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life sciences
separation process principles chemical

Separation Process Principles Chemical And Biochemical Principles 3rd Edition By J. D. Seader, Ernest J. Henley, D. Keith Roper - Solutions

What is a tridiagonal-matrix (TDM) equation? How is it developed from the MESH equations? In the matrix equation, what are the variables and what are the tear variables? What is a tear variable? Is there one TDM equation for each component? If so, can each equation be solved independently of the
Solve by the Newton–Raphson method the simultaneous, nonlinear equationsfor x1 and x2 to within ± 0.001. As initial guesses, assume:(a) x1 = 2, x2 = 5; (b) x1 = 4, x2 = 5; (c) x1 = 1, x2 = 1; (d) x1 = 8, x2 = 1. x² + x² = 17 (8x₁) ¹/3 + x₂/2 = 4
What is meant by normalization of a set of variables?
In the BP method, which of the MESH equations is used to compute a new set (i.e., update) of total molar vapor flow rates leaving each stage?
Solve by the Newton–Raphson method the simultaneous, nonlinear equationsfor x1 and x2 to within ± 0.001. As initial guesses, assume(a) x1 = 0.4, x2 = 0.9; (b) x1 = 0.6, x2 = 0.9; (c) x1 = 1.0, x2 = 1.0. sin (TX₁Xx2) 12X1 exp(2x1₁) [1 - 4 / + exp(1)
Does the SR method use tridiagonal-matrix equations? How does the SR method differ from the BP method? For what types of problems is the SR method preferred over the BP method? What are the tear variables in the SR method?
One thousand kmol/h of a saturated-liquid mixture of 60 mol% methanol, 20 mol% ethanol, and 20 mol% n-propanol is fed to the middle stage of a distillation column having three equilibrium stages, a total condenser, a partial reboiler, and an operating pressure of 1 atm. The distillate rate is 600
Solve the nine simultaneous linear equations below, which have a block-tridiagonal-matrix structure, by the Thomas algorithm: x2 + 2x3 +2x4+x6 = 7 X₁ + x3 + x4 + 3x5 = 6 x₁ + x₂ + x3 + x5 + x6 = 6 X4 + 2x5 + X6 + 2x7 + 2x8 + X9 = 11 x4+x5 + 2x6 + 3x7 +x9 = 8 x5 + X6 + X7 + 2x8 + x9 = 8 x₁ +
What limitations of the BP and SR methods are overcome by the NR methods? How do the NR methods differ from the BP and SR methods?
Derivatives of properties are needed in the Naphtali–Sandholm NR method. For the Chao–Seader correlation, determine analytical derivatives for Ә ƏKƏKƏKij Juj,k Əlik ak AT ат
What is the difference between a tridiagonal-matrix (TDM) equation and a block-tridiagonal-matrix (BTDM) equation? How do the algorithms for solving these two types of equations differ?
What is a Jacobian matrix? How is the Jacobian formulated?
Revise (10-58) to (10-60) to allow two interlinked columns of the type shown in Figure 10.31 to be solved simultaneously by the NR method. Is the matrix equation that results from the NR procedure still block tridiagonal? Thermally coupled distillation
What types of calculations consume the most time in the BP, SR, and NR methods? How does the inside-out method reduce this time?
