Detailed Examination of Energy Flows and Entropy Generation in Low

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Thermodynamics, Transport, and Fluid Mechanics

Detailed Examination of Energy Flows and Entropy Generation in Low Pressure Binary Distillation Columns John Paul O’Connell Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04832 • Publication Date (Web): 20 Jul 2018 Downloaded from http://pubs.acs.org on July 22, 2018

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Industrial & Engineering Chemistry Research

Detailed Examination of Energy Flows and Entropy Generation in Low Pressure Binary Distillation Columns John P. O’Connell* University of Virginia, Charlottesville, VA 22904 California Polytechnic State University, San Luis Obispo, CA 93401 Abstract Variations of the heat flows and entropy generation for binary distillation systems are investigated with varying feed composition, feed condition, and feed stage for a fixed number of stages and product purities, along with the effects of imposed irreversibilities. For ambient feed and products, both full system and column-only results were obtained using AspenPlus V9 for the systems benzene-toluene and methanol-water at one bar pressure. An optimum feed stage exists at the Maximum Driving Force composition. Reboiler heat input is strongly correlated with reflux rate and with feed enthalpy. While system heat input is linearly correlated with entropy generation, the relation of reboiler heat to entropy generation depends on the selected material basis. Full system energy input and entropy generation are minimized for cold feed, though they are maximized when considering only the column. Entropy generation for heat transfer over a 5K temperature difference is equivalent to tray efficiencies reduced to 60%. Introduction Binary distillation systems have been thoroughly studied for many years, with a variety of approaches to thermodynamic efficiencies1-6. Chapter 10 of Seider, et al.6 presents a thorough treatment of Second Law Analyses for many chemical processes, with a focus on lost work and generalized efficiency. The present study is less ambitious, but complementary to that work, by elucidating in detail the energy requirements and thermodynamic irreversibility differences between a column only and a full system for various column feed conditions, heat transfer temperature differences, and tray efficiencies, as measured by entropy generation. It extends the analysis of Agrawal and Herron2 on optimal feed conditions for ideal binary columns to also treat whole systems. Finally, connections are made with the Maximum Driving Force concept of Gani and Bek-Peteresen7. Two sets of boundaries around the units were chosen to find the effects of different feed preparations on the whole system, as well as on only the column. Process simulations were done for the essentially ideal solution of benzene with toluene and the strongly nonideal system of methanol with water at one bar. The properties of the mixtures and calculations for heaters/coolers and a Radfrac column were found using AspenPlus V9. The symbols of the fixed and variable quantities are listed in the Nomenclature of the Supporting Information.

ACS Paragon Plus Environment

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Theory As is well known, there are two principal thermodynamic balance relationships for an open system operating in steady state. q

∑

w

Q& m +

m = heat modes

∑

n = work modes

W&n +

p

∑

h j n& j = 0

(1)

j = ports

p Q& m s j n& j + S& gen = 0 + ∑ ∑ T m = heat modes bm j = ports q

(2)

where heat transfers across the system boundaries, Q& m , through various modes, m, with the temperature of the heat on the outside of the system of Tbm, and work effects, W& n , are transferred through modes n. The material streams flow through ports, j, at molar flow rates, n& j , and must obey material balances. The sign convention is for heat, work, and material into the system to be positive. The stream properties of molar enthalpy, hj, and entropy, sj, are obtained from the stream conditions of temperature, Tj, pressure, Pj, and mole fractions, {x}j via property models. The value of the entropy generation rate, S& , which must not be negative, is a measure of gen

process irreversibilities due to heat transferring over finite temperature differences, momentum transfer over finite pressure differences (fluid and surface friction), and mass transfer and mixing involving finite concentration differences. The effects of different processing rates can be included as well, with S& gen increasing with higher flow rates. Though not present here, de Nevers and Seader7 add irreversible mechanisms of nonequilibrium chemical reaction, electrical current rev through a resistor, and magnetic field loss to this list. If a process is reversible, S& gen =0. Entropy production in distillation columns has also been related to fluxes and driving forces through irreversible thermodynamics9,10. The approach here does not require details of the irreversible mechanism, though reduction and redistribution of S& might need to be based on gen

such analyses. Alternative expressions of the effects of irreversibilities include the rate of lost work, W&lost , and rate of exergy loss/consumption/dissipation, E& x , which are related to S&gen by the Gouy-Stodola theorem3,11

W&lost = E& x = T0 S& gen

(3)

where T0 is the temperature of the surroundings at which rejected heat cannot be utilized to produce work. This is often the value one or more of the Tbm. The general goal in designing


