and plot the operating equation for binary flash distillation on a y-x diagram. Solve sequential and simultaneous binary flash distillation problems using y-x digrams and T-xy diagrams. Define and use: K values Raoult’s law Relative volatility Compare and contrast multicomponent flash distillation with binary flash distillation 1 Vapor-liquid equilibria of pure (single) fluid For a sealed container at a given temperature, the pressure of the vapour of a pure liquid at equilibrium or saturation is defined as the vapour pressure (VP). The Antoine equation is commonly used to estimate the vapour pressure: 𝐵𝐵 VP log10 𝑉𝑉𝑃𝑃 = 𝐴𝐴 − P given in mmHg 𝑇𝑇 + 𝐶𝐶 Parameter Benzene Toluene A 6.89272 6.95805 B (°C) 1203.531 1346.773 C (°C) 219.888 219.693 Single Component 2  Vapor-liquid equilibria of binary mixtures Definitions: A = more volatile component B = less volatile component x = mole fraction of A in liquid phase 1 − x = mole fraction of B in liquid phase y = mole fraction of A in vapour phase 1 − y = mole fraction of B in vapour phase VP Single Component Binary Mixture 3 Ideal mixtures Dalton’s law for ideal gas mixture: 𝑝𝑝𝐴𝐴 = 𝑃𝑃𝑦𝑦𝐴𝐴 pA=partial pressure of component A P= total pressure Remember: Raoult’s law for ideal systems: 𝑝𝑝𝐴𝐴 = (𝑉𝑉𝑉𝑉)𝐴𝐴 𝑥𝑥𝐴𝐴 VP depends on temperature Combining the two laws, Raoult-Dalton law: (𝑉𝑉𝑉𝑉)𝐴𝐴 (𝑉𝑉𝑉𝑉)𝐵𝐵 𝑦𝑦𝐴𝐴 = 𝑥𝑥𝐴𝐴 1 − 𝑦𝑦𝐴𝐴 = 1 − 𝑥𝑥𝐴𝐴 𝑃𝑃 𝑃𝑃 Therefore, knowing (VP)A and (VP)B as functions of temperature (e.g. Antoine equation) allows construction of the T-xy and y-x equilibrium diagrams at constant pressure. 4  Constant Pressure Binary System Vapour-Liquid Phase Diagrams Which point represents the b.p. of K b.p. component b.p.ofof B B superheated Superheated superheated vapour vapour boiling temperature of the pure pureBB vapour phase (LVC) I J most volatile component? H dew dew point Sat’d curve pointvapour/dew curve point curve Which point represents the * (y vs. T) boiling temperature of the G (y* vs. T) Temperature, T Temperature, T liquid-vapour mixture E D least volatile component? F C b.p. b.p. b.p. ofofof component A (MVC) Sat’d liquid/bubblebubble point bubble curve point curve point curve pureAA pure A subcooled (x vs. (x vs.T)T) subcooled liquid subcooled liquid liquid phase 0 Mole fraction, Mole fraction A, x,x,y*y* 1 isotherm Tie line (connecting points CED) is an ________________. It defines the composition of the liquid phase (i.e. C) and vapour phase (i.e. D) which are in equilibrium. Vapour-liquid mixture with overall composition zA,E at equilibrium consists of: xA,c Liquid phase with composition _______ yA,D Vapour phase with composition________ 5  Constant Pressure Binary System Vapour-Liquid Phase Diagrams K b.p. b.p.ofof B superheated superheated vapour Apply the lever rule to find relative pure pureBB I J vapour phase amounts of liquid and vapour