In (10-63), why is the variable order selected as y, T, l? What would be the consequence of changing the order to l, y, T ? In (10-64), why is the function order selected as H, M, E? What would be the consequence of changing the order to E, M, H? Thermally coupled distillation
Calculate product compositions, stage temperatures, interstage vapor and liquid flow rates and compositions, reboiler duty, and condenser duty for the following column specifications. Feed (bubble-point liquid at 250 psia and 213.9F):Column pressure = 250 psia; partial condenser and partial
In Exercise 10.20 provide a 200,000 Btu/hr intercooler on the fourth stage from the top and a 300,000 Btu/h interheater on the fourth stage from the bottom.Data From Problem Exercise 10.20Calculate product compositions, stage temperatures, interstage vapor and liquid flow rates and compositions,
A depropanizer distillation column is designed to operate at a feed stage pressure of 315 psia for separating a feed into distillate and bottoms with the following flow rates:The feed is 66 mol% vapor at tower pressure. Steam at 315 psia and cooling water at 65F are available for the reboiler and
Toluene is to be separated from biphenyl by ordinary distillation.The specifications for the separation are as follows:Temperature = 264οF; pressure = 37.1 psia for the feed; reflux ratio = 1.3 times minimum reflux with total condenser; top pressure = 36 psia; bottom pressure = 38.2 psia. (a)
A feed at 100F and 480 psia is to be separated by two ordinary distillation columns into the indicated products.Two distillation sequences (see §1.7.3) are to be examined. In the first, CH4 is the LK in the first column. In the second, toluene is the HK in the first column. Compute the two
A multiple recycle-loop problem, formulated by Cavett2 and shown in Figure 10.36, has been used to test tearing, sequencing, and convergence procedures. The flowsheet is the equivalent of a four-theoretical-stage, near-isothermal distillation (rather than the conventional near-isobaric type), for
An absorber is to be designed for a pressure of 75 psia to handle 2,000 lbmol/h of gas at 60F having the following composition:The absorbent is an oil, which can be treated as a pure component having a molecular weight of 161. Calculate product rates and compositions, stage temperatures, and
Calculate product rates and compositions, stage temperatures, and interstage vapor and liquid flow rates and compositions for the absorber shown in Figure 10.38. Lean oil, 80°F, 400 psia 250 lbmol/h Secondary oil, 80°F, 400 psia Ibmol/h 13 C1 C2 C3 588888 nC4 nC5 Oil 55556 C₂ C₂ 3445 Rich
The liquid–liquid extractor in Figure 8.1 operates at 100F and a nominal pressure of 15 psia. For the feed and solvent flows shown, determine the number of equilibrium stages to extract 99.5% of the acetic acid, using the NRTL equation for activity coefficients. The NRTL constants may be taken as
What is meant by enhanced distillation? When should it be considered?
What is the difference between extractive distillation and azeotropic distillation?
What is the difference between homogeneous and heterogeneous azeotropic distillation?
What are the two reasons for conducting reactive distillation?
What is a distillation boundary? Why is it important?
To what type of a distillation does a residue curve apply? What is a residue-curve map?
Is a residue curve computed from an algebraic or a differential equation? Does a residue curve follow the composition of the distillate or the residue?
Develop the feasible-product-composition regions for the system of Figure 11.13, using feed F1. H (a) K F₁ Region B₁- 1 F₂. L D D₁ Bd B₂ D4 D₂ (b) Region 2 -B3 B₁ Figure 11.13 Feasible and infeasible crossings of distillation boundaries for an azeotropic system. [From S. Widagdo and
Develop the feasible-product-composition regions for the system of Figure 11.10 if the feed is 50 mol% chloroform, 25 mol% methanol, and 25 mol% acetone. Chloroform (61.8°C) (53.9°C) Methanol (64.5°C) 1 3 A (65.5°C) B (57.6°C) D ■ Azeotrope 2 (55.3°C) Acetone (56.1°C) Figure 11.10
Residue curves involve nodes. What is the difference between a stable and an unstable node? What is a saddle?
What is a distillation-curve map? How does it differ from a residue-curve map?
What is a region of feasible-product compositions? How is it determined? Why is it important?
Under what conditions can a distillation boundary be crossed by a material-balance line?
In extractive distillation, why is a large concentration of solvent required in the liquid phase? Why doesn’t the solvent enter the column at the top tray?
Four hundred lbmol/h of an equimolar mixture of n-heptane and toluene at 200οF and 20 psia is to be separated by extractive distillation at 20 psia, using phenol at 220οF as the solvent, at a flow rate of 1,200 lbmol/h. Design a suitable two-column system to obtain reasonable product purities
Why is heterogeneous azeotropic distillation a more feasible technique than homogeneous azeotropic distillation?
What is meant by multiplicity? What kinds of multiplicity are there? Why is it important to obtain all multiple solutions when they exist?
A monoacidic sugar extracted from water into hexanol has distribution coefficients of 6.0 and 0.47 moles per liter at pH 4.0 and 5.5, respectively. Estimate the value of KD at pH 7.2.
For each of the distillations D-1 and D-2 indicated in Figure 9.20, establish the type of condenser and an operating pressure.
