Chapter 2. Flash Distillation

1. Explain and sketch the basic flash distillation process

2. Find desired VLE data in the literature or on the Web

3. Plot and use y-x, temperature-composition, and enthalpy-composition diagrams; explain the relationship between these three types of diagrams

4. Derive and plot the operating equation for a binary flash distillation on a y-x diagram; solve both sequential and simultaneous binary flash distillation problems

5. Define and use K values, Raoult’s law, and relative volatility

6. Derive the Rachford-Rice equation for multicomponent flash distillation, and use it with Newtonian convergence to determine V/F

7. Solve sequential multicomponent flash distillation problems

8. Determine the length and diameter of a flash drum

9. Use existing flash drums for a new separation problem

10. Use Aspen Plus to simulate two- and three-phase flash distillation

The equipment needed for flash distillation is shown in Figure 2-1 for a liquid feed. The fluid is pressurized and heated and is then passed through a throttling valve or nozzle into the flash drum. Because of the large drop in pressure, part of the fluid vaporizes. The vapor is taken off overhead, while the liquid drains to the bottom of the drum, where it is withdrawn. A demister or entrainment eliminator is often employed to prevent liquid droplets from being entrained in the vapor. The system is called “flash” distillation because the vaporization is extremely rapid after the feed enters the drum. Because of the intimate contact between liquid and vapor, the system in the flash chamber is very close to an equilibrium stage. Figure 2-1 shows a vertical flash drum, but horizontal drums (shown later in Figure 2-14) are also common. Partial condensation is similar to Figure 2-1, except the vapor is cooled before entering the drum.

The designer of a flash system needs to know the pressure and temperature of the flash drum, the size of the drum, and the liquid and vapor compositions and flow rates. He or she also wishes to know the pressure, temperature, and flow rate of the feed entering the drum. In addition, he or she needs to know how much the original feed has to be pressurized and heated. The pressures must be chosen so that at the feed pressure, p_F, the feed is below its boiling point and remains liquid, while at the pressure of the flash drum, p_drum, the feed is above its boiling point and some of it vaporizes. Because the energy for vaporization comes from the hot feed, T_F > T_drum, if the feed is already hot and/or the pressure of the flash drum is quite low, the pump and heater shown in Figure 2-1 may not be needed.

The designer has six degrees of freedom to work with for design of a binary flash distillation. Usually, the original feed specifications take up four of these degrees of freedom:

Feed flow rate, F

Feed composition, z (mole fraction of the more volatile component)

Temperature, T₁

Pressure, p₁

Of the remaining, the designer will usually select first:

Drum pressure, p_drum

The drum pressure must be below the critical pressure for the mixture so that a liquid phase can exist. An approximate value of the critical pressure can be calculated from

where x_i are the liquid mole fractions and p_c,i and p_{c,mixture,approx} are the critical pressures of the pure components and of the mixture (Biegler et al., 1997). In addition, as the pressure increases, the pressure and temperature of the feed and the condensation temperature of the vapor increase. We prefer a feed temperature that can be readily obtained with the available steam (T_F < T_steam + 5°C), and if the vapor product will be condensed, we prefer a condensation temperature that is at least 5°C above the available cooling water temperature.

A number of other variables are available to fulfill the last degree of freedom.

As is true in the design of many separation techniques, the choice of specified design variables controls the choice of the design method. For the flash chamber, we can use either a sequential solution method or a simultaneous solution method. In the sequential procedure, we solve the mass balances and equilibrium relationships first and then solve the energy balances and enthalpy equations. In the simultaneous solution method, all equations must be solved at the same time. In both cases, we solve for flow rates, compositions, and temperatures before we size the flash drum.

We will assume that the flash drum shown in Figure 2-1 acts as an equilibrium stage. Then vapor and liquid are in equilibrium. For a binary system the mole fraction of the more volatile component in the vapor y and its mole fraction in the liquid x and T_drum can be determined from the equilibrium expressions:

To use Eq. (2-2) in the design of binary flash distillation systems, we must take a short tangent and first discuss binary vapor-liquid equilibrium (VLE).

If we obtained equilibrium measurements for a binary mixture of ethanol and water at 1 atm, we would generate data similar to those shown in Table 2-1. The mole fractions in each phase must sum to 1.0. Thus for this binary system,

where x is mole fraction in the liquid and y is mole fraction in the vapor. Very often, only the composition of the more volatile component (MVC, the component that has y > x; ethanol in this case) will be given. The mole fraction of the less volatile component (LVC) can be found from Eqs. (2-3). Equilibrium depends on pressure. (Data in Table 2-1 are specified for a pressure of 1 atm.) Table 2-1 is only one source of equilibrium data for the ethanol-water system, and over a dozen studies have explored this system (Wankat, 1988), and data are contained in the more general sources listed in Table 2-2. The data in different references do not agree perfectly, and care must be taken in choosing good data. We will refer back to this (and other) data quite often. If you have difficulty finding it, either look in the index under ethanol data or water data or look in Appendix D, “Data Locations,” under ethanol-water VLE.

We see in Table 2-1 that if pressure and temperature are set, then there is only one possible vapor composition for ethanol, y_Etoh, and one possible liquid composition, x_Etoh. Thus we cannot arbitrarily set as many variables as we might wish. For example, at 1 atm we cannot arbitrarily decide that we want vapor and liquid to be in equilibrium at 95°C and x_Etoh = 0.1.

The number of variables that we can arbitrarily specify for a system at equilibrium, known as the degrees of freedom, is determined by subtracting the number of thermodynamic equilibrium equations from the number of variables. For nonreacting systems the resulting Gibbs phase rule is

where F = degrees of freedom, C = number of components, and P = number of phases. For the binary system in Table 2-1, C = 2 (ethanol and water) and P = 2 (vapor and liquid). Thus

F = 2 – 2 + 2 = 2

When pressure and temperature are set, all the degrees of freedom are used, and at equilibrium all compositions are determined from the experiment. Alternatively, we could set pressure and x_Etoh or x_w and determine temperature and the other mole fractions.

The amount of material and its flow rate are not controlled by the Gibbs phase rule. The phase rule refers to intensive variables such as pressure, temperature, or mole fraction, which do not depend on the total amount of material present. The extensive variables, such as number of moles, flow rate, and volume, do depend on the amount of material and are not included in the degrees of freedom for equilibrium. Thus a mixture in equilibrium must follow Table 2-1 whether there are 0.1, 1.0, 10, 100, or 1000 moles present. Note that the degrees of freedom for the entire design includes setting extensive variables and feed conditions, which are not included in Gibbs phase rule.

Binary systems with only two degrees of freedom can be conveniently represented in tabular or graphical form by setting one variable (usually pressure) constant. VLE data have been determined for many binary systems. Sources for these data are listed in Table 2-2; you should become familiar with several of these sources. Note that the data are not of equal quality. Methods for testing the thermodynamic consistency of equilibrium data are discussed in detail by Barnicki (2002), Walas (1985), and Van Ness and Abbott (1982). Errors in the equilibrium data can have a profound effect on the design of the separation method (e.g., see Carlson, 1996, or Nelson et al., 1983).

Table 2-1 gives the equilibrium data for ethanol and water at 1 atm. With pressure set, there is only one degree of freedom remaining. Thus we can select any of the intensive variables as the independent variable and plot one or more of the other intensive variable as the dependent variable(s). The simplest such graph is the y versus x graph shown in Figure 2-2. Typically, we plot the mole fraction of the MVC. This diagram is also called a McCabe-Thiele diagram when it is used for calculations. Pressure is constant, but the temperature is different at each point on the equilibrium curve. Points on the equilibrium curve represent two phases in equilibrium. Any point not on the equilibrium curve represents a system that may have both liquid and vapor, but they are not in equilibrium. As we will discover later, y-x diagrams are extremely convenient for calculation.

The data in Table 2-1 can also be plotted on a temperature-composition diagram, as shown in Figure 2-3. The result is actually two graphs: One is liquid temperature versus x_E, and the other is vapor temperature versus y_E. These curves are called saturated liquid and saturated vapor lines because they represent all possible liquid and vapor systems that can be in equilibrium at a pressure of 1 atm. Any point below the saturated liquid curve represents a subcooled liquid (liquid below its boiling point), whereas any point above the saturated vapor curve would be a superheated vapor. Points between the two saturation curves represent streams consisting of both liquid and vapor. If allowed to separate, these streams will give a liquid and vapor in equilibrium. Liquid and vapor in equilibrium must be at the same temperature; therefore, these streams will be connected by a horizontal isotherm, as shown in Figure 2-3 for x_E = 0.2.

Even more information can be shown on an enthalpy-composition or Ponchon-Savarit diagram, as illustrated for ethanol and water in Figure 2-4. Note that the units in Figure 2-4 are weight fractions, not the mole fractions used in Figures 2-2 and 2-3. Again, there are really two plots: one for liquid and one for vapor. The isotherms shown in Figure 2-4 show the change in enthalpy at constant temperature as weight fraction varies. Because liquid and vapor in equilibrium must be at the same temperature, these points are connected by an isotherm. Points between the saturated vapor and liquid curves represent two-phase systems. An isotherm through any point can be generated using the auxiliary line with the construction shown in Figure 2-5. To find an isotherm, go vertically from the saturated liquid curve to the auxiliary line. Then go horizontally to the saturated vapor line. The line connecting the points on the saturated vapor and saturated liquid curves is the isotherm. If an isotherm is desired through a point in the two-phase region, a simple trial-and-error procedure is required.

Isotherms on the enthalpy-composition diagram can also be generated from the y-x and temperature-composition diagrams. Since these diagrams represent the same data, the vapor composition in equilibrium with a given liquid composition can be found from either the y-x or temperature-composition graph, and the value transferred to the enthalpy-composition diagram. This procedure can also be done graphically, as shown in Figure 2-6, if the units are the same in all figures. In Figure 2-6a we can start at point A and draw a vertical line to point A′ (constant x value). At constant temperature, we can find the equilibrium vapor composition (point B′). Following the vertical line (constant y), we proceed to point B. The isotherm connects points A and B. A similar procedure is used in Figure 2-6b, except now the y-x line must be used on the McCabe-Thiele graph. This is necessary because points A and B in equilibrium appear as a single point, A′/B′, on the y-x graph. The y = x line allows us to convert the ordinate value (y) on the y-x diagram to an abscissa value (also y) on the enthalpy-composition diagram. Thus the procedure is to start at point A and go up to point A′/B′ on the y-x graph. Then go horizontally to the y = x line and finally drop vertically to point B on the vapor curve. The isotherm now connects points A and B.

The data presented in Table 2-1 and illustrated in Figures 2-2, 2-3, and 2-4 show a minimum-boiling azeotrope; that is, the liquid and vapor are of exactly the same composition at a mole fraction ethanol of 0.8943. This can be found from Figure 2-2 by drawing the y = x line and finding the intersection with the equilibrium curve (e.g., see Figure 2-8). In Figure 2-3 the saturated liquid and vapor curves touch, while in Figure 2-4 the isotherm is vertical at the azeotrope. Note that the azeotrope composition is numerically different in Figure 2-4, but actually it is essentially the same, since Figure 2-4 is in weight fractions, whereas the other figures are in mole fractions. Below the azeotrope composition, ethanol is the MVC; above it, ethanol is the LVC. The system is called a minimum-boiling azeotrope because the azeotrope boils at 78.15°C, which is a lower boiling point than that of either pure ethanol or pure water. The azeotrope location is a function of pressure. Below 70 mm Hg no azeotrope exists for ethanol-water. Maximum-boiling azeotropes, although rare, also occur (see Figure 2-7). Only the temperature-composition diagram will look significantly different. Another type of azeotrope occurs when there are two partially miscible liquid phases. Equilibrium for partially miscible systems is considered in Chapter 8.

and the component balance for the MVC,

The energy balance is

where h_F, H_v, and h_L are the enthalpies of the feed, vapor, and liquid streams. Usually Q_flash = 0, since the flash drum is insulated and the flash is considered to be adiabatic.

To use the energy balance equations, we need to know the enthalpies. Their general form is

For binary systems, if the data is available, it is convenient to represent the enthalpy functions graphically on an enthalpy-composition diagram such as Figure 2-4. For ideal mixtures, the enthalpies can be calculated from heat capacities and latent heats. Then,

where x_A and y_A are mole fractions of component A in liquid and vapor, respectively. C_P is the molar heat capacity, T_ref is the chosen reference temperature, and λ is the latent heat of vaporization at T_ref. For binary systems, x_B = 1 – x_A, and y_B = 1 – y_A.

