Experimental results (Figure 19-15) and shock wave analysis showed that after an entry region, wave shape for constant pattern waves is independent of distance traveled. Analysis can be done in two parts. First, shock wave analysis tracks movement of the center of the wave. Second, the partial differential equation for the column mass balance can be simplified to an ordinary differential equation by using a variable = t – z/u_sh that defines the deviation from the center of the wave. This approach is detailed in more advanced sources (e.g., Ruthven, 1984; Sherwood et al., 1975; Wankat, 1990).

A simplified analysis procedure called length of unused bed (LUB), or mass transfer zone (MTZ), method that uses experimental data to design columns during constant pattern operation is used in industry. This method is based on original ion exchange analysis by Michaels (1952) that was extended to adsorption by Lukchis (1973). The constant pattern wave inside the bed is shown schematically in Figure 19-23A. After being fully developed, the pattern does not change shape as it moves through the bed. The pattern width (length of the MTZ, L_MTZ) is usually arbitrarily measured from 0.05 c_F to 0.95 c_F. Concentrations of zero and the feed concentration are not used because it is very difficult to determine exactly when these values are left or attained. During operation, feed is stopped at breakthrough time t_br when outlet concentration reaches a predetermined level, often 5% of feed concentration. A fraction of the bed is not fully used for adsorption, since feed is stopped before the bed was fully saturated.

Of course, it is difficult to measure what is happening inside the bed; however, if we run a column to saturation and measure outlet concentrations, we can infer what happened inside the bed. The outlet concentration profile is shown schematically in Figure 19-23B. The MTZ width, t_MTZ (which is again arbitrarily measured from 0.05 c_F to 0.95 c_F), is now easy to measure. The MTZ length inside the bed, L_MTZ, is

Shock wave velocity can be calculated from Eq. (19-34) or from experimental data:

where t_center is the time the pattern center, 0.5 (c_F – c_initial), exits.

All of the bed up to the MTZ is fully utilized for adsorption. Within the MTZ the fraction of bed not used is = (Area unused bed in MTZ)/(Total area of MTZ). This ratio can be determined from Figure 19-23A, or from measurements shown in Figure 19-23B. Thus, fractional bed use is

Measuring the ratio of areas isn’t necessary if the adsorption system produces a symmetric breakthrough curve (e.g., as shown in Figure 19-23B). For symmetric breakthrough curves the ratio of areas is always one half. Thus for symmetric breakthrough curves, fractional bed use is

For symmetric breakthrough curves if L/ L_MTZ = 1.0, fractional bed use = 0.5; L/ L_MTZ = 2.0, fractional bed use = 0.75; L/ L_MTZ = 3.0, fractional bed use = 0.833; L/ L_MTZ =4.0, fractional bed use = 0.875, and so forth. Optimal bed length for adsorption is often between two to three times L_MTZ. If a fractional bed use is specified, column length can be determined:

Once fractional bed use is known, we can determine bed capacity:

where q_F is amount adsorbed at the feed concentration in appropriate units. q_F can be determined from the equilibrium isotherm for an isothermal adsorber or from experimentally determined value of u_sh.

We often measure pattern velocity u_p = u_sh and width of the MTZ t_MTZ experimentally with a laboratory column. To scale up, laboratory measurements need to use design values for initial and final concentrations. It is most convenient if the same velocity and same particle sizes are used as in large-scale units; however, if pore diffusion controls, we can adjust results for changes in velocity and particle diameter. For constant pattern systems width of the MTZ t_MTZ is inversely proportional to k_m,qa_p (Wankat, 1990):

If pore diffusion controls, k_m,qa_p can be estimated from Eq. (19-58b). The result is

The use of these equations in LUB analysis is illustrated in Example 19-11.

The LUB approach is used for the adsorption step. During desorption a proportional pattern (diffuse) wave usually results, as shown in Figure 19-15B (monovalent-divalent ion exchange can be an exception to this—see Example 19-8). Since pattern shape changes with length, the LUB approach cannot be used for desorption. However, results of solute movement theory for diffuse waves are usually reasonably accurate. Thus diffuse wave predictions can be used for preliminary design. Desorption step calculations should be checked with experimental data.

1. Broadly speaking, the sorption (feed) step makes money, and the regeneration step costs money. The optimum sorbent is often a trade-off between these two steps (relatively strong sorption to process the feed, but not so strong that regeneration is not feasible).

2. Regeneration (broadly defined) is always a key cost and often controls costs. Regeneration costs are TSA—energy for heating, PSA—energy for compression, chromatography and SMB—solvent or desorbent recovery (ultimately energy if distillation or evaporation is used), ion exchange—regeneration chemicals.

3. Sorption methods of separation always compete with other separation methods, such as distillation or gas permeation. Always consider alternatives.

4. Compression costs are significant in large-scale gas adsorption systems; thus pressure drop is critically important, since it controls compression costs. A reasonable gas velocity is 100 ft/min (Seider et al., 2009). Pressure drop can be calculated from well-known correlations for flow in packed beds. For example, in a packed bed of rigid particles in laminar flow (Bird et al., 2006),

5. Pressure drop is also important in liquid systems but for different reasons than in gas systems. Because liquids are almost incompressible, obtaining high pressures, and thus from Eq. (19-90) high velocities and high throughputs (A_cρ_fv_superficial), is easy and inexpensive. High throughput reduces cross-sectional area and hence adsorber cost. A common industrial design procedure is to operate at the highest maximum pressure that the equipment is designed for. The highest design pressure gives the highest allowable Δp and hence the highest possible throughput. Of course, increase in length of the MTZ has to be accounted for in the design.

6. Theories assume the column is well packed. If it isn’t, it won’t work well. We want D_col/d_p > ∼30. This limit is often important in lab columns.

a. Special equipment is needed to pack small particles. Packing large-diameter columns with small particles needs to be done by experts.

b. If a wet column is allowed to dry out, the packing often cracks, which causes channeling.

c. Packed beds are efficient depth filters. To prevent clogging, feeds containing particulates must be filtered. It is common, particularly in ion exchange, to use upward flow wash steps to remove particulates from the column.

d. Pressure and flow spikes can be very detrimental if they cause the bed to shift, since shifting can result in channeling or attrition. Unfortunately, spikes naturally occur when concentrated feeds are adsorbed. They are greatly reduced if concentrated feed is introduced in steps (e.g., go from 0% to 45% and then to 90% in two steps instead of a single step from 0% to 90%).

e. Bed movement can also cause attrition of brittle packings, such as activated carbon and zeolites. The resulting fines can clog the bed or frits. Use a hold-down plate, frit, or net to prevent bed movement.

f. Soft packing materials (e.g., Sephadex and agarose) require different packing procedures than rigid packings. The swelling and contracting of polymer packings, particularly ion exchange resins, must be designed for.

7. Simulations and other solutions to theories can only include phenomena that were built into the model. Experiments are usually needed to find the unexpected.

8. If fluid velocity is high and mass transfer rate is low, there may not be enough residence time for some of the solute to diffuse into the sorbent. This solute, which bypasses the packing, does not undergo separation and exits at the feed concentration. Equation (19-66) presents conditions to prevent bypassing. If separation problems are observed, try reducing fluid velocity by one or more orders of magnitude. A reasonable liquid velocity is 1.0 ft/min (Seider et al., 2009).

9. Many adsorbents, particularly activated carbon, show a very high initial adsorption capacity. After regeneration, this capacity is not fully regained. When testing adsorbents, do extensive cleaning and/or washing first, and then do several complete cycles. Do not use initial results for design of cyclic processes.

10. Slow decay of adsorbents due to irreversible adsorption of trace components or thermal deactivation of active sites is common. When slow decay occurs, operating conditions must be adjusted.

11. Because adsorption processes use surface phenomena, they are often much more sensitive to trace chemicals than distillation and other separation techniques that rely on bulk properties. An occasional wash, cleaning, or extreme regeneration step may be needed. Short sorbent life, which can be a problem in biological operations, often makes processes uneconomical. Long-term pilot plant tests with actual feed from the plant are useful to determine the seriousness of these problems.

12. Surface properties and surface morphology of sorbents is critically important. Different batches of what is supposed to be the same sorbent may differ significantly. Thus, batches should be sampled and tested before being used on a large scale.

13. Temperature increases must be controlled. Adsorbates may be thermally sensitive and some adsorbents, such as activated carbon, readily burn. Hot adsorbents are also more likely to catalyze unwanted reactions.

14. Beds in series are often treated as if they were equivalent to a single long bed. However, their transient behavior is different and depends on connecting pipes and valves.

15. For safety reasons, personnel must always wear respirators when entering chromatography or adsorption columns. Many adsorbents adsorb oxygen, and others may desorb toxic gases. Strong acid and strong base ion exchange resins are solid acids and bases that can cause chemical burns, particularly in the eyes. Use of eye protection and normal protective clothing is recommended (Shuey, 1990). Spills of any adsorbent or ion exchange resin should be cleaned up immediately because they “can act as miniature ball bearings” (Shuey, 1990, p. 278) and cause falls. Resin expansion can fracture vessels if sufficient room for expansion is not available.

16. Ion exchange columns need to be backwashed periodically to remove solids and fines and to relieve pressure built up by periodic contraction and expansion. Backwashing reduces pressure drop and extends resin life (Shuey, 1990).

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A1. Column is initially clean (c_init = 0). Feed is c_F > 0.

1. If solute follows a linear isotherm, the resulting solute wave will be

(a) diffuse wave, (b) shock wave, (c) simple wave.

2. If solute follows a favorable isotherm, the resulting solute wave will be

(a) diffuse wave, (b) shock wave, (c) simple wave.

3. If solute follows an unfavorable isotherm, the resulting solute wave will be

(a) diffuse wave, (b) shock wave, (c) simple wave.

A2. Column initially is saturated with solute at concentration c_init > 0. Feed is c_F = 0.

1. If solute follows a linear isotherm, the resulting solute wave will be

(a) diffuse wave, (b) shock wave, (c) simple wave.

2. If solute follows a favorable isotherm, the resulting solute wave will be

(a) diffuse wave, (b) shock wave, (c) simple wave.

3. If solute follows an unfavorable isotherm, the resulting solute wave will be

(a) diffuse wave, (b) shock wave, (c) simple wave.

A3. Sorption separations are not always used in industry in cases where they would be most economical. What are some noneconomic barriers to more use of sorption separations?

A4. Explain why an adsorption isotherm that is too steep may not work well in a PSA process.

A5. Briefly explain why the SMB system is much more efficient (i.e., uses less solvent and less adsorbent) than an elution chromatograph doing the same binary separation. Assume that both systems are operating in migration mode using isocratic elution. Both systems are optimized. Elution chromatography uses repeated pulses of feed.

A6. Although a number of important industrial separations can be operated as either gas or liquid, all SMB applications are operated as liquids. What are the advantages of operation as a liquid compared to operation as a gas?

A7. In an SMB suppose A product purity is okay, but B product purity is too low. We can increase B product purity while maintaining A product purity by

a. increasing all M_i.

b. decreasing all M_i.

c. increasing M₄ and increasing M₃.

d. decreasing M₁ and increasing M₃.

e. increasing M₄ and decreasing M₂.

f. decreasing M₄ and decreasing M₂.

A8. Under what conditions can the LUB approach be used for monovalent-monovalent ion exchange? Under what conditions can the LUB approach be used for monovalent-divalent ion exchange?

A9. A dilute ternary mixture consisting of A, B, and C dissolved in D (A is least strongly adsorbed and C is most strongly adsorbed) is separated in a normal SMB (modify Figure 19-14b for the ternary separation). One product is A (plus D), and the other product is B + C (plus D). The four SMB design Eqs. (19-29) are

a. unchanged.

b. the same except Eq. (19-29b) becomes u_c,2 = M_2c u_port (M_2c ≤ 1.0).

c. the same except Eq. (19-29c) becomes u_B,3 = M_3B u_port (M_3B ≥ 1.0).

d. the same except Eq. (19-29d) becomes u_C,4 = M_4C u_port (M_4C > 1.0).

e. the same except change Eq. (19-29b) as in answer b and change Eq. (19-29d) as in answer d.

A10. You are designing a large-scale chromatographic system for separation of two optical isomers. You talk to a chemist who has a lot of experience with analytical chromatography. He recommends operating at low feed concentrations so that you will be in the linear range of the isotherms. Is this good advice? Explain.

A11. Many variations of the basic Skarstrom cycle shown in Figure 19-11 have been developed. One variation is to include a partial co-flow blowdown step before the counterflow blowdown shown in Figure 19-11. What are the likely advantages and disadvantages of doing this?

B. Generation of Alternatives

B1. Brainstorm some possible alternative adsorbents made from common agricultural and/or forest products or wastes.

B2. The PSA cycle used in Example 19-4 does not produce pure hydrogen throughout the entire feed step. Brainstorm what can be done to change the cycle so that it will produce pure hydrogen.

B3. Separation in chromatography is often limited because selectivity is too close to 1.0. For both liquid and gas systems, list as many ways as possible that the equilibrium constants can be changed.

B4. What can be done to develop more economical sorption separations?

C. Derivations

C1. A molecular sieve zeolite adsorbent consists of pellets that are agglomerates of zeolite crystals with density ρ_crystal scattered in a continuous phase of clay binder with a density ρ_clay. In this case, there is an interpellet porosity ε_e (between pellets—this is normal ε_e), an intercrystal porosity ε_p1 (which is porosity in the binder), and an intracrystal porosity ε_p2 (inside the crystals). If the fraction of the particle volume that is crystals (including porosity within the crystals) is f_cry, derive formulas for the total porosity, V_available, and particle and bulk densities.

C2. Developments of Eqs. (19-14, a-d) are efficient but tend to hide the reasons the solute velocity equations are different. Start with Eq. (19-9) and derive solute velocity equations when c and q are in different units.

a. Derive Eq. (19-14a).

b. Derive Eq. (19-14b).

c. Derive Eq. (19-14c).

d. Derive Eq. (19-14d).

C3. Use mass action expression to prove Eqs. (19-40a) and (19-41).

C4. Derive Eq. (19-44) by modifying development used for adsorption in Eqs. (19-10) to (19-14).

C5. Derive the equation for solute velocity for linear isotherms q_i = K′_ic_i using a single-porosity model (equivalent to setting ε_e = 0). Result obtained should be

C6. Derive appropriate mass balance equation and solutions equivalent to Eqs. (19-22) to (19-24) but for the case where u_s(T_hot) > u_s(T_cold) > u_th. Hint: Start by redrawing the differential control volume in Figure 19-7B noting that concentration, amount adsorbed, and temperature above c₂, q₂, and T₂ are c_change, q_change, and T₁, where c_change is concentration caused by the temperature change, which moves ahead of the thermal wave.

