Temperature-Specified Bubble Point

FIGURE 8.17 Temperature-composition diagram for ethanol-water at 1 atm, using data points from [1]. The curves are simple smooth interpolations. The arrows show the graphical solution for the bubble point (temperature-specified) and vapor composition. 

ERF error flag, integer variable normally zero ERF= 1 indicates parameters are not available for one or more binary pairs in the mixture ERF = 2 indicates no solution was obtained ERF = 3 or 4 indicates the specified flash temperature is less than the bubble-point temperature or greater than the dew-point temperature respectively ERF = 5 indicates bad input arguments. 

BUDET calculates the bubble-point temperature or dew-point temperature for a mixture of N components (N < 20) at specified pressure and liquid or vapor composition. The subroutine also furnishes the composition of the incipient vapor or liquid and the vaporization equilibrium ratios. 

From Table 13-5 it can be seen that the variables subject to the designer s control are C -i- 3 in number. The most common way to utilize these is to specify the feed rate, composition, and pressure (C -i- 1 variables) plus the drum temperature To and pressure To. This operation will give one point on the equilihrium-flash cuive shown in Fig. 13-26. This cui ve shows the relation at constant pressure between the fraction V/F of the feed flashed and the drum temperature. The temperature at V/F = 0.0 when the first bubble of vapor is about to form (saturated liquid) is the bubble-point temperature of the feed mixture, and the value at V/F = 1.0 when the first droplet of liquid is about to form (saturated hquid) is the dew-point temperature. 

For a given drum pressure and feed composition, the bubble- and dew-point temperatures bracket the temperature range of the equilibrium flash. At the bubble-point temperature, the total vapor pressure exerted by the mixture becomes equal to the confining drum pressure, and it follows that X = 1.0 in the bubble formed. Since yj = KjXi and since the x/s stiU equal the feed concentrations (denoted bv Zi s), calculation of the bubble-point temperature involves a trial-and-error search for the temperature which, at the specified pressure, makes X KjZi = 1.0. If instead the temperature is specified, one can find the bubble-point pressure that satisfies this relationship. 

Compute a new set of values of tear variables by computing, one at a time, the bubble-point temperature at each stage based on the specified stage pressure and corresponding normalized values. The equation used is obtained by combining Eqs. (13-69) and (13-70) to eliminate yj j to give... 

The overhead purity is specified as Xp = 0.95. The reflux temperature is the bubble point temperature (saturated reflux), and the external reflux ratio is set at R = 4.5. 

For a total condenser, the vapor composition used in the equilibrium relations is that determined during a bubble point calculation based on the actual pressure and liquid compositions found in the condenser. These vapor mole fractions are not used in the component mass balances since there is no vapor stream from a total condenser. It often happens that the temperature of the reflux stream is below the bubble point temperature of the condensed liquid (subcooled condenser). In such cases it is necessary to specify either the actual temperature of the reflux stream or the difference in temperature between the reflux stream and the bubble point of the condensate. 

Explain in your own words the terms bubble point, boiling point, and dew point of a mixture of condensable species, and the difference between vaporization and boiling. Use Raoult s law to determine (a) the bubble-point temperature (or pressure) of a liquid mixture of known composition at a specified pressure (or temperature) and the composition of the first bubble... 

Bubble point temperatures and vapor compositions on a stage are calculated iteratively by assuming a temperature and computing the bubble point pressure. A solution is reached when the calculated pressure matches the specified value (110 kPa). The calculations below demonstrate the final iteration for the solvent feed stage Ng. 

If the equation is not satisfied to within a specified small tolerance, the summation is repeated using a new estimated temperature until convergence is obtained The converged T is the bubble-point temperature. The method is a one-dimensional temperature search. 

Example 1-2 (a) If for a three-component mixture, the following information is available, compute the bubble-point temperature at the specified pressure of P = 1 atm by use of Newton s method. Take the first assumed value of Tn to be equal to 100°F. 

Since the a/s are independent of temperature, they may be computed by use of the values of and Kb evaluated at any arbitrary value of T and at the specified pressure. After Kb has been evaluated by use of Eq. (1-21), the desired bubble-point temperature is found from the known relationship between Kb and T. 

The boiling-point diagram (Fig. 1-6) is useful for the visualization of the necessary conditions required for a flash to occur. Suppose that feed to be flashed has the composition Xt = xu (xlf A and xlt B), and further suppose that this liquid mixture at the temperature T0 and the pressure P = 1 atm is to be flashed by raising the temperature to the specified flash temperature T,. = T2 at the specified flash pressure P = 1 atm. First observe that the bubble-point temperature of the feed TBP at P = 1 atm is Tv The dew-point temperature, TOP, of the feed at the pressure P = 1 atm is seen to be T3. Then it is obvious from Fig. 1-6 that a necessary condition for a flash to occur at the specified pressure is that... 

In the determination of the bubble-point temperature corresponding to a specified system pressure and liquid-phase composition, the procedure described might appear to lead to a trial determination of both the system temperature and the convergence pressure. However, because of the relatively small dependence of the Ki s on the convergence pressure, the trial-and-error procedure is reduced primarily to the finding of the bubble-point temperature. This characteristic relationship between the K, s and PK permits the use of a single convergence pressure over either the entire column or several plates. 

Equation (7-19) is useful for calculating bubble-point temperature at a specified pressure or bubble-point pressure at a specified temperature. 

It is important when specifying the control valves to select the correct valid phase. If the stream is aU liquid, select Liquid-Only in the Valid Phases under Flash options on the Operation page tab of the valve block. If the stream is all vapor, select Vapor-Only. Some valves have both phases (particularly when the inlet is liquid at its bubble point temperature and pressure, which means flashing occurs when the pressure decreases as the fluid flows through the valve) and Vapor-Liquid should be selected. Numerical problems can occur in Aspen Dynamics if these valid phases are not correct. 

Next, the relative volatilities, a, are determined as averages of estimated s obtained from T-value calculations at overhead and bottoms conditions. These conditions include the operating pressure, the estimated overhead and bottoms compositions, and the estimated dew point and bubble point temperatures. With a starting set of relative volatihties, the minimum trays, N , and the overhead and bottoms compositions at total reflux are calculated by the Fenske method (Equations 12.17 and 12.17a) for the specified separation. The new compositions may be used to recalculate more accurately the temperatures, pressures, and relative volatihties. The process is repeated until the a s stabilize. 

The results obtained were incorporated in a program which specified first whether the conditions are those of (1) the compressed liquid, (2) the liquid at a bubble point of specified temperature,... 

Figure 10.54 The BubbleT.m file that defines f(T), the root of which represents the bubble-point temperature for the given liquid mixture at the specified conditions of mole fraction and total pressure.

Feed stream is fully specified (filling in feed flow rate, compositions, pressure and feed at bubble point temperature). 

At the dew-point temperature y still equals Zj, and the relationshm X Xi = X i/K-i = 1.0 must be satisfied. As in the case of the bubble point, a trial-and-error search for the dew-point temperature at a specified pressure is involved. Or, if the temperature is specified, the dew-point pressure can be calculated. 

Thus, to calculate the bubble point for a given mixture and at a specified pressure, a search is made for a temperature to satisfy Equation 4.58. Alternatively, temperature can be... 

To ensure that the predicted two-phase region corresponds with that for the saturated vapor-liquid-liquid equilibrium, the temperature must be specified to be bubble-point predicted by the NRTL equation at either x = 0.59 or x = 0.98 (366.4 K in this case). 

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