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processes is for W&lost and E& x , and thus S& gen , to be minimized, so that the required input energy, and therefore the output heat rejection, will be minimum. Mullins and Berry12 discuss the minimization of entropy production in distillation and find an analytic expression for the optimization of various methods for increasing the efficiency of a distillation for an idealized separation. de Nevers and Seader8 discuss the history of eq. (2) and thoroughly describe the options for such analyses, especially for systems where the desired effect involves other outcomes besides work, including absorption refrigerators or distillation columns. They also clearly distinguish between the “availability function”, which always involves differences so no complex reference states are involved, and “availability” which does require standard references states that can be complicated for chemical mixtures. de Nevers and Seader78 note that, when properly defined, the outcomes based on the quantities of eq. (3) are all essentially the same. They advocate using W& because it is more intuitive than S& and more lost

gen

convenient than E& x . However, they combine eqs. (1) and (2), and so potentially obscure the fact that two variables must be found by solving the two separate equations. Here, S&gen is preferred for the general reasons articulated by Bejan11 and Sekulic13 and those expressed by Mullins and Berry12 for modifications of distillation systems. For treatment of systems with multiple sections, such as distillation columns with trays and heat exchangers, the concept of distributing entropy generation can significantly improve efficiency9,10,14 though these may involve major equipment changes15. Also, there are various definitions of distillation column efficiency1,6; their relationship to the quantities of eq. (3) are discussed later. An advantage of using efficiency is that it is usually confined to a fixed range, such as zero to unity, while the only constraint on S&gen is that it is nonnegative. Since all of these quantities for characterizing irreversibilities are simply related, the decision of which to use becomes personal. Thermodynamic analysis chooses the boundaries of a system and then specifies the locations and transports of mass, energy, and entropy across the boundaries. The analysis here of the simple binary distillation system of Figure 1 chooses two sets of boundaries, “system”, with all units (solid line boundary) and “column”, with reboiler and condenser (dashed line boundary). The irreversibilities of the column arise from mixing on the stages in the column and heat transfer in the reboiler and condenser, while those for the system also include heat transfers in the preheater, top cooler, and bottom cooler. This division differs from the work of Benyounes, et al16, that treats extractive distillation where mixing effects are of greatest interest, and who do not include the reboiler and condenser with the column. No work effects are included here, and pressure drops within the system have been ignored. For each set of feed conditions, the process simulator evaluated all stream enthalpies and entropies, as well as the heats transferred in all units. The temperatures for heat transfer were set constant at typical conditions, but alternatives are explored, as are the impact of varying Murphree column efficiencies. If a simulation converges



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properly, eq. (1) is satisfied to within a small percentage; here, this balance was checked for every simulation, and for data transfers among spreadsheets to insure reliability. From the heat effects and stream properties, the value of S& is found from eq. (2); it must be positive. The gen

entropy generated in the whole system should be larger than for only the column, which provided another check on the reliability of the calculations and data transfers. Figure 2 shows graphically the locations of the feed and the intersections of the operating lines on McCabe-Thiele (2a: yi vs. xi) and Driving Force diagrams (2b: yi -xi vs. xi) (see below). The equilibrium line of Figure 2a was obtained from Aspen and the intersection of the operating lines at (xI, yI), which is at the optimal feed stage, was computed from eqs. (4) and (5), as given by Wankat17 with additional manipulation to obtain eq. (6) xI =

− ( q − 1)(1 − L& / V& ) x D − z F ( q − 1)( L& / V& ) − q

(4)

 L&   L&  y I =   xI +  1 −  xD  V&   V&   L&  y I − x I =  1 −  ( xD − x I )  V&  where q =

(5) (6)

L& − L& , with L& being the liquid flow (reflux rate) in the rectifying (above feed) F&

section, L& the liquid flow in the stripping (below feed) section, and V& = L& + D& the vapor flow in the rectifying section with D& the distillate (top product) rate. The value of q indicates the feed condition: q > 1 is subcooled liquid; q = 1 is saturated liquid; 0 < q < 1 is 2-phase; q = 0 is saturated vapor; and q < 0 is superheated vapor. The process simulations specified distillate composition, xD, bottoms composition, xB, feed composition, zF, the number of stages, N, the feed stage, NF, and q, with the feed rate set at 1 kmol sec-1. In the simulations, the optimum reflux, ( L& / V& ) , can be found by manual iteration opt

to meet the specified product compositions.

Then, eqs. (4) and (5) provide the precise intersection compositions, (xI, yI). Using simulations to find L& / V& and q for intersection-matching of different feed compositions at the same xD requires double manual iteration. Note that when the feed rate basis and the product purities are fixed, the product flow rates will vary with feed composition, such that when the feed mole fraction of lighter component decreases, the top product rate must decrease. This can influence the relative order of heating and reflux rates with conditions.


