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Absorption and Stripping Some important definitions • In distillation, heat drives the separation of the more volatile from the less volatile component; this unit op is always counter-current. • In stripping/absorption, separation is induced by addition of a third component; these unit ops can be either counter-current or co-current. stripping: a volatile component of a liquid stream vaporizes into a carrier gas stream absorption: a soluble component of a gas stream dissolves in an extracting liquid stream - physical absorption: the desired component is soluble in the - extracting liquid chemical absorption: the desired component reacts with the extracting liquid • irreversible chemical absorption: generates product/waste • reversible chemical absorption: solvent is recycled by stripping Stripping and absorption are often used together. Ex.: Integrated system for removing CO2 from syn gas solvent cooler H2, CO H2NCH2CH2OH (MEA) N2 + CO2 MEA + CO2 heat exchanger stripper absorber hot feed gas H2, CO, CO2 syn gas MEA + CO2 N2 Gases in at the bottom. Liquids in at the top. (Why?) MEA Key simplifying assumptions 1. stripping gas/carrier gas is insoluble in solvent 2. solvent is non-volatile - therefore all streams are either pure or binary 3. columns are isothermal and isobaric 4. heat of absorption is negligible - therefore energy balance is automatically satisfied Degrees of freedom analysis: D.o.F. = C – P + 2 = 3 – 2 + 2 = 3 (A,B,C) (V,L) When T, P are fixed (assumption 3), can specify only one more variable: xB or yB Labeling streams Vn yn xn, yn: Vn: Ln: Ln xn H E T HETP nth stage Vn+1 yn+1 Packed columns are used more often than tray (plate) columns in absorption/stripping, because of low mass transfer efficiencies. Ln-1 xn-1 HETP ≡ height (of packing) equivalent to a theoretical plate. Fractional stages are possible with packed columns. mole fractions of solute A at equilibrium leaving the nth stage total gas flow rate = (moles solute A + moles carrier gas B) / time total liquid flow rate = (moles solute A + moles solvent C) / time Since A is transferred in one direction only (liq → gas, or gas are not constant. Therefore CMO is not valid. → liq), V and L Using mole ratios what is constant? vapor mole ratio: G ≡ carrier gas flow rate, moles B/time since B is presumed insoluble, Gn = Gn+1 = G S ≡ solvent flow rate, moles C/time since C is presumed non-volatile, Sn = Sn-1 = S yA moles A in gas stream y A YA = = = moles B in gas stream y B 1- y A moles A moles B moles A YAG = ´ = in gas stream moles B time time liquid mole ratio: XA = x moles A in liquid stream xA = = A moles C in liquid stream xB 1- xA X AS = moles A moles C moles A ´ = in liquid stream moles C time time McCabe-Thiele analysis of stripping feed S, X0 G, Y1 stage 1 CMB: GYj+1 + SX0 = GY1 + SXj operating line equation: Yj+1 = (S/G)Xj + [Y1 – (S/G)X0] slope = S/G stage j Yint = [Y1 – (S/G)X0] analogous to operating line for stripping section of distillation column G, Yj+1 S, Xj usually specified: X0, YN+1, S/G, XN stage N stripping gas G, YN+1 S, XN fast plotting of operating line: • the point (XN, YN+1) lies on the operating line • calculate Y1 from CMB • the point (X0, Y1) also lies on the operating line Ex.: Analysis of counter-current stripper Given X0, XN, YN+1 and S/G, find N. 1. Plot VLE data as mole ratios (unless x0 < 0.05) Note: y = x line has no use here. •X0 1• 2. Plot (XN, YN+1) and (X0, Y1) and draw operating line. It will be below the VLE line. 3. Step off stages (use Murphree efficiencies if available). 