UGPA2043 Unit Operation I Petrochemical Engineering

MulticomponentDistillationContinuous Distillation with Reflux

Multicomponent Distillation:IntroductionThe objective of distillation is to separate the feed into streams of nearly pure products.Multicomponent distillation involved several components and is more complex than binary distillation due to the increase of variables.The Fenske-Underwood-Gilliland method is a method widely used for making preliminary designs.In practice, multicomponent distillation is solved by using computers due to the numerous variables and the many iterations required to obtain convergence of the solutions to the equations.

Multicomponent Distillation:IntroductionIn multicomponent distillation, specifying the concentrations of one component in each of the top and bottom products does not fully characterise them.

If more than one concentration are specified for each of the top and bottom products, it is generally impossible to meet these specifications exactly.

Multicomponent Distillation:IntroductionThe desired separation usually refers to the amount of light key and heavy recovered in the distillate and bottom products respectively.

The actual mole fractions of the key components in the products are not usually specified, since they depend on the amount of non-keys in the feed.

Small changes of non-keys in the feed would significantly change the product compositions without significantly affecting the basic separation of light and heavy keys.

Multicomponent Distillation:Key ComponentsGenerally two components, known as the key components, are chosen whose concentrations or fractional recoveries in the top and bottom products are a good index of the separation achieved.The more volatile component is the light key (LK) The less volatile component is the heavy key (HK)The rest of the components are non-keys.If the non-key is more volatile than LK, it is called light non-key (LNK). If less volatile than HK, then is called heavy non-key (HNK).

Multicomponent Distillation:Key ComponentsThe distillate may be pure LK if the keys are the two most volatile components, since components heavier than the HK will tend to concentrate in the liquid phase.Often, there are components lighter than the LK, and they are nearly completely recovered in the distillate. xB,LNK = 0Any components heavier than the HK are usually completely recovered in the bottoms. xD,HNK = 0Although any two components can be nominated as keys, usually they are adjacent in the rank order of volatility. Such a choice is called a sharp separation.In sharp separations, the keys are the only components that appear in both top and bottom products in appreciable concentrations.

Multicomponent Distillation:Fenske Equation - NminThe minimum number of equilibrium stages (including partial reboiler) corresponds to total reflux:L/V = 1, hence top and bottom operating line reduced to yn = xn+1 (numbered from bottom up).Other assumptions:Constant molal overflow is valid.Relative volatility is taken as constant.

Multicomponent Distillation:Fenske Equation - NminFor component i at Stage-1:...... (1.39)From operating line, yn = xn+1 :...... (1.40)Similarly for Stage-2:...... (1.41)

Multicomponent Distillation:Fenske Equation - NminCombining Eq.(1.40) and (1.41):...... (1.42)Eq.(1.42) is readily extended into:...... (1.43)Similarly for component j :...... (1.44)

Multicomponent Distillation:Fenske Equation - NminCombining Eq.(1.43) and (1.44):... (1.45)

Multicomponent Distillation:Fenske Equation - NminWith the assumption that ij is constant:...... (1.46)Fenske EquationTop: xn+1 = xDBot: x1 = xB

Multicomponent Distillation:Fenske Equation - NminA more convenient form of Eq.(1.46) is obtained by using distillate and bottom flowrates (di , bi), and replaced by a geometric mean of the top and bottom stage values....... (1.47)where

Multicomponent Distillation:Fenske Equation - NminThe minimum number of equilibrium stages depends on the degree of separation of the two key components and their relative volatility.It is independent of feed-phase condition.Fenske equation is quite reliable except when the relative volatility varies appreciably over the column, and/or when the mixture forms nonideal liquid solutions.

Distributed &Undistributed ComponentsDistributed component is found in both distillate and bottom products. LK and HK are always distributed, as are any components having volatilities between those two keys.Undistributed component is only found in one product. LNK are almost completely recovered in the distillate and HNK are found almost completely in bottom products.

Location of Invariant Zonesat Minimum Reflux, RminAt invariant (pinch-point) zone, there is no change in either liquid or vapour concentrations from plate to plate, so xn-1 = xn and yn+1 = yn .For binary distillation at Rmin, pinch-point occurs at the feed plate (refer McCabe-Thiele diagram at Rmin).For multicomponent distillation, there are pinch-point zones at or above and/or below the feed plate.

