CALCULATION PROCEDURES
COMPUTER-AIDED CALCULATIONS (SIMULATIONS) A number of process simulation programs such as Aspen Plus ® from
Aspen Technology, HYSYS® from Honeywell, ChemCAD® from Chemstations, and PRO/II®from SimSci Esscor, among others, can
ln 1.85 1− 1 1.85 m′S′ R′ S′ − E′ R′ F′ R′ 1 1.85 1 1.85 0.251− 0.0016/0.656 0.01− 0.0016/0.656 (80− 67.5)(0.01) 199.8 (199.8− 198.7)(0.0983) 80 (0.740)(199.8) 80
facilitate rigorous calculation of the number of theoretical stages required by a given application, provided an accurate liquid-liquid equilibrium model is employed. At the time of this writing, commer- cially available simulation packages do not include rate-based programs specifically designed for extraction process simulation; how- ever, the equivalent number of transfer units at each stage can be cal- culated from knowledge of the extraction factor by using Eq. (15-73). Process simulation programs are particularly useful for concentrated systems that exhibit highly nonlinear equilibrium and operating lines, significant change in extract and raffinate flow rates within the process due to transfer of solute from one phase to the other, significant changes in the mutual solubility of the two phases as solute concen- tration changes, or nonisothermal operation. They also facilitate con- venient calculation for complex extraction configurations such as fractional extraction with extract reflux as well as calculations involv- ing more than three components (more than one solute). They can also facilitate process optimization by allowing rapid evaluation of numerous design cases. These programs do not provide information about mass-transfer performance in terms of stage efficiencies or extraction column height requirements, or information about the throughput and flooding characteristics of the equipment; these fac- tors must be determined separately by using other methods. The use of simulation software to analyze extraction processes is illustrated in Examples 4 and 5.
In using simulation software, it is important to keep in mind that the quality of the results is highly dependent upon the quality of the liquid-liquid equilibrium (LLE) model programmed into the simula- tion. In most cases, an experimentally validated model will be needed because UNIFAC and other estimation methods are not sufficiently accurate. It also is important to recognize, as mentioned in earlier dis- cussions, that binary interaction parameters determined by regression of vapor-liquid equilibrium (VLE) data cannot be relied upon to accu- rately model the LLE behavior for the same system. On the other hand, a set of binary interaction parameters that model LLE behavior properly often will provide a reasonable VLE fit for the same sys- tem—because pure-component vapor pressures often dominate the calculation of VLE.
Commercially available simulation programs often are used in a fashion similar to the classic graphical methods. When separation of specific solutes is important, the design of a new process generally focuses on determining the optimum solvent rates and number of the- oretical stages needed to comply with the separation specifications according to relative K values for solutes of interest. Calculations often are made by focusing on a “soluble” key solute with a relatively high K value, and an “insoluble” key solute, expressing the design specification in terms of the maximum concentration of soluble key left in the raffinate and the maximum concentration of insoluble key contaminating the extract (analogous to light and heavy key compo- nents in distillation design). Then solutes with K values higher than that of the soluble key will go out with the extract to a greater extent, and solutes with K values less than that of the insoluble key will go out with the raffinate. If the desired separation is not feasible using a stan- dard extraction scheme, then fractional extraction schemes should be evaluated.
For rating an existing extractor, the designer must make an estimate of the number of theoretical stages the unit can deliver and then determine the concentrations of key solutes in extract and raffinate streams as a function of the solvent-to-feed ratio, keeping in mind the fact that the number of theoretical stages a unit can deliver can vary depending upon operating conditions.
