Temperature enthalpy curve for energy targeting of distillation columns

Transcription

1 Temperature enthalpy curve for energy targeting of distillation columns Santanu Bandyopadhyay, Ranjan K. Malik and Uday V. Shenoy * Energy Systems Engineering, Department of Mechanical Engineering, Computer Aided Design Centre and Department of Chemical Engineering, Department of Chemical Engineering and Computer Aided Design Centre, Indian Institute of Technology, Powai, Bombay , India Abstract The temperature enthalpy (¹ H) diagram of a distillation column at practical near-minimum thermodynamic condition (PNMTC) or the column grand composite curve (CGCC) is a useful representation for energy targeting studies and may be generated from a converged simulation of a base-case column design. The calculation procedure for the CGCC involves determination of the net enthalpy deficit at each stage by generating envelopes from either the condenser end (top-down approach) or the reboiler end (bottom-up approach). However, the values calculated by the two approaches differ for stages with feeds because existing procedures for CGCC generation do not consider the enthalpy balances at the feed stages. In fact, the net enthalpy deficits at feed stages calculated by both approaches are erroneous even for the simplest case of binary distillation. A feed stage correction (FSC) that rigorously considers the mass and enthalpy balance equations at feed stages is proposed in this work to resolve the discrepancy. Instead of assuming that the compositions obtained from the converged simulation for a feed stage will remain unchanged at PNMTC, the pinched compositions for the feed are determined by the intersection of the equilibrium curve and the feed q-line. Rather than perform an additional flash calculation to establish the pinched feed compositions, a quadratic approximation is developed here for column targeting purposes by assuming the relative volatility obtained from the simulation to remain constant in the neighborhood of the feed stage. The proposed FSC ensures that the CGCC is identical whether the calculations are performed by the top-down approach or the bottom-up approach. The effect of the FSC on the targets for energy conservation by reflux modification, feed conditioning, and introduction of side reboilers/condensers is discussed. As the energy target for reflux modification is determined by the CGCC pinch which typically occurs at or close to the feed location, the significance of the FSC on the reflux modification target is highlighted through several case studies including a complex column featuring multiple feeds and consequently multiple pinch points. The CGCCs for these case studies are generated by a computer program based on the FSC and a single analytical equation for the calculation of the net enthalpy deficits that allows every stage to have a feed, liquid product, vapor product, and side exchanger. The studies show that the reflux modification targets may be erroneous in many cases, if the FSC is ignored. Keywords: distillation; thermodynamic minimum; energy targeting; temperature enthalpy diagram; pinch analysis; grand composite 1. Introduction The temperature enthalpy (¹ H) diagram for a distillation column or the column grand composite curve (CGCC) is a useful representation to quantitatively address the energy-saving potential for possible stand-alone modifications such as reflux reduction, feed conditioning, and scope for side reboiler/condenser (Naka et al., 1980; Terranova and Westerberg, 1989; Dhole and Linnhoff, 1993; Ognisty, 1995; Hall et al., 1995; Trivedi et al., 1996). It may be further used to explore opportunities for integration of the distillation column with the background process. The ¹ H curve of a binary distillation column is generated by solving the coupled mass and enthalpy balances for the reversible separation scheme (Benedict, 1947; Fonyó, 1974; King, 1980; Fitzmorris and Mah, 1980; Ho and Keller, 1987). Reversible operation corresponds to minimum net work consumption and involves minimization of the driving forces for heat and mass transfer within individual stages (or, in 1733