H dew dewpoint curve point curve G (y** vs. (y vs.T)T) Temperature, T Derived from overall and Temperature, T liquid-vapour mixture component MB E D F C b.p.ofof b.p. bubble point bubble pointcurve curve A pureAA pure subcooled (x vs. (x vs.T)T) subcooled liquid liquid phase 0 Mole fraction, Mole fraction A, x,x,y*y* 1 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝐿𝐿 𝑧𝑧𝐴𝐴 − 𝑦𝑦𝐴𝐴 𝑑𝑑𝑑𝑑 𝑉𝑉 𝑥𝑥𝐴𝐴 − 𝑧𝑧𝐴𝐴 𝑐𝑐𝑐𝑐 𝑉𝑉 𝑥𝑥𝐴𝐴 − 𝑧𝑧𝐴𝐴 𝑐𝑐𝑐𝑐 = = = = = = 𝐹𝐹 𝑥𝑥𝐴𝐴 − 𝑦𝑦𝐴𝐴 𝑐𝑐𝑐𝑐 𝐹𝐹 𝑥𝑥𝐴𝐴 − 𝑦𝑦𝐴𝐴 𝑐𝑐𝑐𝑐 𝐿𝐿 𝑧𝑧𝐴𝐴 − 𝑦𝑦𝐴𝐴 𝑑𝑑𝑑𝑑 6 Boiling of a Binary Mixture For a pure fluid, transition from Tbp,A liquid to gas (boiling) occurs at a single T (for a given P) Mixture boils in the range of Tbubble < T < Tdew For a mixture, transition from liquid to gas occurs at a range of temperatures – from bubble Two phases are present point to dew point within this envelope. 7  Constant Pressure Vapour-Liquid Phase Diagrams: y-x plot or McCabe-Thiele plot 1 K b.p. b.p.ofof B superheated superheated vapour pure pureBB vapour phase Vapour Mole Fraction, y y D* J I eq’m line (y* = feq(x)) H dew dewpoint curve point curve 45° line G (y** vs. (y vs.T)T) Temperature, T yyH (y = x) Temperature, T liquid-vapour mixture E D F C b.p.ofof b.p. bubble point bubble pointcurve curve A pureAA pure subcooled (x vs. (x vs.T)T) subcooled liquid liquid phase 0 xC 0 xF x Liquid 1 Mole Fraction, x 0 Mole fraction, Mole fraction A, x,x,y*y* 1 Consider a binary system at vapour-liquid equilibrium. If the composition of the sat’d liquid is xF, what is the composition of the sat’d vapour? 1. yH or 2. yJ No Is the temperature constant along the y-x equilibrium line? __________ 8  Enthalpy Heat capacity is the change in energy of a fluid that results from a unit change in temperature. Cp is usually varies with temperature. Must specify a temperature when reporting value. When the fluid is heated or cooled, it absorbs/releases heat. If the fluid does not undergo a phase change, this amount of heat is proportional to the heat capacity. If the fluid undergoes a phase transition, then additional energy is absorbed/released do to the transition of the molecules from one phase to another. SPECIFIC LATENT SPECIFIC HEAT HEAT HEAT SUBCOOLED λ SAT LIQUID SAT GAS SUPERHEATED GAS LIQUID λ=latent heat of vaporization For ideal mixtures: 9 Enthalpy diagram (Ponchan‐Savarit, corrected) For ideal solutions Vapor ℎ 𝑥 𝐶 , 𝑥 𝐶 · 𝑇 𝑇 F , Enthalpy TEF 𝐻 E 𝑦 · 𝐶 , 𝑇 𝑇 𝜆 𝐶 , 𝑇 𝑇 , Liquid 0 1 where A and B are the molal heats of vaporization of Temperature re pure Vapor components A and B, respectively. F TEF Tb is the bubble point temperature E Td is the dew point temperature Tref is the reference temperature chosen for all enthalpy calculations. Liquid xE 0 1 Mole fraction A 10  Relative volatility, 𝛼𝛼 mole ratio of A to B in vapour phase 𝑦𝑦𝐴𝐴 ⁄ 1 − 𝑦𝑦𝐴𝐴 𝑦𝑦𝐴𝐴 1 − 𝑥𝑥𝐴𝐴 𝛼𝛼 ≡ ≡ = mole ratio of A to B in liquid phase 𝑥𝑥𝐴𝐴 ⁄ 1 − 𝑥𝑥𝐴𝐴 𝑥𝑥𝐴𝐴 1 − 𝑦𝑦𝐴𝐴 1 For an ideal mixture, α↑ α=1 y 𝑃𝑃𝐴𝐴𝑠𝑠𝑠𝑠𝑠𝑠 𝑥𝑥 𝑃𝑃𝐵𝐵𝑠𝑠𝑠𝑠𝑠𝑠 1 − 𝑥𝑥 y= and 1 − 𝑦𝑦 = 𝑃𝑃 𝑃𝑃 Then 0 0 1 𝑃𝑃𝐴𝐴𝑠𝑠𝑠𝑠𝑠𝑠 𝑥𝑥 ⁄𝑃𝑃 ⁄𝑃𝑃𝐵𝐵𝑠𝑠𝑠𝑠𝑠𝑠 1 − 𝑥𝑥 ⁄𝑃𝑃 𝑃𝑃𝐴𝐴𝑠𝑠𝑠𝑠𝑠𝑠 x 𝛼𝛼 = = 𝑥𝑥 ⁄ 1 − 𝑥𝑥 𝑃𝑃𝐵𝐵𝑠𝑠𝑠𝑠𝑠𝑠 The more α exceeds unity, the greater is the separation achieved by distillation. 