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The work of Agrawal and Herron2,18-20 examined the effects on column efficiencies (see below) with variable zF and q values over the range of saturated liquid to saturated vapor of ideal solutions for various relative volatilities assumed to be constant over mixture compositions. The principal conclusions were that columns with single phase-saturated feeds can be more efficient than 2-phase feeds except at equimolar composition, and the greatest inefficiencies arise from heat transfers in the reboiler and condenser. The present work adds subcooled liquid feed, varies the feed stage, and treats a nonideal system where the relative volatility is not constant. Other workers, including Soares Pinto, et al21 and Kiss, et al22 describe modifications with intermediate heat exchange, heat pumps, and heat integration, periodic stage flow manipulations. The methodology used here can be applied for such cases; process simulators allow exploration without making system simplifications. The Maximum Driving Force (MDF) approach of Gani and Bek-Petersen7 is intended to predict conditions that lead directly to column configurations of optimal efficiency in terms of reboiler heat. Figure 2b, plotting the Driving Force difference of vapor to liquid mole fractions of the light component, FDi η yi - xi versus xi, shows the essence of the concept. The greatest driving force is at point (Dx, Dy) corresponding to minimum reflux. The operating lines for specified product purities of components A and B intersect at the point (Dx, Dy), connected to xI and yI of eqs. (4) and (5). The shapes of the curves are similar to those of Agrawal and Herron2 for efficiency versus feed composition. In fact, their Figure 4 has relative volatilities of 2 and 5, which are similar to the systems studied here, and the efficiency is maximum very near the maximum driving force liquid composition. Prez-Cisneros and Sales-Cruz23 have determined the thermodynamic relations connecting Gibbs energy and driving force, noting that solution nonideality effects cancel out at the maximum. For real columns, it is claimed that the lowest heat requirement and location of the feed stage are where the operating lines intersect at a point (Dx, D), with the feed stage, NF, being obtained from the formula NF = N (1- Dx), obtained by geometric analysis of the operating lines. This approach is not to be confused with the minimum driving force analysis of Soares Pinto, et al21 which refers to targeting optimally configuring side reboilers and condensers by reducing irreversibilities.

System Details Table S1 lists the values of the input variables and results found here for 1-bar distillation of the benzene-toluene system to 95% purity in 17 stages and the methanol-water system to 99.99% purity in 22 stages. The latter was to reproduce one of the cases of Gani and Bek-Petersen7. For each mixture, there were three feed compositions with two to four feed conditions evaluated for three to five different feed stages. Most of the 118 completed simulations were for heating streams by sources at 400K and for cooling streams at 290K with 100% Murphree stage efficiencies, though some were done with reduced efficiencies or utilities at different temperatures (see below). Figure 3 shows the McCabe-Thiele and Driving Force Diagrams for



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some cases of the benzene-toluene system where zF was 0.35, 0.4 and 0.5. The benzene-toluene system is relatively symmetric, while there is strong asymmetry in the methanol-water system as shown in Figure S1 of the Supporting Information. The MDF composition was Dx = 0.4 for benzene-toluene and Dx = 0.23 for methanol-water. The latter is slightly different from that of Gani and Bek-Petersen7 probably because a different phase equilibrium model was used here (NRTL for activity coefficients and Hayden-O’Connell 2nd virial for vapor nonideality). For benzene-toluene, D = 0.596, while for methanol-water, D = 0.409. The dashed lines of the figure show how the q lines of different feed compositions must vary to match the operating line intersection for zF = 0.4 when q = 1, for a reflux of L& / V& = 0.644. For zF = 0.35 the feed condition to match was q = 1.253 while for zF = 0.50, it was q = 0.481. With the specified column input conditions, it was possible to simulate the benzene-toluene system for all cases of Figure 3. However, for methanol with water, no feed conditions of the selected system with zF = 0.15 and zF = 0.5 could match the intersection point for zF = 0.23.

Results and Discussion Tables S1 and S2 of the Supporting Information list the results for all the cases studied here. Varying Feed Stage The first set of calculations determined that for each feed composition and condition, there was a feed stage that gave the lowest system and column (reboiler) energy requirements. The minimum reboiler heat had a weak minimum with variation within !1-2 stages being less than 2% in system heat for benzene-toluene and less than 5% for methanol-water. The feed stage with minimum energy also gave the lowest entropy generation rates. Benyounes et al16 also found a minimum with feed location. Figure 4 shows example reboiler and system heats and S& gen

for different benzene-toluene feed conditions when the feed composition was zF = 0.5. The results at zF = 0.35 and zF = 0.4, are similar, though the variations with NF are smaller. It is seen that feed stage NF = 9!1 generally has the lowest heat requirements and S& . For all the gen

methanol-water feeds, the variations were somewhat greater with changing feed stage, the minimum being at stage 16!1 and a sharp rise for stages closer to the reboiler, as shown in Figure S2 of the Supporting Information. Therefore, from here on, results will be presented only for benzene-toluene feed at stage 9 and for methanol-water at stage 16, since these were nearly always optimal. The MDF formula for the feed stage of Gani and Bek-Petersen6 predicts stages 10.2 and 16, respectively, when the latter is rescaled according to their procedure. The Kirkbride relation23 gives 12.0 and 13.7, while the Brown and Martin method24 gives 10.7 and 10.3, respectively. The MDF formula is the simplest, most general, and also the closest in both cases here.