The use of process simulation software for process design is dis- cussed by Seider, Seader, and Lewin [Product and Process Design Principles: Synthesis, Analysis, and Evaluation, 2d ed. (Wiley, 2004)] and by Turton et al. [Analysis, Synthesis, and Design of Chemical Processes, 2d ed. (Prentice-Hall, 2002)]. Various computational pro- cedures for extraction simulation are discussed by Steiner [Chap. 6 in Liquid-Liquid Extraction Equipment, Godfrey and Slater, eds. (Wiley, 1994)]. In addition, a number of authors have developed specialized methods of analysis. For example, Sanpui, Singh, and Khanna [AIChE J., 50(2), pp. 368–381 (2004)] outline a computer-based approach to rate-based, nonisothermal modeling of extraction processes. Harjo,
Ng, and Wibowo [Ind. Eng. Chem. Res., 43(14), pp. 3566–3576 (2004)] describe methods for visualization of high-dimensional liquid- liquid equilibrium phase diagrams as an aid to process conceptualiza- tion. Since in general it is not economically feasible to generate precise phase equilibrium data for the entire multicomponent phase diagram, this methodology can help focus the design effort by identi- fying specific composition regions where the design analysis will be particularly sensitive to uncertainties in the equilibrium behavior. The method of Minotti, Doherty, and Malone [Ind. Eng. Chem. Res., 35(8), pp. 2672–2681 (1996)] facilitates a feasibility analysis of poten- tial solvents and process options by locating fixed points or pinches in the composition profiles determined by equilibrium and operating constraints. Marcilla et al. [Ind. Eng. Chem., Res., 38(8), pp. 3083–3095 (1999)] developed a method involving correlation of tie lines to calculate equilibrium compositions at each stage without iter- ations. To optimize the design and operating parameters of an extrac- tion cascade, Reyes-Labarta and Grossmann [AIChE J., 47(10), pp. 2243–2252 (2001)] have proposed a calculation framework that employs nonlinear programming techniques to systematically evalu- ate a wide range of potential process configurations and interconnec- tions. Focusing on another aspect of process design, Ravi and Rao [Ind. Eng. Chem. Res., 44(26), pp. 10016–10020 (2005)] provide an analysis of the phase rule (number of degrees of freedom) for liquid- liquid extraction processes. For discussion of reactive extraction process conceptualization methods, see Samant and Ng, AIChE J., 44(12), pp. 2689–2702 (1998); and Gorissen, Chem. Eng. Sci., 58, pp. 809–814 (2003).
Example 4: Extraction of Phenol from Wastewater The amount of 350 gpm (79.5 m3/h) of wastewater from a coke oven plant contains an aver-
age of 700 ppm phenol by weight that needs to be reduced to 1 ppm or less to meet environmental requirements [Karr and Ramanujam, St. Louis AIChE
Symp. (March 19, 1987)]. The wastewater comes from the bottom of an ammo-
nia stripping tower at 105°C and is to be extracted at 1.7 atm with recycle methylisobutyl ketone (MIBK) containing 5 ppm phenol. The extraction will be carried out by using a reciprocating-plate extractor (Karr column). How many theoretical stages will be required in the extractor at a solvent-to-feed ratio of 1:15, and what is the resulting extract composition?
The Aspen Plus®process simulation program is used in this example, but it
should be recognized that any of a number of process simulation programs such as mentioned above may be used for this purpose. In Aspen Plus, the EXTRACT liquid-liquid extraction unit-operation block is used to model the phenol wastewater extraction. As is typical in process simulation programs, the EXTRACT block is fundamentally a rating calculation rather than a design cal- culation, so the determination of the required number of stages for the separa- tion cannot be made directly. In addition, since the EXTRACT block can only handle integral numbers of theoretical stages, the fractional number of required theoretical stages must be determined by an interpolation method.
The partition ratio for transfer of phenol from water into MIBK at 105°C is
K″ = 34 on a mass fraction basis [Greminger et al., Ind. Eng. Chem. Process Des.
Dev., 21(1), pp. 51–54 (1982)]. Because the partition ratio is so high, a fairly low
solvent-to-feed ratio of 1:15 can be used and still give an extraction factor of about 2. In the EXTRACT block, a property option is available that allows the user to specify liquid-liquid K value correlations (designated as “KLL Correla- tion” in Aspen Plus) for the components involved in the extraction rather than a complete set of binary interaction parameters to define the liquid-liquid equi- libria. In this example, it is time-consuming to regress a set of liquid-liquid binary interaction parameters that results in representative partition ratios, so the option of simply specifying K values directly is highly recommended.