2 1734 other words, decrease of the gap between the operating and equilibrium curves on the x y diagram) as discussed in detail by King (1980). The operating curves come closer to the equilibrium curve (and exhibit a single pinch point on the x y diagram) at the minimum reflux condition (i.e. infinite stages). The reversibility in a binary distillation process can be further increased (away from the single pinch) by introducing side reboilers and side condensers (which correspond to different operating curves and introduce more pinches on the x y diagram). The limit of the minimum thermodynamic condition is achieved with infinite stages and infinitely many side exchangers such that the operating and equilibrium curves coincide (or complete pinching occurs on the x y diagram). In contrast to binary distillation, the sharpness of separation is generally limited in multicomponent reversible distillation (Fonyó, 1974) and it is impossible to devise a reversible separation scheme for many practical multicomponent separations (Franklin and Wilkinson, 1982). The limitation in sharpness of reversible multicomponent distillation can be circumvented, for the purposes of generation of the ¹ H curve, by using the pseudo-binary concept of light and heavy key model (Fonyó, 1974; Dhole and Linnhoff, 1993). Dhole and Linnhoff (1993) describe a procedure for generating the CGCC from a converged simulation of the base-case distillation column and thus inherently account for the inevitable feed loss, pressure loss, sharp-separation loss, and loss due to chosen configuration. The calculation procedure involves generating envelopes from one end of the column and evaluating the net enthalpy deficit at each stage after determining the minimum vapor and liquid flows through that stage. When the net enthalpy deficit is added to (subtracted from) the existing condenser (reboiler) duty and plotted against the stage temperature, a close approximation to the ¹ H curve of the column is obtained at the practical near-minimum thermodynamic condition (PNMTC). The CGCC may be generated by two different approaches depending on the envelope chosen for the material and energy balances. The envelope (Fig. 1) generated from the top of the column (i.e. condenser end) considers the stage with the liquid flowing out and the vapor flowing in. This calculation procedure may be referred to as top-down, and has been discussed by Dhole and Linnhoff (1993) and Shenoy (1995). On the other hand, the envelope (Fig. 2) generated from the bottom of the column (i.e., reboiler end) leads to the bottom-up calculation procedure that considers the stage with the liquid flowing in and the vapor flowing out. Both calculation procedures are employed by the ColumnTarget (1994) software. For a stage without any feed, the enthalpy value for the CGCC obtained by the two approaches is the same. However, this is not the case at a stage with a feed because the finite feed flow induces a finite Fig. 1. Envelope for CGCC generation by top-down calculation procedure. Fig. 2. Envelope for CGCC generation by bottom-up calculation procedure. composition difference in the ideal column assumed to be reversible. The different results obtained from the top-down and bottom-up approaches lead to ambiguity in the CGCC at a feed stage. In this paper, the

3 1735 ambiguity is eliminated and a fundamentally appropriate feed stage correction (FSC) is proposed. 2. Column grand composite curve The generation of the CGCC by the top-down and bottom-up procedures is outlined below with the relevant equations. The form of the equations is different from that used by Dhole and Linnhoff (1993) who utilized all the component balances rather than the overall material balance Top-down calculation procedure For the envelope in Fig. 1, the overall material balance and the component balance are given below.» #F" #D, (1)» y*#fz " x*#dx. (2) On solving equations (1) and (2), the minimum liquid flow ( ) leaving and the minimum vapor flow (» ) entering the stage are obtained as "[D(x!y*)!F(z!y*)]/(y*!x*), (3)» "[D(x!x*)!F(z!x*)]/(y*!x*). (4) Next, the net enthalpy deficit ( ) for the envelope in Fig. 1 may be evaluated from the following enthalpy balance:» #F # " #D. (5) The stage enthalpy deficit may be added to the condenser duty (Q ) to obtain the enthalpy values for plotting the CGCC (H ). Thus, equations (3) (5) may be combined to yield the final equation given below: H "Q #H "Q (#D H #[H!H )x #(H x*!h y*)]/(y*!x*)!f #[(! )z #( x*! y*)]/(y*!x*). (6) The right-hand side of equation (6) is directly evaluated from the output of a converged simulation of a distillation column as it involves only the enthalpies, compositions, and molar flows for the feed, the product and the stage. For a column with a single feed, the third term on the right-hand side of equation (6) will be zero for stages above the feed stage Bottom-up calculation procedure For the envelope in Fig. 2, the overall material balance and the component balance are #F"» #B, (7) x*#fz "» y*#bx. (8) Thus, the minimum liquid flow ( ) entering and the minimum vapor flow (» ) leaving the stage are "[!B(x!y*)#F(z!y*)]/(y*!x*), (9)» "[!B(x!x*)#F(z!x*)]/(y*!x*). (10) The net enthalpy deficit ( ) for the envelope in Fig. 2 may be determined from: #F # "» #B. (11) Equations (9) (11) are combined, and the stage enthalpy deficit then subtracted from the reboiler duty (Q ) to obtain the enthalpy values for plotting the CGCC (H ) as given by the following expression: H "Q!H "Q!B H #[(H!H )x #(H x*!h y*)]/(y*!x*) #F H #[(H!H )z #(H x*!h y*)]/(y*!x*). (12) For a column with a single feed, the last term on the right-hand side of the above equation is zero for stages below the feed stage. In deriving equations (6) and (12), the fact that enthalpy surpluses can be cascaded from higher to lower temperatures and enthalpy deficits can be cascaded from lower to higher temperatures has been utilized Comparison of top-down and bottom-up calculation procedures This section compares the results,», and ( H ) of the two calculation procedures. The material balance, component balance and enthalpy balance for the overall column as given below may be used for this purpose. F"D#B, (13) Fz "Dx #Bx, (14) F #Q "D #B #Q. (15) Denoting the difference between the top-down and bottom-up values by, equations (3), (4), (9), (10), (13) and (14) may be simplified to give "F(y*!z )/(y*!x*), (16)» "!F(z!x*)/(y*!x*). (17) The above equations along with equations (5), (6), (11), (12) and (15) yield H H!» H!FH " "F[H (y*!z )/(y*!x*) # (z!x*)/(y*!x*)! ]. (18)

