Bubble-point type determination

The calculation is readily performed for the condition F/F — 0, analogous to the bubble-point type determination. If, however, F/F — 1, then the dew-point type determination must be used, such that... 

The bubble-point type determination at each point is, as noted,... 

A membrane separation is to be conducted with a continuous withdrawal of the permeate. At each linear point along the membrane during the separation, the reject phase composition is governed by a bubble-point type determination, starting with the initial feed composition. 

The latter approach, using L instead of V, is utilized in the spreadsheet calculations of Appendix 6. Note that the initial composition for L = Lj = f is the feed composition, and a bubble-point type determination establishes the initial composition (y,), of V = V,. (And note that the bubble-point type determination assumes that V7F = 0, where the notation V" is used for the permeate flux in a flash-vaporization type calculation.)... 

The bubble-point and dew-point type calculations are presented in Chapter 3 for a single-stage separation with perfect mixing. For the bubble-point type determination, the criterion is V/F = 0, and it is possible to determine the flux V" where... 

For the first circumstance, where no permeate outflow is produced, V2 0 and F = = L- and the bubble-point type determination on the... 

Since V" = V" is already known from a the bubble-point type determination on the feedstream, it follows that... 

The calculations are therefore the same up to and including the bubble-point type determination for the feedstream F, which also establishes the (same) value for the permeate flux V" (and the corresponding K-values). 

Given the (xf), these calculations would establish the respective values of F" for each of the limiting conditions, along with the respective compositions x, and y,. These limiting bubble-point type and dew-point type determinations have been previously described. 

A dew and bubble-point type of apparatus was developed that permitted direct determinations of the phase boundaries at low temperatures. The general principle of this method, the experimental apparatus and its operation, and the experimental results are presented below the data analysis with respect to refrigerants has been given previously [ ]. 

Furthermore, when V/F = 1, no finite separation occurs, albeit a dew-point type calculation gives a value for the degree or sharpness of separation in terms of mole fraction ratios or K-values. When V/F 0, again no finite separation occurs, albeit a bubble-point type calculation gives a value for the degree or sharpness of separation in terms of mole fraction ratios or K-values. (It may be added that, for a single pure component, whether or not a reject phase can be said to exist is of no concern, since V/F and L/F do not enter into the determination and calculations.)... 

Note that a bubble-point type calculation on the feedstream composition is used to arrive at a value for K, (or K. Albeit this value, in principle, varies from cell to cell as the composition changes, it nevertheless furnishes a means for determining a value. Whereas in vapor-liquid operations such as absorption, the operating temperature and pressure are used to assign a constant value for the liquid-vapor equilibrium vaporization ratio K for a particular component namely, the key component or components. (And, in general, the equilibrium vaporization ratio is also a function of composition, especially near the critical point of the mixture, and even in absorption, the temperature varies somewhat up and down the column due to enthalpic effects.)... 

It was determined in the bubble-point type calculation for Example 3.1, where V/F = 0, that... 

This determination is, first, for the purposes of assigning X-values for estimating the degree of separation. Other V/F ratios could have been used as well via the calculations of Example 3.1, but the bubble-point type calculation is the simplest. Moreover, the values of K do not change... 

In concurrent flow, V, and its composition yfj- may also be specified. If Vj = 0, its composition may be determined from a bubble-point type calculation on L, that is, the composition of V, is that of the first drop of permeate produced. Simultaneous numerical integrations can, in principle, be carried out to a specified value for any of the variables at point 2. 

In countercurrent flow, V-, and its composition (y,), may be specified. If Vj = 0, then its composition necessarily is determined from a bubble-point type calculation on L,. Unfortunately, neither L, nor its composition (X2), would yet be known. This introduces an extra or double trial-and-error element into the solution, even for a two-component system, where, say,... 

If Vj = 0, which is the usual case, then its composition can be determined from a bubble-point type calculation on F = L,. The overall solution does not, in principle, invoke trial and error, save for the special case of establishing the initial bubble-point determination to determine (yj) , starting at point 1 and proceeding to point 2. 

Note, for instance, that, if V, = 0, then its composition introduces the extra element of trial and error, since its composition has to be determined from a bubble-point type calculation on stream L but whose flow rate and composition are not yet known and must be assumed. 