11  Basic Method of Flash Distillation Consider a mixture of A (MVC) and B. How will the components separate after a “flash”? [1 min] Designer needs to know: Pdrum Tdrum Liquid and vapour compositions: xA and yA Flow rates, L and V Drum size (height and diameter) PF TF Throttle High-Pressure Water F Demonstration (opens in new window) 12  D, y1, y2 Equations (corrected) F, z1, z2, PF, TF P,T Mole/mass balance: overall 𝐹 𝑊 𝐷 (i) component 𝐹𝑧 𝑊𝑥 𝐷𝑦 (ii) Equilibrium: component1 𝑦 𝐾𝑥 iii W, x1, x2 component2 𝑦 𝐾𝑥 iv Summation: feed 𝑧 𝑧 1 v liquid 𝑥 𝑥 1 vi vapour 𝑦 𝑦 1 vii Energy Balance (adiabatic): 𝐹ℎ 𝑊ℎ 𝐷𝐻 viii Auxiliary relations: 𝐾 𝐾 𝑇, 𝑃 ix 𝐾 𝐾 𝑇, 𝑃 x ideal ℎ ℎ 𝑇 ,𝑧 ,𝑧 xi ℎ ℎ 𝑇, 𝑥 , 𝑥 xii 𝐻 𝐻 𝑇, 𝑦 , 𝑦 xiii Number of independent equations: 8 Number of degrees of freedom: 13 – 8 = 5 ∴ 5 variables need to be specified in order to use the 14 8 equations to determine the remaining unknowns. Equations (corrected) Mole/mass balance: overall 𝐹𝐹 = 𝑊𝑊 + 𝐷𝐷 (i) component 𝐹𝐹𝑧𝑧1 = 𝑊𝑊𝑥𝑥1 + 𝐷𝐷𝑦𝑦1 (ii) Equilibrium: component1 𝑦𝑦1 = 𝐾𝐾1 𝑥𝑥1 (iii) component2 𝑦𝑦2 = 𝐾𝐾2 𝑥𝑥2 iv Summation: feed 𝑧𝑧1 + 𝑧𝑧2 = 1 (v) liquid 𝑥𝑥1 + 𝑥𝑥2 = 1 (vi) vapour 𝑦𝑦1 + 𝑦𝑦2 = 1 (vii) Energy Balance (adiabatic): 𝐹𝐹ℎ𝐹𝐹 = 𝑊𝑊ℎ𝑊𝑊 + 𝐷𝐷𝐻𝐻𝐷𝐷 (viii) Auxiliary relations: 𝐾𝐾1 = 𝐾𝐾1 (𝑇𝑇, 𝑃𝑃) (ix) 𝐾𝐾2 = 𝐾𝐾2 (𝑇𝑇, 𝑃𝑃) (x) ideal ℎ𝐹𝐹 = ℎ𝐹𝐹 (𝑇𝑇𝐹𝐹 , 𝑧𝑧1 , 𝑧𝑧2 ) (xi) ℎ𝑊𝑊 = ℎ𝑊𝑊 (𝑇𝑇, 𝑥𝑥1 , 𝑥𝑥2 ) (xii) 𝐻𝐻𝐷𝐷 = 𝐻𝐻𝐷𝐷 (𝑇𝑇, 𝑦𝑦1 , 𝑦𝑦2 ) (xiii) Number of independent equations: 8 Number of degrees of freedom: 13 – 8 = 5 ∴ 5 variables need to be specified in order to use the 14 8 equations to determine the remaining unknowns.  Graphical Solution- Case (a)- Pdrum and Tdrum Temperature Tdrum 3 feed specifications: Find: Feed flow rate, F c L Feed composition, zA x a 0 x1 z1 y1 1 Pressure, PF V Mole fraction b y a ℎ𝐹𝐹 = 𝑊𝑊𝐻𝐻𝑊𝑊 + 𝐷𝐷𝐻𝐻𝐷𝐷 /𝐹𝐹 d hF TF e ℎ𝐹𝐹 𝑇𝑇𝐹𝐹 = 𝑇𝑇𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑧𝑧1 ∗ 𝐶𝐶𝑝𝑝𝑝𝑝,1 + 𝑧𝑧2 ∗ 𝐶𝐶𝑝𝑝𝑝𝑝,2 16 Sequential Solution- Case a- Pdrum, Tdrum Approach also applies for following (Pdrum, xA) (Pdrum,yA) i.e. two conditions inside drum are known Order in which the other variables is determined will change. 