Compare the required solvent volume, stage number, and purity obtained when penicillin F is extracted from water preferentially to penicillin K into amyl acetate at pH 3.1 relative to the values at pH 3.75. The respective pKa values for penicillin F and K are 3.51 and 2.77, and the respective KoD
Based on chemical equilibrium, obtain a general expression for dependence of the distribution coefficient of a weak base bioproduct B(2) described by the equilibrium expression in Exercise 8.43 that interacts with an organic solvent extractant X(1) at the interface of an organic (1)
Steroid in water at 6.8 mg/L is extracted using initially pure methylene dichloride in a volume ratio of 1% vol/vol. The distribution constant is 175. Estimate the concentration of steroid in the organic solvent and the fraction of steroid removed.
Two distillation columns are used to produce the products indicated in Figure 9.19. Establish the type of condenser and an operating pressure for each column for the: (a) Direct sequence (C2 / C3 separation first) and (b) Indirect sequence (C3 / nC4 separation first). Use
The enzyme alcohol dehydrogenase (ADH) catalyzes oxidation of primary and secondary alcohols to aldehydes and ketones. It can be produced from a culture of Lactobacillus brevis, and recovered from the lysed broth by countercurrent ATPE with a PEG 8000– dextran T-500–water system at 10°C.
Rigorous, computer-based methods for multicomponent distillation are readily available in process simulators. Why, then, is the FUG method still useful and widely applied for distillation?
A mixture of propionic and n-butyric acids, which can be assumed to form ideal solutions, is to be separated by distillation into a distillate containing 95 mol% propionic acid and a bottoms of 98 mol% n-butyric acid. Determine the type of condenser and estimate the distillation operating pressure.
When calculating multicomponent distillation, why is it best to list the components in order of decreasing volatility? In such a list, do the two key components have to be adjacent?
One thousand kmol/h of rich gas at 70F with 25% C1, 15% C2, 25% C3, 20% nC4, and 15% nC5 by moles is to be absorbed by 500 kmol/h of nC10 at 90°F in an absorber at 4 atm. Calculate by the Kremser method the % absorption of each component for: (a) 4 theoretical stages, (b) 10
A vapor–liquid mixture at 250ºF and 500 psia contains N2, H2S, CO2, and all the normal paraffins from methane to heptane. Use Figure 2.4 to estimate the K-value of each component. Which components will be present to a greater extent in the equilibrium vapor? 2 Cr PRESSURE, PSIA 3 A COMPARISON OF
Benzene can break the ethanol/water azeotrope to produce nearly pure ethanol. Wilson constants for the ethanol (1)/benzene (2) system at 45οC are L12 = 0.124 and L21 = 0.523. Use these with theWilson equation to predict liquid-phase activity coefficients over the composition range and compare
For the deethanizer in Figure 9.21, estimate the number of stages, assuming it is equal to 2.5 times Nmin. Comp. kmol/h 160 370 55836 C₁ C₂ 90°F C₂ RCA RC₂ 240 25 5 a, average Comp. relative volatility 55530 2 kmol/h of C₂ C₂ RC₂ Cs 8.22 2.42 1.00 0.378 0.150 2 kmol/h of C₂
What does the Fenske equation compute? What assumptions are made in its derivation?
For the complex distillation in Figure 9.22, use the Fenske equation to determine Nmin between the: (a) Distillate and feed, (b) Feed and sidestream, and (c) Sidestream and bottoms. Use Raoult’s law for K-values. 130 kPa Feed 165 kPa kmol/h Benzene 260 80 Toluene Biphenyl 5 200
For the distillation in Figure 9.23, calculate Nmin and the distribution of the nonkey components by the Fenske equation, using Figures 2.4 and 2.5 for K-values. C3 iCa nC4 iC5 nC₂ nC6 kmol/h 2,500 400 600 100 200 40 50 40 700 kPa nC7 nCg Figure 9.23 Data for Exercise 9.7. HK iC5 15
For what conditions should the Fenske equation be used with caution?
For the distillation in Figure 9.24, establish the condenser type and operating pressure, calculate Nmin, and estimate the distribution of the nonkey components. Obtain K-values from Figures 2.4 and 2.5.