C7. Use Lapidus and Amundson solution to derive an equation for t_MTZ for a step input for a system with a linear isotherm. The time for the MTZ is defined as the time required to go from 0.05 (c_feed – c_initial) to 0.95 (c_feed – c_initial). Show that t_MTZ is approximately proportional to L^1/2.

Note: As far as I know, the solution for t_MTZ for a breakthrough curve is not available in the literature. The ability to start with a known solution and derive an equation for a specific case will be very valuable in industry and will help you stand out from most engineers.

C8. Show that if the entire column is heated (or cooled) simultaneously (known as direct heating), Eq. (19-24) simplifies to

Explain why direct heating is practical for laboratory-sized columns (small diameter) but not for commercial units with large diameters. (Hint: Consider heat transfer characteristics.)

C9. For divalent-monovalent exchange, show that when a total ion wave passes through a segment of the column, y_i,after = y_i,before.

Hint: Use balance envelope in Figure 19-7B and Eq. (19-22), but with Δz/Δt = u_{total ion} = v_inter.

C10. The SMB in Figure 19-14B is doing a binary separation at (D/F)_min. Volumetric feed rate F and cross-sectional area of column A_c are specified. Derive equations for u_port, v₁, v₂, v₃, v₄, v_A,product, v_B,product, v_D, and D/F = v_D/v_Feed that will satisfy Eqs. (19-29) and (19-30) using Eq. (19-15e). Show that Eq. (19-31b) is correct. After simplification, you should obtain following result:

Show that this result becomes D/F = 1.0 when all M_i = 1.0.

Hint: Start with equations for zones 2 and 3 and v₂ = v₃ + v_Feed, and solve for u_port, v₂ and v₃.

C11. Derive the mass action equilibrium expression for trivalent-trivalent ion exchange and derive derivative of y_tri with respect to x_tri.

D. Problems

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

D1.* Find K_A and q_max for methane adsorption on PCB activated carbon at 296 and 480 K (Table 19-3).

D2.* Adsorption of anthracene from cyclohexane on activated alumina follows a Langmuir isotherm, q = 22c /(1 + 375 c), where c is in mol/L and q is in mol/kg (Thomas, 1948).

Convert this to the form of Eq. (19-6a) in terms of q_max and K_Ac in units of g/L for c and g/kg for q. Range of validity should be from c = 0.0 to 0.012 mol/L.

Data: density of cyclohexane = 0.78 kg/L, MW cyclohexane = 84, MW anthracene = 178.22, ρ_p = 1.47 kg/L, ε_e = 0.4, ε_p = 0.0.

D3. We are separating acetonaphthalene (AN) from dinitronaphthalene (DN). For a very small feed pulse, resolution should be R = 0.97. Linear equilibrium parameters and column parameters are K′_AN = 0.00301, K′_DN = 0.00316, with K′ in units L/g adsorbent. ε_e = 0.40, ε_p = 0.46, K_d = 1.0, v_super = 100cm/min, ρ_s = 2200kg/m³, L=200 cm.

a. At what time does AN peak exit the column?

b. At what time does DN peak exit the column?

c. If resolution R = 0.97, what values of N and HETP are required?

d. If resolution R = 0.97, what are width of the AN peak at half height and value of σ_t in minutes?

D4. A thermal swing adsorption process is removing traces of toluene from n-heptane using silica gel adsorbent. Operation is at 1.0 atm. Feed is 0.11 wt% toluene and 99.89 wt% n-heptane at 0°C. Feed step is continued until breakthrough occurs. Adsorber is 2.0 meters long and during feed step is at 0°C. Purge is counterflow with pure n-heptane at 80°C. Column is cooled to 0°C before next feed step. Superficial velocity is 10.0 cm/min during both feed and purge steps. Use Eq. (19-15c) for solute velocities. Assume that wall heat capacities can be ignored, heat of adsorption is negligible,and no adsorption of n-heptane. Use solute movement theory to

a. determine breakthrough time for toluene during feed step.

b. determine time for thermal wave to break through.

c. determine time to remove all toluene from column.

d. determine outlet concentration profile of toluene in purge fluid.

Data: At low concentrations isotherms for toluene: q = 17.46x at 0°C, q = 7.77x at 30°C, q = 5.16x at 35°C, q = 1.23x at 80°C, q and x are in g solute/g adsorbent and g solute/g fluid (mass fraction), respectively (Matz and Knaebel, 1991). ρ_s = 2100 kg/m³, ρ_f = 684 kg/m³, C_ps = 920 J/(kg °C), C_pf = 1841 J/(kg °C), ε_e = 0.43, ε_p = 0.48, K_d = 1.0.

D5. A 50 cm long column is packed with a resin that immobilizes a liquid stationary phase. The column is initially clean, c_A = 0. At t = 0, we input a feed that is c_A.feed = 1.5 g/L. Superficial velocity is 20 cm/min. The packing has ε_e = 0.4, ε_p = 0.54, K_d = 1.0, ρ_s = 1.124 kg/L, and equilibrium for component A is an unfavorable isotherm,

q = 1.2 c_A/(1 – 0.46 c_A) where q is in g/kg and c_A is in g/L.

Use solute movement theory to predict the outlet concentration profile of A (c_out vs. time).

D6. We are adsorbing p-xylene from n-heptane on silica gel. Column is initially clean (c = q = 0) and is at 30°C. At t = 0, we start input of a 0.010 mass fraction p-xylene feed at 30°C. At t = 40 min, we stop feed and input clean solvent (x_xy = 0) at 80°C. Interstitial velocity is constant, v_inter = 30 cm/min. L = 50 cm, ε_e = 0.43, ε_p = 0.50, K_d = 1.0, ρ_s = 2100 kg/m³, ρ_f = 684 kg/m³, C_p,s = 920 J/kg/K, C_p,f = 2240 J/kg/K, and heat storage in the wall can be neglected. Column is adiabatic. n-heptane does not adsorb, and p-xylene isotherm is (Matz and Knaebel, 1991). q =12.03x_xy at 30°C & q = 2.01x_xy at 80°C. q is g xylene/g adsorbent & x is mass fraction xylene.

a. Find u_s (T = 30°C), u_s (T = 80°C), and u_th.

b. Find the breakthrough time for the thermal wave.

c. Predict the outlet concentration profile (x_xy,out vs. time).

D7.* An initially clean 60.0 cm long column contains activated carbon. At t = 0, we feed a dilute aqueous solution of acetic acid (c = 0.01 kmol/m³) at 4°C in an upward direction. Superficial velocity of feed is 15.0 cm/min. After a very long time (1200 min) and when the column is certainly totally saturated (c = 0.01 everywhere), feed is stopped, flow direction is reversed, and the column is eluted with pure water at 60°C at a superficial velocity of 15.0 cm/min. This elution continues for another 1200 minutes.

Data: Equilibrium at 4°C, q = 0.08943c; equilibrium at 60°C, q = 0.045305c, with c in kmol/m³ and q in kmol/kg carbon; ρ_f = 1000 and ρ_s = 1820.0 kg/m³; K_d =1.0; ε_e = 0.434; ε_p = 0.57; and C_ps = 0.25 and C_pf = 1.00 cal/(g°C). Ignore wall heat capacity effects.

a. From t = 0 to 1200 minutes, predict outlet concentration profile (top of column).

b. Predict outlet concentration profile (bottom of column) for the 1200 minutes of elution.

D8. Redo Example 19-3 but with co-current thermal regeneration. Input the hot thermal wave (co-current purge step at superficial velocity of 11.0 cm/min) so that it exits at same time xylene breaks through at the product end. Stop the hot thermal wave as soon as thermal breakthrough occurs, and input cold feed (at superficial velocity of 8.0 cm/min). Find feed time, time last solute leaves the column, average mass fraction of peak from initial breakthrough to last solute leaving, and time that gas exiting the column becomes cold again. Compare average outlet mass fraction of peak to average mass fraction of gas exiting during regeneration in Example 19-3.

D9. A very simple PSA cycle consists of three steps: (1) Pressurize column with feed. (2) Feed step withdrawing product gas at p_H. (3) Counterflow blowdown to pressure p_L. This cycle is used with a single column to process a feed that contains 0.3 mol% methane in hydrogen using Calgon Carbon PCB activated carbon adsorbent. Operation is at 480 K. The feed step has a superficial velocity of 0.05 m/s, column is 0.75 m long, p_H = 4.0 atm, p_L = 1.0 atm, and data are available in Example 19-4. Column is initially clean (filled with hydrogen that does not adsorb).

a.

Is there breakthrough of methane in the first cycle? Is all of the methane removed in the blowdown step? What are the highest and the lowest mole fractions of methane in the blowdown step?

b. With the same repressurization and blowdown steps, how long should the feed step be to just remove all of the methane in the blowdown step? Interpret your result.

D10.* Intermediate concentrations in the outlet concentration profile for trace PSA systems can be estimated using Eqs. (19-28a) to (19-28c). For Example 19-4,

a. Show that point 10 in Figure 19-13B can be determined by starting with t = 1 s (end of blowdown) at z_after = 0.40 m (0.10 m from feed end) by using Eq. (19-28c) to find p_before and Eq. (19-28a) to find y_M,after. Since solute of this mole fraction moves as a wave at the known velocity u_M during the feed step, the time it exits the top of the column can be determined.

b. Starting at the point t = 1 s, z_after = 0.48m, calculate point 11 in Figure 19-13B.

D11. Repeat Example 19-4 but using repressurization with pure product.

D12. A column packed with activated carbon is used for adsorbing acetone from water at 25°C. The isotherm can be approximated as a Langmuir isotherm (Seader and Henley, 1998), q = (0.190 c)/(1 + 0.146c), q is mol/kg carbon and c is mol/m³. Bed properties are K_d = 1.0, ρ_s = 1820 kg/m³, ρ_f = 1000 kg/m³, ε_e = 0.434, ε_p = 0.57. The bed is 0.50 m long and has an internal diameter of 0.08 m. The flow rate is 0.32 L/min for both parts a and b.

a. If the bed is initially clean (c = q = 0), determine outlet concentration curve (c_out vs. time) if a feed containing 50 mol/m³ of acetone is fed to it starting at t = 0.

b. If bed is initially saturated with a fluid containing 50 mol/m³ of acetone, predict outlet concentration profile when bed is eluted with pure water (c = 0) starting at t = 0. Find outlet times for concentrations of c = 50, 40, 30, 15, 5, and 0 mol/m³. Plot concentration out versus time.

Note: Solute movement theory works just as well for mole balances as for mass balances.

D13. Use the local equilibrium model to estimate reasonable flow rates for separation of dextran and fructose using an SMB. Isotherms are linear, and both q and c are in g/L. Linear equilibrium constants are dextran, 0.23 and fructose, 0.69. Interparticle void fraction = 0.4 and intraparticle void fraction = 0.0. Columns are 40.0 cm in diameter and 60.0 cm long. Feed flow rate is 1.0 L/min, and feed has 50.0 g/L of each component. Desorbent is water. Lumped parameter mass transfer coefficients using fluid concentration differences as driving force are 2.84 1/min for both dextran and fructose. Operation is isothermal. Use multiplier values (see notation in Figure 19-14) of M₁ = 0.97, M₂ = 0.99, M₃ = 1.01, and M₄ = 1.03. Determine flow rates of desorbent, dextran product, fructose product, and recycle rate; and find ratio D/F.

D14. A 50 cm long column is packed with a strong acid cation exchange resin (c_RT = 2.2 eq/L, ε_e = 0.42). Fluid superficial velocity is 25.0 cm/min. Cations are not excluded. Anions are excluded. Anderson (1997) lists K_H–Li = 1.3 & K_K–Li = 2.9. Dechow (1989) lists K_H–Li = 1.26 and K_K–Li = 2.63.

a. If resin is initially in H⁺ form in equilibrium with a 0.1 eq/L solution of HCl and an aqueous feed that is 0.1 eq/L KCl is fed to the column, calculate times that K⁺ shock wave exits for both sets of equilibrium parameters.

b. If resin is initially in equilibrium with a 1.0 eq/L solution of HCl and an aqueous feed that is 1.0 eq/L KCl is fed to the column, calculate times that K⁺ shock wave exits for both sets of equilibrium parameters.

c. If resin is initially in equilibrium with a 1.0 eq/L solution of HCl and KCl (x_H = 0.8, x_K = 0.2) and an aqueous feed that is 1.0 eq/L solution of HCl and KCl (x_H = 0.15, x_K = 0.85) is fed to the column, calculate times that K⁺ shock wave exits for both sets of equilibrium parameters.

d. Discuss your results.

D15. A 50 cm long column is packed with a strong acid cation exchange resin (c_RT = 2.2 eq/L, ε_e = 0.42). Fluid superficial velocity is 25.0 cm/min. Cations are not excluded. Anions are excluded. Anderson (1997) lists K_H–Li = 1.3 and K_K–Li = 2.9 and K_Na–Li = 2.0.

a. Resin is initially in the H⁺ form in equilibrium with a 0.5 eq/L solution of HCl. Your technician does two experiments: (1) an aqueous feed that is 0.5 eq/L KCl is fed to the column, and (2) after re-equilibrating the column with 0.5 eq/L HCL, an aqueous feed that is 0.5 eq/L NaCl is fed to the column. The results show that the K⁺ shock wave and the Na⁺ shock wave in the two separate experiments exit the column at the same times. The technician believes this result cannot be correct. Determine from calculations if this result is correct.

b. The technician then takes a column in equilibrium with x_Na = 0.4 (C_T = 0.5) and feeds with a solution with x_Na = 0.9 (C_T = 0.5). He repeats the experiment with x_K = 0.4 (C_T = 0.5) and feeds with a solution with x_K = 0.9 (C_T = 0.5). At what time do these two waves exit?

c. The technician then decides to take a column saturated with K⁺ and elute it with 0.5 N HCl and to separately take a column saturated with Na⁺ and elute it with 0.5 N HCl. Much to the technician’s surprise, the center (x_K = 0.5) of the K⁺ and the center (x_Na = 0.5) of the Na⁺ waves do not occur at the same time, and the K⁺ center exits earlier than the Na⁺ center. Calculate when the centers of these diffuse waves exit the column.

d. The technician then looks at when the tails of the two elution curves exit (x_K → 0.0) and (x_Na → 0.0). The Na⁺ tail exits before the K⁺ tail. Calculate the times that these two tails exit.

e. Next, the technician looks at the times when (x_K = 0.90) and (x_Na = 0.90). The K⁺ at this concentration exits before the Na⁺ exits. Calculate the times that these two concentrations exit.

f. Finally, the technician notices that for the two diffuse waves there is a concentration of solute (Na⁺ or K⁺) that exits at the same time. What is this concentration (x_Na = x_K)?

g. The technician is thoroughly confused and does not understand why Na⁺ and K⁺ come out at the same time in one experiment, the K⁺ comes out ahead in some experiments, and the Na⁺ comes out ahead in different experiments. Explain the results to the technician.