Because phenol will be relatively dilute in both the raffinate and extract phases, appropriate liquid-liquid K values for distribution of water and MIBK between phases at 105°C can be estimated from water-MIBK liquid-liquid equilibrium data [Rehak et al., Collect. Czech Chem. Commun., 65, pp. 1471–1486 (2000)] to yield K″water= 0.0532 and K″MIBK= 53.8 (mass fraction basis). It is important in
Aspen Plus to specify K values for all the components in the extractor in order to properly model the liquid-liquid equilibria with this approach.
The temperatures and compositions of the wastewater and solvent feed streams, as well as the wastewater feed flow rate, are specified in the problem statement. The solvent flow rate is specified as one-fifteenth of the wastewater flow rate as described above. In the EXTRACT block, the number of stages will be manually varied from 2 to 10 to observe the effect on the raffinate and extract concentrations, and it will be specified as operating adiabatically at 1.7 atm. Water is specified as the key component in the first liquid phase, and MIBK is specified as the key component in the second liquid phase. The rest of the block parameters (convergence, report, and miscellaneous block options) are allowed to remain at their default values.
The raffinate and extract concentrations resulting from successive simulation runs for 2 through 10 theoretical stages are given in Table 15-9, and the raffinate phenol concentrations are presented graphically in Fig. 15-28. Examining the results, we can see that the number of theoretical stages required to achieve the 1 ppm phenol discharge limitation falls somewhere between 7 and 8. In addi- tion, we can see from Fig. 15-28 that the dependence of raffinate phenol con- centration on number of stages yields nearly a straight line on a semilog plot. As a result, performing a linear interpolation of the log of the raffinate concentra- tion between 7 and 8 stages yields the number of stages required to achieve 1 ppm phenol in the raffinate:
N= 7 + (8 − 7)
= 7.53 theoretical stages From examining the extract phenol concentrations in Table 15-9, it is clear that for 5 or more stages, they varied little with number of stages, as is expected since nearly all the phenol contained in the wastewater feed was extracted in stages 1 through 4. As a result, the extract will contain 1.3 wt % phenol, 5.2% water, and 93.5% MIBK.
The simulation results can be checked by using a shortcut calculation—to provide confidence that the simulation is delivering a reasonable result. The KSB equation [Eq. (15-48)] can be used for this purpose with values taken from the problem specification and estimates of the phenol K′ value (in Bancroft coordinates). Since phenol is always quite dilute in both the extract and raffinate phases, its K′ value can be calculated from the component mass fraction K″ val- ues according to the following approximation:
K′PhOH≅ K″PhOH
= 34 = 35.24This value compares favorably with the value of 35.28 calculated directly from phenol mass ratios taken from extractor internal profile data in the simulation output. The extraction factor [Eq. (15-11)] is then calculated with the dilute sys- tem approximation that mPhOH≅ KPhOHand solute-free water and MIBK feed
rates of 159,841 and 10,668 lb/h taken from the simulation output:
EPhOH= mPhOH ≅ K″PhOH = K′PhOH = 35.24 × = 2.35
It is interesting to note that this value of the extraction factor, 2.35, is the same as those calculated on mole fraction, mass fraction, and Bancroft coordinate bases from extractor internal profile data in the simulation, a confirmation that the extraction factor is indeed independent of units as long as consistent values of m, S, and F are used. By substituting the above values into Eq. (15-48) along
10,668 159,841 S′ F′ S″ F″ S F 53.8− 1 53.8(1− 0.0532) KMIBK− 1 KMIBK(1− KH2O) log 1.47− log 1 log 1.47− log 0.707
TABLE 15-9 Simulation Results for Extraction of Phenol from Wastewater Using MIBK (Example 4)
Raffinate compositions Extract compositions
X″H2O, X″MIBK, Y″PhOH, Y″H2O, Y″MIBK,
N X″PhOH, ppm mass fraction mass fraction mass fraction mass fraction mass fraction
2 101 0.98235 0.01755 0.01146 0.05223 0.93631 3 41.8 0.98237 0.01759 0.01260 0.05223 0.93517 4 17.7 0.98238 0.01761 0.01306 0.05223 0.93471 5 7.55 0.98238 0.01761 0.01326 0.05223 0.93451 6 3.28 0.98238 0.01762 0.01334 0.05223 0.93443 7 1.47 0.98238 0.01762 0.01337 0.05223 0.93440 8 0.707 0.98238 0.01762 0.01339 0.05223 0.93438 9 0.381 0.98238 0.01762 0.01340 0.05223 0.93437 10 0.242 0.98238 0.01762 0.01340 0.05223 0.93437