Vapor mole fraction, y

Liquid mole fraction, x

Fraction feed vaporized, f = V/F

Fraction feed remaining liquid, q = L/F

Temperature of flash drum, T_drum

If one of the equilibrium conditions, y, x, or T_drum, is specified, then the other two can be found from Eqs. (2-2a) and (2-2b) or from the graphical representation of equilibrium data. For example, if y is specified, x is obtained from Eq. (2-2a) or Figure 2-2 and T_drum from Eq. (2-2b) or Figure 2-3. In the mass balances, Eqs. (2-5) and (2-6), the only unknowns are L and V, and the two equations can be solved simultaneously.

If either the fraction vaporized or fraction remaining liquid is specified, Eqs. (2-2a), (2-2b), and (2-6) must be solved simultaneously. The most convenient way to do this is to combine the mass balances. Solving Eq. (2-6) for y, we obtain

Equation (2-11) is the operating equation, which for a single-stage system relates the compositions of the two streams leaving the stage. Equation (2-11) can be rewritten in terms of either the fraction vaporized, f = V/F, or the fraction remaining liquid, q = L/F.

From the overall mass balance, Eq. (2-5),

Then the operating equation becomes

The alternative in terms of L/F is

and the operating equation becomes

Although they have different forms, Eqs. (2-11), (2-13), and (2-15) are equivalent operating equations, the use of fraction vapor in the feed is most common. We will use whichever operating equation is most convenient.

Now the equilibrium and the operating equation (Eq. 2-11, 2-13, or 2-15) must be solved simultaneously. The exact way to do this depends on the form of the equilibrium data. For binary systems, a graphical solution is very convenient. Equations (2-11), (2-13), and (2-15) represent a single straight line, called the operating line, on a graph of y versus x. This straight line will have

and

The equilibrium data at pressure p_drum can also be plotted on the y-x diagram. The intersection of the equilibrium curve and the operating line is the simultaneous solution of the mass balances and equilibrium. This plot of y versus x showing both equilibrium and operating lines is called a McCabe-Thiele diagram and is shown in Figure 2-8 for an ethanol-water separation. The equilibrium data are from Table 2-1 and the equilibrium curve is identical to Figure 2-2. The solution point gives the vapor and liquid compositions leaving the flash drum. Figure 2-8 shows three different operating lines as V/F varies from 0 (line a) to 2/3 (line c) to 1.0 (line b) (see Example 2-1). T_drum can be found from Eq. (2-4), from Table 2-1, or from a temperature-composition diagram, Figure 2-3.

Two other points often used on the McCabe-Thiele diagram are the x intercept (y = 0) of the operating line and the intersection of the operating line with the y = x line. Either of these points can also be located algebraically and then used to plot the operating line.

The intersection of the operating line and the y = x line is often used because it is simple to plot. This point can be determined by simultaneously solving Eq. (2-11) and the equation y = x (see Problem 2.C4). The result is that the intersection is at the feed mole fraction.

The y = x line is often used in graphical solution methods because it simplifies the calculation. However, do not use it blindly, because for other separations the y = x line may have no significance.

Why, other than the mathematics shows that Eq. (2-18) is valid, do the y = x line and the operating line intersect at the feed mole fraction? Since the operating equation (i.e., the mass balances) are independent of the equilibrium behavior, the operating equation has to be valid for any equilibrium. If the feed is at the composition of an azeotrope, then there is no separation and vapor and liquid mole fractions are equal (y = x). The only way this can be true is if y = x = z. Because the operating equation is valid for all separation systems, y = x = z is a point on the operating equation for all binary flash distillations.

The graphical technique can be used if y, x, or T_drum is specified. The order in which you find points on the diagram will depend on what information you have to begin with.

For binary systems,

y_B = 1 – y_A, x_B = 1 – x_A

and the relative volatility is

Solving Eq. (2-22) for y_A, we obtain

Alternatively, solving for x_A, we obtain

If Raoult’s law is valid [see Eq. (2-30)], then we can determine relative volatility as

The relative volatility α may also be fit to experimental data.

If we solve Eqs. (2-21) and (2-11) simultaneously, we obtain

Equation (2-24) is easily solved for x with the quadratic equation. This can be done conveniently with a spreadsheet.

If the temperature of the feed to the drum, T_F, is the specified variable, the mass and energy balances and the equilibrium equations must be solved simultaneously. You can see from the energy balance, Eq. (2-7) why this is true. The feed enthalpy, h_F, can be calculated, but the vapor and liquid enthalpies, H_v and h_L, depend upon T_drum, y, and x, which are unknown. Thus a sequential solution is not possible.

We could write Eqs. (2-3) to (2-8) and solve seven equations simultaneously for the seven unknowns y, x, L, V, H_v, h_L, and T_drum. This is feasible but rather difficult, particularly since Eqs. (2-3) and (2-4) and often Eqs. (2-8) are nonlinear, so we resort to a trial-and-error (or guess-and-check) procedure. This method is: Guess the value of one of the variables, calculate the other variables, and then check the guessed value of the trial variable. For a binary system, we can select any one of several trial variables, such as y, x, T_drum, V/F, or L/F. For example, if we select the temperature of the drum, T_drum, as the trial variable, the calculation procedure is

1. Calculate h_F(T_F, z) [e.g., use Eq. (2-9b)].

2. Guess the value of T_drum.

3. Calculate x and y from the equilibrium equations (2-3) and (2-4) or graphically (use temperature-composition diagram).

4. Find L and V by solving the mass balance equations (2-5) and (2-6), or find L/V from Figure 2-8 and use the overall mass balance, Eq. (2-5).

5. Calculate h_L(T_drum, x) and H_v(T_drum, y) from Eqs. (2-8) or (2-9a) and (2-10) or from the enthalpy-composition diagram.

6. Check: Is the energy balance equation (2-7) satisfied? If it is satisfied, we are finished. Otherwise, return to step 2.

The procedures are similar for other trial variables.

Determining the isotherm through the feed point requires a minor trial-and-error procedure. Pick a y (or x), draw the isotherm with the aid of the auxiliary line (see Figure 2-5), and check whether it goes through the feed point. If not, repeat with a new y (or x). Once y and x in equilibrium are determined, liquid and vapor flow rates can be found from Eq. (2-20) and L = F – V.

The equations used are equilibrium, mass and energy balances, and stoichiometric relations. The mass and energy balances are very similar to those used in the binary case, but the equilibrium equations are usually written in terms of K values. The equilibrium form is

where in general

Equations (2-25) and (2-26) are written once for each component. In general, the K values depend on temperature, pressure, and composition. These nonideal K values are discussed in detail by Smith (1963) and Walas (1985), in thermodynamics textbooks, and in the references in Table 2-2.

Fortunately, for many systems the K values are approximately independent of composition. Thus

For light hydrocarbons, the approximate K values can be determined from the nomographs prepared by DePriester. These are shown in Figures 2-10 and 2-11, which cover different temperature ranges. If temperature and/or pressure of the equilibrium mixture are unknown, a trial-and-error procedure is required. DePriester charts in other temperature and pressure units are given by Green and Perry (2008), Perry and Green (1997), and Smith et al. (2005). The DePriester charts have been fit to the following equation (McWilliams, 1973):

Note that T is in ºR and p is in psia in Eq. (2-28). The constants a_T1, a_T2, a_T6, a_p1, a_p2, and a_p3 are given in Table 2-3. The last line gives the mean errors in the K values compared to the values from the DePriester charts. This equation is valid from –70°C (365.7°R) to 200°C (851.7°R) and for pressures from 101.3 kPa (14.69 psia) to 6000 kPa (870.1 psia). If K and p are known, then Eq. (2-28) can be solved for T. The obvious advantage of an equation compared to the charts is that it can be programmed into a computer or calculator. Equation (2-28) can be simplified for all components except n-octane and n-decane [see Eq. (5-14)]. It is doubtful that all of the 7-10 digits presented by McWilliams (1973) in Table 2-3 are significant.

The K values are used along with the stoichiometric equations, which state the mole fractions in liquid and vapor phases must sum to 1.0.

where C is the number of components. Bubble-point and dew-point calculations that determine the pressure and temperature that satisfy Eqs. (2-29a) and (2-29b) are discussed in detail in Section 5.3.

If only one component is present, then y = 1.0 and x = 1.0. This implies that K_i = y/x = 1.0. This gives a simple way of determining the boiling temperature of a pure compound at any pressure. For example, if we wish to find the boiling point of isobutane at p = 150.0 kPa, we set our straightedge on p = 150.0 and at 1.0 on the isobutane scale on Figure 2-10. Then read T = –1.5°C as the boiling point. Alternatively, Eq. (2-28) with values from Table 2-3 can be solved for T. This gives T = 488.68°R or –1.6°C.

For ideal systems Raoult’s law holds (Franses, 2014; Koretsky, 2013). Raoult’s law states that the partial pressure of a component is equal to its vapor pressure multiplied by its mole fraction in the liquid. Thus

where vapor pressure (VP) depends on temperature. By Dalton’s law of partial pressures,

Combining these equations,

Comparing Eqs. (2-32) and (2-25), the Raoult’s law K value is

and the Raoult’s law relative volatility was already given in Eq. (2-23). Because extensive tables of vapor pressures are available, Eqs. (2-23) and (2-33) are handy. The Antoine equation is often used to correlate vapor pressure data

where A, B, and C are constants for each pure compound. These constants are tabulated in various data sources (Boublik et al., 1984; Speight, 2005; Yaws et al., 2005). The equations based on Raoult’s law should be used with great care, since deviations from Raoult’s law are extremely common.

Nonidealities in the liquid phase can be taken into account with a liquid-phase activity coefficient, γ_i. Then Eq. (2-33) becomes

The activity coefficient depends on temperature, pressure, and concentration. Excellent correlation procedures for activity coefficients such as the Margules, Van Laar, Wilson, nonrandom two-liquid (NRTL), and UNIQUAC methods have been developed (Dahm and Visco, 2015; Poling et al., 2001; Sandler, 2006; Van Ness and Abbott, 1982; Walas, 1985). The coefficients for these equations for a wide variety of mixtures have been tabulated along with the experimental data (see Table 2-2). When the binary data are not available, one can use infinite dilution coefficients (Table 2-2; Carlson, 1996; Lazzaroni et al., 2005; Schad, 1998) or the UNIFAC group contribution method (Fredenslund et al., 1977; Prausnitz et al., 1980) to predict the missing data. Many distillation simulators use Eqs. (2-34), (2-35), and an appropriate activity coefficient equation. Although a detailed description of these methods is beyond the scope of this book, a guide to choosing VLE correlations for use in computer simulations is presented in Table 2-4. The books by Gmehling et al. (2012) and Sandler (2015) that focus on thermodynamic models for simulations are also useful for selecting correlations. For final designs, you must be confident in the VLE correlation used. Check the predictions with experimental data such as VLE data, flash distillation results, or distillation column results.

and the energy balance, Eq. (2-7). Equation (2-36) is very similar to the binary mass balance, Eq. (2-6).

Usually the feed flow rate, F, and the feed mole fractions z_i for C – 1 of the components will be specified. If p_drum and T_drum or one liquid or vapor composition are also specified, then a sequential procedure can be used. That is, the mass balances, stoichiometric equations, and equilibrium equations are solved simultaneously, and then the energy balances are solved.

Now consider for a minute what this means. Suppose we have 10 components (C = 10). Then we must find 10 K values, 10 x’s, one L, and one V, which is 32 variables. To do this we must solve 32 equations [10 Eq. (2-25), 10 Eq. (2-26), Eqs. (2-29a) and (2-29b), and 10 independent mass balances, Eq. (2-36)] simultaneously. And this is the simpler sequential solution for a relatively simple problem.

How do we solve 32 simultaneous equations? In general, the K value relations could be nonlinear functions of composition. However, for hand calculations we will restrict ourselves to ideal solutions where Eq. (2-27) is valid and

K_i = K_i(T_drum, p_drum)

Since T_drum and p_drum are known, the 10 K_i can be determined [say, from the DePriester charts or Eq. (2-28)]. Now there are only 22 linear equations to solve simultaneously. This can be done, but trial-and-error procedures are simpler.

First use equilibrium, y_i = K_i x_i, to remove y_i from Eq. (2-36):

Fz_i = Lx_i + VK_i x_i i = 1, C

Solving for x_i, we have

If we solve Eq. (2-5) for L, L = F – V, and substitute this into the last equation, we have

Now if the unknown V is determined, all of the x_i can be determined. It is usual to divide the numerator and denominator of Eq. (2-37) by the feed rate F and work in terms of the variable V/F because V/F is bounded between 0 and 1.0 for all possible problems. Upon rearrangement we have

Once V/F is determined, x_i and y_i are easily found from Eqs. (2-38) and (2-39):

How can we derive an equation that allows us to calculate V/F?