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Varying Feed Condition Figure 4a also shows that the ordering of the system heats and reboiler heats vary oppositely as the feed condition varies from cold to saturated vapor. Note that the cold feed has no preheat, so the system and reboiler values are the same. The calculations show that the total system heat increases with preheating while the column (reboiler) heat decreases. Similar behavior is shown in Figure 4b for the system and column entropy generations. These results show that focusing only on the column can ignore significant energy requirements for the whole system. Further, when cold feed is available, it is best to be fed directly to the column. Figure 5a shows that the reflux rate increases with preheat amount while Figure 5b shows that the reboiler heat decreases with increased reflux rate. It should be mentioned that Agrawal and Herron1 state that when the feed has more than 50% light component, saturated vapor is most efficient. Such higher mole fraction cases were not investigated here. It is not obvious why increasing preheat should mean that the system requires increased energy input and that decreasing reboiler heat results in increased reflux rate. The origin of these effects is revealed by the order of system entropy generations in Figure 4b, where S& values increase gen

from subcooled liquid to saturated vapor, in the order of amount of preheat. Increasing S&gen means more input heat energy that the system does not utilize for separation. The principal sources of entropy generation are from heat transfer over finite temperatures in the various heat exchangers of the system. Here, the product coolers remove heat at a constant rate. Thus, the condenser must remove all the rest of the energy put in by the preheater and the reboiler. Increased reflux rate is the mechanism to take care of this. This is similar to the findings of Benyounes, et al15 who observed that entropy production in extractive distillation increased directly with reflux rate and entrainer flow, regardless of the feed condition. Figure 6 shows that the system heat input linearly increases with entropy generation as expected from eq. (2). This variation is consistent with the assumption by Tondeur and Kvaalen9 and of Ratkje, et al10 that operating cost (heat input here) increases linearly with entropy production. This led to their common assertion that the uniform distribution of irreversibility among units of a process is optimal. In general, the column and system heat effects vary directly with S&gen . The only exception is for the benzene-toluene system where column S&gen for cold feed is higher than that for saturated liquid. This effect arises because there is entropy generated when the feed and column conditions are not matched. Saturated and 2-phase feeds match the temperature and composition of the feed stage liquid, while subcooled liquid feed does not, so there is entropy generated when cold feed mixes with the column flow. Apparently, this mixing effect is greater than the relatively small impact of lower reflux rate for the subcooled feed. Note, however, that the



system heat still only increases with S&gen , reinforcing the connection of cost to S&gen . Fully similar results were found for the methanol-water system. Benyounes et al16 found the greatest entropy production at the entrainer and main feed stages, as well as in the reboiler. The condenser in their case was less important because the entrainer condensed inside the column. Maximum Driving Force Conditions The Maximum Driving Force concept7 was developed mainly to determine optimum feed stages and focuses on saturated liquid feed at the composition, Dx, where the driving force is maximum as shown in Figure 2b. Here, different feed compositions were chosen with feed conditions including cold, saturated liquid, saturated vapor, and where the operating lines all intersected at point Dx, D in Figure 3b. Thus, for benzene-toluene in Figure 3 where, for zF = 0.35, the adjusted preheat was for less subcooling (q > 1) and for zF = 0.5, the preheat gave the required amounts of two phases (0 < q < 1). Figure 7 shows the system and reboiler heats as well as system and column S& for varying degrees of preheat when the feed stage, NF = 9. The symbols with circles gen

are the conditions of operating line intersection for MDF. The system entropy generation increases with increasing preheat while the column S&gen shows a minimum. As with the results of Gani and Bek-Petersen7, the lowest system and column heats are with the smallest mole fraction of the light component (benzene with zF = 0.35). The system entropy generations are lowest for cold feed with the lowest concentration of benzene. The column entropy generation is lowest for the smallest mole fraction of benzene at the matched operating line intersection for zF = 0.35, but is lowest for saturated liquid at higher zF concentrations. Where the operating lines intersected for different feed compositions, the entropy generated increased with concentration of benzene, while q decreased and the reflux rate increased. For the methanol-water system, the reflux ratio for zF = 0.50 was slightly higher than reported by Gani and Bek-Petersen7. While the reboiler heat rates for different saturated liquid feed compositions found here were much higher than in their Figure 3a, the ordering of the heat rates was the same and their ratio was essentially constant. This probably was caused by the different thermodynamic models and product purities. Also, their feed basis was not stated. It should be remembered that the basis for the calculations here is unit feed rate. If the basis is changed to unit rate of top product, the order of energy requirements is inverted; the case with feed of zF = 0.5 has the least heat input and entropy generation per mole of distillate, while that of zF = 0.35 has the greatest heats and entropy generations. The variations with feed conditions do not change, since each one is multiplied by the same factor when the feed composition is fixed. This variation of basis with feed composition explains the relative placement of the curves of Figure 5, which might appear to contradict the Maximum Driving Force concept, but may not. To the degree that the variety of set conditions for benzene-toluene was reproduced by the methanol-water system, the outcomes were generally similar.


