2Some 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 streamabsorption: 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 strippingStripping and absorption are often used together.
3Ex.: Integrated system for removing CO2 from syn gas solvent coolerabsorberstripperH2NCH2CH2OH(MEA)hot feed gasH2, CO, CO2syn gasN2 + CO2MEAH2, COMEA + CO2MEA + CO2N2heat exchangerGases in at the bottom.Liquids in at the top. (Why?)
4Key simplifying assumptions stripping gas/carrier gas is insoluble in solventsolvent is non-volatile- therefore all streams are either pure or binarycolumns are isothermal and isobaricheat of absorption is negligible- therefore energy balance is automatically satisfiedDegrees of freedom analysis:D.o.F. = C – P = – = 3(A,B,C) (V,L)When T, P are fixed (assumption 3), can specify only one more variable: xB or yB
5Labeling streamsLn-1xn-1VnynLnxnVn+1yn+1Packed columns are used more often than tray (plate) columns in absorption/stripping, because of low mass transfer efficiencies.HETP ≡ height (of packing) equivalent to a theoretical plate.nth stageHETHETPFractional stages are possible with packed columns.xn, yn: mole fractions of solute A at equilibrium leaving the nth stageVn: total gas flow rate = (moles solute A + moles carrier gas B) / timeLn: total liquid flow rate = (moles solute A + moles solvent C) / timeSince A is transferred in one direction only (liq → gas, or gas → liq), V and L are not constant. Therefore CMO is not valid.
6Using mole ratioswhat is constant? 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 = Svapor mole ratio:liquid mole ratio:
7McCabe-Thiele analysis of stripping CMB: GYj SX0 = GY1 + SXjoperating line equation:Yj+1 = (S/G)Xj + [Y1 – (S/G)X0]slope = S/G Yint = [Y1 – (S/G)X0]analogous to operating line for stripping section of distillation columnusually specified: X0, YN+1, S/G, XNfast 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 linefeedS, X0stripping gasG, YN+1G, Y1S, XNstage 1stage jG, Yj+1S, Xjstage N
8Ex.: Analysis of counter-current stripper VLE (may be curved)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(S/G)max•1•(X0,Y1)2. Plot (XN, YN+1) and (X0, Y1) and draw operating line.It will be below the VLE line.operating lineslope = S/G••2•3. Step off stages (use Murphree efficiencies if available).•3N = 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)maxRule-of-thumb: (S/G)opt ≡ 0.7 (S/G)max
10McCabe-Thiele analysis of absorber CMB: GYN SXk-1 = GYk + SXNoperating line equation:Yk = (S/G)Xk [YN+1 – (S/G)XN]slope = S/G Yint = [YN+1 – (S/G)XN]analogous to operating line for rectifying section of distillation columnusually specified: X0, YN+1, S/G, Y1fast 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 lineSolventS, X0feedG, YN+1G, Y1S, XNstage 1G, YkS, Xk-1stage kstage N
11Ex.: 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.VLE (may be curved)(XN,YN+1)•YN+1 •(S/G)minoperating lineslope = S/G2. 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).••213••3. Step off stages (use Murphree efficiencies if available).(X0,Y1)••N = 3Find 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)minRule-of-thumb: (S/G)opt ≡ 1.4 (S/G)min
12Multiple 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) ≈ yiXi = xi / (1 - xi) ≈ xiS/G ≈ L/V
13Ex.: 2-component absorber Specify yA,N+1, yD,N+1, xA,0, xD,0Specify L/V and yA,1. Find N and yD,1(xD,N,yD,N+1)•yA,1yD,1xA,0xD,0slope = L/VSeparation of A requires N = 3.1VLE(A)(xA,N,yA,N+1)•operating lineslope = L/Vy••VLE(D)••231231N•••Separation of D must also use N = 3 and same L/V.Trial-and-error: guess yD,1•yA,N+1yD,N+1xA,NxD,N(xA,0,yA,1)••(xD,0,yD,1)••xProbably a good idea to use a different graph for each component…
14Irreversible 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 + H2OEquilibrium lies far to the right: xA ≅ and yA ≅ 0Equation of the VLE line: yA = 0
16Ex.: Irreversible absorption with low efficiency Specify yN+1, x0, L/V, y1 ≠ 0By1 ≠ 0C + Rx0 = 0More than one actual equilibrium stage required …1operating lineslope = L/VyN+1•pseudo-VLE••EMV = 0.25265431y••••N••A + ByN+1A + R•AxN = 0••(x0,y1)••VLEx(A + R•A)
17Co-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 absorptionSpecify y0, x0 = 0, xN, yN = 0L, x0V, yNV, y0L, xNjOnly one theoretical equilibrium stage required, if the reaction is irreversible and mass transfer is fast …(x0,y0)•operating lineslope = -L/VyL, xjV, yj(x1,y1)•VLEx(A + R•A)
18VLE for dilute streamsWhen streams are dilute, VLE data can be approximated by a straight line.y = mxObtain 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.
19Analytical solution, when both VLE and op. line are straight change in vapor composition between adjacent stages:Op. line(x2,y3) •VLE: y = mx(Δy)2CMB:(x1,y2) ••(x2,y2)(Δy)1 = y2 - y1VLE:(x0,y1)••(x1,y1)general case: L/V ≠ m, then (Δy)j ≠ (Δy)j+1special case: if L/V = m, then (Δy)j = Δy.Δy1 + Δy2 + Δy3 + … = yN+1 – y1 = NΔyOR
20Kremser equation: L/V ≠ m use VLE:where A = L/mV ≡ absorption factorKremser equation:➠where y0 = mx0
21Other forms of Kremser equation For gas phase compositions (absorber columns):where S = mV/L ≡ stripping factor, and xN+1 = yN+1/mFor liquid phase compositions (stripper columns):solve for N:include Murphree vapor efficiency:More forms shown in Wankat, chapter 12.4
22Counter-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