Thus, the limiting conditions presumably mark the limits for the degree of separation attainable, although the recovery in either the reject outflow or permeate outflow is nil. That is, the feed is regarded as recovered either as reject only or permeate only. In the former circumstance, the composition of the minute amount or drop of permeate is determined from a bubble-point type calculation on the feed. In the latter, everything is recovered as permeate, so that the last drop of reject transformed to permeate is determined by a dew-point calculation on the permeate, which necessarily is of the same composition as the feed. These are the two extremes. In the one case, the bubble-point type calculation applies, in the other the dew-point type calculation applies. 

In turn, the permeate phase compositions for both the rectifying and the stripping sections are assumed to have the same common value at the feed location here, the requirement for continuity. This permeate composition can be determined by a flash-type calculation on the feedstream composition, in particular, a bubble-point type calculation. 

On determining V" = V" from the bubble-point type calculation on the feedstream F, the corresponding value of D can be determined from the previously assigned external reflux or recyde ratio LID and the yalue of B from the assigned external recycle ratio VIB. In turn, L and L can be determined, where as previously noted, L = L + F and V = V. It is built in that the various flow rates are mutually consistent. 

The feed composition, membrane permeability, and operating pressure levels are assigned as before, and a trial-and-error bubble-point type calculation performed for V/F = 0. This results in a value for V", which is not directly required for determining the degree of separation, other than being incorporated into the K -values but would be necessary in further determining membrane areal requirements. Thus, the bubble-point type calculation simultaneously establishes the values for K and K-, which are used in the separation calculations. 

The corresponding calculations are performed for the stripping section Jn term qf the stripping factors 5, and S, which depend on the value for V/6 or LIV (or V/L), which is assumed, as well as the values for the Kj, as determined from the bubble-point type calculation on the feed-stream composition. 

A third fundamental type of laboratory distillation, which is the most tedious to perform of the three types of laboratory distillations, is equilibrium-flash distillation (EFV), for which no standard test exists. The sample is heated in such a manner that the total vapor produced remains in contact with the total remaining liquid until the desired temperature is reached at a set pressure. The volume percent vaporized at these conditions is recorded. To determine the complete flash curve, a series of runs at a fixed pressure is conducted over a range of temperature sufficient to cover the range of vaporization from 0 to 100 percent. As seen in Fig. 13-84, the component separation achieved by an EFV distillation is much less than by the ASTM or TBP distillation tests. The initial and final EFN- points are the bubble point and the dew point respectively of the sample. If desired, EFN- curves can be established at a series of pressures. 

BP (bubble-point) methods. Temperatures are corrected iteratively by determinations of bubblepoints. The method is satisfactory for mixtures with relatively narrow ranges of volatilities. The parent program of this type is that of Wang and Henke (1966) which is flowsketched on Figure 13.16 and described in the next section. The availability of a FORTRAN program was cited earlier in this section. 

By simply knowing the phase equilibrium behavior and the composition within the beaker at the start of the experiment (x ), one can easily construct a residue curve by integrating Equation 2.8. Such integration is usually performed with the use of a numerical integration method (see later, Section 2.5.3), such as Runge Kutta type methods, remembering that at each function evaluation, a bubble point calculation must be performed in order to determine y(x). 

The apparatus can be also used to establish the dew point-bubble point locus. The great advantage of Kay s apparatus over most types of apparatus for determining critical properties is that it is relatively simple to operate. However, it does have the disadvantage that the samples are not degassed. This could lead to errors of 0.01 to 0.06 MPa in the critical pressure and up to 1 K in the critical temperature. 

The equilibrium curve, or IC-value, is for the most part represented by a straight line with slope K (or K,). Since this pertains to the more-permeable component, the slope is greater than unity. Furthermore, the K-value line lies above the 45° diagonal, albeit the actual determination is to a certain extent arbitrary, as per Example 3.1 of Chapter 3 that is, is it determined from a bubble-point, dew-point, or in-between type calculation on the feedstream composition ... 

Therefore, specifying or knowing L/V or V/L (or LID) yields V/F, from which a flash-type determination can be made that yields a value for V". As already indicated, however, this value expectedly does not vary appreciably using different values of V/f between the bubble-point and the dew-point types of calculation. 

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