D16. A column packed with gas-phase activated carbon is initially filled with clean air. At t = 0, a feed gas containing y = 0.05 wt% toluene in air is started. This feed continues until t = 100.0 hours at which time a feed that is y = 0.15 wt% toluene is introduced and continued throughout the remainder of the operation. The superficial velocity is always 20.0 cm/s. Find the minimum column length required to have a single shock wave exit the column.

Data: Equilibrium (Basmadjian, 1997)

q = kg toluene/kg carbon and y = wt frac, which is essentially kg toluene/kg air. T = 298 K, P_tot = 50 kPa. Assume gas has density of pure air, which acts as an ideal gas.

, , K_d = 1.0, ε_e = 0.40, ε_p = 0.65, ρ_s = 1500kg/m³.

Watch your units.

D17. A 25 cm long column packed with gas-phase activated carbon is initially filled with air containing y = 0.10 wt% toluene. At t = 0, a feed gas containing y = 0.05 wt% toluene in air is started. This feed continues until t = 20.0 hours at which time a feed that is pure air (y = 0.0000) is introduced and continued throughout the remainder of the operation. The superficial velocity is always 21.0 cm/s. Pressure is 50 kPa. Data are in problem 19.D16.

Predict the outlet concentration profile. Specifically, find when the following exit: y = 0.10, 0.075, 0.05, 0.025, and 0.0 wt%. Sketch the outlet concentration profile (y vs. t), and label the times when these concentrations exit the column. Watch your units.

D18. Glucose (G) is separated from fructose (F) on an ion exchange resin in Ca⁺² form. (Note: This is NOT an ion exchange problem—sugars complex with Ca⁺² and there is no exchange of ions.) Linear equilibrium parameter for glucose and values of ε_e, ε_p, E_eff, and K_d are given in Example 19-9. Equilibrium for fructose (Table 19-2) is q = 0.88 c with q and c in g sugar/100 ml. Interstitial velocity is 20.0 cm/min. For a very small pulse of feed, we desire a resolution between the two peaks of R = 1.05.

a. How long should the column be?

b. At what times do the glucose and fructose peaks exit the column?

c. What are the values of σ_t for glucose and fructose?

d. If we want resolution between the two peaks R = 1.0, repeat parts a to c.

D19. We are exchanging Ag⁺ and K⁺ on a strong acid resin with 8% divinylbenzene (DVB). Total resin capacity is c_RT = 2.0 eq/L, and ionic concentration of feed solution is c_T = 1.2 eq/L, all of which is Ag⁺. Column is initially at a solution concentration of c_T = 0.2 eq/L, all of which is K⁺.

a. How long does it take for the total ion wave to break through?

b. At what time does Ag⁺ shock wave break through?

c. After Ag⁺ shock wave breaks through, regenerate column with pure K⁺ solution with c_T = 1.2 eq/L. Predict shape of ensuing diffuse wave. (Reset t = 0 when start K⁺ regeneration solution.)

Data: ε_e = 0.4, ε_p = 0.0, K_E = 1.0, v_super = 3.0 cm/min, L = 50 cm.

D20. A column packed with a strong cation exchanger is initially in the K⁺ form, c_T = 0.02 eq/L. The column is 75.0 cm long, superficial velocity is 20.0 cm/min, and flow is in same direction for all steps, ε_p = 0, ε_e = 0.4, K_E = 1.0 (cations), and c_RT = 2.0 eq/L. Equilibrium data are in Table 19-5.

a. At t = 0, feed column with a solution with c_T = 0.02 eq/L, x_Ca = 0.80, x_K = 0.20. Plot outlet value of x_Ca vs. time.

b. At t = 500 minutes, column is regenerated with a pure aqueous solution of K⁺ with x_K = 1.0, x_Ca = 0.0, and c_T = 1.0 eq/L. Plot outlet values of c_T and x_Ca vs. time.

c. As an alternate regeneration procedure, at t = 500 minutes, regenerate with a pure aqueous solution of K⁺ with x_K = 1.0, x_Ca = 0.0, and c_T = 1.4 eq/L. Plot outlet c_T and x_Ca vs. time.

Note: If any of these steps require you to calculate a diffuse wave, calculate velocities and breakthrough times at three values of x_Ca: at highest and lowest mole fractions and at x_Ca = 0.5.

D21. Isotherms for dilute amounts of toluene and xylene adsorbed on silica gel from n-heptane are linear at low concentrations (Matz and Knaebel, 1991). For toluene, q_Tol = K′_Tol(T)x_Tol where q_Tol is g toluene/g adsorbent and x_Tol is in g toluene/g solution (mass fraction) (Matz and Knaebel, 1991). The linear “constants” are functions of temperature. For toluene, q_Tol = 17.46x_Tol at 0°C, q_Tol = 7.77x_Tol at 30°C, q_Tol = 5.16x_Tol at 35°C, and q_Tol = 1.23x_Tol at 80°C. Isotherms for xylene at low concentrations have similar form to those for toluene, q_xy = K′_xy(T)x_Txyl where q_xy is g xylene/g adsorbent and x_xy is in g xylene/g solution (mass fraction). Isotherms for xylene: q_xy = 22.36x_xy at 0°C, q_xy = 12.03x_xy at 30°C, q_xy = 6.28x_xy at 35°C, and q_xy = 2.01x_xy at 80°C. Wall heat capacities can be ignored, heat of adsorption is negligible, and no adsorption of n-heptane. Find appropriate zone, product, and desorbent interstitial velocities (based on column diameter) for an SMB separating toluene and xylene if interstitial feed velocity = 1.0 cm/min and temperature is 30°C. Switching time is 100 min. Choose M₁ = M₂ = 0.95, M₃ = M₄ = 1.05. Physical properties: ε_e = 0.43, ε_p = 0.48. ρ_s = 2100 kg/m³, ρ_f = 684kg/m³, K_d = 1.0, C_ps = 920 J/kg °C, and C_pf = 1841 J/(kg °C).

D22. Use the Lapidus and Amundson solution to predict the behavior of fructose in a column packed with silica gel. Column is initially clean (contains no fructose). Feed is 50 g/L, feed pulse lasts for 8 minutes, and after 8 minutes elution is with water. Flow rate is 20 ml/min. The other values are as follows:

Lumped parameter with concentration driving force, k_m,ca_p = 5.52 1/min. Isotherm is linear, K′_fructose = 0.69. Isotherm parameters, q and c, are in g/L. Calculate E_effective, and then calculate enough points on the curve to plot it. This is a step up followed 8 minutes later by a step down.

D23. For a linear system, breakthrough solution is c_out/c_feed = X (z,t). At t = 0, we have an adsorption column that is initially at a uniform concentration c_initial, and feed concentration is c_initial. At t = 17.5 minutes, the feed concentration is reduced to c_F1 (c_F1 < c_initial). At t = 28 minutes, the feed concentration is increased to c_F2 (c_F2 > c_F1). At t = 36 minutes, the feed concentration is reduced to 0.0. Write the solution for c_out in terms of c_initial, c_F1, c_F2, and breakthrough solution X.

D24. Isotherms for dilute amounts of toluene and xylene adsorbed on silica gel from n-heptane and physical properties are given in Problem 19.D21. Find appropriate zone, product, and desorbent interstitial velocities (based on column diameter) for an SMB separating toluene and xylene if interstitial feed velocity = 1.0 cm/min and temperature is constant at 30°C. Switching time is 100 min. Choose M₁ = M₂ = 0.9, M₃ = M₄ = 1.10. Compare results with Problem 19.D21.

D25. TSA regeneration can be combined with an SMB to reduce desorbent usage (Kim et al., 2005; Wankat, 1986). For the separation of toluene and xylene, repeat Problem 19.D21 except operate zones 2 and 3 at 30°C with M₂ = 0.95 and M₃ = 1.05, operate zone 4 at 80°C with M₄ = 4.0, and operate zone 1 at 0°C with M₁ = 0.5. This will give a better separation than M values in Problem 19.D21. A very large value of M₄ and small value of M₁ are necessary to have a workable process.

D26. A chromatograph is separating acetonaphthalene (A) from dinitronaphthalene (Dinitro) on 20-micron silica gel. For a single-porosity model, [(1 – ε) ρ_s K′_A/ε] = 5.5, and [(1 – ε) ρ_s K′_Dinitro/ε] = 5.8 in a solvent with 23% methylene chloride and 77% n-pentane. When the interstitial velocity v = 1.0 cm/s, HETP is 0.05 cm.

a. What column length is required for a resolution of R = 1.5 for an infinitesimal pulse of feed,?

b. Plot the outlet curve for A as c/c_max, vs. time using the Gaussian solution for R = 1.5.

Note: In the chromatography literature the parameter is known as the relative retention. The relative retention is easily determined from experiments.

D27. For a linear system breakthrough solution is c_out = X (z,t). We have an adsorption column that is initially at a uniform concentration c_initial = 0, and feed concentration is c_initial = 0. At t = 10 minutes, feed concentration is increased to 0.30c_F (c_F > 0). At t = 20 minutes, feed concentration is increased to c_F. At t = 25 minutes, feed concentration is increased to 2.0 c_F. At t = 30 minutes, feed concentration is decreased to 0.55 c_F. Finally, at t = 50 minutes, feed concentration is reduced to 0.0. Write a solution for c_out in terms of c_F, time, and breakthrough solution X.

D28.* An initially clean 25.0 cm long laboratory column is packed with particles that have an average diameter of 0.12 mm. At a superficial velocity of 9.0 cm/min with a step input, the symmetrical breakthrough curve center exits at 35.4 minutes, and the width (measured from 0.05 c_F to 0.95 c_F) is 2.8 minutes. Pore diffusion controls and isotherm has a Langmuir type shape.

a. What is L_MTZ in the lab unit?

b. Design a large-scale unit with 0.80 fractional bed use. Average particle diameter is 1.0 mm, and superficial velocity is 12 cm/min. How long should this unit be? What is t_br (c_out = 0.05 c_F)? Assume ε_e is same in both units.

D29. A 90 cm long laboratory column is packed with a strong acid cation exchange resin (c_RT = 2.5 eq/L, ε_e = 0.39). Cations are not excluded. Anions are excluded. Anderson (1997) lists K_H–Li = 1.3 and K_K–Li = 2.9 and K_Ca–Li = 5.2. The resin is initially in the K⁺ form in equilibrium with a solution of KCl that is 0.03 eq/L.

a. First, a 0.03 eq/L solution with x_Ca+2 =0.70 is fed to the column at a fluid superficial velocity of 25.0 cm/min at time t = 0. Does a shock or diffuse wave occur? What is the velocity and breakthrough time of this wave?

b. After column is totally saturated with 0.03 eq/L solution with x_Ca+2 =0.70, reset clock to t = 0 and feed in counterflow a regenerant fluid that is 1.1 eq/L of KCl (no calcium) with a superficial velocity of 35.0 cm/min. How long does it take for total ion wave to breakthrough?

A diffuse calcium wave occurs during elution. Calculate the velocity and breakthrough time of the fastest C_a⁺² wave, the velocity and breakthrough time of the slowest C_a⁺² wave, and the velocity and breakthrough time of the C_a⁺² wave with x_Ca+2 equal to 0.5.

c. What concentration of regenerant fluid is required to not have a diffuse wave during the regeneration step?

D30. A 500 cm long column is packed with a strong acid resin (c_RT = 2.2 eq/L, ε_e = 0.42). Superficial velocity is 25.0 cm/min. Counter-ions are not excluded. Co-ions are excluded. Dechow (1989) lists K_H–Li = 1.26 and K_K–Li = 2.63. Note: The questions ask for three exit times—if there is a shock wave, these times will be identical.

a. If the resin is initially in equilibrium with a 1.0 eq/L solution of HCl and KCl (x_H = 0.8, x_K = 0.2) and an aqueous feed that is 1.0 eq/L solution of HCl and KCl (x_H = 0.15, x_K = 0.85) is fed to the column, calculate the predicted times the K⁺ wave exits the column (give exit times for K⁺ concentrations of 0.01, 0.5, and 0.85 eq/L).

b. If the resin is initially in equilibrium with a 1.0 eq/L solution of HCl and KCl (x_H = 0.2, x_K = 0.8) and an aqueous feed that is 1.0 eq/L solution of HCl and KCl (x_H = 0.85, x_K = 0.15) is fed to the column, calculate predicted times the K⁺ wave exits the column (give exit times for K⁺ concentrations of 0.15, 0.5, and 0.8 eq/L).

D31. We have a 30.0 cm long laboratory column packed with a strong acid cation exchange resin (c_RT = 2.4 eq/L, ε_e = 0.40). Cations are not excluded. Anions are excluded. Anderson (1997) lists K_H–Li = 2.9 and K_Na–Li = 2.0. The resin is initially in the Na⁺ form in equilibrium with a 1.10 eq/L solution of NaCl. Then a 1.10 eq/L solution of KCl is fed to the column at a fluid superficial velocity of 10.0 cm/min. Breakthrough starts (x_K = 0.005) at 7.06 minutes, the center of breakthrough wave exits at 7.31 minutes, and the end of breakthrough wave (x_K = 0.95) at 7.57 minutes.

a. Calculate the time that the wave center is expected to leave the column (this is when shock wave exits) and the error between the experimental time and the calculated time.

b. The error could be caused by a number of small errors, such as an incorrect value for c_RT and/or ε_e. Use experimental data to determine an experimental value of shock velocity.

c. Calculate the value of c_RT/ ε_e required if this ratio is the only cause of errors. Is this amount of error a reasonable explanation? Give an example of values that would cause this amount of error.

d. From experimental values for shock wave velocity and times, calculate L_MTZ and fractional bed use of lab unit.

e. A large-scale column (L = 200 cm) with same resin (c_RT = 2.4 eq/L, ε_e = 0.40), but with beads that are four times the diameter of beads in the lab column, is being designed. Superficial velocity is increased to 20 cm/min. Initial and feed concentrations are the same as in laboratory column. Calculate L_MTZ, fractional bed use, and time that breakthrough starts (x_K = 0.05) for large-scale column. Use experimental values.

D32. Complete the mole balance check in step E of Example 19-7 and show that mole balance agrees with results of solute movement analysis.

D33. Show that pressure drops of columns designed in parts b and c of Example 19-11 are equal. Assume ε_e is the same in the two designs.

D34.* We are separating dextran and fructose in a four-zone SMB. Isotherms are linear, and both q and c are in g/liter. Linear equilibrium constants are dextran, 0.23, and fructose, 0.69. Interparticle void fraction = 0.4, and intraparticle void fraction = 0.0. Columns are 20 cm in diameter and 60 cm long. Feed flow rate is 1.0 L/min. Feed has 50 g/L of each component. Desorbent is water. Feed and desorbent are at 2.0 bar. Lumped parameter mass transfer coefficients using fluid concentration differences as driving force are 2.84 1/min for both dextran and fructose. Dispersion coefficient is 0.30 cm²/min for both solutes. Operation is isothermal. Use the local equilibrium model to estimate reasonable flow rates with multiplier values (see notation in Figure 19-14) of M₁ = 0.97, M₂ = 0.97, M₃ = 1.03, and M₄ = 1.03. Determine the linear velocity and volumetric flow rates of desorbent, dextran product, fructose product, and recycle rate; and find ratio D/F. Compare answer with 19.D13.

