Page 310 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

312 Chapter 11 Distillation

Other shortcut methods
A conservative design of multicomponent distillation can be quickly arrived at by considering the
light key component and all lighter components as one group, and the heavy key component and all
heavier components as another group to get X F ,X D ,X B . The a of the keys themselves are used for
calculation.
The presence of components having a molar ratio (D/B) in distillate (D) to bottoms (B) greater than
100 or less than 0.01 can be neglected for quick calculations. The group a values are found by plotting
log(D/B) versus log(a) with a straight line drawn through the major points. The a value for each group
is read at the corresponding D/B value for the group. This procedure was introduced by Hengstebeck.
Rigorous methods
Rigorous methods involve tray-to-tray calculation. This considers mass balances and equilibrium
relationship equations, or in the fullest form includes both heat as well mass balances across each tray
along with equilibrium relationship equations.
There are several approaches, all of which are quite intricate and are more amenable to be pro-
grammed and solved using computers. These are primarily for simulating the operation of a column
where the total number of trays (N) and the feed tray location (N F ) are known and the key operating
parameters (reflux ratio, column pressure, bottom tray temperature, etc.) are known. The basic approach
is to guess (i) the temperature and pressure profile in the column, (ii) the molar composition of top and
bottom product (or top and bottom tray compositions), (iii) stream flows, etc., and then follow an
iterative procedure to arrive at the steady-state stream flows, compositions and stage temperatures.
In case of a design problem, simulations are carried out with several options of N, N F , etc., to arrive
at the configurations delivering the functional requirements of the design objectives and meeting
constraints for the specific design problem, e.g., top and bottom compositions and limits on specific
components in product streams. The most suitable design option is chosen based on economic eval-
uation of these competing alternatives.
A distillation column is conceived to be represented by a set of equations known as the MESH
equation and these are
(M) e Material or flow balance equations
(E) e Equilibrium equations including bubble point and dew point equations
(S) e Summation or stoichiometric equations
(H) e Heat balance equations
These equations are framed around the stages of vapoureliquid contacting. The condenser and
the reboiler are also considered as stages. The simple contacting stages, feed stage(s), product draw
stage(s) along with the reboiler and condenser constitute the column model. Fig. 11.13A shows the
overall structure of a column with two feed, two product draws, partial condenser and reboiler. The
top products are vapour ‘V top ’ and liquid ‘L top ’ and the reflux is ‘L 1 ’ and hence the reflux ratio is
R ¼ L 1 /(V top þ L top ). V i , j and L i,j stand for the ith component flow rates leaving stage j in vapour and
liquid phase. V j ,L j are the total molar flow rates of vapour and liquid leaving stage j and their
corresponding molar enthalpies are H V , j and H L , j , respectively. The contacting stage, feed stage,
product draw stage are schematically shown in Fig. 11.13BeD, respectively. There F i and F are the
flow rates of the i-th component and the total feed. K i,F is the distribution coefficient of the i-th
component in feed after flashing at the conditions of the feed tray. H F is the molar enthalpy of the
feed. In Fig. 11.13D, molar flow rates of the i-thcomponentinthe vapourand liquidproduct streams
, and the total product flow rates are V and L. Molar enthalpy of these streams are
are V i;N P and L i;N P
, respectively.
H V;N P and H L;N P