To answer this question, first consider what equations have not been used. These are the two stoichiometric equations, ∑ x_i = 1.0 and ∑ y_i = 1.0. If we substitute Eqs. (2-38) and (2-39) into these equations, we obtain

Either of these equations can be used to solve for V/F. If we clear fractions, these are Cth-order polynomials. Thus, if C is greater than 3, a trial-and-error procedure or root-finding technique must be used to find V/F. Although Eqs. (2-40a) and (2-40b) are both valid, they do not have good convergence properties. That is, if the wrong V/F is chosen, the V/F that is chosen next may not be better.

Fortunately, an equation that has good convergence properties is easy to derive. Start with

∑y_i - ∑x_i = 0

Subtract Eq. (2-40a) from (2-40b) term-by-term,

Equation (2-41), the Rachford-Rice equation, has excellent convergence properties. It can also be modified for three-phase (liquid-liquid-vapor) flash systems (see Section 2.8).

Since the feed compositions, z_i, are specified and K_i can be calculated when T_drum and p_drum are given, the only unknown in Eq. (2-41) is the fraction vaporized, V/F. This equation can be solved by many different convergence procedures or root finding methods. For example, a Newtonian convergence procedure will converge quickly. Newtonian convergence estimates the next value of f(V/F) from the derivative,

where f_k is the value of the function for trial k and df_k/d(V/F) is the value of the derivative of the function for trial k. We desire to have f_k+1 equal zero, so we set f_k+1 = 0 and solve for (V/F)_k+1,

This equation gives us the best next guess for the fraction vaporized. To use it, however, we need equations for both the function and the derivative. For f_k, use the Rachford-Rice equation, (2-41). Then the derivative is

Equation (2-43) gives a good estimate for the next trial. Once (V/F)_k+1 is calculated the value of the Rachford-Rice function can be determined. If

with ε_R = 0.005 the calculation is finished; otherwise continue Newtonian convergence.

Newtonian convergence procedures do not always converge. One advantage of using the Rachford-Rice equation with the Newtonian convergence procedure is that there is always rapid convergence. This is illustrated in Example 2-2.

Once V/F has been found, x_i and y_i are calculated from Eqs. (2-38) and (2-39). L and V are determined from the overall mass balance, Eq. (2-5). The enthalpies h_L and H_v can now be calculated. For ideal solutions the enthalpies can be determined from the sum of the pure component enthalpies and multiplied by the corresponding mole fractions:

If the solutions are not ideal, heats of mixing are required. The energy balance, Eq. (2-7), is solved for h_F, and T_F can be determined from

If V/F and p_drum are specified, then T_drum must be determined. This can be done by picking a value for T_drum, calculating K_i, and checking with the Rachford-Rice equation, (2-41). A plot of f(V/F) versus T_drum will help select the temperature value for the next trial. Alternatively, an approximate convergence procedure similar to that employed for bubble- and dew-point calculations can be used (see Section 5-3). The new K_ref can be determined from

where the damping factor df ≤ 1.0. In some cases this may overcorrect unless the initial guess is close to the correct answer. If we set V/F = 0, this calculation gives us the bubble-point temperature (liquid starts to boil), and if we set V/F = 1.0, the calculation gives the dew-point temperature (vapor starts to condense).

If the specified variables are F, z_i, p_drum, and either x or y for one component, we can follow a sequential convergence procedure using Eq. (2-38) or (2-39) to relate to the specified composition (the reference component) to either K_ref or V/F. We can do this in either of two ways. The first is to guess T_drum and use Eq. (2-38) or (2-39) to solve for V/F. The Rachford-Rice equation is then the check equation on T_drum. If the Rachford-Rice equation is not satisfied, we select a new temperature – using Eq. (2-48) – and repeat the procedure. In the second approach, we guess V/F and calculate K_ref from Eq. (2-38) or (2-39). We then determine the drum temperature from this K_ref. The Rachford-Rice equation is again the check. If it is not satisfied, we select a new V/F and continue the process.

If there are nonvolatile compounds present, the K_i values for these compounds are zero. The presence of these compounds will cause no difficulties for Eqs. (2-38) to (2-49). However, if there are noncondensable compounds present, the K_i for these compounds will be very large, particularly if the solubilities are small. It is tempting to set these K_i values to infinity, but then Eq. (2-41) becomes undefined. This difficulty is easily handled by rearranging Eq. (2-41) (Hatfield, 2008). If we divide numerator and denominator of the noncondensable (NC) term of Eq. (2-41) by K_NC, this term becomes

Substitution of this term into Eq. (2-41) results in a well-behaved equation in the presence of noncondensable compounds. Equations (2-38) and (2-39) become x_NC = 0 and y_NC = Fz_NC/V.

The first question to ask in setting up a trial-and-error procedure is: Which trial variables shall we use? Almost always, temperature is chosen as a trial variable, since it is required to calculate all K_i, , and and is difficult to solve for. The second trial variable for flash distillation is V/F, because we can use the Rachford-Rice approach with Newtonian convergence.

Should we converge on both variables simultaneously (that is, change both T_drum and V/F at the same time), or should we converge sequentially? Both techniques will work, but sequential convergence tends to be more stable. If we use sequential convergence, then we need to decide if we should converge V/F or T_drum first. To answer this question we need to consider the chemical system we are separating. If the mixture is wide-boiling – that is, if the dew point and bubble point are far apart (say more than 80°C to 100°C) – then a small change in T_drum cannot have much effect on V/F, so we should converge on V/F first. Then when T_drum is changed, we will be close to the correct answer for V/F. For a significant separation in a flash system, the volatilities must be very different, so this is the typical situation for flash distillation.

The procedure for wide-boiling feeds is shown in Figure 2-12. Note that the energy balance is used last. This is standard procedure, since accurate values of x_i and y_i are available to calculate enthalpies for the energy balance. Several methods can be used to estimate the next flash drum temperature. One of the fastest and easiest to use is a Newtonian convergence procedure. To do this we rearrange the energy balance (Eq. 2-7) into the functional form,

The subscript k again refers to the trial number. When E_k is zero, the problem has been solved. The Newtonian procedure estimates E_k+1(T_drum) from the derivative,

dE_k/dT_drum is the variation of E_k as temperature changes. Since a sequential convergence routine is being used and we do not want to vary V and L in this loop, set both dV/dT and dL/dT equal to zero. The last two terms in Eq. (2-50) do not depend on T_drum. The derivative is

where we have used the definition of the heat capacity. We want the energy balance to be satisfied after the next trial. Thus we set E_k+1 = 0. Now Eq. (2-51) can be solved for T_{drum k+1}:

In this equation E_k is the calculated numerical value of the energy balance function from Eq. (2-50), and dE_k/dT_drum is the numerical value of the derivative calculated from Eq. (2-52).

The procedure has converged when

For computer calculations, ε_T = 0.01°C is a reasonable choice. For hand calculations, a less stringent limit such as ε_T = 0.2°C would be used. This procedure is illustrated in Example 2-3.

It is possible that this convergence scheme may oscillate with a growing amplitude and not converge. To discourage this behavior, the temperature change can be damped:

where the damping factor df is about 0.5. When df = 1.0, this is just the Newtonian approach.

The drum temperature should always lie between the bubble- and dew-point temperatures of the feed. In addition, the temperature should converge toward some central value. If either of these criteria is violated, then the convergence scheme should be damped or an alternative convergence scheme should be used.

With three phases, the component mass balance for a flash distillation system is

which is equivalent to Eq. (2-36). There are i independent component mass balances, but the overall balance is not independent, since it is obtained by summing all of the component balances.

When there are three phases, we can write three equilibrium distribution relationships for each component i,

Solving Eq. (2-57a) for y_i and substituting the result into Eq. (2-57b), rearranging and comparing to Eq. (2-57c), we obtain

Thus only two of the three K values for each component are independent. Of course, all the K values are, in general, functions of temperature, pressure, and composition.

We can now follow exactly the same steps used to derive the Rachford-Rice equation [Eqs. (2-37) to (2-41)] to derive two equations for the three-phase flash (Chien, 1994).

If temperature and pressure are specified and correlations for the equilibrium parameters are available, these two forms of the Rachford-Rice equation can be solved simultaneously for L_{liquid_1} /F and V/F. Then y_i, x_{i,liquid_1}, and x_{i,liquid_2} can be calculated from the three-phase equations equivalent to Eqs. (2-38) and (2-39) (see Problem 2.C9). Process simulators can do these calculations (e.g., Problem 2.G5), but the equilibrium correlations, particularly the liquid-liquid equilibrium correlations, need to be checked against data.

Step 1. Calculate the permissible vapor velocity, u_perm, that prevents excessive entrainment:

u_perm is the maximum permissible vapor velocity in feet per second at the maximum cross-sectional area. ρ_L and ρ_v are the liquid and vapor densities. K_drum is in ft/s.

K_drum is an empirical constant that depends on the type of drum. For vertical drums the value has been correlated graphically by Watkins (1967) for 85.0% of flood with no demister. Approximately 5.0% liquid will be entrained with the vapor. Use of the same design with a demister will reduce entrainment to less than 1.0%. The demister traps small liquid droplets on fine wires and prevents them from exiting. The droplets then coalesce into larger droplets, which fall off the wire and through the rising vapor into the liquid pool at the bottom of the flash chamber. Blackwell (1984) fit Watkins correlation to the equation

where

and constant = 1.0 ft/s, W_L and W_v are the liquid and vapor flow rates in weight units per hour (e.g., lb/h). The constants are (Blackwell, 1984)

A = –1.877478097

B = –0.8145804597

C = –0.1870744085

D = –0.0145228667

E = –0.0010148518

The resulting value for K_drum typically ranges from 0.1 to 0.35.

Step 2. Using the known vapor rate, V, convert u_perm into a horizontal area. The vapor flow rate, V, in lbmol/h is

Solving for the cross-sectional area,

For a vertical drum, diameter D is

Usually, the diameter is increased to the next largest 6-in. increment.

Step 3. Set the length/diameter ratio either by rule of thumb or by the required liquid surge volume. For vertical flash drums, the rule of thumb is that h_total/D ranges from 3.0 to 5.0. The appropriate value of h_total/D within this range can be found by minimizing the total vessel weight (which minimizes cost).

Flash drums are often used as liquid surge tanks in addition to separating liquid and vapor. The design procedure for this case is discussed by Watkins (1967) for petrochemical applications. The height of the drum above the centerline of the feed nozzle, h_v, should be 36 in. plus one-half the diameter of the feed line (see Figure 2-13). The minimum of this distance is 48 in.

The height of the center of the feed line above the maximum level of the liquid pool, h_f, should be 12 in. plus one-half the diameter of the feed line. The minimum distance for this free space is 18 in. The depth of the liquid pool, h_L, can be determined from the desired surge volume, V_surge:

The geometry can now be checked, since

These procedures are illustrated in Example 2-4. If h_total/D < 3, a larger liquid surge volume should be allowed. If h_total/D > 5, a horizontal flash drum should be used.

Horizontal flash drums (Figure 2-14) are used when large liquid surge volumes are required because additional surge volume is formed by increasing the length (Evans, 1980). The cross sectional area required for vapor flow is given by Eq. (2-66) except the area is relabeled as A_vap because it is not the final cross sectional area of the horizontal drum. If the time required to respond to an upset (the surge time) and the average residence time of fluid (the holding time) in the drum are known, the full liquid volume V_liq is

Practical experience shows that this full amount of liquid can be held in the drum using 80.0% of the total area. The remaining 20.0% of the total area is left for the vapor flow and must equal A_c from Eq. (2-63):

The minimum diameter of the drum is

The length of the drum h that can hold the full volume of surge liquid is

The vapor flow pattern in the drum is quite complicated, but u_perm for Eq. (2-63) can be found from Eq. (2-61) (Evans, 1980) with

where K_vertical is determined from Eq. (2-62a).

The range for a vertical drum is typically h/D from 3 to 5, and for a horizontal drum h/D is typically 5 or larger. Horizontal drums are particularly useful when large liquid surge capacities are needed. More detailed design procedures and methods for horizontal drums are presented by Evans (1980), Blackwell (1984), and Watkins (1967). Note that in industries other than petrochemicals, that sizing may vary.

The existing flash drum has its dimensions h_total and D specified. Solving Eqs. (2-63) and (2-64) for a vertical drum for V, we have

This vapor velocity is the maximum for this existing drum, since it will give a linear vapor velocity equal to u_perm.