4 1736 The CGCC must be independent of the calculation procedure and therefore H must be zero. This requires that either the stage not have a feed (i.e. F"0), or the term in square brackets in equation (18) be zero. This second condition may be rewritten in the following form: (! )/(! )"(y*!z )/(y*!x*). (19) Equation (19) highlights the fundamental reason for the ambiguity in the CGCC at a stage with a feed. It will be satisfied only at the minimum reflux condition, where a practical simulation is clearly not possible because it would call for an infinite number of stages. Using the x* and y* values from a converged simulation at a feed stage will never lead to equation (19) being satisfied, and therefore will always result in different values for H from a top-down and bottom-up calculation at a feed stage. It must be emphasized that a similar analysis may be performed for a product drawn at a stage and the equations readily rewritten. However, no ambiguity occurs in the CGCC at a stage with a product withdrawal because the product composition will necessarily be identical to the equilibrium stage composition. In other words, if a liquid product (with molar flow D ) and/or a vapor product (with molar flow D ) are withdrawn at a stage, then "!D and» "D but H "0. Though the minimum internal flows computed by the two approaches are different for stages with product withdrawals, the CGCC values are identical. 3. Proposed approach based on feed stage correction It is clear from the previous section that the CGCC is uniquely defined at all stages except those with feeds. The ambiguity at stages with feeds may be eliminated through a fundamental analysis of a feed stage Fundamental analysis of feed stage Figure 3 shows a feed stage (generalized to include liquid and vapor products) for a column operating at the PNMTC. The material balance, component balance and enthalpy balance at such a feed stage are as follows: #» #F" #», (20) x* #» y* #Fz " x* #» y* x* y*, #» #F " #» (21). (22) Equations (21) and (22) assume the composition and molar enthalpy changes of the saturated liquids and Fig. 3. Fundamental analysis of a generalized feed stage with liquid and vapor products for a PNMTC column. vapors over the feed stage are negligible. This assumption holds when the feed stage is pinched or the column is operating at the PNMTC. Furthermore, in equation (21), the product compositions correspond to the equilibrium compositions (x*, y*) of the feed stage (for the simulated finite column operating at greater than minimum reflux). Note that these product compositions are different from the equilibrium compositions (x*, y* ) of the feed pinch (for an infinite reversible column at minimum reflux) in order to satisfy the column mass balance. Denoting (! )/F"1!(»!» )/F by q, equations (20) (22) give q"(! )/(! ) "[(y*!z )!(y*!y*)d /F!(x*!x*)D /F]/(y* ). (23) Equation (23) reduces to the well-known definition of q (Treybal, 1981) for a feed stage without product withdrawals (i.e. D "D "0). Importantly, equations (19) and (23) indicate that it is appropriate to use x* (and not use x* and y* values from a converged simulation) during the CGCC calculation at a feed stage. Thus, at a feed stage, the value of H from the top-down and bottom-up calculation procedures will be identical provided x* are used Computation of feed stage correction (FSC) A separate computation is required for every feed during the generation of a CGCC because x* and y* values from a converged simulation are not appropriate at a feed stage. The feed stage correction (FSC) involves solving equation (23) simultaneously with the equilibrium relationship to determine x*.once appropriate values of x* are obtained, then the following modified forms of equations (6) and (12) may be used for calculating the enthalpy value of the