D35. A 28 cm long column packed with gas-phase activated carbon is initially filled with clean air. At t = 0, a feed gas containing y = 0.10 wt% toluene in air is started. This feed continues until t = 30.0 hours at which time pure air is introduced and continued throughout the remainder of operation. Superficial velocity is always 24.0 cm/s. Find the breakthrough time of shock wave and times the following outlet concentrations exit: y = 0.10, 0.075, 0.050, 0.025, and 0.0 wt%. Pressure is 150 kPa. Data are in problem 19.D16.

D36. At very low concentrations, isotherms for separation of enantiomers of 1,1’-bi-2-naphtol using a 3,5-dinitrobenzoyl phenylglycine bonded silica gel adsorbent with heptane-isopropanol (72:28) solvent at operating temperature of 25°C become linear.

q_A = 2.79 c_A and q_B = 4.03 c_B, q and c are both in g/L, A is the least retained enantiomer, and B is the most retained enantiomer (see Lab AC3 in this chapter’s appendix for isotherms for concentrated systems and for reference). Superficial velocity is 2.0 cm/min, and column is 30 cm long.

Data: Fluid density = 713 kg/m³, bulk density of adsorbent = 705 kg/m³, and viscosity of fluid is 0.876 cp. Average MW of solvent is 82.77, ε_e = 0.4, ε_p = 0.42, K_d,A = K_d,B = 1.0.

a. If a feed pulse containing equal concentrations, c_F, of A and B is input at t = 0, at what times do waves first start to exit?

b. How long should the feed pulse be if we want the trailing edge of A wave to just start to be separated from the leading edge of B wave?

c. At what time should a second feed pulse be injected if we want the leading edge of A wave from the second feed pulse to just start to intersect the trailing edge of B wave from the first feed pulse?

D37. Use a thermal swing adsorption process to remove traces of toluene from liquid n-heptane using silica gel as adsorbent. Adsorber operates at 1.0 atm. Feed is 0.11 wt%toluene and 99.89 wt% n-heptane at 35°C. Superficial velocity of feed is 5.50 cm/min. Adsorber is 0.85 meters long and during feed step is at 35°C. Feed is continued until toluene breakthrough occurs. Thermal regeneration/purge is done with counterflow of pure n-heptane at 80°C continued until all xylene is removed. Superficial velocity during thermal regeneration/purge is 9.0 cm/min. Data are in problem 19.D21. Use solute movement theory to

a. determine breakthrough time for toluene during feed step.

b. determine thermal breakthrough time during both purge and feed steps.

c. determine xylene outlet concentration profile during regeneration/purge.

D38. An adsorption with thermal regeneration experiment was done in laboratory with a 17 cm long adiabatic column that was initially clean (filled with pure n-heptane) and at 30°C. The student put in a hot feed (80°C) containing x_xy,feed = 0.6 wt% xylene in n-heptane at a superficial velocity of 8.6 cm/min. After breakthrough of xylene just started, flow was reversed and a pure solvent purge at 30°C was input to column at a superficial velocity of 12.9 cm/min (clock was reset to zero at start of purge). Data are in problem 19.D21.

a. What is breakthrough time for hot thermal wave during feed step?

b. What is breakthrough time for xylene during feed step?

c. What is breakthrough time for cold thermal wave during purge step?

d1. What is xylene outlet mass fraction during purge step before cold thermal wave breaks through?

d2. What is xylene outlet mass fraction during purge step after cold thermal wave breaks through but before pure solvent breaks through?

d3. At what time does pure solvent break through in outlet during purge step?

D39. A column packed with gas-phase activated carbon is initially filled with clean air. At t = 0, a feed gas A containing y_FA = 0.05 wt% toluene in air is started. This feed continues until t = 30.0 hours at which time feed gas B containing y_FB = 0.10 wt% toluene in air is introduced and continued throughout remainder of operation. Superficial velocity is always 24.0 cm/s. Data are in problem 19.D16. Find breakthrough time of resulting shock wave(s) for

a. a 20.0 cm long column.

b. a 25.0 cm long column.

D40. A 50.0 cm long column contains activated carbon and is initially saturated with acetic acid at c = 0.007 kmol/m³ at 4°C. At t = 0, column is eluted with pure water (C = 0) at 60°C at a superficial velocity of 12.0 cm/min. Data are in problem 19.D7.

a. At what time does temperature increase?

b. What does the outlet concentration profile look like? Give concentration values and times for changes in exiting fluid.

D41. Adsorption of anthracene from cyclohexane on activated alumina follows a Langmuir isotherm, q = 22c/(1 + 375 c), where c is in mol anthracene/L and q is in mol anthracene/kg adsorbent. A 40 cm long column is initially clean (c = 0, q = 0). A feed that is c_feed = 0.0008 is fed at t = 0 until column is totally saturated. Superficial velocity is 16 cm/min. Data are in problem 19.D2.

a. How long does it take to saturate column (what is breakthrough time)?

b. Saturated column is eluted with pure cyclohexane at a superficial velocity of 20 cm/min. Reset t = 0 and predict times it takes for anthracene concentrations of 0.0008 mol/L, 0.0004 mol/L, and 0.0000 mol/L to exit column.

E. Complex Problems

E1. Do Problem 19.D35 first, as results of that problem help set up this problem. A 28 cm long column packed with gas-phase activated carbon is initially filled with a gas containing y = 0.10 wt% toluene in air. At t = 0 pure air is fed into column. This feed continues until t = 15.0 hours at which time a feed gas containing y = 0.10 wt% toluene in air is started and continued throughout the remainder of the experiment. Superficial velocity is always 24.0 cm/s. Find the approximate time shock wave exits column and approximate exiting weight fraction of toluene in diffuse wave at time shock wave exits. Pressure is 150 kPa. Data are in problem 19.D16.

F. Problems Requiring Other Resources

F1. An adsorbent gas dryer has been sized to contain 2580 cubic feet of adsorbent. Dryer is a horizontal cylindrical vessel with a circular cross-section and flow from top to bottom of vessel (across circular cross-section). Adsorbent will be supported above the vessel’s bottom. Area (width × length) of adsorbent layer at adsorbent support should be 860 ft². Determine vessel dimensions that will minimize vessel weight (minimum weight will be minimum cost) subject to constraints that vessel is designed for an operating pressure of 6 atm, a maximum temperature of 500°C, a maximum diameter of 16 feet, and a maximum length of 60 feet.

a. Report diameter, length, and shell thickness of vessel and width of adsorbent layer. (Note: A spreadsheet is suggested for determining vessel dimensions. Sizing pressure vessels is covered in Chapter 16 of Seider et al., 2004.)

b. What was the purchase cost of vessel FOB in mid-2000? (Use weight method in Seider et al., 2004.) Note: FOB is Free on Board, which specifies the point at which the buyer becomes the owner of the vessel. Since the owner is responsible for damage during shipping, the point at which goods transfer ownership is important.

c. What was the purchase cost of molecular sieve adsorbent for this dryer in mid-2000? Ignore curvature when finding amount of adsorbent.

d. What are purchase cost FOB and installed cost of vessel at current prices? (Update cost with Chemical Engineering Plant Cost index.)

e. What is the current purchase cost of molecular sieve adsorbent for this dryer?

G. Computer Simulation Problems (These problems assume you have access to a simulator such as Aspen Chromatography)

G1.

a. Repeat Problem 19.D22 on the simulator.

b. Rerun Problem 19.D22 on the simulator but with k_m,ca_p = 100,000 1/min and E_D = E_effective.

c. Compare your two simulator runs.

d. Compare Lapidus and Amundson solution to Aspen Chromatography solutions. Note: You need to consider convergence and accuracy of Aspen Chromatography runs.

G2. Set up a chromatographic column with one feed, a column, and one product. Components that adsorb are acetonaphthalene (A) and dinitronaphthalene (DN). Use a model with convection with constant axial dispersion coefficients (0.25 cm²/min for both A and DN), constant pressure, and constant velocity. Use a linear lumped parameter model with driving force of (c – c*) and constant mass transfer coefficients (k_m,ca_p = 50.0 1/min for A and 45.0 1/min for DN). Isotherms are both linear, q = 0.003056 c (for A) and q = 0.003222 c (for DN) where q is in g adsorbed/kg adsorbent and c is in g solute/m³ of solution. Operation is isothermal. Column is 50.0 cm long with a 2.0 cm diameter. Adsorbent has the following properties: ε_e =0.40, ε_p = 0.46, K_D = 1.0, and ρ_s = 2222 kg/m³. Feed flow rate is 0.10 L/min, feed pressure = 3.0 bar, and feed concentration for A is 2.0 g/L, while feed concentration of DN is 1.0 g/L.

a. Run a breakthrough curve for 10 minutes. Print, label, and turn in your plot. Accurately determine t_MTZ for component A where t_MTZ is measured from 0.05 times A feed concentration to 0.95 times A feed concentration. Show this calculation.

b. Input a 0.010-min feed pulse, and develop with pure solvent for a total time of 10 minutes. Print your plot.

G3. We want to separate component 1 from component 2 using an SMB. In the feed, both compounds are dissolved in water, component 1 is 40 g/L, and component 2 is 60 g/L. Feed rate is 141.55 ml/min. The components both have linear isotherms where both q and c are in g/L. Equilibrium: component 1 is q₁ = 1.5 c₁; component 2 is q₂ = 3.5 c₂. SMB has six columns: two columns between feed and extract (B) product (zone 3 in Figure 19-14B) and two columns between feed and raffinate (A) product (zone 2). There is one column between desorbent addition and extract (B) product (zone 4). SMB has closed recycle, and there is one column between raffinate (A) product and desorbent addition (zone 1). Use constant pressure and volume (pressure = 3.0 bars), linear lumped parameter with (c – c*) driving force, and isothermal operation. Each column is 50.0 cm long and has a diameter of 10.0 cm. Data: ε_e = 0.40, ε_p = 0.45, K_D = 1.0, and ρ_bulk = 800 kg/m³. Fluid density is 1000 g/L. Values of both axial dispersion coefficients are 0.35 cm²/min; mass transfer coefficient (k_m,ca_p) for component 1 is 150 1/min and for component 2 is 100 1/min.

a. First, design your SMB to operate at optimum point for D/F = 1.0 (all M_i = 1.0). Calculate D, E, and R, switching time and recycle rate; and report these values. Run system for at least 10 complete cycles (a cycle is 6 switching times). Turn in a plot of raffinate concentrations (components 1 and 2) and a plot of extract concentrations (components 1 and 2). Also, report average mass fraction over last cycle for component 1 in raffinate and average mass fraction over last cycle for component 2 in extract.

b. Next, increase D/F to 2.0 (there are, of course, many ways to do this). Calculate and report D, E, and R, switching time and recycle rate. Briefly, explain your rationale for the method you used to increase D/F to 2. Run the system for at least 10 complete cycles. Turn in a plot of raffinate concentrations (components 1 and 2) and a plot of extract concentrations (components 1 and 2). Also, report average mass fraction over last cycle for component 1 in raffinate and average mass fraction over last cycle for component 2 in extract.

G4. Ion exchange. Bed is 50 cm long and 20 cm in diameter. External porosity = 0.4, internal porosity = 0.0. Use axial dispersion coefficients of 0.2 cm²/min for all components. Mass transfer coefficients (k_m,ca_p) are 10.0 1/min for all components. For a strong acid resin, use c_RT = 2.0 eq/L. K_H-H = 1.0, K_Na-H = 1.54. Operate with a feed rate of 5.0 L/min. Pressure is 2.0 bar.

a. Set feed component concentration of H⁺ equal to 0.0. Use a feed concentration of 1.0 eq/L for Na⁺. Column is initially in H⁺ form with c_T = 1.0 eq/L. Do a breakthrough run.

b. After column is converted to Na⁺ form, feed it with pure acid (H⁺) at 1.0 eq/L (Na⁺ is 0.0 and 1.0 eq/L H⁺). Do a breakthrough curve.

c. Now do a wash step with pure water (feed concentrations of all components are zero). Continue run until concentrations all become zero. Explain why this is so quick.

G5. Water softening. Use the same column, same resin, and same mass transfer and axial dispersion coefficients as in Problem 19.G4, except exchange Mg⁺⁺ with H⁺. K_Mg-H = 1.9527. The column is initially in H⁺ form with c_T = 0.10 eq/L. Feed is 0.0 eq/L of H⁺ and 0.10 eq/L of Mg⁺⁺ (c_T = 0.10 eq/L). The value of c_RT = 2.0 eq/L is unchanged. (There is no Na⁺ involved in this operation.) To reduce run time, operate with a column length of 10.0 cm. Do a breakthrough run and report results.

Unfortunately, most simulators will find this problem to be difficult, since equations are very stiff. Change convergence settings and discretization procedure as needed to obtain convergence.

G6. Separation of ternary mixture with a feed consisting of dextran, fructose, and a heavy impurity. A 25.0 cm long column with a diameter of 2.0 cm is used. External porosity = 0.4, internal porosity = 0.0. Pressure is constant at 2.0 bar. Use axial dispersion coefficients of 0.35 cm²/min for all components. Mass transfer coefficients (k_m,ca_p) are 2.84 1/min for dextran and fructose and 1.5 1/min for the heavy impurity. Driving force for mass transfer is concentration differences. Isotherms are linear with q and c both in g/L. Isotherm parameters are 0.23 for dextran, 0.69 for fructose, and 10.0 for heavy impurity. Feed flow rate is 20.0 ml/min, overall concentration of feed is 100.0 g/L, and feed is 48 wt% dextran, 48 wt% fructose, and 4.0 wt% heavy impurity.

a. Input a 1.5-minute feed pulse followed by pure solvent (water). Set up a plot with outlet concentrations of dextran, fructose, and heavy, and run for 100 minutes.

Where is the heavy? If your plot uses the same scale for all three components, it will be difficult to see the heavy. To find it, set up plot with a separate scale for heavy concentration. Note that heavy has an initial peak and then a main, very broad peak (all at low concentrations). Initial peak occurs because with a low mass transfer coefficient, some of the heavy exits the column without ever entering the packing material. This is called bypassing or “instantaneous breakthrough and is obviously undesirable. Check to see if Eq. (19-66) is satisfied, and interpret your results.

b. Change heavy mass transfer coefficient (k_m,ca_p) to 10.0 1/min and run again. Now it should look more normal, except concentrations of the heavy component are very low. This type of problem (at least two components that are difficult to separate plus very slow components) is known as the general elution problem. Column length needs to be set to separate difficult separation, but then slow components take a long time to come out.

c. (All mass transfer coefficients are k_m,ca_p = 10.0 1/min for this step.) Input a 1.0-minute pulse of feed followed by 4.5 minutes of pure solvent. Then reverse flow of solvent and elute for 15 minutes. Develop plots for both forward flow and reverse flow.