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Distillation Efficiency There are several different definitions of distillation column efficiency, connecting the input energy flow of the real process to a suitable minimum energy rate1,2,6,7,16,27. Most agree that the reversible distillation case should be based on the reversible, isothermal work rate required to do the separation, as related to the negative of the Gibbs energy of mixing W& rev = − F& ∆ g mix = −  F& ( hF − Ts F ) − D& ( hD − Ts D ) − ( F& − D& ) ( hB − Ts B ) 

(7)

One form of efficiency is where the real energy rate is equal to the total lost work plus the reversible work rate16,22. While the systems here have feed and products at the same temperature, the column does not, so this relation cannot strictly apply. Instead, the reversible work can be the difference of availabilities or exergies where T in eq. (7) is set as the surroundings temperature, T0. Then, using W& from eq. (3) the efficiency is lost

ηA =

−  F& ( hF − T0 sF ) − D& ( hD − T0 sD ) − ( F& − D& ) ( hB − To sB ) 

(8)

W&lost −  F& ( hF − T0 sF ) − D& ( hD − T0 sD ) − ( F& − D& ) ( hB − T0 sB ) 

Since heat is the separation agent in distillation, it may be more appropriate to use the heat input rate as the measure of actual energy. Ho and Keller21 chose the reboiler rate, Q& , so their R

efficiency is

− F ( hF − T0 sF ) − D ( hD − T0 sD ) − ( F − D ) ( hB − T0 sB )  ηH =  &

&

&

&

&



QR

(9)

Another approach is to find the reversible work from a Carnot engine producing work from heat put in at a high temperature, TH, and rejected at a low temperature, TL.

 T  W&rev = Q& rev 1 − L  (10) T H   & Then Qrev is found from setting equal the right-hand-sides of eqs. (7) and (8), giving this efficiency as & & & & Q& rev −  F ( hF − T0 sF ) − D ( hD − T0 sD ) − ( F − D ) ( hB − T0 sB )   TH  ηQ = & =   QR Q& R  TH − TL 

(11)

Agrawal and Herron2 suggest that ηQ is preferable to ηH, while also stating that “correct practice” would use ηA. In the present work, the property values for the streams were used to compute efficiencies from eqs. (8)-(11). To obtain ηQ, TL was set to T0 = 300K. For column efficiency, TH was the temperature of the reboiling liquid, though other values could have been used. For the bottom product of benzene with toluene, TH = 381.06 K. Then for zF = 0.4, NF = 9, and F& = 1 kmol s-1,



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D& = 0.388889 kmol s-1. The result was Q& rev = 5.56 MW. This is much less than the total heat

inputs from simulations that ranged from 42 MW for cold feed to 65 MW for saturated vapor feed. Table 1 shows the results for the benzene-toluene and methanol-water systems. The various efficiencies have significantly different values for the same case, and thus should not be compared to each other. The variations for different conditions are large, but all are quite low in the range of 0.05 to 0.2 for benzene and toluene - with those for the methanol-water system being even less. The system efficiencies are less than those of only the columns, implying that the full analysis is more indicative of separation energy losses. These observations are generally understood and motivate implementation of alternative separation processes6. Imposed Irreversibilities Recall that for the above results, the external temperatures for the preheater and reboiler were arbitrarily set to 400 K and the condenser and coolers were 290 K. Variations of the temperature differences of the external heating/cooling utilities and the streams can be made to indicate reductions in entropy generation from heat integration. Again, the case of zF = 0.4, NF = 9, and F& = 1 kmol s-1 for benzene with toluene is examined. To illustrate the effects of temperature differences for heat transfer, the heat exchanger temperatures can be set to other values or even to no temperature differences with the process streams (described below). While these changes would not affect the heat effects for the column and system, they would decrease the entropy generations and reduce the amounts of energy needed to create the heating and cooling utilities, as mentioned by Agrawal and Herron2. The preheater temperature would depend on feed composition. For zF = 0.4 with NF = 9 when the basis is F& = 1 kmol s-1, The condensing overhead temperature is 353.87 K, while the boiling bottom temperature is 381.06 K. The highest temperature reached in the preheater is for saturated phases which is 367.89 K. Calculations were done with utilities that were realistically close to the stream temperatures (5 K) lower or higher for cooling and heating. Table 2 shows the reductions in S& for this case. gen

The reductions in S&gen ranged from 62 - 72% for the system, with the amount increasing with preheat, while for the column it was 81% for all feed conditions. The principal effect was on the condenser, where the heat transferred is greatest and the utility temperature was changed the most. It is also possible to introduce designed amounts of irreversibility into calculations for process system behavior without specifying the mechanisms involved. In analyses done for previous work with entropy generation in chemical processes28-31, a series was done of overall and subsection calculations with specified S& , to obtain the consequences for external and gen

intersectional stream properties. Distillation systems are simpler, but the same kind of analysis is possible, as explored here for the benzene-toluene system. Figure 8 shows how the reboiler and condenser heats found from eqs. (1) and (2) vary with imposed S& for the benzene-toluene with gen