For Nmin = 15 at 250 psia, calculate and plot the percent recovery of C3 in the distillate as a function of distillate flow rate for the distillation of 1,000 lbmol/h of a feed containing by moles: 3% C2, 20% C3, 37% nC4, 35% nC5, and 5% nC6. Obtain K-values from Figures 2.4 and 2.5.
Is use of the Fenske equation restricted to the two key components? If not, what else can the Fenske equation be used for besides the estimation of the minimum number of equilibrium stages, corresponding to total reflux?
For the conditions of Exercise 9.7, with bubble-point liquid feed at column pressure, compute the minimum external reflux and nonkey distribution at Rmin by the Class 2 Underwood equations.Data From Exercise 9.7For the distillation in Figure 9.23, calculate Nmin and the distribution of the
What is a pinch point or region? For multicomponent distillation, under what conditions is the pinch point located at the feed location? What conditions cause the pinch point to migrate away from the feed location?
What is the difference between a Class 1 and a Class 2 separation? Why is the Class 1 Underwood equation useful even if the separation is Class 2?
What is internal reflux? How does it differ from external reflux? Does the Underwood equation compute internal or external reflux? How can one be determined from the other?
Use the FUG method to determine the reflux ratio required for the distillation in Figure 9.25 if N/Nmin = 2.0, the average relative volatility = 1.11, and the feed is at the bubble-point temperature at feedstage pressure. Assume that external reflux equals internal reflux at the upper pinch zone.
What is the optimal range of values for R/Rmin?
What key parameter is missing from the Gilliland correlation?
When can a serious problem arise with the Gilliland correlation?
The following feed mixture is to be separated by ordinary distillation at 120 psia to obtain 92.5 mol% of the nC4 in the liquid distillate and 82.0 mol% of the iC5 in the bottoms.(a) Estimate Nmin by the Fenske equation. (b) Use the Fenske equation to determine the distribution of
What is the best method for estimating the distribution of nonkey components at the actual (operating) reflux?
One hundred kmol/h of a three-component bubble-point mixture to be separated by distillation has the composition:(a) For a distillate rate of 60 kmol/h, five stages, and total reflux, calculate the distillate and bottoms compositions by the Fenske equation. (b) Using the separation in part (a)
Calculate and plot the external Rmin and Nmin against % product purity for the separation by distillation of an equimolar bubble-point liquid feed of isobutane/n-butane at 100 psia. The distillate is to have the same iC4 purity as the bottoms is to have nC4 purity. Consider purities from 90% to
Is the Kremser method a group method? What is meant by a group method?
Determine, by the Kremser method, the achievable separation for the absorber in Figure 9.26 for the following conditions: (a) Six stages and 75-psia pressure, (b) Three stages and 150-psia pressure, and (c) Six stages and 150-psia pressure. What do you conclude? Feed 130 kPa 165
Under what conditions can the Kremser method be applied to liquid–liquid extraction?
For the flashing and stripping operation in Figure 9.27, determine by the Kremser method the kmol/hr of steam if the stripper is operated at 2 atm with five stages. 145ºF C₁ Ca C₂ nCa NCH NC 2 Valve kmol/h 13.7 101.3 146.9 23.9 5.7 196.7 2 atm -0 150ºF Figure 9.27 Data for Exercise 9.24. 150
For the conditions of Exercise 9.6, determine the ratio of rectifying to stripping equilibrium stages by the: (a) Fenske equation, (b) Kirkbride equation, and (c) McCabe–Thiele diagram. Discuss your results.Data From Exercise 9.6A 25 mol% mixture of acetone (A) in water (W) is to
A feed of 62 mol% para-dichlorobenzene in ortho-dichlorobenzene is separated by distillation at near-atmospheric pressure into a distillate containing 98 mol% para isomer and bottoms of 96 mol% ortho isomer. If a total condenser and partial reboiler are used, α = 0.9, average a = 1.154, and R/Rmin
Starting with equations like (5-46) and (5-47), show that for two stages, Se=√0.25 +S₂(S₁+1)-0.5.
Explain why the Gilliland correlation can give erroneous results when the ratio of rectifying to stripping stages is small.