H. Spreadsheet Problems

H1. Set up a spreadsheet and solve Problem 19.D12.

H2. Solve Problem 19.D22 with a spreadsheet. Note: For unexplained reasons, the argument for the error function in Excel must be positive. An error is returned if the argument is negative. In this case make the argument positive and use equality erf (–a) = –erf (a).

Lab AC1. Introduction to Aspen Chromatography

Goal:

Goal is to get you started in Aspen Chromatography. This lab consists of a cookbook on running Aspen Chromatography, some helpful hints, and simulation of a real separation. The assistance of Dr. Nadia Abunasser in developing the original version of this lab was critically helpful.

Preparation:

Review Sections 19.6.1, 19.6.2, and 19.6.3.

Suggestions: Be patient. Solving partial differential equations numerically is probably two orders of magnitude more difficult than solving algebraic equations. There is a lot more set-up required than with Aspen Plus. It is relatively easy to skip a step and find you did not obtain expected results. Start over. Although mildly frustrating, repeating the process will help you set steps in your mind.

Start-up

1. Log in to your computer. Use your local operating system method of getting into Aspen Chromatography. Most likely, Aspen Tech→Aspen Process Development→Aspen Chromatography.

2. You will first develop a simple chromatography (or adsorption) column system. To do this, go to the menu bar, and on the left-hand side (LHS) select File. Go to Templates. In that window click Blank trace liquid batch flowsheet, and then click Copy. It will ask for a directory name. Use something like column1. This will be saved in your working file. NOTE: In all file names and names for components, columns, streams, and so forth, there must be no spaces. Click OK.

3. In the Contents of Simulation box (LHS), left double-click Component lists. Then in the “Contents of Component Lists” box below, double-click Default. A and B are listed in the pop up screen. Change these names to names of the components to be separated (fructose and dextran T6). First, click the Remove all button. In the window below, type in the first component name (e.g., fructose), and click the Add button. Do the same steps for all other components. Click OK.

4. Draw the column. Click + to the left of Libraries, and then click + to the left of Chromatography in the Exploring Simulation box. This opens other possibilities. Click on the word Chromatography, which gives Contents of Chromatography in a box below. Double-click the model you want to use (Chrom_Reversible—since it is more flexible). Contents now lists Contents of Chrom_Reversible. Click and drag the specific model you want—in this case chrom_r_column (probably at the top row center in the window)—and move it to the center of the Process Flowsheet Window. This gives a column labeled B1. Left-click B1, then right-click to open a menu. Click Rename Block. Call the block something like “column.”

5. Now for some confusion. Click on word Chrom_Nonreversible in the upper box of Exploring Simulation. This will get you new contents. Click and drag a feed stream (chrom_feed), and put it near the top and to the left of the column (nonreversible column has flow downward by arbitrary convention). Now click and drag a product stream (chrom_product) (scroll down to find it), and put it near the bottom and to the right of the column. Rename as feed and product. (We are using code in a reversible model, since it is up to date, but are using nonreversible for feed, product, and connecting lines, as it is simpler and less likely to cause problems. In Lab AC4, when you are more comfortable with Aspen Chromatography, we will switch to reversible streams.)

6. Connect everything together. In Exploring Simulation under Chromatography, click on the word Stream Types. This gives new contents below. Click and drag chrom_Material_Connection (avoid the one with r) into the Process Flowsheet Window, and click the blue arrow of a source (e.g., feed); move over to the inlet blue arrow for the column, and left-click. The stream is labeled S1—you can rename if you want. (If you do not see a label, click the feed arrow and drag it away from the column to make room for a label.) Repeat for column outlet and product arrow. This stream is labeled S2. (Note for Aspen Plus users: In Aspen Plus we would click the Next button; it would tell us that connections were complete and would then lead us through the necessary steps. Aspen Chromatography does not have this feature.)

Column Operating Conditions

7. Set up column operating conditions. Double-left-click the column. This gives a box labeled Configure Block/Stream Column. You should see your two components listed in the box for Adsorbed Components. For now, keep the UDS1 discretization scheme, but change the number of nodes to 50. (Aspen Chromatography has a number of integration schemes that can be used for more complex systems or longer columns, but they are not required for this lab. The important issue of accuracy of numerical integration is explored in detail in Lab AC2.)

a. Click the Material balance tab. Select Convection with constant dispersion. The box for trace liquid assumption should be checked.

b. In the Kinetic Model tab, select Linear Lumped Resistance in the menu for Kinetic Model Assumption. The fructose-dextran T6 data we have uses (c – c*) as the driving force; thus choose fluid in the menu for a lumped resistance film model. For mass transfer coefficient, select constant.

c. In the Isotherm tab, for Isotherm Form Assumed, select linear. For Loading Basis, select Volume base, g/L.

d. In the Energy Balance tab, check Isothermal. Change Global Process Temperature to 30 C.

8. Click Specify button. This opens an imposing table where you specify column dimensions, isotherms, and so forth. It lists fructose and dextran T6 because in step 3 you told it to do so. Use the following values initially: L = Hb = 25 cm, column diameter Db = 2.0 cm, external porosity Ei = 0.4, particle porosity Ep = 0.0, dispersion coefficients Ez = 0.15 for both components. Mass transfer coefficient MTC = 5.52 min^–1 (fructose) and = 2.84 min^–1 (dextran T6). Isotherm coefficients: Aspen uses formula for linear isotherm: q = (IP1) c + IP2. Set IP2 = 0.0 for both components. Adsorbent used was silica gel, and solvent was water. (This information is not entered into Aspen when a template is used.) For fructose IP1 = 0.69, and for dextran T6, IP1 = 0.23. (Units on q and c are g/volume solid and g/volume fluid.) Hit Enter, and close the window (click X).

9. Click the button for Presets/Initials. For an initially clean column (which is what we want), all values should be zero. If they aren’t, insert 0.0 values, hit Enter, and close the window.

10. Click the Initialize button in the Configure Block/Stream column window. This makes all concentrations in column proper values. Close the window.

Feed Conditions

11. To set feed concentrations and flow rates, double-click the feed arrow. This opens a window labeled Configure Block/Stream Feed. For Feed material specification, select Component Concentrations in menu. Then, click the Specify button. Use a feed concentration of 50 g/L for both components. Set pressure at 2 bar (this has little effect). Flow rate of 20.0 cm³ /min is reasonable. (Note: You have to change units in the menu to the right of the number. Change units first, and then enter desired value.) Leave default values for reference concentrations. Hit Enter. Check that your values are correct, close the window, and close the Configure block/stream feed window.

12. Do not touch product stream—specifying something here will overspecify the system.

Integration Details

13. Set integration step size: Go to Run in the toolbar. In the Run menu click Solver Options, which opens Solver Options window. In the Integrator tab, pick Implicit Euler, and under Step Size click Fixed. Typically use a step size that is approximately (run time)/200. Try 0.025 as a first try. For now, ignore other tabs. Click OK.

Setting Up Plots

14. Set up plots. Left-click and then right-click name of your product stream. In menu that opens go to Forms, and click All Variables. This opens an All Variables table for this product stream. We will use this for dragging variables. Click on the white background in the Process Flowsheet Window (this wakes up the toolbar), and in the toolbar click the icon of a star on top of a square donut (if you place your cursor over icon, it says New Form). In the New Flowsheet Form window name plot (e.g., Chromatography1). Click the button for plot. Click OK. This opens a window showing start of a plot. Scroll down in All Variables table until you find Process_in.C(fructose). Drag this variable (you probably have to click it twice) to y axis. Do this for Process_In.C(“dextran T6”) as well. Double-click plot white space to open a window, PfsPlot 25.1 Control Properties. ClickAxisMap tab, and click all in one. Then click OK. This puts the two concentrations on same scale. (Aspen has a tendency to use different ranges if there are two scales, which makes comparisons rather difficult.) Close the All Variables table.

Setup of Breakthrough Run

15. Set up a breakthrough run. Go to Run on the toolbar, and click Run Options in the menu. In the Simulation Control section of the Run Options window, click Pause At. Try 10 minutes. Click OK. Note that your plot now has the x axis set for 10 minutes.

16. Initialize. In the center of the toolbar in the window, choose Initialization (it probably says Dynamic). (This is not strictly necessary, but it is good practice because it allows you to use the Rewind button later.) Click the Play button (a small dark arrow immediately to the right of the menu that reads Initialization). Click OK in the Run complete window after it runs. Run is initialized.

17. Run. Return to the window and select Dynamic. Click the Play button. After it runs, click OK. Right-click on the plot. Select Zoom Full. You can print the plot if you want. Right-click on the plot again. In the menu select, Show as history. This gives a table of both concentrations. This table can be cut and pasted into Excel if further manipulation of numbers is desired. To get back to the plot, right-click history table and select Show table as plot. It is better to not close the plot—we will reuse it. If you minimize it, you can find it under Window. Note: If you close the plot (or close and later reopen the entire file), go to the All Items box in Exploring Simulation, and click the word flowsheet. The plot will be next to an icon that looks like a square donut and will be listed by name in the Contents box. Double-click the name to recover your plot.

18. Pulse input of 1.0 minute. Start with a clean column. If you initialized, then you can simply restart to initial state (this is like a rewind button on a VCR—the fourth button over from Menu in the toolbar). To check that the column is clean, double-click the column, then click the Results button. All concentrations and solid loading values should be zero. If they are not zero, input zero values, and click the Initialize button. Close the windows. There are a number of ways to add a pulse. One easy way is as follows: First, go to Run in the toolbar, and click Run Options. Select Pause At, and insert your pulse length (1.0 minute) and click OK. Initialize the simulation again (using the menu in the center of the toolbar). Click the run button and click OK. Select Dynamic, and click the Start button. (Since a plot was already drawn, you will get one automatically.) Run for this pulse is very short. We have input pulse and now must develop it with pure solvent. Double-click the feed, click Specify, set concentrations to zero (the template, since it is for a dilute system, “knows” there is solvent present), hit Enter, and close the windows. (If you cannot find concentrations, make sure you are in the feed table, not the column table.) Go back to Run (toolbar), click Run Options, and change Pause At time to desired run time (10 minutes will work). Click OK. Do not initialize because we want the pulse to remain in the column. The menu on the toolbar should read Dynamic. Click the Run button. When the run is finished, click OK, and look at the plot and history.

19. When you look at the plot, it will probably appear to be a series of connected straight lines instead of a smooth curve. We can fix this by using more points. Click Rewind to get a clean column. Go to Run (toolbar) and then Run Options. Change Communication to 0.1 minute. Click OK. Follow the procedure for running pulse (input feed for 1 minute [use Pause At] and Run. Then set feed concentration to zero, set Pause At to 10 minutes, and Run.) Look at your plot. It should be smooth curves. Print this plot and label it. Note: Communication sets number of points that are plotted but does not affect integration. Thus you can keep communication at 0.1 minutes for remaining runs. You can also obtain a useful report by right-clicking the column and selecting Forms, then Chromatography Report.

20. The two peaks are not completely separated. There are a number of ways they can be separated more completely, such as by doubling the value of L to L = 50 cm. Hit Rewind, change L in the Column Specify table, hit Enter, close the twindows and rerun 1-minute pulse input. When you run pure solvent, a pause time slightly greater than 10 minutes is needed, since doubling the column length will double the time for material to exit. Do this run and look at the result. Separation is better but still not complete. A more complete separation is done in Lab AC2.

21. Save your file (remember the file name), and exit Aspen. There is no lab report.

Lab AC2. Convergence for Linear Isotherms

Goals:

• Explore numerical convergence and accuracy of Aspen Chromatography simulator for linear isotherms.

• Continue exploration of adsorption and chromatography.

Preparation:

• Review procedures in Aspen Chromatography Lab AC1.

• Read or reread Sections 19.2, 19.7.1 and 19.7.2.

1. Open your file from Lab AC1. You need to increase the accuracy of the discretization procedure. You first increase the number of nodes with UDS1. Rerun the breakthrough curve from Lab AC1 (step 16), but use UDS1 with 200 nodes. To do this, repeat step 7 from Lab AC1. (Double-click the column, and in the Configure Block/Stream Column window, use the General tab. Change the number of nodes from 50 to 200, and then hit Enter.) The integration method should still be Implicit Euler with time step at 0.025 min. Check that preset/initials are all zero or essentially zero, and initialize in this block. Feed is 50g/L for both components, and column length is 25 cm. Then set run time for 10 minutes, initialize run, and do run. Compare to your previous result with 50 nodes. If there is significant change, 50 nodes was not enough.

2. To make comparisons quantitative, you need a metric that can be measured. One common metric for adsorption is width of mass transfer zone (MTZ) for each solute. Width of MTZ in time units, t_MTZ, is measured from c = c_initial + 0.05(c_feed – c_initial) to c = c_initial + 0.95(c_feed – c_initial). If initial concentration is zero, measure from 0.05c_feed to 0.95c_feed. (The reason for using 5% and 95% of the change is that with experiments it is very difficult to tell when one is exactly at c_initial or at c_feed.) Calculate MTZ widths for each component separately for 25 cm columns with both 50 and 200 nodes. Save results, as they will be useful in step 8. Note: Graphs are not accurate enough—use history (right-click the plot and select Show as history) for calculation of t_MTZ.

3. Try UDS1 with 400 nodes (repeat all parts of step 2). Calculate t_MTZ values and compare to previous runs. Note that with 400 nodes, many steps take a longer time.

4. Change to either BUDS or QDS integration schemes with 50 nodes. Integration is still Implicit Euler with a time step of 0.025. (Change the number of nodes [no need to hit Enter], and then change to BUDS or QDS using the menu. Hit Enter [probably not necessary], check your presets/initials and change if necessary, and initialize with button in Configure Block/Stream column menu. Then initialize run using the Initialization command in the menu bar window. If the plot has gone blank, initialization is not required.) Run (use dynamic) and compare qualitatively. Both BUDS and QDS work pretty well on this linear problem. Calculate t_MTZ for both components and compare to previous values.

5. Repeat breakthrough runs for L = 50 cm and 100 cm, but using BUDS or QDS with 100 nodes and integration time step of 0.025. Remember to increase your Pause At time in the Run Options window. To see the entire plot, left-click the plot and click Zoom Full. Calculate t_MTZ for both components for each run. Theory says that widths should be proportional to L^1/2. Note: BUDs and QDS are great for linear isotherms but often have convergence and/or oscillation problems with nonlinear isotherms. Thus we may be forced to use UDS1 or a similar approach.