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cold feed (Figure 8a) and with saturated liquid feed (Figure 8b). For benzene with toluene, decreasing the entropy generation by 50% reduces the reboiler and condenser heat effects by 50%. For methanol with water, the decrease is somewhat less. For distillation, it is also possible to see the effects of tray efficiencies. Process simulations were made with Murphree stage efficiencies of 60% and 75% for comparison with 100% when the feed was cold and when it was saturated liquid. The detailed conditions and results are given in Table S2. Vertical lines in Figures 8 and 9 show values of system S& for these tray efficiencies. gen

The impact of increasing stage efficiency is considerably less than for decreasing heat transfer temperature differences, as found by comparing results in Table 2 and Figure 8. Decreasing the temperature difference by 2 degrees is equivalent to increasing the stage efficiency from 60% to 75%. Given this analysis for entropy generation, it is appropriate to consider alternative column configurations and utility conditions. Agrawal et al.2,18-20 suggest using multiple feeds and internal heating. Soares Pinto et al21 and Kiss et al22 describe a number of different ways for increasing efficiency. Tondeur and Kvaalen9 and Ratkje, et al10 demonstrate that uniform distribution of S& among process units is optimal. Minimizing entropy generation in fluid flow gen

and heat transfer are described in detail by Bejan11. Tula, et al.32 suggest using hybrid separation processes where only a portion of the separation is done by distillation augmented by more efficient techniques such as with membranes. The present macroscopic approach could provide guidance about where to focus distillation process modifications for maximum benefit.

Conclusions Simulations of distillation systems and columns have determined heat requirements and entropy generation as a function of feed composition, feed condition, feed stage location, utility temperatures, and stage efficiencies for separation of an ideal and of a nonideal binary mixture. Input heat rates and entropy generation rates trend together, consistent with operating costs increasing linearly with greater irreversibilities. They generally increase with higher reflux rate. Cold feed at the lowest concentration of the light component generates the least system entropy and requires the least energy, while a system with feed preheated to saturated vapor takes the most heat and generates the most entropy. The results are generally consistent with the Maximum Driving Force concept for the column, though additional considerations arise when feed preheating and product cooling are used. The greatest irreversibilities are from heat flows over finite temperature differences, with stage inefficiencies having much less impact. The present analysis is consistent with, and complementary to, other work aiming to improve distillation efficiency.



ASSOCIATED CONTENT Supporting information Nomenclature; Figure S1: Methanol Vapor Mole Fraction and Driving Force vs. Methanol Liquid Mole Fraction; Figure S2: Reboiler Heat Rate and System Heat Rate for varying feed stage location of methanol-water system; Table S1: Details of Simulated Distillation Cases with 100% Murphree Efficiency; Table S2. Details of Simulated Distillation Cases with Various Murphree Efficiencies. (PDF) AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Tel: +1 805 343 1939. Fax: +1 805 343 1939 ORCID John O’Connell: 0000-0003-0817-5887 Funding Sources None. ACKNOWLEDGMENT The author is grateful to Professor R. Gani, Danish Technical University, and to Professor M. Doherty, University of California, Santa Barbara, for valuable comments about content and for suggestions of relevant literature. REFERENCES (1) Fitzmorris, R.E.; Mah, R.S. Improving Distillation Column Design Using Thermodynamic Availability Analysis. AIChE J., 1980, 26(2), 265-273. (2) Agrawal, R.; Herron, D.M. Optimal Thermodynamic Feed Conditions for Distillation of Ideal Binary Mixtures. AIChE J. 1997, 43(11), 2984-96. (3) de Koeijer, G.; Rivero, R. Entropy production and exergy loss in experimental distillation columns. Chem. Eng. Sci. 2003, 58, 1587-1597. (4) Demeril, Y. Thermodynamic Analysis of Separation Systems. Sep. Sci. Tech. 2014, 39(16), 3897-3942. (5) Blahusiak, M.; Kiss, A.A.; Kersten, S. R. A.; Schuur, B. Quick assessment of binary distillation efficiency using a heat engine perspective. Energy, 2016, 116, 20-31. (6) Seider, W.D., Lewin, D.R., Seader, J.D., Widagdo, S., Gani, R., Ng, K.M. Product and Process Design Principles, 4th Ed., Wiley, New York, 2017. (7) Gani, R.; Bek-Petersen, E. Simple New Algorithm for Distillation Column Design. AIChE J. 2000, 46(6), 1271-1274. (8) de Nevers, N.; Seader, J.D. Lost Work: A Measure of Thermodynamic Efficiency. Energy 1980, 5, 757-769. (9) Tondeur, D.; Kvaalen, E. Equipartition of Entropy Production. An Optimality Criterion for Transfer and Separation Processes. Ind. Eng. Chem. Res. 1987, 26, 50-56.