The hydrocarbon feed to a distillation column is a bubble-point liquid at 300 psia with mole fractions: C2 = 0.08, C3 = 0.15, nC4 = 0.20, nC5 = 0.27, nC6 = 0.20, and nC7 = 0.10. Determine:(a) Column pressure and type of condenser, if condenser outlet temperature is 120°F, for a
One hundred kmol/h of an equimolar mixture of benzene (B), toluene (T), n-hexane (C6), and n-heptane (C7) is to be extracted at 150°C by 300 kmol/h of diethylene glycol (DEG) in a countercurrent, liquid–liquid extractor having five equilibrium stages. Estimate the flow rates and compositions of
Use the Thomas algorithm to solve the following tridiagonal matrix equation for the x vector. -6 3 0 1.5 0 0 3 0 -4.5 3 0 0 0 0 3 4.5 -7.5 0 4.5 -7.5 0 0 0 3 -4.5 X1 X2 X3 X4 X5 0 100 0 0
Ethanol and benzene are separated in a network of distillation and membrane separation steps. In one step, a near-azeotropic liquid mixture of 8,000 kg/h of 23 wt% ethanol in benzene is fed to a pervaporation membrane consisting of an ionomeric film of Ethanol and benzene are separated in a network
A stripper at 50 psia with three stages is used to strip 1,000 kmol/h of liquid at 250F with molar composition 0.03% C1, 0.22% C2, 1.82% C3, 4.47% nC4, 8.59% nC5, and 84.87% nC10. The stripping agent is 100 kmol/h of superheated steam at 300F and 50 psia. Use the Kremser method to estimate
Use the Thomas algorithm to solve the following matrix equation for x1, x2, and x3. -160 200 50 -350 0 X1 ]]-[] X2 -50 X3 180 150-230 0 0
Why are rigorous solution procedures difficult and tedious for multicomponent, multistage separation operations?
Hydrocarbon Processing published a petroleum-refining handbook in November 1990, with process-flow diagrams and data for commercial processes. For the ethers process on page 128, list the separation operations of the type given in Table 1.1 and indicate what chemical(s) is (are) being separated.
In the equilibrium-stage model, can each stage have a feed, a vapor sidestream, and/or a liquid sidestream? How many independent equations apply to each stage for C components?
In the equilibrium-stage model equations, are K-values and enthalpies counted as variables? Are the equations used to compute these properties counted as equations?
Derive a general expression for the total solubility of a zwitterionic amino acid in terms of pH, pKca, and pKaa from definitions of the respective acid dissociation constants, the expression for total solubility,and the definition of solubility of the uncharged species, ST = So + M-NH3 +
For a cascade of N countercurrent equilibrium stages, what is the number of variables, number of equations, and number of degrees of freedom? What are typical specifications, and what are the typical computed (output) variables? Why is it necessary to specify the number of equilibrium stages and
For the seven-phase equilibrium system shown in Figure 4.30, assume air consists of N2, O2, and argon. What is the number of degrees of freedom? What variables might be specified? Air n-hexane-rich. liquid Aniline-rich liquid Water-rich liquid Phosphorous liquid Gallium liquid Mercury liquid Figure
Early attempts to solve the MESH equations by hand calculations were the Lewis–Matheson and Thiele–Geddes methods. Why are they not favored for computer calculations?
For a mixture with mole fractions 0.005 methane, 0.595 ethane, and the balance n-butane at 50 psia, and using K-values from Figure 2.4: (a) Find the bubble-point temperature. (b) Find the temperature that results in 25% vaporization at this pressure, and determine the liquid and vapor
Figure 4.36 shows a system to cool reactor effluent and separate light gases from hydrocarbons. K-values at 500 psia and 100οF are:(a) Calculate composition and flow rate of vapor leaving the flash drum. (b) Does the liquid-quench flow rate influence the result? Prove your answer
One hundred kmol/h of a saturated-liquid mixture of 12 mol% ethyl alcohol in water is distilled continuously using open steam at 1 atm introduced directly to the bottom plate. The distillate required is 85 mol% alcohol, representing 90% recovery of the alcohol in the feed. The reflux is saturated
It is proposed that oxygen be separated from nitrogen by absorbing and desorbing air in water. Pressures from 101.3 to 10,130 kPa and temperatures between 0 and 100οC are to be used. (a) Devise a scheme for the separation if the air is 79 mol% N2 and 21 mol% O2.(b) Henry’s law constants for

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