The maximum vapor capacity of the drum limits the product (V/F) F, since we must have

If Eq. (2-69) is satisfied, then use of the drum is straightforward. If Eq. (2-69) is violated, something has to give. Some of the possible adjustments include the following:

a. Add chevrons or a demister to increase V_Max or to reduce entrainment (Woinsky, 1994).

b. Reduce feed rate to the drum.

c. Reduce V/F. Less vapor product with more of the more volatile components will be produced.

d. Use existing drums in parallel. This reduces feed rate to each drum.

e. Use existing drums in series (see Problems 2.D2 and 2.D5).

f. Try increasing the pressure (note that this changes everything—see Problem 2.C1).

g. Buy a different flash drum, or build a new one.

h. Use some combination of these alternatives.

i. The engineer can use ingenuity to solve the problem in the cheapest and quickest way.

Biegler, L. T., I. E. Grossmann, and A. W. Westerberg, Systematic Methods of Chemical Process Design, Prentice Hall, Upper Saddle River, NJ, 1997.

Binous, H., “Equilibrium-Staged Separations Using MATLAB and Mathmatica,” Chem. Engr. Educ., 42 (2), 69 (Spring 2008).

Blackwell, W. W., Chemical Process Design on a Programmable Calculator, McGraw-Hill, New York, 1984, chapter 3.

Bošnjakovic, F., Technische Thermodynamik, T. Steinkopff, Leipzig, Germany, 1935.

Boublik, T., V. Fried, and E. Hala, Vapour Pressures of Pure Substances, Elsevier, Amsterdam, 1984.

Carlson, E. C., “Don’t Gamble with Physical Properties for Simulators,” Chem. Engr. Progress, 92 (10), 35 (Oct. 1996).

Chien, H. H.-Y., “Formulations for Three-Phase Flash Calculations,” AIChE Journal, 40 (6), 957 (1994).

Dadyburjor, D. B., “SI Units for Distribution Coefficients,” Chem. Engr. Progress, 74 (4), 85 (April 1978).

Dahm, K. D., and D. P. Visco, Jr., Fundamentals of Chemical Engineering Thermodynamics, Cengage Learning, Stamford, CT, 2015.

Evans, F. L., Jr., Equipment Design Handbook for Refineries and Chemical Plants, Vol. 2, 2nd ed., Gulf Publishing Co., Houston, TX, 1980.

Franses, E. I., Thermodynamics with Chemical Engineering Applications, Cambridge University Press, Cambridge, UK, 2014.

Fredenslund, A., J. Gmehling, and P. Rasmussen, Vapor-Liquid Equilibria Using UNIFAC: A Group-Contribution Method, Elsevier, Amsterdam, 1977.

Gmehling, J., B. Kolbe, M. Kleiber, and J. Rarey, Chemical Thermodynamics for Process Simulation, Wiley-VCH, Weinheim, Germany, 2012.

Green, D. W., and R. H. Perry (Eds.), Perry’s Chemical Engineers’ Handbook, 8th ed., McGraw-Hill, New York, 2008.

Hatfield, A., “Analyzing Equilibrium When Noncondensables Are Present,” Chem. Engr. Progress, 42 (April 2008).

Himmelblau, D. M., Basic Principles and Calculations in Chemical Engineering, 3rd ed., Prentice Hall, Upper Saddle River, NJ, 1974.

Jordan, P., Foundations of Excel for Engineers and Scientists, Pearson, Auckland, N. Z., 2012.

Koretsky, M., Engineering and Chemical Thermodynamics, 2nd Ed., Wiley, New York, 2013.

Larsen, R. W., Engineering with Excel, 4th Ed., Pearson (published as Prentice-Hall), Upper Saddle River, NJ, 2013.

Lazzaroni, M. J., D. Bush, C. A. Eckert, T. C. Frank, S. Gupta, and J. D. Olsen, “Revision of MOSCED Parameters and Extension to Solid Solubility Calculations,” Ind. Eng. Chem. Research, 44, 4075 (2005).

McWilliams, M. L., “An Equation to Relate K-factors to Pressure and Temperature,” Chem. Engineering, 80 (25), 138 (Oct. 29, 1973).

Marsh, K. N., “The Measurement of Thermodynamic Excess Functions of Binary Liquid Mixtures,” Chemical Thermodynamics, Vol. 2, Chemical Society, London, 1978, pp. 1-45.

Nelson, A. R., J. H. Olson, and S. I. Sandler, “Sensitivity of Distillation Process Design and Operation to VLE Data,” Ind. Eng. Chem. Process Des. Develop., 22, 547 (1983).

O’Connell, J. P., R. Gani, P. M. Mathias, G. Maurer, J. D. Olson, and P. A. Crafts, “Thermo-dynamic Property Modeling for Chemical Process and Product Engineering: Some Perspectives,” Ind. Engr. Chem. Research, 48, 4619 (2009).

Perry, R. H., C. H. Chilton and S. D. Kirkpatrick (Eds.), Chemical Engineer’s Handbook, 4th ed., McGraw-Hill, New York, 1981.

Perry, R. H. and D. Green (Eds.), Perry’s Chemical Engineer’s Handbook, 7th ed., McGraw-Hill, New York, 1997.

Poling, B. E., J. M. Prausnitz, and J. P. O’Connell, The Properties of Gases and Liquids, 5th ed., McGraw-Hill, New York, 2001.

Prausnitz, J. M., R. N. Lichtenthaler, and E. G. de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed., Prentice Hall, Upper Saddle River, NJ, 1999.

Sandler, S. I., Chemical and Engineering Thermodynamics, 4th ed., Wiley, New York, 2006.

Sandler, S. I., Using Aspen Plus^® in Thermodynamics Instruction, AIChE and John Wiley & Sons, Hoboken, NJ, 2015.

Schad, R. C., “Make the Most of Process Simulation,” Chem. Engr. Progress, 94 (1), 21 (Jan. 1998).

Schefflan, R., Teach Yourself the Basics of Aspen Plus, AIChE and John Wiley & Sons, Hoboken, NJ, 2011.

Seider, W. D., J. D. Seader, D. R. Lewin, and S. Widago, Product and Process Design Principles, 3rd ed., Wiley, New York, 2009.

Shacham, M., N. Brauner, W. R. Ashurst, and M. B. Cutlip, “Can I Trust This Software Package: An Exercise in Validation of Computational Results,” Chem. Engr. Educ., 42 (1), 53 (Winter 2008).

Smith, B. D., Design of Equilibrium Stage Processes, McGraw-Hill, New York, 1963.

Smith, J. M., H. C. Van Ness, and M. M. Abbott, Introduction to Chemical Engineering Thermodynamics, 7th ed., McGraw-Hill, New York, 2005.

Speight, J. (Ed.) Lange’s Handbook of Chemistry, 70th Anniversary Edition, 16th ed., McGraw-Hill, New York, 2005.

Van Ness, H. C., and M. M. Abbott, Classical Thermodynamics of Non-Electrolyte Solutions. With Applications to Phase Equilibria, McGraw-Hill, New York, 1982.

Walas, S. M., Phase Equilibria in Chemical Engineering, Butterworth, Boston, 1985.

Wankat, P. C., Equilibrium-Staged Separations, Prentice Hall, Upper Saddle River, NJ, 1988.

Watkins, R. N., “Sizing Separators and Accumulators,” Hydrocarbon Processing, 46 (1), 253 (Nov. 1967).

Woinsky, S. G., “Help Cut Pollution with Vapor/Liquid and Liquid/Liquid Separators,” Chem. Engr. Progress, 90 (10), 55 (Oct. 1994).

Yaws, C. L., P. K. Narasimhan, and C. Gabbula, Yaws Handbook of Antoine Coefficients for Vapor Pressure (electronic edition), Knovel, 2005.

A1. In Figure 2-9 the feed plots as a two-phase mixture, whereas it is a liquid before introduction to the flash chamber. Explain why. Why can’t the feed location be plotted directly from known values of T_F and z? In other words, why does h_F have to be calculated separately from an equation such as Eq. (2-9b)?

A2. Can weight units be used in the flash calculations instead of molar units?

A3. Flash distillation is usually operated adiabatically. Where does the energy to vaporize part of the feed come from?

A4. In the flash distillation of salt water, the salt is totally nonvolatile (this is the equilibrium statement). Show a McCabe-Thiele diagram for feed water containing 3.5 wt% salt. Be sure to plot weight fraction of more volatile component.

A5. Develop your own key relations chart for this chapter. That is, on one page summarize everything you would want to know to solve problems in flash distillation. Include sketches, equations, and key words.

A6. In a flash drum separating a multicomponent mixture, raising the pressure will

a. increase the drum diameter and increase the relative volatilities.

b. increase the drum diameter and cause no change to the relative volatilities.

c. increase the drum diameter and decrease the relative volatilities.

d. not change the drum diameter but increase the relative volatilities.

e. not change the drum diameter and not change the relative volatilities.

f. not change the drum diameter but decrease the relative volatilities.

g. decrease the drum diameter and increase the relative volatilities.

h. decrease the drum diameter and not change the relative volatilities.

i. decrease the drum diameter and decrease the relative volatilities.

A7.

a. What would Figure 2-2 look like if we plotted y₂ versus x₂ (i.e., plot less volatile component mole fractions)?

b. What would Figure 2-3 look like if we plotted T versus x₂ or y₂ (less volatile component)?

c. What would Figure 2-4 look like if we plotted H or h versus y₂ or x₂ (less volatile component)?

A8. Use the DePriester chart:

a. At 100°C and a pressure of 200.0 kPa, what is the K value of n-hexane?

b. As the pressure increases, does the K value (a) increase, (b) decrease, or (c) stay constant?

c. Within a homologous series such as light hydrocarbons as the molecular weight increases, does the K value (at constant pressure and temperature) (a) increase, (b) decrease, or (c) stay constant?

d. At what pressure does pure propane boil at a temperature of –30°C?

A9. Use the DePriester chart:

a. What is the K value of propane at 240.0 kPa and 25°C?

b. What is the normal boiling point of n-pentane?

c. What is the boiling point of n-pentane at p = 600.0 kPa?

A10. Use the vapor-liquid equilibrium data at 1.0 atm for methanol-water (Table 2-7 in Problem 2.D1) for the following:

a. If the methanol vapor mole fraction is 0.60, what is the methanol liquid mole fraction?

b. Is there an azeotrope in the methanol-water system at a pressure of 1.0 atm?

c. If water liquid mole fraction is 0.35, what is the water vapor mole fraction?

d. What are the K value of methanol and of water at a methanol mole fraction in the liquid of 0.20?

e. What is the relative volatility α_M-W at a methanol mole fraction in the liquid of 0.20?

A11. An open glass of an alcoholic beverage that is 15.0 mol% ethanol and 85.0% water has been sitting on the table for a long time and is at 1.0 atm pressure and 25°C. The temperature and mole fractions are not even close to values in Table 2-1. Explain why not.

A12. Why is there a difference between degrees of freedom for equilibrium and degrees of freedom for complete design? Example: binary flash. Gibbs phase rule, F = C – P + 2 =2; entire design F = 6.

A13. Is a binary flash distillation system fully specified if we specify F, T₁, p₁, z, T_drum, and V even though V is an extensive variable? If it is, explain how Gibbs phase rule is satisfied.

A14. Table 2-4 is at a pressure of 1.0 kg/cm² (actually kgf/cm²), which was formerly a fairly common pressure unit. What is the pressure in bar and in atm?

B. Generation of Alternatives

B1. Think of all the ways a binary flash distillation problem can be specified. For example, we have usually specified F, z, T_drum, p_drum in addition to T₁ and p₁. If T₁ and p₁ are constant, what other combinations of variables can be used? (I have over 20.) Then consider how you would solve the resulting problems.

B2. An existing flash drum is available. The vertical drum has a demister and is 4 ft in diameter and 12 ft tall. The feed is 30.0 mol% methanol and 70.0 mol% water. A vapor product that is 58.0 mol% methanol is desired. We have a feed rate of 25,000 lbmol/h. Operation is at 1.0 atm pressure. Since this feed rate is too high for the existing drum, what can be done to produce a vapor of the desired composition? Design processes using both the existing plus new equipment (if needed). You should devise at least three alternatives. Data are given in Problem 2.D1.

C. Derivations

C1. Determine the effect of pressure on the temperature, separation and diameter of a flash drum.

C2. Analytically solve the Rachford-Rice equation for V/F for a binary system.

C3. Assume that vapor pressure can be calculated from the Antoine equation and that Raoult’s law can be used to calculate K values. For a binary flash system, solve for the drum pressure if drum temperature and V/F are given.

C4. Prove that the operating and y = x lines for binary flash distillation intersect at y = x = z.

C5. Choosing to use V/F to develop the Rachford-Rice equation is conventional but arbitrary. We could also use L/F, the fraction remaining liquid, as the trial variable. Develop the Rachford-Rice equation as f(L/F).

C6. In flash distillation a liquid mixture is partially vaporized. We could also take a vapor mixture and partially condense it. Draw a schematic diagram of partial condensation equipment. Derive the equations for this process. Are they different from flash distillation? If so, how?