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(10) Ratkje, S.K.; Sauar, E.; Hansen, E.M.; Lien, K.M.; Hafskjold, B. Analysis of Entropy Production Rates for Design of Distillation Columns. Ind. Eng. Chem. Res. 1995, 34, 3001-3007. (11) Bejan, A. Entropy Generation Minimization; CRC: Boca Raton, FL, 1996. (12) Mullins, O.C.; Berry, R.S. Minimization of Entropy Production in Distillation. J. Phys. Chem. 1984, 88, 723-728. (13) Sekulic D.P. An Entropy-Based Metric for Transformational Technology Development, in Thermodynamics and the Destruction of Resources; Bakshi, B.R.; T.G. Gutowski, T.G.; Sekulic, D.P. (Eds.), Cambridge, New York, 133-162, 2011. (14) Johannessen, E.; Rsjorde, A. Equipartition of entropy production as an approximation to the state of minimum entropy production in diabatic distillation. Energy, 2007, 32, 467473. (15) Kiss, A.A.; Olujić, Ž. A Review on Process Intensification in Internally Heat-Integrated Distillation Columns. Chem. Eng. Processing: Proc. Intensification, 2014, 86, 125-144. (16) Benyounes, H.; Shen, W.; Gerbaud, V. Entropy Flow and Energy Efficiency Analysis of Extractive Distillation with a Heavy Entrainer. Ind. Eng. Chem. Res. 2014, 53, 4778-4791. (17) Wankat, P.C. Separation Process Engineering, 3rd Ed.; Prentice-Hall: Upper Saddle River, NJ, 2012. (18) Agrawal, R.; Herron, D.M. Efficient Use of an Intermediate Reboiler or Condenser in a Binary Distillation. AIChE J. 1998, 44(6), 1303-1315. (19) Agrawal, R.; Herron, D.M. Intermediate Reboiler and Condenser Arrangement for Binary Distillation Columns AIChE J. 1998, 44(6), 1316-1324. (20) Agrawal, R.; Herron, D.M. Feed Pretreatment for Binary Distillation Efficiency Improvement, European Symposium on Computer Aided Process Engineering – 11, R. Gani, R.; Jorgensen, S.B. (Eds); Elsevier Science, N.V.: Amsterdam, 2001. (21) Soares Pinto, F.; Zemp, R.; Jobson, M.; Smith, R. Thermodynamic Optimization of Distillation Columns. Chem. Eng. Sci. 2011, 66, 2920-2934. (22) Kiss, A.; Flores Landaeta, S.J.; Infante Ferreira, C.A. Towards Energy Efficient Distillation Technologies – Making the Right Choice. Energy, 2012, 47, 531-542. (23) Prez-Cisneros, E.S.; Sales-Cruz, M. Thermodynamic Analysis of the Driving Force Approach: Nonreactive Systems. Comp. Chem. Eng. 2017, 107, 37-48. (24) Kirkbride, C.G. Process Design Procedure for Multicomponent Fractionators. Petroleum Refiner 1944, 23(9), 87-102. (25) Brown, G.G.; Martin, T.Z. An empirical relationship between reflux ratio and the number of equilibrium plates in fractionating columns. Trans. AIChE 1939 35, 679-708. (26) Ho, F.G.; Keller, G.E. Process Integration, in Recent Developments in Chemical Process and Plant Design, Liu, Y.A.; McGee, H.A.; Epperly, W.R. (eds.). Wiley: New York, 101134, 1987. (27) Agrawal, R.; Woodward, D.W. Efficient Cryogenic Nitrogen Generators: An Exergy Analysis. Gas Separation & Purification, 1991, 5, 139-150.



(28) O'Connell, J.P. Thermodynamic Analysis of Processes for Hydrogen Generation by Decomposition of Water. Energy Education & Outreach, CEI Education Modules; 2012, http://www.aiche.org/cei/resources/overview/energy-education-outreach (accessed 7.10.18) (29) O'Connell, J. P.; Narkprasert, P.; Gorensek, M.B. Process Model-Free Analysis for Thermodynamic Efficiencies. Int. J. Hydrogen Energy, 2009, 34, 4033-4040. (30) O’Connell, J.P.; Chemical Process Systems Analysis Using Thermodynamic Balance Equations with Entropy Generation, Comp. Chem. Eng., 2017, 107, 3-25. (31) O’Connell, J.P.; Chemical Process Systems Analysis Using Thermodynamic Balance Equations with Entropy Generation: Reevaluation and Extension, Comp. Chem. Eng., 2018, 111, 37-42. (32) Tula, A.K., Befort, B., Garga, N., Camarda, K.V., Gani, R. “Sustainable Process Design & Analysis of Hybrid Separations”, Comp. Chem. Eng., 2017, 105, 96–104.


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Figure 1. Distillation process diagram with column only (dashed line) and whole system (solid line) boundaries.



