IDEAL STAGE Feed F, x F Distillate D, x D Bottom Product B, x B SINGLE-STAGE (FLASH) DISTILLATION UNECONOMICAL

F, x F V1V1 V2V2 V3V3 V5V5 V4V4 V6V6 L5L5 L4L4 L3L3 L2L2 L1L1 L0L0 Countercurrent multistage contact

Simple counter-current flow cannot give as complete a separation as required N =  More concentrated L 0 uneconomical x 0 is fixed by other consideration Where does L 0 come from?

Multistage cascade with reflux at both ends for distillation V1V1 -q C m p LCLC D F Enriching section Stripping section F-1 F+1 N 1 B C S qSqS L0L0 Condenser Reboiler F

ZERO REFLUX No liquid returned to stage 1 No condensation of V 2 to supply liquid leaving stage 1 The vapor leaving stage 1 would be the same quantity and composition of the vapor leaving stage 2. The vapor leaving stage 2 would be the same quantity and composition of the vapor leaving stage 3. Etc. V1V1 -q C LCLC D F F 1 C 2 V2V2 V3V3 3 Multistage cascade with no liquid reflux

F N-2 N-1 N F B S qSqS If the vapor reflux were eliminated: No vapor returned to stage N No vaporization of to supply vapor leaving stage N The liquid leaving stage N would be the same quantity and composition of the liquid leaving stage N-1. The liquid leaving stage N-1 would be the same quantity and composition of the liquid leaving stage N-2. Etc. Multistage cascade with no vapor reflux

A fractionating column by its inherent nature has two limits of operation based upon reflux ratio: Minimum reflux Total reflux

MINIMUM REFLUX D B F L0L0 There is insufficient liquid returned to the column There is only an infinitesimal change in vapor and liquid compositions through the plates. Infinite number of plates would be needed. Actual operation of a column below or at minimum reflux is impossible. Schematic representation of minimum reflux operation

TOTAL REFLUX All condensate is returned to the column It requires the least number of stages. Practically no overhead product and no bottom product can be made and no feed is introduced. It is possible to operate experimentally a fractionating column at total reflux when the system inventory is large and only very small samples of distillate and bottoms are removed. D = 0 B = 0 F = 0 Schematic representation of total reflux operation

MINIMUM REFLUX VS TOTAL REFLUX Large reflux ratio Small reflux ratio More coolant More heating medium Greater operating cost Greater number of plates Greater investment cost $/unit product Number of stages N min Total cost Operating cost Equipment cost Optimum design at minimum cost Schematic relationship between reflux ratio and number of stages

V 1, y 1, H 1 L 1, x 1, h 1 L0x0h0L0x0h0 DxDhDDxDhD qDqD Total condenser 1 2

Over-all: Component i: (1) (2) (3) (4) (5) V 1 = L 0 + D MATERIAL BALANCE AROUND TOTAL CONDENSER

V 1 H 1 + q D = L 0 h 0 + D h D (6) ENTHALPY BALANCE AROUND TOTAL CONDENSER The total heat removed in the condenser can be expressed in terms of heat per unit mass of distillate stream times the mass of stream. q D = D Q D V 1 H 1 + D Q D = L 0 h 0 + D h D V 1 H 1 + (V 1 – L 0 ) Q D = L 0 h 0 + (V 1 – L 0 ) h D (7) (8) (9) Introducing eq. (1) into eq. (8) to eliminate D yields:

(10) (11) V 1 H 1 + (V 1 – L 0 ) Q D = L 0 h 0 + (V 1 – L 0 ) h D Introducing eq. (1) into eq. (8) to eliminate V 1 yields:

MATERIAL BALANCE IN ENRICHING SECTION V 1, y 1, H 1 L 1, x 1, h 1 L0x0h0L0x0h0 DxDhDDxDhD qDqD V m+1 y m+1 H m+1 LmxmhmLmxmhm F

Over-all: Component i: (12) (13) (14) V m+1 = L m + D Introducing eq. (12) into eq. (13) to eliminate D results in

(15) Introducing eq. (12) into eq. (13) to eliminate V m+1 results in:

ENTHALPY BALANCE IN ENRICHING SECTION (16) Introducing eq. (12) into eq. (16) to eliminate D results in (17)

(18) Introducing eq. (12) into eq. (16) to eliminate V m+1 results in:

Partial condenser MATERIAL AND ENTHALPY BALANCES AROUND PARTIAL CONDENSER V 1, y 1, H 1 L 1, x 1, h 1 L0x0h0L0x0h0 DyDHDDyDHD qDqD

Over-all: Component i: (19) (20) (21) V 1 = L 0 + D (22)

(23)

ENTHALPY BALANCE: V 1 H 1 + q D = L 0 h 0 + D H D (24) The total heat removed in the condenser (q D ) can be expressed in terms of heat per unit mass of distillate stream times the mass of stream. q D = D Q D V 1 H 1 + D Q D = L 0 h 0 + D H D (25) (26)

V 1 H 1 + (V 1 – L 0 ) Q D = L 0 h 0 + (V 1 – L 0 ) H D (27) Replacing D in equation (26) with (V 1 – L 0 ):

(28) (L 0 + D) H 1 + D Q D = L 0 h 0 + D H D Replacing V 1 in equation (26) by (L 0 + D):

MATERIAL BALANCE IN ENRICHING SECTION WITH PARTIAL CONDENSER V 1, y 1, H 1 L 1, x 1, h 1 L0x0h0L0x0h0 DyDhDDyDhD qDqD V m+1 y m+1 H m+1 LmxmhmLmxmhm F m

Over-all: Component i: (29) (30) (31) V m+1 = L m + D D is eliminated from equation (30) by substituting D with (V m+1 – L m ):

(32) V m+1 is eliminated from equation (30) by substituting V m+1 with L m + D

ENTHALPY BALANCE IN ENRICHING SECTION V 1, y 1, H 1 L 1, x 1, h 1 L0x0h0L0x0h0 DxDhDDxDhD qDqD V m+1 y m+1 H m+1 LmxmhmLmxmhm F

(33) (34) D is eliminated from equation (33) by substituting D with V m+1 – L m

V m+1 is eliminated from equation (33) by substituting V m+1 with L m + D (35)

MATERIAL BALANCE IN STRIPPING SECTION qBqB BxBhBBxBhB y p+1 H p+1 xphpxphp F

Over-all: Component i: (36) (37) (38) Replacing B in equation (37) with

ENTHALPY BALANCE: q B = B Q B (39) (40) (41)

MATERIAL & ENTHALPY BALANCES ABOUT REBOILER qBqB BxBhBBxBhB y N+1 H N+1 yNHNyNHN

Over-all: Component i: (42) (43) (44) Replacing B in equation (43) with

MATERIAL BALANCE AROUND THE FEED PLATE F = F V + F L H p+1 y p+1 hpxphpxp V m+1 H m+1 y m+1 LmhmxmLmhmxm

Over-all: Component i: (45) (48) (46) (47)

(49) If the feed is a saturated liquid, the last term in eq. (49) drops out. If the feed is a saturated vapor, the middle term on the right side of eq. (49) drops out.

ENTHALPY BALANCE AROUND THE FEED PLATE (50) (51) If the feed is a saturated liquid, the last term in eq. (51) drops out. If the feed is a saturated vapor, the middle term on the right side of eq. (51) drops out.

In liquid mixture / solution the molal enthalpy of the mixture at a given T and P is the sum of the partial molal enthalpies of the components composing the mixture. (52) In “regular” / ideal mixtures: (53) For gaseous / vapor mixtures at normal T and P: (54)