C7. Plot Eq. (2-40a) versus V/F for Example 2-2 to illustrate that convergence is not as linear as the Rachford-Rice equation.

C8. For a vapor-liquid-liquid flash distillation, derive Eqs. (2-59) and (2-60) and the equations that allow calculation of all the mole fractions once V/F and L_liquid–1/F are known.

D. Problems

*Answers to problems with an asterisk are at the back of the book.

D1.* We are separating a mixture of methanol and water in a flash drum at 1.0 atm pressure. Equilibrium data are listed in Table 2-7.

a. Feed is 60.0 mol% methanol, and 40.0% of the feed is vaporized. What are the vapor and liquid mole fractions and flow rates? Feed rate is 100 kmol/h.

b. Repeat part a for a feed rate of 1500.0 kmol/h.

c. If the feed is 30.0 mol% methanol and we desire a liquid product that is 20.0 mol% methanol, what V/F must be used? For a feed rate of 1000.0 lbmol/h, find product flow rates and compositions.

d. We are operating the flash drum so that the liquid mole fraction is 45.0 mol% methanol. L = 1500.0 kmol/h, and V/F = 0.2. What must the flow rate and composition of the feed be?

e. Find the dimensions of a vertical flash drum for Problem 2.D1c.

Data: ρ_w = 1.00 g/cm³, ρ_m,L = 0.7914 g/cm³, MW_w = 18.01, MW_m = 32.04. Assume vapors are ideal gas.

f. If z = 0.4, p = 1.0 atm, and T_drum = 77°C, find V/F, x_m, and y_m.

g. If F = 50.0 mol/h, z = 0.8, p = 1.0 atm, and y_m = 0.892 mole fraction methanol, find V, L, and x_m.

D2.* Two flash distillation chambers are hooked together as shown in the diagram. Both are at 1.0 atm pressure. The feed to the first drum is a binary mixture of methanol and water that is 55.0 mol% methanol. Feed flow rate is 10,000 kmol/h. The second flash drum operates with (V/F)₂ = 0.7 and the liquid product composition is 25.0 mol% methanol. Equilibrium data are given in Table 2-7.

a. What is the fraction vaporized in the first flash drum?

b. What are y₁, y₂, x₁, T₁, and T₂?

D3. A flash drum operating at 700.0 kPa is separating binary mixtures of ethane and n-butane.

a. The following partial equilibrium results were generated using Eq. (2-28). Complete the table and use these equilibrium results to answer the remaining parts of this problem.

b. If the feed is z_E = 0.20 mole fraction ethane, p = 700 kPa, and V/F can assume any value from 0 to 1.0; what are the highest and lowest possible ethane vapor mole fractions? What are the highest and lowest possible ethane liquid mole fractions? What are the highest and lowest temperatures of the flash drum?

c. If the feed is z_E = 0.30 mole fraction ethane, p = 700 kPa, and V/F =0.4, what are the outlet vapor and liquid mole fractions and the drum temperature?

d. If the feed is z_E = 0.30 mole fraction ethane, p = 700 kPa, and x_E = 0.2, what value of V/F was used and what is the outlet vapor mole fraction ethane?

e. If the feed is z_E = 0.18 mole fraction ethane, p = 700 kPa, and T_drum = 45^oC, what are the values of V/F, x_E, and y_E?

D4. We have a mixture that is 20 mol% propane, 35 mol% n-butane, and 45 mol% n-hexane. If a flash drum operates at 400 kPa, what is the highest temperature at which the flash drum can operate and still have vapor and liquid present? Use the DePriester chart for equilibrium.

D5. We have a feed that is a binary mixture of methanol and water (55.0 mol% methanol) that is sent to a system of two flash drums hooked together. The vapor from the first drum is cooled, which partially condenses the vapor, and then is fed to the second flash drum. Both drums operate at a pressure of 1.0 atm and are adiabatic. The feed rate to the first drum is 1000 kmol/h. We desire a liquid product from the first drum that is 30.0 mol% methanol (x₁ = 0.30). The second drum operates at a fraction vaporized of (V/F)₂ = 0.25. The equilibrium data are in Table 2-7.

a. Sketch the process labeling the different streams.

b. Find the following for the first drum: vapor mole fraction y₁, fraction vaporized (V/F)₁, and vapor flow rate V₁.

c. Find the following for the second drum: vapor mole fraction y₂, liquid mole fraction x₂, and vapor flow rate V₂.

D6. One form of the Antoine equation is log₁₀(VP) = A – B/(T + C) where VP is in mm Hg and T is in ^oC. For 1-octanol, A = 6.8379, B = 1310.62, C = 136.05.

a. At 1.5 atm and 100°C, what is vapor pressure of 1-octanol in mm Hg?

b. Assuming Raoult’s law is valid, what is the K value of 1-octanol at 1.5 atm and 100°C?

D7. Your plant feeds 100 kmol/h of a mixture that is 46.0 mol% ethanol and 54.0 mol % water to a flash drum. Your boss thinks that results will be better with two flash drums (same configuration as in Problem 2.D2.) with V₁ = 30.0 kmol/h and V₂ = 30.0 kmol/h.

a. Find L₁, L₂, and x₂.

b. Compare x₂ to the liquid mole fraction from a single flash drum with V/F = 0.60.

D8.* You want to flash a mixture with a drum pressure of 2.0 atm and a drum temperature of 25°C. The feed is 2000.0 kmol/h. The feed is 5.0 mol% methane, 10.0 mol% propane, and the rest n-hexane. Find the fraction vaporized, vapor mole fractions, liquid mole fractions, and vapor and liquid flow rates. Use DePriester charts.

D9.* We wish to flash distil an ethanol-water mixture that is 30.0 wt% ethanol and has a feed flow of 1000.0 kg/h. Feed is at 200°C. The flash drum operates at a pressure of 1.0 kg/cm². Find T_drum, weight fraction of liquid and vapor products, and liquid and vapor flow rates.

Data:

C_PL,EtOH = 37.96 at 100°C, kcal/(kmol°C)

C_PL,W = 18.0, kcal/(kmol°C)

C_PV,EtOH = 14.66 + 3.758 × 10^–2T – 2.091 × 10^–5T² + 4.74 × 10^–9T³

C_PV,W = 7.88 + 0.32 × 10^–2T–0.04833 × 10^–5T²

Both C_PV values are in kcal/(kmol°C), with T in °C.

ρ_EtOH = 0.789 g/mL, ρ_W = 1.0 g/mL, MW_EtOH = 46.07, MW_W = 18.016, λ_EtOH = 9.22 kcal/mol at 351.7 K, and λ_W = 9.7171 kcal/mol at 373.16 K.

Enthalpy composition diagram at p = 1 kg/cm² is in Figure 2-4. Note: Be careful with units.

D10. We have a mixture that is 35.0 mol% n-butane with unknown amounts of propane and n-hexane. We are able to operate a flash drum at 400 kPa and 70°C with x_C6 = 0.7. Find the mole fraction of n-hexane in the feed, z_C6, and the value of V/F.

D11. An equilibrium mixture of ethylene and propylene is at 2500.0 kPa and 25°C. Find the vapor and liquid mole fractions of ethylene. Note: This is not a guess-and-check problem.

D12. Find h_total and D for a horizontal flash drum for Problem 2.D1c. Use h_total/D = 4.

D13. We flash distil a mixture that is 36% ethane (C2) and 64% n-butane (C4). The flash drum operates as an equilibrium stage. We measure the outlet concentrations of ethane as x_C2 = 0.088 and y_C2 = 0.546. Find x_C4, y_C4, T_drum, p_drum, and V/F. Note: This is not trial and error.

D14. A flash drum is separating a mixture that is 12.0 mol% methane (C1), 48.0 mol% n-butane (C4), and 40.0 mol% n-pentane (C5). Feed rate is 122.0 kmol/h. The feed is partially liquid and partially vapor at a pressure of 5.0 bar and temperature of 50.4°C. The flash drum is at 3.0 bar and T = 36°C. Find V/F, the K values, and vapor and liquid mole fractions.

D15.* We have a flash drum separating 50.0 kmol/h of a mixture of ethane, isobutane, and n-butane. The ratio of isobutane to n-butane is held constant at 0.8 (that is, z_iC4/z_nC4 = 0.8). The mole fractions of all three components in the feed can change. The flash drum operates at a pressure of 100 kPa and a temperature of 20°C. If the drum is operating at V/F = 0.4, what must the mole fractions of all three components in the feed be?

D16. A feed that is 50.0 mol% methane, 10.0 mol% n-butane, 15.0 mol% n-pentane, and 25.0 mol% n-hexane is flash distilled. F = 150.0 kmol/h. Drum pressure = 250.0 kPa, drum temperature = 10°C. Use the DePriester charts. Find V/F, x_i, y_i, V, and L.

D17. We are separating a mixture of acetone (MVC) from ethanol by flash distillation at p = 1 atm. Equilibrium data are listed in Problem 4.D7. Solve graphically.

a. 1000.0 kmol/day of a feed that is 70.0 mol% acetone is flash distilled. If 40% of the feed is vaporized, find the flow rates and mole fractions of the vapor and liquid products.

b. Repeat part a for a feed rate of 5000.0 kmol/day.

c. If feed is 30.0 mol% acetone, what are the lowest possible liquid mole fraction and the highest possible vapor mole fraction?

d. If we want to obtain a liquid product that is 40.0 mol% acetone while flashing 60% of the feed, what must the mole fraction of the feed be?

D18.* 10.0 kmol/h of a feed that is 10.0 mol% propane, 30.0 mol% n-butane, and 60.0 mol% n-hexane is flash distilled at a drum pressure of 200.0 kPa. We desire a liquid that is 85.0 mol% n-hexane. Use DePriester charts. Find T_drum and V/F. Continue until your answer is within 0.5°C of the correct answer. Note: This is a single trial and error, not a simultaneous mass and energy balance convergence problem.

D19.* A flash drum operating at 300.0 kPa is separating a mixture that is 40.0 mol% isobutane, 25.0 mol% n-pentane, and 35.0 mol% n-hexane. We wish a 90% recovery of n-hexane in the liquid. F = 1000.0 kmol/h. Find T_drum, x_j, y_j, V/F.

D20. 200.0 kmol/h of a feed that is 10.0 mol% ethanol and 90.0 mol% water is separated in a pair of flash drums. The vapor from drum 1 is partially condensed and fed to drum 2 (F₂ = V₁). If y₂ = 0.45 and V₂/F₂ = 0.6, find V₁, L₁, V₂, L₂, x₁, y₁, and x₂. Both drums are at 1.0 atm.

D21. We wish to flash distil a feed that is 55.0 mol% ethane and 45.0 mol% n-pentane. The drum operates p_drum = 700.0 kPa and T_drum = 30°C. Feed flow rate is 100,000 kg/h.

a. Find V/F, V, L, liquid mole fraction, and vapor mole fraction.

b. Find the dimensions in metric units required for a vertical flash drum. Assume the vapor is an ideal gas to calculate vapor densities. Use DePriester chart for VLE. Be careful of units. Arbitrarily pick h_total/D = 4. MW_ethane = 30.07, MW_pentane = 72.15. Liquid densities are = 0.54 g/ml (estimated), = 0.63 g/ml.

D22. 50.0 kmol/h of a vapor feed that is 70.0 mol% methanol and 30.0 mol% water is partially condensed in a heat exchanger and then fed to a flash drum operating at a pressure of 1.0 atm. 20.0 kmol/h of liquid product is collected.

a. Find mole fractions of methanol in the liquid and in the vapor.

b. Find the temperature of the drum.

D23.

a. Design a new vertical flash drum for Example 2-4 but with a feed of 1500.0 kmol/h.

b. If a vertical flash drum 4.0 feet in diameter has been built, what size additional vertical flash drum is needed if the drums will be operated in parallel to separate 1500.0 kmol/h?

D24. We plan to separate a mixture of propane and n-hexane at 300.0 kPa.

a. Using the data in the DePriester charts, plot y propane versus x propane for this mixture at this pressure.

b. If the feed is 30.0 mol% propane, and 40.0 mol% of the feed is vaporized, what are the liquid and vapor mole fractions, and what is the drum temperature? Solve graphically.

c. What is the drum temperature in part b?

d. If y = 0.8 and the feed is 0.6 (both mole fraction propane), what is the value of V/F?

e. Use the Rachford-Rice equation to check the answers obtained in parts b and c.

D25. We wish to flash distil a mixture of methane and n-butane in a flash drum operating at 50°C. The feed is 20.0 mol% methane and 80.0 mol% n-butane. Feed rate is 100.0 kmol/h. Feed is at a pressure and temperature such that in the drum V/F = 0.40. Use the DePriester charts.

a. Find the drum pressure.

b. Find the methane mole fraction in the liquid and the vapor.