2• 3• •(X0,Y1) • • N=3 •(XN,YN+1) To find minimum stripping gas flow rate (Gmin): 1. Plot X0 on VLE line (watch for earlier pinch point, if VLE is curved). 2. Calculate Gmin = S / (S/G)max Rule-of-thumb: (S/G)opt ≡ 0.7 (S/G)max Estimating fractional stages Y VLE op. line (X4, Y4) • X4 • •(X , Y ) 3 4 • XN X X3 • • XN XN - X3 fractional stage = requirement X 4 - X3 McCabe-Thiele analysis of absorber Solvent S, X0 G, Y1 stage 1 G, Yk CMB: GYN+1 + SXk-1 = GYk + SXN operating line equation: Yk = (S/G)Xk-1 + [YN+1 – (S/G)XN] S, Xk-1 slope = S/G Yint = [YN+1 – (S/G)XN] analogous to operating line for rectifying section of distillation column stage k usually specified: X0, YN+1, S/G, Y1 stage N feed G, YN+1 S, XN fast plotting of operating line: • the point (X0, Y1) lies on the operating line • calculate XN from CMB • the point (XN, YN+1) lies on the operating line Ex.: Analysis of counter-current absorber Given X0, Y1, YN+1 and S/G, find N. 1. Convert VLE data to mole ratios (unless x0 < 0.05) Note: y = x line has no use here. (XN,YN+1)• 2. Plot (X0, Y1) and (XN, YN+1) and draw operating line. It will be above the VLE line (because mass is transferred in opposite direction, gas → liq). 3. Step off stages (use Murphree efficiencies if available). • • (X0,Y1)• • 1 YN+1 • • 3 •2 N=3 Find minimum extracting solvent flow rate (Smin) for given G: 1. Plot YN+1 on VLE line (watch for earlier pinch point, if VLE is curved). 2. Calculate Smin = G • (S/G)min Rule-of-thumb: (S/G)opt ≡ 1.4 (S/G)min Multiple non-interacting solutes Multiple soluble components (A, D, E…) in solvent C, to be stripped using gas B, OR Multiple components (A, D, E…) in carrier gas B, to be absorbed using solvent C. If streams are dilute and components do not interact with each other, assume VLE for each component is independent. Treat each as a single-component problem, and solve sequentially. For dilute streams, Yi = yi / (1 - yi) ≈ yi Xi = xi / (1 - xi) ≈ xi S/G ≈ L/V Ex.: 2-component absorber Specify yA,N+1, yD,N+1, xA,0, xD,0 Specify L/V and yA,1. Find N and yD,1 (xD,N,yD,N+1)• xA,0 xD,0 yA,1 yD,1 Separation of A requires N = 3. 1 y (xA,N,yA,N+1)• • • N yA,N+1 yD,N+1 xA,N xD,N (xA,0,yA,1)• (xD,0,yD,1)• • • •3 •3 •2 • 2 •1 • 1 Separation of D must also use N = 3 and same L/V. Trial-and-error: guess yD,1 x Probably a good idea to use a different graph for each component… Irreversible absorption Add reagent R to solvent. R reacts essentially irreversibly with solute A to form non-volatile products R + A(g) → R•A(l) e.g., NaOH + H2S(g) → Na2S + H2O Equilibrium lies far to the right: Equation of the VLE line: xA ≅ 0 yA = 0 and yA ≅ 0 Ex. Irreversible absorption Specify