6. Runs with UDS1 with 50 nodes are not accurate enough and will not agree with theory. Try running UDS1 with 50 nodes for 50 and 100 cm lengths to see how inaccurate the results are. Plot your widths for 25 cm (from step 3), 50 cm and 100 cm (for each component separately) vs. L^1/2. Do they agree with theory?

7. Set the number of nodes to 200 and run lengths of 50 and 100 cm (you have 25 cm results from step 3) with UDS1. Plot your widths (for each component separately) vs. L^1/2. Do they agree with theory?

8. a. Repeat conditions for Lab AC1, steps 8 and 11 but using BUDS with 50 nodes. Do a breakthrough run until the column is saturated (exit fluid is at feed concentration—a pause time of 10 minutes works). Then set feed concentrations to zero, do not initialize, set pause time at 20 minutes, and continue the run until everything exits. This second part is an elution run. The entire process can be thought of as putting in a very big pulse. Compare your breakthrough and elution curves. Do this by printing the plot and cutting it in half vertically, then see if you can superimpose the curves (try different ways to do this).

b. Repeat run 8a but with dispersion coefficients Ez = 0.0. Superimpose the curves.

9. Return to standard conditions (Lab AC1, steps 8 and 11), but increase feed concentrations to 500 g/liter. Run a breakthrough experiment followed by elution. Compare this run to the run from 8a. Calculate c_out/c_feed from history and compare for the two runs.

10. Save your file, and exit Aspen Chromatography.

Reflect:

1. What have you learned about running Aspen Chromatography?

2. What have you learned about adsorption?

3. Are there additional runs that will help your current understanding?

Turn in:

Your instructor may ask you to turn in your values of MTZ widths for different runs.

Lab AC3. Convergence for Nonlinear Isotherms

This lab explores numerical convergence and accuracy of the simulator for nonlinear isotherms.

Goals:

• Explore numerical convergence and accuracy of Aspen Chromatography for nonlinear isotherms.

• Continue exploration of adsorption and chromatography.

Preparation:

• Review procedures in Aspen Chromatography Labs AC1 and AC2.

• Read or reread Sections 19.4 and 19.8.

Start Up

1. If you saved your file from linear runs in Lab AC2, open that file. If not, you need to repeat steps 1 to 14 from Lab AC1. Although this takes time, the practice is probably useful.

Problem Statement

2. Difficult to converge nonlinear isotherm. This problem pushed the numerical capabilities of older versions of Aspen Chromatography, but V8.8 has improved integration capabilities. Separation of enantiomers of 1,1’-bi-2-naphtol is studied (Pais et al., 1997). Adsorbent used is 3,5-dinitrobenzoyl phenylglycine bonded silica gel, desorbent is heptane-isopropanol (72:28), and operation temperature is 25°C. Average MW of solvent is 82.77.

3. Double click on the column to obtain the Configure Block/Stream column window. In the General tab select UDS1 from the PDE Discretization Method menu and the Number of Elements is 50. Hit Enter. In the Material Balance tab select Convection with Estimated Dispersion from the menu for the Material Balance Assumption, and check the box for trace liquid assumption. In the Kinetic Model tab select Linear LumpedResistance from the menu for Kinetic Model Assumption and in the menu for Lumped Resistance Film Model select Fluid. The Mass Transfer/Film Coefficient is Constant. In the Isotherm tab choose Dual-site Langmuir in the menu for Isotherm Form Assumed. For Loading Basis choose Volume Base g/l. In the Energy Balance tab check the box for Isothermal Operation and pick a Global Process Temperature of 30.00 C. Hit Enter.

4. Click the Specify button. Column length (Hb) is 21.0 cm and internal diameter of packed section (Db) is 2.6 cm. Ei = 0.4, Ep = 0.0. Diameter of particles is 32 microns (radius Rp = 16µm = 0.0016 cm). Use an SFac =1.0. Fluid density RHOI = 0.713 g/ml, and viscosity of fluid MUI is 0.876 cp. Note that a place to input values for dispersion coefficients no longer appears in this table. The mass transfer coefficients MTC for both components is 0.5 s^–1.

5. The isotherms are fit by dual-site Langmuir model (Pais et al, 1997):

where A is the less retained component, and both adsorbent loadings and fluid concentrations are in g/liter. To see how Aspen labels isotherm variables, go to Help, then Help index, then look up isotherm tab—trace liquid, and select General Liquid Process: Isotherm Form Assumed. Click Dual-site Langmuir. Write down the formula for the dual-site Langmuir model and match the formula to isotherms given previously to determine IP values and input them in specify table for the column.

Hint: IP(1, A) or, if you did not change the name, IP(1, dextran T6) = 2.69/0.0336, not 2.69.

Input all these values in the column Specify Table. Recheck your input to be sure it is correct, hit Enter and close the table. In the Configure Block/Stream column window check the Presets/Initials. If they are not zero, make them zero, and hit Enter. Initialize in this window, hit Enter, and close the window.

6. If you have time, you can relabel components as A and B, and redraw the plot. A faster (but sloppy) approach is to leave the labels you have and use dextran as A and fructose as B.

7. Nonlinear systems are more difficult to solve and converge. Since this problem is stiff, you need to adjust the parameters in Solver Options.

Integrator tab: Use Implicit Euler method with a 0.0250 fixed step size.

Tolerances tab: Set all tolerances at 0.0001, except absolute equation tolerance should be .001.

8. Double click on the feed arrow and click on the Specify button. Flow rate is 4.0 ml/min, and pressure is 5.0 bar. For pure component A set feed to 10 g/L, and set feed concentration of B = 0.0. Hit Enter, close the Table, and close the Configure Block/Stream feed window. Set up a breakthough run with pause at 70 minutes followed by an elution run (both feed concentrations are zero) with pause at 170 min. Then do a breakthrough run for pure B with feed of 10 g/L (set feed concentration of A = 0.0) with pause at 70 followed by an elution run (pause at 200 min). Compare the two runs and explain any differences.

9. Do a breakthrough run with both components present at 10 g/L followed by an elution run. Compare with pure breakthrough and elution runs. Try to explain what happened.

10. Try running step 9 with USD1 with 200 nodes. Compare to results of step 9.

11. Try repeating step 9 using BUDS with 50 elements. Note that there is an obvious oscillation in breakthrough curve and a less obvious irregular bump in elution curve. These phenomena are caused by numerical instabilities and do not represent physical phenomena.

12. Try step 9 again with OSPRE with 10 elements. Then repeat with 20 elements. Which advanced PDE discretization method appeared to work best on this problem?

13. Repeat step 6 for only component B using OSPRE with 20 elements. Calculate Δt_MTZ for OSPRE runs for both breakthrough and elution.

14. Increase column length to 42.0 cm. Repeat step 13 for only component B (at 10.0 g/L), with OSPRE method with 20 elements. Calculate Δt_MTZ values for breakthough and elution.

15. Compare Δt_MTZ values for steps 13 and 14. Do these results agree with what you expect? Explain.

16. Save your file and exit Aspen.

Note: If you have convergence problems, try using Gear instead of implicit Euler.

Turn in:

Your instructor may ask you to turn in your values of widths of MTZs for steps 13 and 14 and your theoretical predictions for step 15.

Lab AC4. Cycle Organizer

This lab explores developing repeated chromatographic pulses with Cycle Organizer.

Goals:

• Explore use of Cycle Organizer in Aspen Chromatography simulator.

• Continue exploration of chromatography for preparative purposes.

Preparation:

• Review procedures in Aspen Chromatography Labs AC1, AC2, and AC3.

• Read or reread sections 19.2.3 and 19.7.3.

Start-up

1. You can either start with a blank template or copy the file used for separating dextran and fructose. If you start from a blank template, set up a system with dextran and fructose. All models used should be reversible. Use Lab AC1 in this chapter as a guide to building or rebuilding process. If you use your existing file, delete feed, product, and both streams, and then rebuild with reversible models. Use models chrom_r_feed, chrom_r_product, and chrom_r_Material_Connection. Rename the feed stream as feed and the product stream as product. You also need to delete your plot and develop another one (follow step 14 in Lab AC1) using appropriate concentrations from the name of your product stream. (The old plot won’t work because it uses names of variables that no longer exist in flow sheet.) Name the plot chromatography4 to keep it separate from other plots. In the All Variables table find Process_r_in.C(“fructose”). Drag this variable (you probably have to click it twice) to the y axis. Do this for Process_r_in.C(“dextran T6”) also.

2. Double-click the column to obtain the Configure Block/Stream column window and fill in all tabs. They will be same as in Lab AC1 except use QDS with 50 nodes. If you kept your file from Lab AC3, change it back to the Lab AC1 settings.

3. Click Specify. Use these values:

If there is no place to add the dispersion coefficient Ez in the table and/or if IP4 and IP4 values are listed, you need to return to the Configure Block/Stream column window and change the settings for dispersion coefficient (Material Balance tab) and/or isotherm (Isotherm tab). Close the table. Set all presets to zero and initialize. Close the window.

4. Set up feed with concentrations of 50 g/L, flow rate of 20 ml/min (listed as cm³/min), and pressure of 5.0 bar. Click Enter, and close the box.

5. In Run Options choose 0.1 minutes for communication. In Solver Options, Integrator tab, choose Implicit Euler with fixed time step and a step size of 0.025.

6. Save your file. Then choose Initialize from the toolbar and do a dynamic run to make sure everything is working. If you do not have a Pause At time, hit the Stop button. Rewind.

Cycle Organizer

7. This finishes preliminary steps. You will now set up Cycle Organizer, which allows you to automatically repeat a number of steps (we have been manually been putting in pulses—Cycle Organizer automates the process). You will set up a series of chromatographic pulses followed by development with pure solvent. Go to Tools, and select Cycle Organizer. This gives a window and an icon.

8. In the Cycle Organizer window, click Cycle. This gives a window for options: list maximum number of cycles = 4 and hit Enter. In the Cycle Organizer toolbar click Step. You should get step 1. (If not, go to the tab next to Step and select Add/Insert Step. If you are asked where you want to put additional step compared to step 1, click Cancel. Now, step 1 should appear.) For step 1, you can name the step (optional). We will use Time driven, which is the default. Choose 1.5 minutes—this will be length of feed pulse. Hit Enter. In the tab (downward-pointing arrow) next to Step (in the Cycle Organizer toolbar) select Manipulated. This adds a blue icon labeled Variable to the toolbar. In the tab next to Variable, select Add variables. A pop-up box called Variable Selector will appear. There are a huge number of variables listed. From this list, you choose variables you want to change during the cycle. You want to change feed concentrations from 50 to 0 (pure solvent). Choose feed.Component_Concentration(“fructose”) and feed.Component_Concentration(“dextran T6”). Select them one at a time and click the Select button in the Variable Selector box (if the box disappears, click the tab next to the blue Variable icon in the toolbar and click Add variables). Then add the second variable. Concentration variables should now appear in the Cycle Organizer under step 1 for cycle 1. If not already at 50 g/L, set both values at 50 g/L. Hit Enter. Spec is Fixed. Ramped should be No, since we are not using a gradient. Next, add step 2. Go to the tab next to Step and select Add/Insert Step. When asked if insertion should be before or after, choose after. When asked if you want the new stage to be a copy of data in step 1, choose Yes. Change concentrations to zero. Go to the tab next to Step in the Cycle Organizer toolbar and click control. Click Time driven and set time to 5 minutes. Hit Enter. This completes the cycle.

9. To finish the Cycle Organizer, in the tab next to Cycle (in the Cycle Organizer toolbar) select Generate task. Every time you are done changing settings in Cycle Organizer, you have to generate task. At the bottom of the Cycle Organizer there should be a checkmark by Cycle Active. Save your file. (Details about the Cycle Organizer can be found in Help in the Cycle Organizer toolbar. You will get an “Overview of Cyclic Operation.” Read these pages when you have time outside of lab.)

Runs

10. When you get a check that says Cycle active, you are ready to run. But first, initialize run and make sure the Pause At box is checked in Run Options with a time longer than the cycle. Set the window in the main toolbar to Dynamic, do run, and print the plot. Note that you don’t see four complete cycles. That is because with each cycle 6.5 minutes long, four cycles take 26 minutes and the fourth cycle is still in the column. You can see more cycles by clicking the Run button.

IF THE PROGRAM DOES NOT WORK PROPERLY AT THIS POINT (e.g., you get only one feed pulse), DELETE CYCLE ORGANIZER AND REBUILD IT FOLLOWING DIRECTIONS STEP-BY-STEP. IF CYCLE ORGANIZER STILL DOES NOT WORK, SAVE THE PROGRAM, CLOSE ASPEN CHROMATOGRAPHY, THEN REOPEN ASPEN CHROMATOGRAPHY WITH THE SAVED PROGRAM AND SEE IF CYCLE ORGANIZER WILL WORK.

11. a. Separation within one pulse is not too good. For a better separation, you can reduce feed time and/or increase column length and/or increase time between pulses. Rewind. Try keeping the same pulse feed time and time between pulses, but increase column length to 100 cm. Initialize to zero by setting presets/initials to zero, initializing and running again for four cycles. Note: In steps 11a and 11b keep column.specify and column.initials tables and Cycle Organizer open to make sure you do not accidentally revert to a previous condition (it can happen if you rewind at the wrong time).

b. Rewind and THEN change development time. (Recover Cycle Organizer box by double-clicking the icon.) This run should have L = 100 cm, pulse time = 1.5 minutes, QDS discretization with 50 nodes, and use implicit Euler integrator with a fixed time step of 0.025. Change the time to 10 minutes in step 2. Now go to Cycle and select Generate task. Initialize the system to zero (as above) and run again for four cycles. Print plot.

12. A mass balance check can be made by double-clicking the product arrow. When a box appears, select the Accumulation button (this is accumulation of product, not accumulation in column). The variable CCompAccumFwd(“fructose”) is the accumulated amount of fructose from the last cycle. At cyclic steady state, which it should be, this number should be 1.5 grams, the amount input during one cycle. The Results button allows you to watch concentrations as the run continues to see how numbers—instantaneous concentrations exiting column—change during the run.

13. If you don’t finish, finish doing the simulations after lab.

Challenge Assignment (Optional). Develop repeating separation of a nonlinear system (1,1’-bi-2-napthol enantiomers) from Lab AC3. It is probably easiest to copy your Lab AC3 simulation. You may use either reversible or nonreversible models. First, use a 40 cm column and find operating conditions that give a reasonable separation. Do a single pulse of 0.1 minutes with feed concentrations of 10.0 g/L for both A and B. Limit elution time to 200 minutes. SMART with 50 nodes and Implicit Euler with 0.025 fixed time step worked quite well. Separation is adequate. Assume that this column length and pulse time is okay. Now decide on a time for step 2 and run the cycle four times. You can choose to use Cycle Organizer or manual operation to do six cycles. Separation between B and A from the following feed pulse should be as good as or somewhat better than separation of A and B from the same feed pulse. If it is worse, increase time for development in the second steps of your cycle. Print out results for at least two complete cycles.