Location of Invariant Zonesat Minimum Reflux, RminFor class 1 (one pinch-point) separation, all components in the feed distribute to both the distillate and bottom products. The single pinch point bridges the feed stage.FeedinvariantzoneFeedClass 1(one pinch point)Class 2(two pinch point)

Location of Invariant Zonesat Minimum Reflux, RminFor class 2 (two pinch-point) separation, one or more of the components appear in only one of the products. (feed with undistributed components)Stages between the feed stage and the rectifying section invariant zone remove heavy components that do not appear in the distillate.Stages between the feed stage and the stripping section invariant zone remove light components that do not appear in the bottom.

Multicomponent Distillation:Underwood Equation - RminFrom top operating line,At invariant zone, yn+1,i = yn,i and n = ,

Multicomponent Distillation:Underwood Equation - RminRearrange,......(1.48)Similarly for stripping section,......(1.49)

Multicomponent Distillation:Underwood Equation - RminTo solve Eq.(1.48) and (1.49), an approximate but fairly accurate method to determine Rmin was developed by Underwood, by introducing a term .Assumptions:constant molal overflow for each component is the same in the upper and lower invariant zones,

HK usually taken as ref.

Multicomponent Distillation:Underwood Equation - RminRectifying section:......(1.50)Similarly for stripping section,......(1.51)

Multicomponent Distillation:Underwood Equation - RminCombine Eq.(1.50), (1.51), feed line:......(1.52)Underwood Equation

Multicomponent Distillation:Underwood Equation - RminWhen only the two key components distribute, Eq.(1.52) is solved iteratively for a root of that satisfies:HK < < LK The value of is then used to get Rmin by Eq.(1.50),......(1.53)

Multicomponent Distillation:Underwood Equation - RminIf any non-key components are suspected of distributing, Underwood equation Eq.(1.52) is solved for m roots of , where m = C - 1 and C = number of distributing components.Each root of lies between an adjacent pair of relative volatilities of distributing components.LNK > 1 > LK > 2 > HK > 3 > HNK

Multicomponent Distillation:Underwood Equation - RminWith these m roots of , Eq.(1.53) is written m times and solved simultaneously to yield Rmin and the unknown value of xD,i .And the solution must satisfy the condition

Underwood Equation - Rmin:ExampleA mixture of 4 mol% n-pentane, 40% n-hexane, 50% n-heptane and the rest n-octane is to be distilled at 1 atm with 98% of the hexane and 1% of the heptane recovered in the distillate.Find the minimum reflux ratio for a liquid feed at the boiling point.

Example Solution

Only for saturated liquid. Terms in () are the fractional recovery of A & B in distillate.

Example Solution

(1.52)

Multicomponent Distillation:Gilliland Correlation R, NA simple empirical method by Gilliland is much used for preliminary estimates, although precise calculation is best accomplished by computer.Gilliland correlation relates the actual number of stage, N, with minimum reflux ratio, Rmin and minimum number of stages, Nmin .The correlation is based mainly on calculations for systems with nearly constant relative volatility and may be considered in error for nonideal systems.

Multicomponent Distillation:Gilliland Correlation R, NThe data for Gilliland correlation cover the following ranges of conditions:Number of component = 2 to 11 q = 0.28 to 1.42 P = vacuum to 600 psig = 1.11 to 4.05 Rmin = 0.53 to 9.09 Nmin = 3.4 to 60.3Use this correlation only for rough estimates.The error for N can be 30% but usually is 7%.

Multicomponent Distillation:Gilliland Correlation R, N

Multicomponent Distillation:Gilliland Correlation R, NThe line in the graph can be represent by the following equation developed by Molokanov et. al.:......(1.54)Nmin from Fenske equationRmin from Underwood equation

Multicomponent Distillation:Feed-Stage LocationThe optimum feed stage can be located by assuming that the ratio of stages above the feed to stages below the feed is the same as the ratio determined by simply applying the Fenske equation to the separate section at total reflux conditions to give:Unfortunately, this equation is not reliable except for fairly symmetrical feeds and separations.

Multicomponent Distillation:Feed-Stage LocationA reasonably good approximation of optimum feed-stage location can be made by employing the empirical equation of Kirkbride:......(1.55)

**