chapter_3_distillation_ponchon savarit method

• Ponchon-Savarit method

• takes into account latent heats, heats of solution & sensible heats

• no assumption of molal overflow rates

• graphical procedure combining enthalpy & material balances

• provides information on condenser & reboiler duties

Use enthalpy concentration data

The data that require for enthalpy concentration diagram are:

Heat capacity of the liquid, Cp

Boiling temperature, Tb

Latent heats of vaporization, λ Heat of solution, ∆Hsol

The diagram at a given constant pressure is based on reference states of liquid and temperature such as 273K

Use enthalpy concentration data

The data that require for enthalpy concentration diagram are:

Heat capacity of the liquid, Cp

Boiling temperature, Tb

Latent heats of vaporization, λ Heat of solution, ∆Hsol

The diagram at a given constant pressure is based on reference states of liquid and temperature such as 273K

The saturated liquid line in enthalpy h kJ/kg can be obtained from the following equation below:

(1)

T=boiling point of temperature T0=reference temperature CP=liquid heat capacity ∆Hsol=heat of solution at T0 (usually is

neglected)

The saturated vapor line can be obtained from the following equation below:

(2)

T=boiling point of temperature T0=reference temperature CPy=vapor heat capacity λA, λB=latent heat at T0

Normally value of λA and λB not be given, only the value of λAb and λBb

λAb= latent heat at boiling point of pure component A

λBb=latent heat at boiling point of pure component B

But equation (2) need the value of latent heat at reference temperature (T0), so that;

For simplify, normally we take the value of T0 equal to the boiling point temperature of component that most volatile which is component A. Thus it,

So, only the value of that has to convert to .

Overall balance

F=V+L (3)

Balance on the most volatile component A

FxF=VyD + LxL (4)

From (3) and (4)

(5)

Energy balance

FHF=VHV + LhL (6)

From equation (3) & (6)

(7) If heat input to streams, so equation (6)

become:

(8)

So, total input enthalpies =

Overall balance

(9)

Component material balance

(10)

Rearranging equation (9) and writing for various streams, (11)

The difference between two streams passing each other is constant and has the value of D kg mol/h.

Rearranging equation (10), (12)

The composition of this difference stream is constant a .

Making an enthalpy balance and then rearranging,

(13)

(14)

(15)

Again the difference in enthalpy between the streams passing each other is constant, with the enthalpy of this stream being ,

where qc is the condenser duty in kJ/h.

Number of theoretical steps in the enriching section

This difference point will be called D’. Point D’ is a common operating point for all values of and in enriching section of the distillation tower that having an enthalpy and a composition of . The intersection of is shown in the diagram having the composition y1=xD for a total condenser. The liquid L1 is in equilibrium with V1 and is located by drawing a tie line through V1 intersecting the saturated liquid line at L1. Next, a line is drawn as L1D’, which is intersects saturated vapor line at V2.

Overall balance (16)

Component material balance (17)

Rearranging equation (16) and writing it for various trays, (18)

Again this difference between two streams passing each other is constant at W kgmol/h.

Rearranging equation (17) (19)

The composition of this difference stream is constant at xW.

Making an enthalpy balance with qR kJ/h entering the reboiler and then rearranging,

(20)

(21) (22)

Again the difference in enthalpy between

the streams passing each other is constant, with enthalpy being .

This difference point in the stripping section will be called , having an enthalpy

and a composition . This point is an operating point just as is for the enriching section. The point is plotted below. Starting at point W a tie line is drawn through this point intersecting the saturated vapor line , which is in equilibrium with . Next, line is drawn, which intersects the saturated liquid line at . By rearranging equation (18),

(23)

Hence, must be on the line between and . Next, the tie line is drawn. This

process is continued in stepping off the theoretical plates.

As in the McCabe Thiele analysis, there are two operating points for the entire distillation tower. In order to obtain a relation between these points we make an overall enthalpy balance on the entire column.

(24)

Rearranging,

(25)

The two terms on the right represent the operating points and . The enthalpy of point is and of

is . Hence, the three points , and must all lie on straight line with in between and .

Reflux ratio (R)

Reflux ratio at the top of the tower

A mixture of 50 wt% ethanol and 50% water which is saturated liquid at boiling point is to be distilled at 101.3kPa pressure to give a distillate containing 85 wt% ethanol and a bottoms containing 3 wt% ethanol. The feed rate is 4536 kg/h and a reflux ratio of 1.5 is to be used.

a)Calculate the amounts of distillate and bottoms

b)Calculate the number of theoretical trays needed using enthalpy concentration plot

c) Calculate the condenser and reboiler heat loads

Draw the enthalpy-concentration plot & the xy equilibrium plot on the same graph.

Determine the points xF, xD,xW. Use the following equation to calculate H’

H1=enthalpy of vapor at xD

hD=enthalpy of liquid at xD

Locate point D’ or H’ at (xD, H’) Locate point V1 at (xD, H1) Locate point L0 at (xD, hD) Draw the line from D’ to intersect hF

(enthalpy of saturated liquid at xF) and the vertical line of xW). The point of intersection shows W’ or H’W.

From point V1, draw a line down to 45o line. Then, draw a horizontal tie line to touch the xy equilibrium curve. Draw a line up to the liquid enthalpy curve. This point is L1.

Plot an operating line from L1 to D’, intersecting the vapor enthalpy curve at V2. From V2, draw a vertical line down to the equilibrium curve. Draw yet another line, go up to obtain L2; repeat the process until you exceed xF.

When you exceed xF, draw an operating line from W’ to L3 intersecting the vapor enthalpy curve to obtain V4. Repeat the process until you exceed xW.

Draw a tie line for L1 to V1, L2 to V2, L3 to V3 and so on.

Number of tie lines=number of stages.

Determine H’min from the graph.

-From point, (xF,hF), draw a line down to equilibrium curve. Then, draw a horizontal line to 45o line. Next, draw a line up to saturated vapor line. Let say the point is V.

-Then, draw a line from point (xF,hF) to point V till you reach the vertical line of xD.

-H’min is the point intersect between the line from point (xF,hF) to point V and vertical line

of xD.