yN+1, x0, L/V. Required: xN = y1 = 0 C+R x0 = 0 B y1 = 0 Only one theoretical equilibrium stage required … 1 y yN+1 • N A+B yN+1 C + R•A xN = 0 (x0,y1)• (x1,y1) VLE • x (A + R•A) Ex.: Irreversible absorption with low efficiency Specify yN+1, x0, L/V, y1 ≠ 0 C+R x0 = 0 B y1 ≠ 0 More than one actual equilibrium stage required … 1 yN+1 • y • • • N A+B yN+1 A + R•A xN = 0 • •3 • •2 (x0,y1)• •1 •6 EMV = 0.25 •5 •4 VLE x (A + R•A) Co-current cascade • can use higher vapor velocity to increase mass transfer rate • can use smaller diameter column without risk of flooding • generally used for irreversible absorption Specify y0, x0 = 0, xN, yN = 0 V, y0 L, x0 (x0,y0)• Only one theoretical equilibrium stage required, if the reaction is irreversible and mass transfer is fast … j V, yj L, xj Vy 0 + Lx0 = Vy j + Lx j y=- V, yN L, xN æ L L ö x + ç y 0 + x0 ÷ V V ø è (x1,y1) VLE • x (A + R•A) VLE for dilute streams When streams are dilute, VLE data can be approximated by a straight line. y = mx Obtain the slope, m, from Henry’s Law: PB = HB xB where yB = PB/Ptotal PB is the partial pressure of B, and HB is the Henry’s Law constant. Note: HB = HB(T), like an equilibrium constant. Analytical solution, when both VLE and op. line are straight change in vapor composition between adjacent stages: (x2,y3) • (y)2 (x1,y2) • •(x2,y2) (y)1 = y2 - y1 (x0,y1)• •(x1,y1) ( Dy ) j = y j +1 - y j CMB: æ L L ö y j +1 = x j + ç y1 - x0 ÷ V V ø è VLE: y j = mx j general case: L/V ≠ m, then (y)j ≠ (y)j+1 special case: if L/V = m, then (y)j = y. y1 + y2 + y3 + … = yN+1 – y1 = Ny OR N= x0 - xN ( V) xN - L -1 y N+1 Kremser equation: L/V ≠ m use VLE: ( Dy ) ( ) Dy ( ) Dy ( ) - Dy j +1 j j y j = mx j æL ö yj æ ö æ L ö æ L L ö = ç - m÷ + ç y1 - x0 ÷ = ç -1 y + y - x V ø è mV ÷ø j çè 1 V 0 ÷ø èV øm è æ L ö æ L ö = 1 y + y çè mV ÷ø j +1 çè 1 V x0 ÷ø j +1 æ L ö æ L ö =ç - 1÷ y j +1 - y j = ç - 1÷ Dy è mV ø è mV ø ( ) Dy ( ) æ L ö = çè mV ÷ø Dy j +1 ( ) j ( ) ( ) = A Dy j where A = L/mV ≡ absorption factor j ( )( ) ( ) 1- AN y N+1 - y1 = Dy 1 + Dy 2 + Dy 3 + Dy 4 + ... = Dy 1 1+ A + A + A + ... = Dy 1 1- A Kremser equation: ( ) ( ) ( ) ( ) y N+1 - y1 ( Dy ) 1 = y N+1 - y N ( ) A Dy 0 1- AN = 1- A ➠ 2 3 y N+1 - y1 A - AN+1 = y1 - y 0 1- A where y0 = mx0 Other forms of Kremser equation For gas phase compositions (absorber columns): For liquid phase compositions (stripper columns): y N+1 - y1 A - AN+1 = y1 - y 0 1- A xN - xN+1 1- S = x0 - xN+1 1- S (N+1) where and S = mV/L ≡ stripping factor, xN+1 = yN+1/m solve for N: é ù æ y - y0 ö -1 ln ê 1- A-1 ç N+1 + A ú ÷ y y è ø ê úû 1 0 N= ë ln A ( ) N= é lnê 1- S -1 êë ( ) ù æx -x ö -1 0 N+1 çç ÷÷ + S ú úû è xN - x N+1 ø lnS include Murphree vapor efficiency: é ù æ y N+1 - y 0 ö -1 -1 ln ê 1- A ç ÷+A ú y y è 1 ê úû 0 ø N=- ë ln éë1+ EMV A-1 - 1 ùû ( ) ( ) More forms shown in Wankat, chapter 12.4 Counter-current column sizing Height: 1. measure HETP 2. measure EMV 3. obtain N Diameter: 1. key parameter is V, total gas flow rate (not constant) 2. Vj is largest at the top of a stripper column, or at the bottom of an absorber column 3. calculate D using same procedure as distillation column