with concentrations taken from the problem statement and Table 15-9, the required number of stages is estimated as
ln
(1− 1/2.35) + 1/2.35N≈
ln 2.35 = 7.18 theoretical stages
The simulation result of 7.53 theoretical stages is close to this shortcut estimate, indicating that the simulation is indeed delivering reasonable results. FRACTIONAL EXTRACTION CALCULATIONS
Dual-Solvent Fractional Extraction As discussed in “Commer- cial Process Schemes,” under “Introduction and Overview,” fractional extraction often may be viewed as combining product purification with product recovery by adding a washing section to the stripping section of a standard extraction process. In the stripping section, the mass transfer we focus on is the transfer of the product solute from the wash solvent into the extraction solvent. If we assume dilute conditions and use short- cut calculations for illustration, the extraction factor is given by
Es= K′s (15-99)
where Es= stripping section extraction factor (dimensionless)
K′s= stripping section partition ratio, defined as equilibrium
concentration of product solute in extraction solvent divided by that in wash solvent (Bancroft coordinates) S′s= mass flow rate of extraction solvent within stripping sec-
tion (solute-free basis)
W′s= mass flow rate of wash solvent in stripping section (solute-
free basis)
The change in the concentration of product dissolved in the wash sol- vent, within the stripping section, can be calculated by using the KSB equation
product ≈1− 1/Es (15-100) (Es)Ns− 1/Es X′out X′in S′s W′s 0.0007/0.9993− (0.000005)/(0.999995) 35.24 0.000001/0.9824− (0.000005)/(0.999995) 35.24
where Ns= number of theoretical stages in stripping section
X′in= concentration of product solute in wash solvent at inlet to stripping section (feed stage)
X′out= concentration of product solute in wash solvent at outlet from stripping section (raffinate end of overall process) In the washing section, we focus on transfer of impurity solute from the extraction solvent into the wash solvent. A washing extraction fac- tor can be defined as
Ew= (15-101)
where Ew= washing section extraction factor (dimensionless)
K′w= washing section partition ratio (equilibrium concentration
of impurity solute in extraction solvent divided by that in wash solvent, in Bancroft coordinates)
S′w= mass flow rate of extraction solvent within washing section
(solute-free basis)
W′w= mass flow rate of wash solvent in washing section (solute-
free basis)
Then the change in the concentration of impurity solute dissolved in the extraction solvent, within the washing section, is given by
impurities≈ (15-102)
where Nw= number of theoretical stages in washing section
Y′in= concentration of impurity solute in extraction solvent at inlet to washing section (feed stage)
Y′out= concentration of impurity solute in extraction solvent at outlet from washing section (extract end of overall process) The ratio of extraction solvent to wash solvent in each section will be different if either solvent enters the process with the feed. Note that both K′sand K′ware defined as the ratio of the appropriate solute con-
centration in the extraction solvent to that in the wash solvent. The shortcut calculations outlined above illustrate the general con- siderations involved in analyzing a fractional extraction process. The analysis requires locating the feed stage and matching the calculations for each section with the material balance at the feed stage, an itera- tive procedure. Buford and Brinkley [AIChE J., 6(3), pp. 446–450 (1960)] discuss application of the KSB equation to fractional extrac- tion calculations including the use of reflux. Transfer unit calculations also may be used. When equilibrium and operating lines are not lin- ear, more sophisticated calculations will be needed to take this into account. Commercially available simulation software or other com- puter programs often are used to carry out this procedure (see “Com- puter-Aided Calculations”). Note that with dual-solvent fractional extraction, solute concentrations always are highest at the feed stage. This can lead to undesired behavior such as tendencies toward emul- sion formation or even formation of a single liquid phase at the plait point. The minimum amounts of solvent needed to avoid these effects can be determined in laboratory tests.