D26. We are feeding 100.0 kmol/h of a 45.0 mol% propane, 55.0 mol% n-pentane feed to a flash distillation system. We measure the outlet vapor and liquid mole fractions leaving the flash drum, which is an equilibrium stage, and obtain, y_propane = 0.8, x_propane = 0.2162.

Find (a) L and V. (b) x_pentane and y_pentane. (c) T_drum and p_drum.

Use the DePriester charts. Note: This is not trial and error.

D27. For the Antoine equation in the form

with VP in mm Hg and T in °C, the constants for n-pentane are A = 6.853, B = 1064.8, C = 233.01. n-hexane constants are A = 6.876, B = 1171.17, C = 224.41 (Speight, 2005).

a. Predict the vapor pressure at 0°C for pure n-pentane.

b. Predict the boiling point of pure n-pentane at 3.0 atm pressure.

c. Predict the boiling pressure if pure n-pentane is boiling at 0°C.

d. At a pressure of 500.0 mm Hg and temperature of 30°C, predict the K values for n-pentane and n-hexane using Raoult’s law.

e. If T = 30°C and p = 500.0 mm Hg, determine the mole fractions in the liquid and vapor phases of an equilibrium mixture of n-pentane and n-hexane.

f. One mole of a mixture that is 75.0 mol% n-pentane and 25.0 mol% n-hexane is placed in a closed chamber. The pressure is adjusted to 500.0 mm Hg, and the temperature to 30°C. The vapor and liquid mole fraction were found in part e. How many moles of liquid and moles of vapor are there at equilibrium?

g. If 1.0 mol/min of a mixture that is 75.0 mol% n-pentane and 25.0 mol% n-hexane is fed continuously to an equilibrium flash chamber operating at 30°C and 500.0 mm Hg, find the flow rates of the liquid and vapor products.

D28. Repeat Example 2-4, but with F = 3000.0 lbmol/h, and use a horizontal flash drum with holding time = 55.0 min and surge time = 85.0 min. Calculate D, h, and h/D.

D29. Design a horizontal flash drum to separate 15,000 kg/h of a feed with the following mass fractions: methane 0.21, propane 0.39, n-butane 0.24, i-butane 0.11, and n-pentane 0.05. The feed is at 0°C and a pressure just high enough that it is all liquid. The drum pressure is 4.0 atm and the drum is adiabatic (heat duty = 0).

a. Find the minimum feed pressure (to within a whole number of atmospheres) that keeps the feed a liquid. Report this pressure and the VLE correlation used, and use this as the feed pressure for the flash calculation.

b. Find L, V (in kg/h and in kmol/h), y_i, x_i (in mole fractions), and T_drum (in °C).

c. If a horizontal drum is used, find D_min. If the holding time is 9 minutes and the ratio of the drum length to diameter is h/D = 6, find the surge time that can be accommodated.

Note: The easiest way to solve this problem is to use Aspen Plus for part a (trial and error) and then obtain the solution for part b. Although Aspen Plus does not do the drum sizing, it does calculate the physical properties needed for drum sizing. Obtain these values and do the drum sizing with a hand calculation.

D30. Data for the equilibrium of water and n-butanol at 1.0 atm is given in Table 8-2. Plot y_w versus x_w. A feed of 100.0 kmol/h that is 20.0 mol% water is fed to flash chamber A in the figure that follows. The vapor from flash chamber A is 40.0 mol% water. This vapor is then partially condensed and fed to flash chamber B. In flash chamber B, 40% of the vapor from chamber A is condensed.

a. What are the flow rates L_A and V_A, and what is the value of x_A?

b. What are the flow rates L_B and V_B, and what are the values of x_B and y_B?

c. Suppose we changed the operation of chamber B so that enough vapor was condensed to give a liquid mole fraction of x_B = 0.20 mole fraction water. If x_B = 0.20, what are y_B, L_B, and V_B? We could now easily recycle this liquid to the feed (also 20% water) and produce only V_B,new and L_A,new as products. Calculate these new flow rates when L_B with mole fraction 0.2 is recycled.

D31. A flash drum is separating n-butane and n-pentane with T_drum = 20°C and p_drum = 101.3 kPa. The feed is 50.0 wt% n-butane and 50.0 wt% n-pentane. Use the Rachford-Rice equation to find V/F (does not require trial-and-error). Then find x and y for n-butane and n-pentane.

Is it possible to do a flash distillation of the 50-50 feed of n-butane and n-pentane with the flash drum operated at T_drum = 0°C and p_drum = 101.3 kPa?

D32. A feed of 100.0 kmol/h that is 60.0 mol% methanol and 40.0 mol% water is sent to a system of three flash drums operating at 1.0 atm. The feed is sent to drum A with (V/F)_A = 1/3. After partial condensation, the vapor product from drum A is the feed to drum B, which operates at (V/F)_B = V_B/V_A = 0.4. The liquid from drum A is partially vaporized and is sent to drum C. The liquid product from drum C is 15.0 mol% methanol. Find flow rates of L_A, L_B, L_C, V_A, V_B, and V_C, and find all unknown vapor and liquid mole fractions.

E. More Complex Problems

E1. A vertical flash drum will be used to separate 1000.0 kmol/h of a feed that is 10.0 mol% isopropanol and 90.0 mol% water. Feed is at 9.0 bar and 75°C. V/F_drum = 0.5 and p_drum = 1.0 bar.

a. Find L, V, x_i, y_i, T_drum, the heat duty in kW, and the drum diameter.

b. Unfortunately, the drum available is 1.0 m in diameter, which is too small. Your boss suggests raising the drum pressure to use the existing drum with V/F = 0.5. Maximum drum pressure is 9.0 bar. Will the current drum work at a pressure < 9.0 bar?

c. If yes, what is the lowest drum pressure that works (that is, for what pressure does D_drum = 1.0 m)? Find L, V, x_i, y_i, T_drum, and the heat duty in kW.

E2. A flash drum is to flash 10,000 lbmol/h of a feed that is 65.0 mol% n-hexane and 35.0 mol% n-octane at 1 atm pressure. V/F = 0.4.

a. Find T_drum, liquid mole fraction, and vapor mole fraction.

b. Find the size required for a vertical flash drum.

c. Note, y, x, T equilibrium data can be determined from the DePriester charts. Other required physical property data are given in Example 2-4.

E3. A flash drum at 1.0 atm is separating a feed consisting of methanol and water. If the feed rate is 2000.0 kg/h and the feed is 45.0 wt% methanol, what are the values of L (kg/h), V (kg/h), y_M, x_M (weight fractions), and T_drum if 35% by weight of the feed is vaporized? VLE data are in Table 2-7. Note: Watch your units.

F. Problems Requiring Other Resources

F1. Benzene-toluene equilibrium is often approximated as α_BT = 2.5. Generate the y-x diagram for this relative volatility. Compare your results with data in the literature (see references in Table 2-2). Also, generate the equilibrium data using Raoult’s law, and compare your results to these.

F2.* Ethylene glycol and water are flash distilled in a cascade of three drums connected as shown in the figure. All drums operate at 228.0 mm Hg. Feed is 40.0 mol% water. One-third of the feed is vaporized in the first drum, two-thirds of the feed to the second drum is vaporized, and one-half the feed to the third drum is vaporized. What are the compositions of streams L₃ and V₃? Note that water is the more volatile component.

F3.* (Long Problem!) We wish to flash distill a mixture that is 51.7 mol% propane, 9.1 mol% n-pentane, and 39.2 mol% n-octane. The feed rate is 100.0 kmol/h. The feed to the flash drum is at 95°C. The flash drum will operate at 250.0 kPa. Find the drum temperature, the value of V/F, and the mole fractions of each component in the liquid and vapor products. Converge |ΔT_drum| to < 0.20°C.

F4. Pure water at a flow rate of 1500.0 kg/minute at p = 5000.0 kPa and T = 500 K is sent to an adiabatic flash system operating at p = 100.0 kPa.

a. Is this feed a liquid, a vapor, or a two-phase mixture?

b. Find T_drum (in K), and the flow rates L and V (in kg/min) leaving the flash drum.

G. Computer Simulation Problems

G1. An adiabatic flash drum operates at a pressure of 1000.0 kPa. The feed is 100.0 kmol/h of a mixture containing 5.3 mol% ethylene, 22.6 mol% ethane, 3.7 mol% propylene, 36.2 mol% propane, and 32.2 mol% n-butane. At the point after the pump and heater—immediately before the valve to the drum where the feed is flashed–the feed is at 10,000 kPa and 100°C.

Find the values of L, V, x_i, and y_i.

G2. 250.0 kmol/h of a feed that is 14 mol% methane (C1), 6.0 mol% ethane (C2), 52.0 mol% n-pentane (C5), and 28.0 mol% n-hexane (C6) is at a temperature of 28°C and a pressure 50.0 kPa higher than the minimum pressure that will keep the feed totally liquid (vapor fraction of feed stream ≤ 0.001). Determine a drum pressure p_drum that allows an adiabatic flash distillation to meet the specification for the liquid product that is in the range 0.042 < (x_C1 + x_C2) ≤ 0.043. Use Peng-Robinson VLE correlation.

a. What is the lowest pressure (kPa) for the feed that will keep the feed all liquid (vapor fraction of feed stream ≤ 0.001)?

b. What feed pressure did you use for feed to flash drum? What was the fraction of vapor in the feed?

c. What are the values of p_drum, V/F, T_drum, and mole fractions of the liquid and vapor product that meet the specification 0.042 < (x_C1 + x_C2) ≤ 0.043?

G3. Use a process simulator to solve Problem 2.D14 using the Peng-Robinson VLE correlation. Also determine the fraction of the feed that is vapor and the amount of cooling or heating required for the process. Compare answers and comment on differences.

G4. Use a process simulator to solve Problem 2.D16. Do “what if?” simulations to see what happens to V/F and product compositions as temperature and/or pressure vary.

G5. One kmol/s of a feed containing 20.0 mol% furfural, 75.0 mol% water, and 5.0 mol% ethanol at 105°C and 3.0 bar is fed to a three-phase flash drum. The drum is at 1.0 bar and operates with V/F = 0.4. The key component in the second liquid (bottom of drum) is water. Find the outlet temperature, heat duty in kW, the ratio of the first liquid/total liquid, and the compositions of the three phases.

G6. Use a process simulator to solve the following flash distillation problem. Feed is 2.0 mol% methane, 30.0 mol% n-butane, 47.0 mol% n-pentane, and 21.0 mol% n-hexane and is a liquid. The flash drum is at 1.0 atm, it is adiabatic (heat duty = 0), and there is no heat exchanger. Initially, for the feed, set vapor fraction = 0 (a saturated liquid) and set the temperature. You want to obtain V/F in the drum of 0.4000 (rounded off to the fourth decimal). Find the feed temperature that gives this value of V/F. (As you do runs, note that feed pressure for a saturated liquid increases as feed temperature is increased. Why?) Once you find the correct feed temperature, remove the feed specification that vapor fraction = 0 and specify a feed pressure that is 1.0 atm above the pressure reported by Aspen Plus when vapor fraction of feed = 0. Liquids that are saturated liquids (this is what Aspen means by vapor fraction = 0) cannot be pumped easily. By raising the pressure, we make pumping easy. Rerun simulation one last time to check that you have met all requirements. Expect to do several Aspen Plus runs to solve this problem. Report the feed temperature and pressure, drum temperature, heat duty in drum, x, and y values.

H. Computer Spreadsheet Problems. Turn in two copies of the spreadsheets—one with numbers in the cells and one with equations in the cells.)

H1. We flash distil a mixture that is 5.0 mol% methane, 12.3 mol% ethane, 11.5 mol% n-butane, 22.2 mol% n-pentane, 25.4 mol% n-hexane, and 23.6 mol% n-heptane. Use Table 2-3 data and a spreadsheet.

a. If p = 14.7 psia and V/F =0.45, what temperature is the drum at?

b. If T = 110°F and p = 19.0 psia, find V/F.

c. If T = 135°F and V/F = 0.62, find p.

H2. Show that the spreadsheet in Figures 2.B-3 and 2.B-4 has convergence difficulties if Goal Seek is used to make cell B19 (∑x_i = 1) equal 1 by changing cell B9 (V/F).

H3. We flash distil a mixture that is 24.1 mol% ethane, 39.7 mol% n-hexane, and 36.2 mol% n-heptane. If p = 101.3 kPa and T = 65°C, find V/F, y_i and x_i values.

H4. We flash distil a mixture that is 28.1 mol% n-butane, 42.8 mol% n-pentane, and 29.1 mol% n-heptane. T_drum = 41°C and (V/F)_drum = 0.35. Find p_drum, y_i and x_i values.