Lab AC5. Flow Reversal

This lab explores use of flow reversal or counterflow operation, which is often a major advantage in adsorption operations.

Goals:

• Explore use of flow reversal in the Aspen Chromatography simulator.

• Continue exploration of adsorption.

Preparation:

• Review procedures in Aspen Chromatography Labs AC1, AC2, AC3, and AC4.

Start-up

If you have forgotten how to do a step, follow procedures in Lab AC1.

1. Go to File in the menu bar and select the template for Blank trace liquid batch flowsheet. Give Aspen a directory name (e.g., Lab AC5). Then, for the default component list, add dextran, fructose, and heavy.

2. Draw a diagram as shown in Figure 19.A1 using one chrom_r_column, two chrom_r_product, two chrom_r_feed, and one chrom_r_select (essentially a multiport valve). Rename everything, rotate product icons as needed, and connect with chrom_r_material_connection. The program requires the following connections: (a) Lines with double arrows should be connected to column and to Select. (b) Connect Select unit’s Select.Process.In.fwd port to feed in your forward flow direction (you may need to rotate Select icon). (c) Product in your reverse flow direction (probably heavy) is connected to Select unit at Process.Out.rev port. Product in forward flow direction is connected to Select unit at Process.Out.fwd port. Feed in reverse direction (probably solvent) is connected to Select unit at Process.In.rev port.

3. Double-click the column. Pick an appropriate discretization method and number of nodes for a linear system. Choose convection with constant dispersion and constant pressure and velocity. Film model assumption is fluid with linear lumped parameter and constant mass transfer coefficient. Isotherm is linear with volume base g/l. Energy balance is isothermal. List the following values in Specify:

4. Double-click forward feed, and pick total concentration and fraction from menu. Input the following values:

5. Double click reverse feed, and pick total concentration and fraction from menu. Input the following values:

6. Make a plot for forward product outlet concentrations. This can be done by using All Variables for product and dragging Process_r_In.C(“dextran”), Process_r_In.C(“fructose”), and Process_r_In.C(“heavy”) to the plot. Then, do all-in-one (see step 14 in Lab AC1).

7. Go to Feed→Forms→All Variables. Scroll down and find Process_r_out.Cr(“”). Change all three values from free to fixed. DO NOT do this for Process_r_out.C(“”). Do the same for RevFeed. Then recheck that you have changed the correct variables.

8. Go to product, double-click it, and click Specify. Make three concentrations = 0.0 and the pressure 2.0 bar. Do the same for RevProduct.

9. You should now have a green light and the word Ready at bottom of the page. If not, recheck the steps. If it still is not green, ask for help.

Runs

10. Go to Solver Options and pick an appropriate integration technique. Go to Run Options and pick an appropriate communication time. Check Pause At box at 1.5 minutes (we will input a 1.5-minute feed pulse). Initialize run. Then run pulse. Change overall concentration of feed to 0.0 (but do NOT change the individual Material fraction %), set Pause At to 101.5 minutes, and press the Run button. Watch the outlet in your plot.

11. Where is the heavy? To find it look at the history or set up a plot with a separate scale for heavy concentration (double-click the plot, go to the axis map, click one-for-each, and click OK).

12. The heavy has an initial peak and then a main, very broad peak (all at low concentrations). Initial peak occurs because with low mass transfer coefficients, part of the heavy is never adsorbed and exits very quickly. Change the heavy MTC to 10.0 1/min and run again. Now it looks more normal. This type of problem (two components that are difficult to separate plus a very slow component) is known as the general elution problem. Column length needs to be set for difficult separation, but then the slow component takes a long time to exit. Set all three MTC to 10.0 1/min for remainder of this lab.

13. Manual operation with flow reversal. You will do a forward pulse, develop fast components, and reverse flow to remove the heavy. First, you need a chromatographic plot for RevProduct. Click the plot icon, open All Variables for RevProduct, and drag the three concentration variables Process_r_In.C(“dextran”), Process_r_In.C (“fructose”), and Process_r_In.C (“heavy”) to plot. Then, do all-in-one. Leave axes separate. (Note: It is important to use correct variables. Be sure that they are listed as free.) Input a 1.0-minute pulse of feed followed by 6.5 minutes of pure solvent (set pause at 7.5 minutes). Be sure feed and reverse feed concentrations are zero In flowsheet double-click the Select block, click Specify, and set flow direction to –1. Then click the Run button. You should get a plot that shows false peaks during feed period (all Aspen Chromatography demos include this) and then real peak for the heavy coming out in reverse direction. If you do not see the heavy, you need to look at the history or set up the plot with a separate scale for heavy concentration. Click Rewind when you are ready to move ahead.

Cycle Organizer

14. First, set up Cycle Organizer without flow reversal (double-click the Select block, click Specify, and set flow direction to +1). Open Cycle Organizer. Label cycle 1 as Forward flow. Set up a cycle with a 1.0-minute feed pulse and maximum number of cycles = 10. In step 1, select the following five variables (values in parentheses are values for step 1): feed.Flowrate (20 ml/min), feed.Overall_Concentration (100 g/l), RevFeed.Flowrate (20), RevFeed.Overall_Concentration (0.0), and Select.Direction (1). The reverse conditions will essentially be ignored for cycle 1. Now step 2 should have 6.5 minutes of development with pure solvent. Add step 2 and copy information from step 1 (this way, you don’t have to find variables again). Change time to 6.5 minutes, and set feed.Overall_Concentration = 0.0 g/l. Click Generate task. When cycle is active, check column presets, initialize, and run (set pause in Run Options at 75 minutes). Look at the product plot in both all-in-one and one-for-each modes. Print results. Explain what has happened to the heavy component. Why isn’t it separating? Bring your plots to class.

15. Cycle Organizer with flow reversal. Go to Cycle Organizer and click New cycle. Copy data from the old cycle to new one. Change the title to reverse flow. Step 1 is unchanged. For step 2, reduce time to 4.5 minutes. Then add step 3 and copy information from step 2. Change Select1.direction to –1 for step 3 (both concentrations should be 0.0 and both flowrates 20.0), and change time for step 3 to 15 minutes. Click Generate task. Check that column presets are all at zero, and initialize. Set Pause At in Run Options to 100, and run. Look at both plots. Note that reverse plot contains false peaks at original feed concentrations.

Lab AC6. Ion Exchange

Goals:

• Explore ion exchange using Aspen Chromatography simulator.

• Study ion exchange behavior, which can be different than adsorption.

Preparation:

• Review procedures in Aspen Chromatography Labs AC1, AC2, AC3, and AC4.

• Read or reread Section 19.5.

Although ion exchange models must take into account electroneutrality and effect of changing total ion concentration, application of these models in Aspen Chromatography is done in a manner quite similar to trace liquid models we have used up to now. We look at monovalent-monovalent and monovalent-divalent exchange in cation exchangers.

Set-up

1. Open a new Aspen file and use a Blank trace-liquid template.

2. In All items click the plus sign for Libraries, then Chromatography and then on the plus sign for Ionx. Double-click Reversible. Select ionx_r_column model, and drag it into the flowsheet area.

3. Double-click Nonreversible, and drag ionx_feed and ionx_product systems onto the flowsheet. Connect column to feed and product using Stream Types. Use ionx_Material_Connection stream.

4. In Component list, double-click Default. Remove A and B. Add Na, H, and Mg. Click OK.

5. Double-click the column. Use UDS1 with 20 nodes. Make Na exchanged ion for initial runs. List H as counter-ion in the menu. Mg should be in the non-exchanged list. Use convection with constant dispersion and constant pressure and velocity. Choose a film model assumption of solid and a lumped parameter model. Isotherm should be mass-action. Procedures should be blank.

6. To understand terms in Aspen’s isotherm, you need to look at Help. Click Help from the Configure Block window while in the Isotherm tab. Look in the Contents until you find Ion-Exchange Process: Mass Action Equilibrium. Note: Aspen’s definition for x is adsorbed phase mole fraction, while in the textbook x is liquid-phase mole fractions. The y’s are also reversed. However, equilibrium constant K_AB has the same meaning. Variable m = 1 for monovalent-monovalent exchange and m =2 for divalent ion (Mg) in divalent-monovalent exchange.

7. Go to Specify. The bed is 50 cm long and 20 cm in diameter. External porosity (E_i) = 0.4, and internal porosity = 0.0. Use Ez values of 0.2 cm²/min for all components. Mass transfer coefficients are 10.0 1/min for all components. For a strong acid resin, use Q = c_RT = 2.0 eq/L. From Table 19-5, K_H-H = 1.0, K_Na-H = K_Na-Li/K_Na-Li =1.54, and K_Mg-H = K_Mg-Li/(K_H-Li)² =1.953. Put in appropriate values for IP2. Note: Initially, only Na will show up in Specify table. You will need to add others later when we change exchanged ions (step 12).

8. Operate with a feed rate of 5.0 L/min. Set feed component concentrations of Mg and H equal to 0.0. Use a feed concentration of 1.0 eq/L for Na. Pressure of 2.0 bar is okay.

9. Preset H concentration on resin (W) at c_RT = 2.0 eq/L and set H concentration in liquid at c_T = 1.0 eq./L. Initialize in the Configure Block window. Develop a plot with Na and H concentrations.

Runs

10. Initialize run using the toolbar. Change to Dynamic, and set your run conditions. Save your file. Then do the run and pause once concentrations line out at constant values. Print your plot. Do NOT rewind. Note: If Aspen Chromatography does not converge, change tolerances as listed in step 13.

11. You now feed the column that is in the Na form with acid (H) at 1.0 eq/liter. Change the feed conditions (Na is 0.0 and 1.0 eq/liter H). Continue the dynamic run. Pause when concentrations line out. Do NOT rewind. Print your plot. Compare with the run for step 9, and explain why they differ.

12. Next do a wash step with pure water (feed concentrations of all components are zero). Set Pause At for 5 minutes after current time. Look at the history to see how long the wash step took. Explain why this is so quick. Rewind.

13. Switch to water softening. Remove Na concentration from your plot and put in Mg concentration instead. Double-click the column. Make Mg exchangeable and remove Na from the exchangeable list. Go to Specify. Put in MTC, IP1, and IP2 values for Mg (see step 7). Feed is 0.0 eq/liter of H and 0.10 eq/liter of Mg (c_T = 0.10 eq/liter). The value of c_RT = 2.0 eq/liter is unchanged. (There is no Na involved in this operation.) To reduce run time, operate with a column length of 10.0 cm. Go to Presets/Initials and set C(H) = 0.1 eq/liter, C (Mg) = 0, W (Mg) = 0, C (Na) = 0.0, W(Na) = 0.0, and W(H) = 2.0 eq/liter.

Aspen finds this problem difficult. Use 20 nodes. Use Implicit Euler integration with a constant time step of 0.01. Change tolerances so that all are 0.0001, except absolute equation tolerance should be 0.001. Initialize run. Then do a dynamic run. If Aspen says Integrator step size is too small, click OK and try clicking on the Play button. Do this five or so times to see if Aspen will get past the problem (sometimes it does).

Print your plot. Look at Presets/Initials (before rewinding). Why is concentration of Mg on resin so much greater than concentration of Mg in feed? Do NOT rewind.

14. The next step is co-flow regeneration using acid. Do NOT rewind and do not change Presets/Initials. Use a regeneration solution that is 0.30 eq H/liter and 0.0 eq Mg/liter. Change the feed to these concentrations. If Aspen says Integrator step size is too small, click OK and try clicking on the Play button. Do this five or so times to see if Aspen will get past problem. Print your plot.

15. Repeat step 12 (rewind and start over) and try step 13 with a 0.50 eq H/liter solution. This may or may not converge.

16. Actual water softening problems have Mg equivalents in the range of less than 0.010 eq/liter, and use concentrated salt solutions for regeneration. I have not been able to get Aspen to run for this problem but have been able to do the following problem: First double-click the column and make counter-ion Na. Try an Mg feed of 0.10 eq/liter with column initially (Presets/Initials) containing Na at 0.10 eq/liter in solution and 2.0 eq/liter Na on resin. In Specify, the IP1 value for Mg should be for Mg with respect to Na = 0.825. In Solver Options set Integrator as Gear with a fixed step size of 0.01. Then, without rewinding, try regeneration with 1.0 eq/liter of Na and 0 eq/L Mg. If Aspen says Integrator step size is too small, click OK and try clicking on the Play button. Take a look at your results and explain what happened.

Aspen Chromatography Lab AC7. SMB and TMB

This lab explores use of simulated moving beds (SMB) and true moving beds (TMB) for large-scale chromatographic separations.

Goals:

• Explore separation with SMB and TMB in Aspen Chromatography simulator.

• Continue exploration of adsorption and chromatography.

Preparation:

• Review procedures in Aspen Chromatography Labs AC1, AC2, AC3, and AC4.

• Read or reread Section 19.3.3. Do preliminary work listed below. Answers to preliminary work are used throughout this lab.

Introduction:

Both SMB and TMB use a number of columns hooked together. Since both solid and fluid move in a TMB, it will eventually reach a steady state. In addition, TMBs can be solved directly for steady state. This makes a TMB a convenient first calculation when doing SMB systems; however, TMB systems are not commercial, and TMB calculations almost always overstate separation achieved in an SMB, particularly when there are a small number of columns per zone. TMB local equilibrium calculation for linear and nonlinear systems is used to estimate flow rates in flow optimizer. The SMB is quite a complicated system, but since Aspen has made the interface user friendly, simulating SMBs with Aspen Chromatography is not difficult; however, because there is a recycle stream, it can take a long time to come to cyclic steady state.

Preliminary Work: Solve Problem 19.D34

Start-up

1. Normally, you would open Aspen Chromatography, and in File go to Templates. The Normal choices are Trace liquid SMB flowsheet and Blank trace liquid SMB flowsheet. You would use Trace liquid SMB flowsheet as it is easier, give Aspen a name for a directory when asked, and record the name. You would then see a figure that looks like Figure 19-A2. Double-clicking on one of the columns would give you the Configure Block/Stream SMB page shown in Figure 19-A3. You would fill this out and then click the Specify button, which allows you to specify column dimensions and mass transfer and isotherm coefficients. At the time this book is written, the Specify button is not working. If Specify is working, these instructions will work in the Normal template. My suggestion is try the normal procedure, particularly if you have an Aspen Chromatography version earlier or later than versions 8.4 and 8.8. If normal procedure does not work, use the workaround procedure.

Workaround Procedure

2. Instead of going to Templates after opening Aspen Chromatography, go to File (in the menu bar), select Demonstrations, and then select Amino Acid Separation Using SMB. Do not select demo of a Fully defined SMB flowsheet. Click Open. A figure similar to Figure 19A2 will appear. We will now do the same steps we would normally do, except we will be changing parameters in the demo. Assistance of Dr. Nicholas Soepriatna was invaluable in developing this workaround procedure.