17 Example 1 A flash drum operating at 700.0 kPa is separating a binary mixture of ethane and n-butane. Temperature-composition data is provided. If zE=0.30, Pdrum=700.0 kPa, and Tdrum=33.4oC, determine the outlet vapour and liquid mole fractions, V/F, and TF. 18  80 Ethane-n-Butane Equilibria, P=700.0 kPa 60 40 Temperature (oC) 20 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -20 -40 -60 Mole Fraction of Ethane (x, y) Liquid Vapour 19 Analysis of problems State briefly what is known (in your own language) State briefly what must be found Draw a schematic of the system List simplifying assumptions Compile physical properties Analyze using conservation laws and rate equations Discuss the results Answers should have 3 significant digits and be clearly identified with a box. Units must be given. e.g. V= 10.0 mol/hr 20 21  Sequential Solution-Graphical, Case (b)- Pdrum and V/F Equations must now be solved simultaneously: 𝑦𝑦 = 𝑓𝑓(𝑥𝑥, 𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 ) Find: L a 𝑇𝑇𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑓𝑓(𝑥𝑥, 𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 ) 3 feed specifications: b x Feed flow rate, F d 𝐹𝐹𝑧𝑧𝐴𝐴 = 𝐿𝐿𝑥𝑥𝐴𝐴 + 𝑉𝑉𝑦𝑦𝐴𝐴 hL Feed composition, zA a Pressure, P1 V b y d Remaining specifications: Hv Pdrum c Tdrum V/F= fraction vaporized e hF f TF 22 Example 2-1 (Wankat, 2017) A flash distillation chamber operating at 101.3 kPa is separating an ethanol-water mixture. The feed mixture is 40.0 mol% ethanol and F=100.0 kmol/hr. a) What is the composition of the liquid and vapour outlets if V/F=2/3? b) What is the drum temperature? c) What is hF? d) How will the composition of the outlet streams change if V/F is increased? Decreased? e) What is the composition if V/F=2/3 and F=1000 kmol/hr? 23 EtOH- Water Equilibria at 1 atm 24 25 26 Sequential Solution- Case b- Pdrum, V/F Approach also applies for following (Pdrum, L/F) Let q=L/F= fraction remaining liquid= quality 𝑞𝑞 1 Re-write operating equation as: 𝑦𝑦 = − 1−𝑞𝑞 𝑥𝑥 + 1−𝑞𝑞 𝑧𝑧 For both Case a and Case b: mass balance equations are uncoupled from energy balance, hence “sequential” Case c: mass and energy balance equations will have to be solved simultaneously 27  Simultaneous Solution- Case c (Pdrum, TF) Consider energy balance: Fhf=LhL+VHV Can find hF=f(z,TF) BUT hL and HV are unknown because 3 feed specifications: composition and Tdrum are unknown. Feed flow rate, F Feed composition, zA Pressure, P1 Remaining specifications: Pdrum TF 28 3 feed specifications: Feed flow rate, F Feed composition, zA Pressure, P1 Remaining specifications: Pdrum TF Type equation here.Have to solve equations simultaneously! Feasible BUT difficult! Circled equations are usually non-linear. 𝐻𝐻𝑉𝑉𝑠𝑠𝑠𝑠𝑠𝑠 29 Trial & error is easier. Simultaneous Solution- Case c (Pdrum, TF) Calculate hF=f(z,TF) Just following Guess Tdrum Basic method: Case a Guess value for one variable. Calculate x and y procedure Calculate the other variables. e.g. by plotting (z,Tdrum) from T-xy chart Check the guessed value. Calculate L and V For a binary system can choose: y, x, e.g. Solve Eq’n 1 & 2 Tdrum, V/F, or L/F e.g. Lever rule on T-xy chart Calculate hL and HV Is energy balance satisfied? No FhF=LhL+VHV Yes? 30 Done!