Page 16 - Applied Process Design For Chemical And Petrochemical Plants Volume II

Distillation 5

position of the equilibrium for the vapor and liquid phas- Interpolation between charts of convergence pressure can
es, and is the critical pressure for a system at a specific be calculated, depending on how close the operating pres
temperature. The convergence pressure represents the sure is to the convergence pressure. The K-factor (or K-val-
pressure of system at a temperature when the vapor-liquid ues) do not change rapidly with convergence pressure, Pk
separation is no longer possible [79]. The convergence (psia) [79].
pressure generally is a function of the liquid phase, and The use of the K-factor charts represents pure compo-
assumes that the liquid composition is known from a flash nents and pseudo binary systems of a light hydrocarbon
calculation using a first estimate for convergence pressure, plus a calculated pseudo heavy component in a mixture,
and is usually the critical pressure of a system at a given when several components are present. It is necessary to
temperature. The following procedure is recommended determine the average molecular weight of the system on
by Reference 79: a methane-free basis, and then interpolate the K-value
between the two binarys whose heavy component lies on
Step 1. Assume the liquid phase composition or make either side of the pseudo-components. If nitrogen is pre-
an approximation. (If there is no guide, use the total feed sent by more than 3-5 mol%, the accuracy becomes poor.
composition.) See Reference 79 to obtain more detailed explanation and
Step 2. Identlfy the lightest hydrocarbon component a more complete set of charts.
that is present at least 0.1 mole % in the liquid phase.
Step 3. Calculate the weight average critical tempera- Non-Ideal Systems
ture and critical pressure for the remaining heavier com-
ponents to form a pseudo binary system. (A shortcut Systems of two or more hydrocarbon, chemical and
approach good for most hydrocarbon systems is to calcu- water components may be non-ideal for a variety of rea-
late the weight average T, only.) sons. In order to accurately predict the distillation perfor-
Step 4. Trace the critical locus of the binary consisting mance of these systems, accurate, experimental data are
of the light component and psuedo heavy component. necessary. Second best is the use of specific empirical rela-
When the averaged pseudo heavy component is between tionships that predict with varying degrees of accuracy the
two real hydrocarbons, an interpolation of the two critical vapor pressure-concentration relationships at specific tem-
loci must be made. peratures and pressures.
Step 5. Read the convergence pressure (ordinate) at the Prausnitz [54] presents a thorough analysis of the appli-
temperature (abscissa) corresponding to that of the cation of empirical techniques in the absence of experi-
desired flash conditions, from Figure 8-3A [79]. mental data.
Step 6. Using the convergence pressure determined in The heart of the question of non-ideality deals with the
Step 5, together with the system temperature and system determination of the distribution of the respective system
pressure, obtain K-values for the components from the components between the liquid and gaseous phases. The
appropriate convergence-pressure Kcharts. concepts of fugacity and activity are fundamental to the
Step 7. Make a flash calculation with the feed composi- interpretation of the non-ideal systems. For a pure ideal
tion and the K-values from Step 6. gas the fugacity is equal to the pressure, and for a compo-
Step 8. Repeat Steps 2 through 7 until the assumed and nent, i, in a mixture of ideal gases it is equal to its partial
calculated convergence pressures check within an accept- pressure yip, where P is the system pressure. As the system
able tolerance, or until the two successive calculations for pressure approaches zero, the fugacity approaches ideal.
the same light and pseudo heavy components agree with- For many systems the deviations from unity are minor at
in an acceptable tolerance. system pressures less than 25 psig.
The ratio f/f is called activity, a. Note: This is not the
The calculation procedure can be iterative after starting activity coefficient. The activity is an indication of how
with the first “guess.” Refer to Figure 8-3A to determine “active” a substance is relative to its standard state (not
the most representative convergence pressure, using necessarily zero pressure), f. The standard state is the ref-
methane as the light component (see Figure 8-3B for erence condition, which may be anything; however, most
selecting K values convergence pressure.) references are to constant temperature, with composition
For a temperature of 1OO”F, the convergence pressure is and pressure varying as required. Fugacity becomes a cor-
approximately 2,500 psia (dotted line) for the pseudo sys- rected pressure, representing a specific component’s devi-
tem methane-n-pentane (see Figure 8-3C). For n-pentane ation from ideal. The fugacity coefficient is:
at convergence pressure of 3,000 psia (nearest chart) the
K-value reads 0.19. The DePriester charts [SO] check this
quite well (see Figures 84 and B, and Figure 8-3D). (text continued on page 12)