H5. 255.0 kmol/h of a liquid feed at a high pressure (see part a) and 15°C that is 2.3 mol% ethane, 12.6 mol% propane, 23.4 mol% n-butane, 28.7 mol% n-pentane, 25.2 mol% n-hexane, and 7.8 mol % n-heptane is sent to a flash drum.

a. What is the minimum pressure (kPa) that will make the feed all liquid?

b. If the drum pressure is 101.3 kPa and the flash drum is at 15°C, report V/F, x_i, and y_i.

c. If the drum pressure is 101.3 kPa and V/F = 0.6, report drum temperature, x_i, and y_i.

d. If the drum pressure is 101.3 kPa and the n-pentane mole fraction in the liquid is 0.300, report T and V/F. Note: There is a rather narrow range of values where this is possible.

H6. Solve Example 2-2 with a spreadsheet and Goal Seek using the K values from the example. Note that this spreadsheet is considerably simpler than the spreadsheets shown in Figures 2-B3 and 2-B4 in this chapter’s Appendix B, section 2.B.2, because K values are not calculated in the spreadsheet.

As you use the simulator, take notes on what you do and what works. If someone shows you how to do something, insist on doing it yourself—and then make a note of how to do it. Without notes, you may find it difficult to repeat some of the steps even if they were done just 15 minutes earlier. In addition, develop the practice of saving your work in a new file each time you make a substantial change. This practice makes the process of going backwards to previous results very easy. If difficulties persist, see Appendix A, “Aspen Plus Troubleshooting Guide for Separations,” at the end of the book.

Lab 1. Introduction to Aspen Plus

This lab introduces you to the Aspen Plus simulator and to simulation of flash distillation.

Goals:

• To become familiar with the Aspen Plus simulator, including drawing and specifying flowsheets and choosing the appropriate physical properties packages

• To explore flash distillation

1. Start-up of Aspen Plus

First, log into your computer. Once you are logged in, use the specific steps for your computer to log into the simulator and request a new simulation and then a blank simulation. This should give you an Aspen Plus (or other simulator) blank screen.

2. Input Data

Aspen Plus v8.8 first shows the tab for selection of components. Select ethanol and water. Component ID is whatever you want to call it. If you decide to name the components ETHANOL and WATER and click Enter after each, Aspen Plus will complete the remainder of the information. If you use a different ID, such as ETOH or H2O, give the appropriate component name (ethanol or water). Then proceed to the next component. Aspen Plus will recognize these two components. If Aspen Plus does not fill in the formula, click on the Find button and proceed. When done with components, click on the blue Next button (on the toolbar in the Home tab) to go to the next required input specification. Aspen Plus can be very picky about the names or the way you write formulas.

Note: If you use W as component ID, Aspen will think this is tungsten. Type WATER as component ID. After you have the compounds entered, click on the blue Next arrow.

You should now have the Global tab with property methods and options. You must select the property method to use. As noted in the references, proper choice of property method is absolutely critical (Carlson, 1996; O’Connell et al, 2009; Schad, 1998). If you pick the wrong model, your results are garbage. A brief selection guide is given in Table 2-4. The Methods Assistant is new in Aspen Plus v8.8 and may also be helpful. We will try different models and compare them to data. Note that data also needs to be checked for consistency (Barnicki, 2002; O’Connell et al, 2009; Van Ness and Abbott, 1982). First, try the IDEAL model. In the center of the tab use the Method Name menu. Then click the blue Next button.

After you have input the properties and clicked Next, you will get a box labeled Required Properties Input Complete. Click OK to Run Property Analysis/Setup. The Control Panel should say “Table generation completed.” Click Next—you should have a box that says “Property analysis and setup completed successfully.” Click OK (If you get a pop-up that says an economics program is being installed click Cancel.) Then click the blue Next button. If you only get a message that “property analysis and setup completed successfully,” click OK. In the Navigation area on the left side of the window you will see that Properties is lit up. Click on Simulation, which is immediately under Properties. This will give you a screen labeled Main Flowsheet.

3. Drawing a Flowsheet in Aspen Plus

Go to the bottom menu and left-click Separators (flash drums). (If you can’t see a bottom menu, go to VIEW and click on Model Palette in the menu bar.) After clicking on Separators, left-click on the downward pointing arrow head to the right of Flash2 (flash drums with two outlets). Click on the icon that you prefer (e.g., see Figure 2-A1). Drag your cursor to the center of the blank space, and left-click. This gives the basic module for a flash drum. You can deselect the Flash2 option (to avoid getting extra copies by accident) by clicking on the arrow in the upper-left corner of the Model Palette. If you hover the cursor over this button, it is labeled “Cancel insert mode”—it is a good idea to click this button after completing each step of setting up the flowsheet. Try left-clicking on the icon (in the working space) to select it and right-clicking the mouse to see the menu of possibilities. Rename the block by left-clicking Rename Block, typing in a name such as, FLASH, and clicking OK.

The basic flash drum needs to have a feed line and two outlets. Left-click on the icon labeled Material Streams on the left side of the Model Palette to get possible ports (after you move the cursor into the white drawing screen). Move the cursor to one of the red arrows until it lights up. Left-click (take your finger off the button) and move the cursor away from the flash drum. Then left-click again to obtain a labeled material stream. Additional streams can be obtained the same way. Put the required (shown in red) feed, vapor product, and liquid product streams on your flowsheet. (DO NOT USE THE BLUE WATER DECANT ARROW. If you inadvertently connect to a blue arrow, right-click on the stream and select Reconnect, and in the menu select either the source or the destination as appropriate. An alternative is to select the stream, cut the stream, and start over.) After clicking the Cancel insert mode button, highlight the stream names by clicking on a stream with the left mouse button, and use the right button to obtain a menu. Rename the streams as desired. The completed flowsheet is shown in Figure 2-A1.

Aspen Plus will happily create mass streams and modules that you do not want (and can hide one behind another), and thus some deletion may be necessary. If a stream is created in error, highlight it with the left button. Then click the right button to obtain a menu that allows you to delete (use “cut”) the stream. Click OK with the left button. Play with the functions until you determine how everything works. If things appear that you don’t want, click the Cancel insert mode button, and then Delete.

When you are happy with your flowsheet, click the Next button (a blue arrow in v8.8 located on the very top ribbon and in the middle of the center ribbon when in the Home tab). If the flowsheet is not complete, a message will tell you there is a problem. If the flowsheet is complete, Aspen Plus will take you to the Material Input for your feed stream to the flash distillation (see Figure 2-A2). Fill in this information. Try a pressure of 1.0 bar, vapor fraction of 0.4 (click on the arrow next to Temperature, and select vapor fraction), total flow of 100.0 kmol/h, ethanol mole fraction of 0.1, and water mole fraction of 0.9 (use the menu under Composition to select mole fraction). Click Enter on the keyboard. Then left-click on the Next button.

Since these instructions assume the use of mole or mass fraction, always use mole fractions or mass fractions for the units for the composition of the stream (use the menu). Other choices may lead to inadvertent errors.

After clicking the Next button, you will see a very similar page asking for the Flash2 input (Figure 2-A3). (Note that confusing these two similar screens will result in wrong answers and a lot of confusion.) This screen wants the actual pressure and temperature in the flash column (the fraction vapor or heat duty can be substituted for either T or P). Fill out the conditions for the flash drum block (for the first run only, use a pressure of 0.9 bar, which has to be less than or equal to the feed pressure, and vapor fraction = 0.6) and click on the Next button. At this point you will probably get a screen that says input is complete, and asks if you want to run the simulation now. Don’t. Click Cancel.

Aspen Plus v8.8 skips the Setup step, which works for this problem, since vapor-liquid is the default but in general is not good practice. On the left side of the Aspen Plus screen in the column of items, click on Setup (top item). In the Valid Phases menu select Vapor-Liquid and Free water = No. Click on the Next arrow.

4. Analysis of VLE Data

Instead of running the simulation, analyze the VLE data. Click on Properties in the Navigation Pane (lower left of Aspen screen). Then click on Binary in the toolbar (be sure you are in the Home tab) to do a binary analysis (see Figure 2-A4). For Analysis type choose Txy from the menu. For Compositions choose Mole fraction as the Basis, and for Vary choose ETHANOL. For valid phases pick Vapor-Liquid and a pressure of 1 bar. Since you selected Ideal as the property method, it should be listed on the form. Scroll down on the form. For number of points choose 100 (see following screenshot). Then click Run Analysis and look at the T-xy graph. (If you get messages, you are in the control panel—go to the BINRY tab and click the button to run analysis.) This should give you the T-xy graph.

Aspen has also produced a table with all the VLE predicted—in the Navigation Pane on left of the Aspen screen under Analysis/BINRY-1/, click on Results. The table is very useful for comparing with data. You can also obtain a y-x plot: In the BINRY tab with the home menu bar on top right side of screen, you will see plots labeled T-xy and T-x. To the right of T-x is a menu bar—click on the bottom part of the bar and then click on the icon for y-x graph. (There is an alternate way to do this, but this method is easier.) Record the x and y values or print the x-y graph. Of course, all of these numbers are wrong, since we used the wrong VLE model.

Note that with the Ideal VLE correlation, the results are not close to the data (Table 2-1). What this means is that we picked the wrong equilibrium data (on purpose). Since Aspen Plus is quite willing to let you be stupid in picking the wrong properties package, it is your responsibility to check that the equilibrium data make sense. With the NRTL VLE correlation there is reasonably good agreement, and we will try that later.

5. Doing a Flash Run with Ideal Model

Cancel any leftover screens from the analysis (this will speed up the simulator). Click on the Next button. If Aspen sees any leftover analysis runs that are unfinished, it will try to run them. If necessary, go to the Navigation Pane, left-click on Analysis, then select any previously created object (e.g., VLE based on Ideal model), right-click to obtain a menu, and select Delete. To return to the flash simulation, select the Simulation button in the Navigation Pane. Click the Next button, and when the dialog box asks if you want to do a run, click OK, and watch Aspen Plus as it calculates (this takes very little time). If you get a box that says Economic Analysis, click “Do not show me this recommendation again,” and then Close. The Control Panel should say “Generating results.” Note: The Control Panel can also be opened from the Home tab of the toolbar. Following are two useful methods of looking at results:

a. In the Navigation Pane, left-click on the arrow to the left of Results Summary. The most important item in the Results Summary is the line that hopefully says, “Calculations were completed normally.” If it says anything else, you may have a problem. Results Summary also gives a menu that allows you to look at the streams and other data.

b. Another useful way to look at results is to go to the Home tab in the toolbar and click on Report, then in the window click on the box next to the block you want to see the report for, and then click OK. This report can be printed using the file column in Notepad. By scrolling in the menu window, you can obtain other reports—the Streams report contains useful results. The folder/Results Summary/Streams/ in the Navigation Pane is also very useful.

The different methods contain slightly different data, so look at them all.

Record the values for vapor and liquid mole flow rates and drum temperature. Of course, all of these numbers are wrong, since we used the wrong VLE model.

6. Rerun Analysis and Simulation with Better VLE Model

Cancel any unused screens. Go to the Properties menu in the Navigation Pane. In the Global tab of the /Methods/Specifications/ folder, change the base method for VLE to NRTL-2. Click on Next. Aspen will open the folder /Methods/Parameters/Binary Interaction/NRTL-2/ to show you the model parameters drawn from the database APV86 VLE-IG that will be used in the simulation. Click on Binary in the Home tab of the toolbar, and redo the analysis. Look at the T-xy plot, the table of data, and the x-y plot. Compare to the VLE data in the textbook (the most accurate comparison is with Table 2-1).

Then go to Simulation. Click on the Next button, and redo the run. Check the results. Write these results down. Compare the vapor and liquid products with this equilibrium data to the previous run.

7. Try Different Inputs

Once you are happy with the previous runs, change the input conditions (using the same flowsheet) to look at different feed compositions and different fraction vaporized. There are at least two ways to input new data:

a. In the main flowsheet, left-click on the block for the flash. Right-click to obtain the dropdown menu, and click on Input. Enter the desired numbers for the flash drum. Left-click on the feed stream, right-click on input (or navigate directly to the folder /Streams/Feed/Input/), and enter the desired feed numbers.

b. Click the Simulation button (lower left), and in the All Items column (left side of screen), click Input for streams or blocks (if Input is not visible, click on the arrowhead next to the desired item). Change the data as desired.

Try feeds that are 10.0, 30.0, 50.0, and 70.0 mol% ethanol and vary Vapor fraction.