3. Input all appropriate values into Aspen Chromatography (start by setting up the component list by clicking on Default, removing Phenylalanine and Tryptophan [in Normal template remove A and B], and adding dextran and fructose. Click OK). Then double-click any column in Aspen Chromatography’s SMB icon (Figure 19-A2) and fill out the page shown in Figure 19-A3: set Adsorbent assumption to Fixed (SMB), set Number of columns in unit to 8 (and click Enter), set Column uniformity to Identical, and set Internal configuration to Carousel. For Port Position & Distribution, put S1-in on initial port 1 and S2-in on initial port 5, and put S3-out on initial port 3 and S4-out on initial port 7. Set Port Switch Control to Synchronous, Valve assumption to Sequential Valve, and Port switching interval to the input value for t_sw you calculated in preliminary work. Set the Recycle assumption to Closed Recycle, and input the recycle volumetric flow rate calculated in preliminary work.

4. Go to Forms in the upper left of the Configure Block/Stream SMB window (Figure 19-A3), and look at the menu. Click Column. Use the tabs to set your operating conditions. Try OSPRE PDE discretization method with 15 elements used in the demo. Other conditions are listed in Preliminary Work (note that many items, such as isotherm, have to be changed).

5. Click Specify. This opens the normal Column Specify table; however, you are now specifying each of eight identical columns in SMB. Input the values listed in Preliminary Work. Close the table. In the Configure Block/Stream SMB window, click Presets/Initials and check they are all zero. Then click Initialize in this window. Close window.

6. Double-click Desorbent arrow in SMB icon (Figure 19-A2). Click Specify and input the flow rate of desorbent you calculated in preliminary work, component concentrations = 0.0, pressure of 2.0 bar. Do not change Cref. Double-click Feed arrow and input values. For Raffinate and Extract products, input your calculated flow rates and pressure of 2.0 bar.

7. Delete Extract and Raffinate plots by clicking on Flowsheet (in Explore All Items), then left-click the plot icon, and right-click to find Delete on the menu. (Since variables no longer exist, you need new plots.) Create plots for extract and raffinate products (follow step 14 of Lab AC1). Use variables Process_In.C(“dextran”) and Process_In.C(“fructose”).

8. In Solver Options use implicit Euler with a fixed step size of 0.25. Change Pause At in Run Options to 200 min.

9. Initialize run, and then do run. During run, you can watch plots, or by right-clicking on a column, select Forms and then Results, and watch the values. If you double-click the column in the Configure Block/Stream SMB page, you can watch switching of ports. If you double-click either the Extract or Raffinate product arrow and select the Accumulation button, you can watch average purities over the last cycle, which is a convenient way to see if things are changing. However, runs may take longer if you have any of these pages open.

10. Look at your results both at Zoom Full and with various zooms on the time axis. You can also look at total concentration chromatograms (right-click the product of interest, go to Forms, and select Chromatogram). If you double-click the product arrow, you can look at Results, which are instantaneous values. The Accumulation button tends to be more useful: scroll down to CCompFraction, which gives the average purities over the last cycle. How would you go from the graphs to these results by a hand calculation?

If you are getting very little separation or the separation is reversed (more fructose in raffinate product), you have done something wrong. A common error is incorrect solution of preliminary work. Carefully check your work to find any errors.

11. Now run SMB with four columns per zone (16 total). Keep the amount of adsorbent constant, which requires reducing column length to 30 cm, cutting the switch time in half so that u_port is unchanged, changing the number of columns to 16, and adjusting locations of input and output streams. Once you have changed column lengths, check Presets/Initials, and set to zero if necessary. Initialize with the button immediately below Presets/Initials, and do an initialization run. Then run SMB until you appear to be at cyclic steady state. Look at plots, and click the Accumulation button for extract and for raffinate, and compare to run with two columns per zone. If you have convergence difficulties, reduce tolerances and use Gear instead of Implicit Euler.

12. Explore the TMB option by double-clicking on a column and selecting TMB in the menu for Adsorbent Assumption. It takes some time to switch from SMB to TMB. Change conditions back to those of step 9 (eight columns, each 60 cm, same switch time as previously). You will need to reposition ports (use initial ports); the figure will redraw. When ready, initialize run. Then, do a steady-state, not dynamic, run (TMB is a steady-state device). Why is the steady-state result produced so quickly compared to dynamic runs? Look at outlet extract and raffinate purities (note that the Results and Accumulation buttons give identical results), and compare them to your SMB run. Which is better? Why do we operate SMB systems instead of TMB systems in practice?

Aspen Chromatography Lab AC8. Thermal Systems

This lab explores systems with temperature changes and energy balances.

Goals:

• Use the Aspen Chromatography simulator to explore separation with temperature changes.

• Continue exploration of adsorption.

Preparation:

• Review procedures in Aspen Chromatography Labs AC1, AC2, AC3, and AC4.

• Read or reread Section 19.3.1 and 19.6.4.

Introduction:

To use systems with temperature changes, you need to set up an Aspen Properties file, connect it to Aspen Chromatography, and then do all your work in Aspen Chromatography.

1. Go to Start→Programs→Aspen Tech→Aspen Engineering Suite→Process Modeling→Aspen Properties, and then open Aspen Properties Desktop. (Getting to Aspen Properties and the exact name of the Aspen Properties User Interface may be somewhat different on different systems.)

2. Click New and then choose Blank Case.

3. Click Components Specifications in the All Items box on the left-hand side. In the selection, type in compounds as you would in Aspen Plus. The solute is toluene and the solvent is n-heptane. Since we will not use a template, you need to add both compounds.

4. Now, click the blue Next button. Input the appropriate VLE method—use Peng Robinson. Click Next again, then OK as needed.

5. In File, go to Save As. Then give your file a name (which you need to remember—I used L8therprop.aprop). Pick the place to save it where you also want to save your Aspen Chromatography file. Save the Aspen Properties file, and then close Aspen Properties.

6. Now open Aspen Chromatography using usual method. Do NOT use a template. Double-click the Component List, and double-click Default. Asked if you want to configure now, say Yes. Then click Import Aspen Properties file. When asked if want to initialize, click Yes. Now browse in the list and find your Aspen Properties file and click OK. Eventually you should get a pop-up that says Physical Properties Configuration: you want to see the green light under Properties status. Click OK. You have toluene adsorbing from n-heptane, so highlight these and hit the arrow to select them. Click OK.

7. Build your system (look at the instructions in Lab AC1 if you forgot the steps). Use chrom_r_column, then double-click Nonreversible (in All Items), and drag and drop chrom_feed and chrom_product. Then double-click Stream Types (in All Items), drag and drop chrom_Material_Connection, and connect the feed to the top of the column and bottom of the column to the product.

8. Save your Aspen Chromatography file.

9. Double-click the column. The Configure Block/Stream window for the column will appear.

General tab: Remove n-heptane from the list of adsorbed components by highlighting it and using the arrow to move it. UDS1 with 100 nodes is a good start.

Material Balance tab: In menu, pick Convection with constant dispersion. Click the Trace Liquid Assumption box, and leave the others blank.

Kinetic Model tab: In menus, pick Linear lumped resistance, Fluid and Constant.

Isotherm tab: In menus for Isotherm Form Assumed pick Langmuir_TD and for Loading Basis pick Volume Base g/l.

Energy Balance tab: Uncheck Isothermal Operation box, pick None for Heat of adsorption, No for Heat of Adsorbed Phase, and Adiabatic for External Heat Transfer.

Presets/Initials button: List initial concentration of n-heptane (the solvent), which is the same as the density of n-heptane (684 kg/m³). (When you used a template, you did not need to do this.) Also, list the initial column and solid temperatures (both 303.15 K). C of toluene and W (loading of toluene) should both be 0.0. Press Enter. Close the Presets/Initials window. Click Initialize.

10. You want to use Aspen Chromatography to simulate thermal adsorption of toluene from n-heptane by silica gel in the linear concentration range. Matz and Knaebel (1991) found the following equilibrium values in the linear range: q = 17.46x at 0°C, q = 7.77x at 30°C, q = 5.16x at 35°C, and q = 1.23x at 80°C; q and x are in g solute/g adsorbent and g solute/g fluid (mass fraction), respectively. Since Aspen does not support a linear equilibrium model with temperature dependence, use the Langmuir TD model, which does support temperature dependence. For the Langmuir isotherm with temperature dependence (TD), Aspen Chromatography uses the form

where T is in K. Although Aspen Chromatography supports loading bases of g/liter and g/g adsorbent, the g/liter loading base appears to work better. This means you need to convert the toluene data into terms for IP1, IP2, and IP3 to fit the Matz and Knaebel data at the operating temperatures of 30°C (303.15 K) and 80°C (353.15 K) with g/liter fluid concentrations. You also want the denominator to ∼ 1.0. This last requirement is achieved by making IP2 very small (e.g., 1.0 × 10^–9). Set IP2 = 1.0 × 10^–9, set x = 0.001 mass fraction, write Eq. (19-A3) for T = 303.15 K and for T = 353.15 K, and set the corresponding values of q to 0.00777 and 0.00123. These values are for g/g adsorbent loading base with fluid in mass fractions. If you multiply q by ρ_adsorbent (2100 g/liter) and multiply x by ρ_solvent (0.684 g/liter), you have converted to the g/liter loading base. You can now solve the resulting two equations (one at each temperature) for values for IP1 and IP3. The values are listed in step 11, and the details are left as an exercise.

11. Click the Specify button. In the Specify Table use these values:

Click Enter, recheck your numbers and the units, and close the Specify Table.

If the IP locations are not available, in the Configure Block/Stream (Name of column block) click the Isotherm tab, select Langmuir_TD in menu and loading basis: Volume Base g/l. Then reopen the Specify Table, and input the IP values. Click Enter, and close the table.

12. Save the Aspen file. Finally, you are done with the extra setup work for the thermal system! Question: How does Aspen obtain values such as fluid heat capacity, which we are not asked to input?

The remainder of this lab is (fortunately) short. If you don’t finish, run it after lab.

13. Use UDS1 with 100 nodes. Now set up the integration with Solver Options. In the Integrator tab, pick Implicit Euler, Step size is Fixed with a Step size of 0.05. Click OK.

14. You will now do a breakthrough curve. Double-click the feed arrow, and in the menu for Feed material specification select Component Concentrations. Then click Specify. Set the feed Flowrate as 16 cm³/min. Use a component concentration for toluene of 0.684 g/liter (this is low to be in the linear range). Component concentration of n-heptane is n-heptane density (684 kg/m³) minus toluene component concentration; the result is 683.316 kg/m³. Pressure is 3.0 atm. Feed temperature is 353.15 K. Click Enter and close the Table. Double-click the column and then on the Presets button, and set the concentration of toluene and the loading of toluene to zero. Temperature should be at the desired initial value 303.15. Heptane concentration should not change (684 kg/m³). Click the Initialize button in the Configure Block/Stream window. Close the window. Do an Initialization run from the menu in the toolbar. Click OK.

Create a plot (check out Lab AC1 if you forgot how). Use toluene concentration or x value and temperature on two separate scales. (Do not include heptane—it will drown out the toluene.)

Click Dynamic in the menu in the toolbar. Set a run time of 75 minutes. Run the system, and print the plot.

15. Rewind, check Presets/Initials, change the feed temperature to 303.15 K, and repeat the breakthrough run. Use a run time of 250 minutes. Run the system, and print the plot. Compare the result with the run in step 14. Do NOT rewind or initialize after this run.

16. You now want to develop this saturated column co-flow using hot pure solvent. Do NOT initialize. Increase the feed temperature to 80°C (353.15 K) and make the toluene concentration 0.0 and the n-heptane concentration 684. Click the Run button. It will run until you stop it (e.g., with the Pause button). Print the plot. Explain the results.

You can also print out a report. If a box for Simulation Messages is not showing at the bottom of the screen, go to View in the Toolbar and click Messages. Right-click in the space for Simulation Messages, and select Clear from the menu. (The purpose of this is to have a clean space for the report, which Aspen prints here.) In the toolbar go to Tools→Report, and select Global Material Balance from the menu. You may also want to go to Tools→Report, and select Open Reports to see what else is available.

17. Do a breakthrough run with a toluene concentration of 0.684 g/liter and feed temperature of 353.15K. Run time is 75 minutes. Without rewinding, change the feed to a toluene concentration of 0 and a feed temperature of 303.15 K. Set the run time to 350 minutes (complete development may be slow). Print and explain the results.

18. If you have time, try other runs such as development at other temperatures.

Your instructor may assign the following Lab assignment:

a. Show that fitting the Matz and Knaebel (1991) equilibrium data gives the values of IP1 and IP3 used.

b. Repeat steps 15 and 16, and step 17, but with

b1. UDS1 with 50 nodes.

b2. UDS1 with 200 nodes.

b3. QDS with 50 nodes, and integrate with Gear with a time step of 0.05.

Turn in your plots (UDS1 with 50, 100, and 200 nodes; and QDS/Gear with 50 nodes), and conclude what the appropriate settings are to run this system.

Note: In comparing the plots, watch the toluene scale—it may change from graph to graph, which will change the relative vertical location of the temperature and concentration curves. The most accurate way to compare results is to use the history.

c. Use the sketch of a solute movement diagram to help briefly explain the results qualitatively for steps 15 and 16 and step 17.

Answer: Where does Aspen gets fluid values? From the Aspen Properties file.

Epilogue: Aspen Chromatography Simulator

In these labs we looked individually at different simulations that can be done with Aspen Chromatography. Hopefully, it is obvious that different simulations can be combined. For example, in Lab AC5 (flow reversal) we used the Cycle Organizer (Lab AC4) to automate repeated cycles. Flow reversal is also commonly used with thermal regeneration of columns (Lab AC8), and we can combine this with the Cycle Organizer. Flow reversal and the Cycle Organizer can also be used with ion exchange (Lab AC8). Although we ran the SMB (Lab AC7) with linear isotherms, we could also use nonlinear isotherms (Lab AC3). SMBs can also be run with temperature differences, but the method we used for SMBs does not support this application; however, a non-isothermal SMB can be built with the Cycle Organizer.

The Aspen Chromatography simulator was designed for liquid systems that are practically incompressible. This means the fluid velocity in each column section is not a function of axial distance. Simulations of very dilute gas systems at constant temperature and pressure are also possible, since fluid velocity is constant. Gas systems that are not isothermal or not isobaric or that are more concentrated cannot be simulated with Aspen Chromatography because it does not have the capability of simulating systems with a velocity that depends on axial distance. Aspen Adsorption can simulate these systems, including pressure swing adsorption; however, Aspen Adsorption is beyond the scope of this introductory chapter.