Continuous countercurrent extraction

Absorption and Stripping

Some important definitionsIn 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 theextracting 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 gasstripperMEA + CO2N2N2 + CO2MEAH2, COMEA + CO2Gases in at the bottom. Liquids in at the top. (Why?)solvent coolerabsorberH2NCH2CH2OH(MEA)hot feed gasH2, CO, CO2syn gasheat exchangerKey simplifying assumptionsstripping 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 + 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 yBLabeling streamsnth stagePacked 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.HETHETPLn-1xn-1VnynLnxnVn+1yn+1xn, 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) / timeFractional stages are possible with packed columns.Since A is transferred in one direction only (liq gas, or gas liq), V and L are not constant. Therefore CMO is not valid. Using mole ratioswhat is constant?G carrier gas flow rate, moles B/time since B is presumed insoluble, Gn = Gn+1 = GS solvent flow rate, moles C/timesince C is presumed non-volatile, Sn = Sn-1 = S

vapor mole ratio:

liquid mole ratio:McCabe-Thiele analysis of strippingfeedS, X0stripping gasG, YN+1G, Y1S, XNstage 1stage Nstage jS, XjG, Yj+1CMB: GYj+1 + SX0 = GY1 + SXj

operating line equation:

Yj+1 = (S/G)Xj + [Y1 (S/G)X0]

slope = S/GYint = [Y1 (S/G)X0]

analogous to operating line for stripping section of distillation column

usually specified: X0, YN+1, S/G, 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 lineEx.: Analysis of counter-current stripper

VLE (may be curved)1. Plot VLE data as mole ratios (unless x0 < 0.05)Note: y = x line has no use here.

2. Plot (XN, YN+1) and (X0, Y1) and draw operating line. It will be below the VLE line.N = 3

(X0,Y1)3. Step off stages (use Murphree efficiencies if available).Given X0, XN, YN+1 and S/G, find N. (S/G)max operating line slope = S/G(XN,YN+1) 1 2 3To find minimum stripping gas flow rate (Gmin):1. Plot X0 on VLE line (watch for earlier pinch point, if VLE is curved).X02. Calculate Gmin = S / (S/G)maxRule-of-thumb: (S/G)opt 0.7 (S/G)maxEstimating fractional stagesYXXN(X3, Y4)(X4, Y4)VLEop. lineX3XNX4

fractional stage requirementMcCabe-Thiele analysis of absorberSolventS, X0feedG, YN+1G, Y1S, XNstage 1stage Nstage kS, Xk-1G, YkCMB: GYN+1 + SXk-1 = GYk + SXN

operating line equation:

Yk = (S/G)Xk-1 + [YN+1 (S/G)XN]

slope = S/GYint = [YN+1 (S/G)XN]

analogous to operating line for rectifying section of distillation column

usually specified: X0, YN+1, S/G, Y1

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

VLE (may be curved)1. Convert VLE data to mole ratios (unless x0 < 0.05)Note: y = x line has no use here.

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).N = 3

(XN,YN+1)3. Step off stages (use Murphree efficiencies if available).Given X0, Y1, YN+1 and S/G, find N. (S/G)min operating line slope = S/G(X0,Y1) 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). 213 YN+1 Ex.: Analysis of counter-current absorber2. Calculate Smin = G (S/G)minRule-of-thumb: (S/G)opt 1.4 (S/G)minMultiple non-interacting solutesMultiple 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

Ex.: 2-component absorber1NxA,0xD,0yA,N+1yD,N+1yA,1yD,1xA,NxD,N

VLE(A)Separation of A requires N = 3.

(xA,N,yA,N+1) operating line slope = L/V(xA,0,yA,1) 231 Specify yA,N+1, yD,N+1, xA,0, xD,0Specify L/V and yA,1. Find N and yD,1VLE(D)Separation of D must also use N = 3 and same L/V.Trial-and-error: guess yD,1

(xD,0,yD,1) 231(xD,N,yD,N+1)slope = L/VProbably a good idea to use a different graph for each componentyxIrreversible absorptionAdd reagent R to solvent. R reacts essentially irreversibly with solute A to form non-volatile products

R + A(g) RA(l)

e.g., NaOH + H2S(g) Na2S + H2OEquilibrium lies far to the right: xA 0 and yA 0Equation of the VLE line:yA = 0Ex. Irreversible absorption1NC + Rx0 = 0A + ByN+1By1 = 0C + RAxN = 0

yN+1 operating line slope = L/V(x0,y1)Specify yN+1, x0, L/V.Required: xN = y1 = 0VLEOnly one theoretical equilibrium stage required (x1,y1) (A + RA)yxEx.: Irreversible absorption with low efficiency1NC + Rx0 = 0A + ByN+1By1 0A + RAxN = 0

yN+1(x0,y1)Specify yN+1, x0, L/V, y1 0VLEMore than one actual equilibrium stage required (A + RA)265431 operating line slope = L/VEMV = 0.25yxpseudo-VLECo-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

(x1,y1)Specify y0, x0 = 0, xN, yN = 0(A + RA)L, x0V, yNV, y0L, xNjL, xjV, yj

(x0,y0)VLE operating line slope = -L/VOnly one theoretical equilibrium stage required, if the reaction is irreversible and mass transfer is fast yxVLE for dilute streamsObtain the slope, m, from Henrys Law:

PB = HB xBwhere yB = PB/Ptotal

PB is the partial pressure of B, and HB is the Henrys Law constant.Note: HB = HB(T), like an equilibrium constant.

When streams are dilute, VLE data can be approximated by a straight line.

y = mx

Analytical solution, when both VLE and op. line are straightVLE: y = mxOp. line(x0,y1)(x1,y1)(x1,y2) (x2,y2)(y)1 = y2 - y1(x2,y3) (y)2

change in vapor composition between adjacent stages:

special case: if L/V = m, then (y)j = y. y1 + y2 + y3 + = yN+1 y1 = Ny

CMB:

VLE:

ORgeneral case: L/V m, then (y)j (y)j+1Kremser equation: L/V m

use VLE:

where A = L/mV absorption factor

where y0 = mx0

Kremser equation:Other forms of Kremser equation

More forms shown in Wankat, chapter 12.4

where S = mV/L stripping factor, and xN+1 = yN+1/mFor liquid phase compositions (stripper columns):

For gas phase compositions (absorber columns):

solve for N:

include Murphree vapor efficiency:Counter-current column sizingHeight: 1. measure HETP2. measure EMV3. 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 column3. calculate D using same procedure as distillation column