Figure 2. Light Component Vapor Mole Fraction of (upper) and Driving Force (lower) vs. Light Component Liquid Mole Fraction with maximum driving force liquid composition (Dx), vapor composition at minimum reflux for maximum driving force liquid (Dy) and vapor composition for a real distillation process (D).


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Figure 3. Benzene Vapor Mole Fraction (upper) and Driving Force (lower) vs. Benzene Liquid Mole Fraction for conditions simulated with benzene product distillate of xD = 0.95 and bottoms of xB = 0.05 with three feed compositions and two feed conditions of saturated liquid (vertical solid lines) and for feed conditions matching Maximum Driving Force operating lines (dashed). Top and bottom operating lines are shown for minimum reflux and for nine stages.



Figure 4. Heat and entropy generation rates for varying feed stage location of benzene-toluene system with total stages n = 17, benzene feed mole fraction, zF = 0.5, and different feed conditions of subcooled liquid, saturated liquid, 2-phase, and saturated vapor. Total System and Reboiler Heat Rates (upper) and Total System and Column Entropy Generation Rates (lower).


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Figure 5. Correlations among Reflux Rate, Preheat Rate, and Reboiler Heat Rate. Upper: Reflux vs Preheat; Lower: Reboiler Heat vs. Reflux Rate.



Figure 6. Heat Rate requirement vs. Entropy Generation Rate for varying feed qualities, compositions and basis. Filled circles for whole system at all conditions. Open symbols for column only: Cold feed; Saturated liquid feed; MDF feed; 2-phase feed; X, Saturated Vapor feed. Upper: Basis 1 kmol s-1 feed. Lower: Basis 1 kmol s-1 top product (95% Benzene).


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Figure 7. Input System and Reboiler Heat Rate (upper) and Entropy Generation Rate (lower) vs. Preheat Rate. Circled points are for Maximum Driving Force feed compositions and conditions.



Figure 8. Input Reboiler and Condenser Heat Rates vs. Entropy Generation Rate for benzenetoluene with cold feed (upper) and saturated liquid feed (lower) at zF = 0.4 for different utility temperature differences (0 K, 5 K, and defaults) in reboiler and condenser. Vertical lines show entropy generations for different column Murphree efficiencies (100, 75, and 60%).


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Table 1. Column Efficiencies for Binary Distillation Systems Benzene-Toluene at 1 bar, zF = 0.40, Wrev, eq (7) = 1.18 MW, F = 1 kmol s-1 q Sgen, kW K-1 Ex, MW ηA, eq (8) ηH, eq. (9) ηQ, eq (11) 1.3342 35.5 10.6 0.100 0.028 0.105 1.0 39.4 11.8 0.091 0.026 0.063 0.373 49.9 15.0 0.073 0.021 0.099 0.0 58.1 17.4 0.064 0.018 0.098 -1 Q Sgen, kW K Ex, MW ηA, eq (8) ηH, eq. (9) ηQ, eq (11) 1.3342 29.5 8.9 0.118 0.028 0.105 1.0 28.3 8.5 0.122 0.034 0.126 .373 34.7 10.4 0.102 0.047 0.175 0.0 40.6 12.2 0.088 0.056 0.208 Methanol-Water at 1 bar, zF = 0.23, Wrev, eq (7) = 1.03 MW, F = 1 kmol s-1 System q Sgen, kW K-1 Ex, MW ηA, eq (8) ηH, eq. (9) ηQ, eq (11) 1.086 112.4 33.7 0.0165 0.0043 0.0175 1.0 125.3 37.6 0.0148 0.0039 0.0159 0.0 196.8 59.0 0.0095 0.0025 0.0106 Column q Sgen, kW K-1 Ex, MW ηA, eq (8) ηH, eq. (9) ηQ, eq (11) 1.086 104.6 31.4 0.0177 0.0043 0.0175 1.0 108.9 32.7 0.0170 0.0043 0.0178 0.0 141.6 42.5 0.0131 0.0092 0.038

Table 2. Entropy Generation for Utility Temperatures Benzene-Toluene at 1 bar, zF = 0.40, F = 1 kmol s-1 q TR, TP, TC, Tb, QR, QC, Sgen System, Sgen Column, K K K K MW MW kW K-1 kW K-1 400 290 290 35.47 29.54 1.3342 386 349 295 41.6 -30.0 9.39 8.33 381 354 300 6.24 5.75 39.44 28.33 400 400 290 290 1.0 386 377 349 295 34.7 -34.0 6.52 5.35 381 372 354 300 2.94 2.84 49.94 34.72 400 400 290 290 0.373 386 377 349 295 25.0 -45.2 8.64 6.18 381 372 354 300 4.03 3.50 58.06 40.61 400 400 290 290 0.0 386 377 349 295 21.1 -53.7 10.92 7.44 381 372 354 300 5.56 4.55



Abstract Graphic


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Detailed Examination of Energy Flows and Entropy Generation in Low

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