Early in a project, it may be useful to consider a simplified case in which the ratio of extraction solvent to wash solvent is constant and the same in the stripping and washing sections (i.e., the amount of sol- vent entering with the feed is negligible) and the extraction factors for each section are equal. For this special case, termed a symmetric sep- aration, the extraction factors are
Es= Ew=αi,j (15-103)
and the ratio of extraction solvent to wash solvent is given by
≈ ≈ = αi,j (15-104) Ks 1 αi,jKw 1 KsKw S W 1− 1/Ew (Ew)Nw− 1/Ew Yout′ Y′ in W′w S′w 1 K′w 0.1 1 10 100 2 6 10
No. of Theoretical Stages
ppm w Phenol in R affinate 4 8
FIG. 15-28 Simulation results showing phenol concentration in the raffinate versus number of theoretical stages (Example 4).
Using these relationships, we find the number of stages required for the stripping and washing sections will be about the same and the total number of stages required likely will be close to the minimum num- ber—assuming symmetric separation requirements. The effects of the separation factor and the number of stages on the separation perfor- mance can be estimated by using expressions given by Brian [Staged Cascades in Chemical Processing (Prentice-Hall, 1972)]. For a process containing two solutes i and j, with the feed entering at the middle stage, it follows from Brian’s analysis that
Si,j= ≈ αi, j(N+1)/2 (15-105)
where Si,jis termed the separation power of the process. Equation
(15-105) is derived by assuming that the ratio of extract phase to raffi- nate phase within the process is constant, and that αi,jis constant.
Interestingly, Eq. (15-105) is very similar in its general form to the equation obtained by using the Fenske equation to calculate fractional distillation performance for a binary feed, assuming that the required number of theoretical stages is twice the minimum number obtained at total reflux. (See Sec. 13, “Distillation.”)
For a proposed symmetric separation, Eqs. (15-104) and (15-105) can be used to gauge the required flow rates, number of theoretical stages, and separation factor. For example, consider a hypothetical application with the goal of transferring 99 percent of a key solute i into the extract and 99 percent of an impurity solute j into the raffi- nate. For illustration, let Ki= 2.0 and Kj= 0.5, so αi, j= 4. From Eq.
(15-104), the extraction solvent to wash solvent ratio should be about S/W= 1.0 for a symmetric separation. The number of theoretical stages is estimated by using Eq. (15-105): Si,j= 99 × 99 = 9801 gives N ≈ 12
total stages for αi,j= 4. When one is evaluating candidate solvent pairs
for a proposed fractional extraction process, a useful first step is to measure the equilibrium K values for product and impurity solutes and then assess process feasibility by using Eqs. (15-104) and (15-105). This can provide a quick way of assessing whether the measured sep- aration factor is sufficiently large to achieve the separation goals, using a reasonable number of stages.
Single-Solvent Fractional Extraction with Extract Reflux As discussed earlier, single-solvent fractional extraction with extract reflux is widely practiced in the petrochemical industry to separate aromatics from crude hydrocarbon feeds. For example, a variety of extraction processes utilizing different high-boiling, polar solvents are used to separate benzene, toluene, and xylene (BTX) from aliphatic hydrocarbons and naphthenes (cycloalkanes), although processes involving extractive distillation are displacing some of the older extrac- tion processes, depending upon the application. A typical hydrocar- bon feed is a distillation cut containing mostly C5to C9components. Commercial extraction processes include the Udex process (employ- ing diethylene and/or triethylene glycol), the AROSOLVAN process (employing N-methyl-2-pyrrolidone), and the Sulfolane process (employing tetrahydrothiophene-1,1-dioxane), among others. Although the flow diagrams for these processes differ, they all involve use of a liquid-liquid extractor followed by a top-fed extract stripper or extractive distillation tower. A number of different processing schemes are used to isolate the aromatics and recycle the heavy sol- vent. For detailed discussion, see Chaps. 18.1 to 18.3 in Handbook of Solvent Extraction, Lo, Baird, and Hanson, eds. (Wiley, 1983; Krieger, 1991); Mueller et al., Ullmann’s Encyclopedia of Industrial Chem-