8. Adiabatic Flash

The most common way to operate a flash system is to feed a hot liquid at elevated pressure through a valve into an insulated (adiabatic) flash chamber that operates at lower pressure. Try a feed of 100.0 kmol/h that is 30.0 mol% ethanol and 70.0 mol% water. The flash chamber operates at 1.0 atm and is adiabatic (set Duty = 0).

a. The feed is at 110°C and a pressure of 50.0 psia. Repeat for 100.0 psia.

b. The feed is at 130°C and a pressure of 100.0 psia.

c. The feed is at 150°C and a pressure of 100.0 psia.

d. The feed is at 151.5°C and a pressure of 100.0 psia.

e. The feed is at 151.5°C and a pressure of 200.0 psia.

For all of these cases, look at the feed stream and the two product streams (e.g., Report→Streams→All→OK, or navigate directly to /Blocks/Flash2/Stream Results/). Is the feed stream entirely liquid? When the feed is not entirely liquid, what happens to the liquid and vapor product flow rates? What is the effect of the feed pressure? Why are the two runs for part a essentially identical, but runs d and e give very different results?

9. Switch to a Ternary Problem

Remove any leftover dialog boxes or screens. Click on Properties, and in the Navigation Pane, click on Components. Left-click on the box to the left of the component ID. Then right-click and delete the row from the dropdown menu. Delete both ethanol and water.

Then add propane, n-butane, and n-pentane as the three components. (You will have to input N-PENTANE in the component name list, since it is too long to fit in component ID.) In the Navigation Pane go to Methods, and change the choice of VLE in the Global tab. Peng-Robinson is a good choice for hydrocarbons. Although the following step can be skipped, good practice is to go to the folder /Methods/Selected Methods/ and delete the entries for NRTL-2 and IDEAL. Click on Simulation in the Navigation Pane. Return to the /Streams/Feed/Input/ folder (or use the Next button) and input the mole fractions (propane 0.2, n-butane 0.3, and n-pentane 0.5). In the /Blocks/Flash2/Input/ folder, set fraction vaporized in feed at 0.4 and pressure of 1.0 bar for now. Go to the Flash input for the flash drum, and set pressure to 1.0 bar and vapor fraction to 0.4. Click on the Next button, and do the simulation run when ready. Record your results (component flow rates, T, y, and x). Then rerun with a feed that has a set temperature instead of fraction vaporized. Compare your results to the previous run. Try different fraction vaporized, different feed compositions, and different temperatures.

10. What Does It All Mean?

Reflect on the meaning of your results for both the binary and the ternary flash systems.

a. Binary: How are the compositions of the vapor and liquid streams from the flash system related? What is the role of the fraction vaporized? How can you do the calculation by hand?

b. Ternary: How are the compositions of the vapor and liquid streams from the flash system related? What is the role of the fraction vaporized? How can you do the calculation by hand? Note that the calculation methods used for hand calculations will be different for the binary and ternary systems, since the equilibrium data are available in different forms (graphically for the binary and DePriester chart for the ternary).

11. Finish

Finish by taking notes on this instruction sheet and save these instructions. The next lab will assume that you know how to do flash calculations in Aspen Plus. Exit Aspen Plus and log out. There is no formal lab report for this lab.

Lab 2. Flash Distillation

This lab is an opportunity to learn more about Aspen Plus v8.8 simulations of flash distillation systems.

Goals:

• Become familiar with use of Flash2 and Flash3 to simulate flash distillation systems.

• Explore the effects of changing operating variables on the results of the flash distillation simulation.

Preparation:

• Find equilibrium data for furfural-water before lab. This data is your ticket to lab—if you do not have the data, you will be told to leave, go find the data, and then return to lab.

• This lab assumes you are familiar with the previous lab and that you are able to do basic steps with Aspen Plus.

• If you need to, use the instructions for Lab 1 to help you use Aspen Plus.

• If problems persist while trying to run the simulations, see Appendix A at the end of the book.

General Instructions:

For part 1a use Flash2 with the Peng-Robinson VLE correlation (if you need to, review Lab 1 on how to input the VLE correlation you want to use). For part 1b use Flash3 and NRTL. For part 1c use Flash3 and a VLE correlation that fits the equilibrium data. Your instructor will collect the equilibrium data at the beginning of the period and then return it before you do part 1c. Use F = 1.0 kmol/h for all cases. Compare the predictions of Analysis with equilibrium data from the literature.

Part 1. Simulations

a. The feed is 45.0 mol% n-butane and 55.0 mol% n-hexane at 1.0 atm. The feed is a saturated liquid (vapor fraction = 0.0). The drum pressure is 0.8 atm. Do for V/F in the drum = 0.2, 0.4, 0.6, and 0.8 (four runs). Report feed temperature, Q, drum T, y, x, V, and L.

b. Delete the block for Flash2, redraw with Flash3, and then reconnect streams and add another liquid product (you need both a first and a second liquid product). Be sure to list valid phases as Vapor-liquid-liquid in both Setup and Analysis. The feed is 55.0 mol% benzene and 45.0 mol% water at 5.0 atm and is a saturated liquid. Use Analysis to generate T-xy data and y-x diagrams with the Ideal and the NRTL VLE correlation. Compare the results. Then run the simulation with the NRTL correlation and a drum temperature of 120°C for V/F in the drum = 0.2, 0.4, 0.6, and 0.8 (four runs), and use the NRTL y-x diagram to explain your results. Record drum pressure (bar), heat duty, and compositions of all three phases for each V/F.

c. Feed is initially 60.0 mol% furfural (a cyclic alcohol) and 40.0 mol% water at 1.0 atm and 50°C. The drum operates at 105°C and V/F = 0.4. Use a VLE correlation that fits the data, Flash3, and list valid phases as Vapor-liquid-liquid. With 40.0 mol% water, the two liquid phases should be identical, which means there is only one liquid phase. Try 60.0, 70.0, 90.0, and 99.0 mol% water in the feed. Generate a y-x diagram with Analysis, and use it to explain your results. (Note that Aspen will not know which property method to use and will list the Property options. Select the best fit correlation.) Report the VLE correlation used, drum pressure, Q, and the compositions of all three phases for each feed composition.

Part 2. Design

Before starting, delete (cut) Flash3 and the second liquid product, add Flash2, and connect streams. (An alternate procedure that you may prefer is to start a new simulation.) List valid phases as Vapor-liquid in Setup. Feed is 100.0 kmol/h that is 3.0 mol% methane, 25.0 mol% n-butane, 44.0 mol% n-pentane, and 28.0 mol% n-hexane and is a liquid. Input the new components and choose an appropriate property method. The flash drum is at 1.0 atm, it is adiabatic (Duty = 0), and there is no heat exchanger. Initially, for the feed, set vapor fraction = 0 (a saturated liquid) and set the temperature. You want to obtain V/F in the drum of 0.4000 (rounded off to fourth decimal). Find the feed temperature that gives this value of V/F. (As you do runs, note that feed pressure for a saturated liquid increases as feed temperature is increased. Why?) Once you find the correct feed temperature, remove the feed specification that vapor fraction = 0 and specify a feed pressure that is 1.0 atm above the pressure reported by Aspen Plus when vapor fraction of feed = 0. Liquids that are saturated liquids (this is what Aspen means by vapor fraction = 0) cannot be pumped easily. By raising the pressure, we make pumping easy. Rerun the simulation one last time to check that you have met all requirements. Expect to do several Aspen Plus runs to solve this problem. Report the property method, feed temperature and pressure, drum temperature, heat duty in drum, vapor and liquid flow rates, and x and y values.

Before you go to part 3, keep your design on Aspen Plus, and show the instructor your handwritten results for part 2. If there is an error, the instructor will ask you to keep working on the problem.

Part 3. Bubble- and Dew-Point Determination

a. Although Aspen Plus does not have a button or command to calculate bubble and dew points, you can easily determine the bubble and dew points with Flash2 or Flash3. Input the components (methane, ethane, propane, and n-butane) and the VLE correlation you want to use. In Simulation you want a flash drum and the appropriate streams. Once the flowsheet is finished, click on the Next arrow in the menu bar. Then input the feed conditions (mole fractions: C1 = 0.2, C2 = 0.25, C3 = 0.25, nC4 = 0.3), pressure = 10.0 bar, vapor fraction = 0, and flow rate 1 kmol/h. Run the simulation. Look at the reports for both blocks and streams. (Alternatively, you can find the results in the Navigation Pane beneath the Block folder for your flash drum, labeled B1 if you used the default, in the Results and Stream Results folders.) You should have the same outlet temperature (which is the bubble point temperature, since vapor fraction = 0) for the feed stream and for the outlet temperature from the block.

b. Change the flash drum setting to a vapor fraction of 1.0 and run the simulation again. Look at the results for blocks. What do these results mean? From the V-L phase equilibrium given in the report for the flash drum, record the mole fractions of liquid and vapor.

c. Aspen Plus is very versatile, and there are often multiple methods to do tasks. For bubble and dew points, an alternative is to use Heater. Determine how to do optional methods by yourself.

Part 4. Boiling Points

You can also use Aspen Plus to determine boiling point of pure compounds at any pressure. Find the boiling point of pure n-hexane at 0.23 bar. Record this value.

Assignment to Hand In

If instructed by the instructor, each group should write a one- to two-page memo addressed to the professor or teaching assistant from the entire group of members. You may attach a few appropriate graphs and tables on a third page (do not attach the entire Aspen results printout). Anything beyond three pages (including cover pages) will not be looked at or graded. The memo needs to have words in addition to numbers. Give a short introduction. Present the numbers in a way that is clearly identified. Mention the graphs or figures you have attached as backup information. (If a group member is absent for the lab and does not help in preparation of the memo, leave his/her name off the memo. Attach a very short note explaining why this member’s name is not included. For example, “Sue Smith did not attend lab and never responded to our attempts to include her in writing the memo.”) Prepare this memo on a word processor. Graphs should be done on the computer (e.g., Aspen or Excel). Proofread everything and do a spell check also!

For the ethanol-water data at 1.0 atm (Table 2-1), the best fit was a sixth-order polynomial. This result is

The alternate function xeq = g(y) was also generated:

An alternative to fitting the data is to input the table of data into Excel and then use the Lookup function built into Excel to linearly interpolate between data points (Jordan, 2012).

Once an equation form of the equilibrium data is available, it is relatively easy to develop a spreadsheet to solve binary flash problems. We need to input the known values, which we will assume are the mole fraction of the more volatile component in the feed, z, and the fraction vaporized, V/F. Then input the constants for the VLE data in the form y_MVC = f(x_MVC). For this example we will separate ethanol and water at 1.0 atm with an ethanol feed that is 30 mol% ethanol and V/F = 0.4. The VLE equation for ethanol-water at 1.0 atm is given by Eq. (2.B-1). Next, input a guessed value for x_ethanol. Now calculate yeq using this value of xguess from Eq. (2.B-1) and calculate yop from Eq. (2-13). Since yop = yeq at the intersection of the equilibrium and operating curves, eq0 = yeq – yop will be zero at the point of intersection. Thus, calculate eq0 and use Goal Seek to make it equal zero by changing the value of xguess. (Note: Goal Seek is hidden in Excel 2010. In the spreadsheet go to Data Tab→What if Analysis→Goal Seek.) The resulting spreadsheet with numerical results is presented in Figure 2-B1 and with cell formulas in Figure 2-B2. Goal Seek was used to set cell B12 to zero by changing cell B8. Cell B12 multiplies eq0 by 1000 to reduce the error tolerance of Goal Seek. (Obviously, this trick only works if the goal is to set the function to zero.) Since eq0 ∼ 0, the answer to this flash problem is x = 0.1555 and y = 0.5168.

Goal Seek was used to find the value of V/F that makes cell D20 equal to 0.0 by changing the value in B9. Cell D20 multiplies the sum in cell D19 by 1000 to make the result obtained from Goal Seek more accurate. Goal Seek converged for any guess of V/F from 0 to 1.0. The results are given in Figure 2-B3 for the conditions given in Problem 2.D16: T = 10°C and p = 250 kPa. Since the constants in Eq. (2-3) are for temperature units in °R and pressure units of psia, the temperature is input in °R (cell B7) and pressure is input in psia (cell D7).

We also tried use of Goal Seek to force the sum of xi in cell B19 to 1.0. For this problem, Goal Seek works for ∑xi = 1.0 with V/Fguess > ∼0.5 but does not work for low values of V/Fguess (see Problem 2.H2.). This difficulty reinforces the need to check results from any software package, even one as common and robust as a spreadsheet (Shacham et al., 2008).

If your skill with spreadsheets is not equal to these spreadsheets or the spreadsheets in later chapters, Jordan (2012) and Larsen (2013) are good resources. Note that there are many other possible approaches to solving this problem with a spreadsheet, and other software tools such as MATLAB or Mathematica could be used as well (Binous, 2008).