5 1737 CGCC at the feed stage. H "Q #D[ # (x!y* )/(y* )! (x )/(y* )] "Q!B[ # (x!y* )/(y* )! (x )/(y* )]. (24) The values of x* may be determined by an adiabatic flash calculation. For a two-phase feed, this flash calculation may be additionally performed on the simulator. For a subcooled or superheated feed, additional thermal energy is exchanged via condensation of the vapor stream or vaporization of the liquid stream, respectively; however, x* can still be calculated from the mathematical solution of the adiabatic flash equations, without their physical counterpart (Shiras et al., 1950). Strictly speaking, superheated vapors and subcooled liquids cannot be fed reversibly into a distillation column (Koehler et al., 1991) even for binary systems. As an alternative to the extra simulation/adiabatic flash calculation, excellent approximations to x* and y* that suffice for targeting purposes may be obtained by simply assuming the relative volatility α for the feed to be equal to that from the converged simulation at the feed stage. Figures 4a and 4b provide geometric interpretations for the FSC on the x y diagram. Figure 4a highlights the difference between the feed stage composition obtained from the simulator and the pinch composition required for the FSC. At the minimum thermodynamic condition, the operating curve coincides with the equilibrium curve (King, 1980). Therefore, the feed should be injected at that point where the q-line of the feed intersects the equilibrium curve. Equation (26) implements the FSC by determining the intersection point in terms of x* assuming α"[y* (1 )]/[x* (1!y* )] "[y*(1!x*)]/[x*(1!y*)]. (25) Then, equation (25) for the equilibrium curve based on constant relative volatility near the feed stage is solved with equation (23) to eliminate y* and obtain the quadratic approximation given below. (α!1)(q!d /F)x* #[α(1!d /F)!D /F!(α!1)(q#z!y*D /F!x*D /F)]x*!z #y*d /F#x*D /F"0. (26) The FSC calculations are performed as follows. The enthalpy and composition values from the converged simulation at the feed stage are used to determine q and α from equations (23) and (25), respectively. Then, equation (26) is solved and only that value of x* is accepted which is between zero and unity. Finally, y* is determined from equation (23) or equation (25), and H is computed from equation (24). As an aside, note that the left-hand-side of equation (26) for the binary case with no product withdrawals can be rearranged [after substituting for α and x* in terms of the K-values for the two components] into the form of the Rachford-Rice (1952) function; however, equation (26) has the advantage of being formulated in terms of α (rather than K-values which are strongly dependent on temperature). If constancy of K is assumed in the neighborhood of the feed, then a linear approximation (rather than a quadratic one) is obtained. Fig. 4(a). Geometric interpretation of FSC on x y diagram: comparison of feed stage composition from simulation with pinch composition from FSC. (b) Geometric interpretation of FSC on x y diagram: comparison of the slope of the line that denotes the minimum liquid to vapor flow ratio ( /» ) at the feed stage by three different approaches.

6 1738 the relative volatility at the feed stage is constant in its neighborhood. Figure 4b highlights the variation of the ratio of the minimum liquid flow to the minimum vapor flow ( /» ) for the top-down, bottom-up and FSC approaches. The ( /» ) ratio for the FSC is given by the slope of the line joining the distillate point with the intersection point of the feed line and the equilibrium curve. The corresponding ratios for the topdown approach and the bottom-up approach are also shown in Figure 4b. The difference between the slopes of these two lines leads to errors in the CGCC calculation as reflected in equation (18) Effect of FSC on reflux modification target The scope for energy conservation (in terms of the reboiler/condenser loads) by reflux modification can be estimated from Q!Q "Q!Q "Dλ(R!R ). (27) The potential for reduction in energy requirements by decreasing reflux ratio is targeted from the CGCC in terms of the enthalpy gap (horizontal distance) of the CGCC pinch from the temperature axis (Dhole and Linnhoff, 1993). The CGCC pinch typically occurs at or near the feed stage except for some non-ideal systems (where the pinch occurs either in the stripping section or the rectifying section). For the case where the CGCC pinch occurs at the feed stage, the R values calculated from the topdown and bottom-up procedures are incorrect, leading to the targets for reflux modification also being inaccurate. The difference between the two targets exactly equals H given in equation (18). It is demonstrated below that the CGCC reflux modification targets based on the top-down and bottom-up procedures are fundamentally in error even for the simplest case of binary distillation unless the FSC is applied. In the case of a binary mixture with constant relative volatility and constant molar overflow for the column, it is well known that the minimum reflux corresponds to the pinch at the feed point. The minimum reflux may be calculated from the slope of the line joining the distillate point to the intersection of the equilibrium curve with the feed q-line. Noting that the slope"(x!y* )/(x )"R /(R #1), the scope for reflux modification is given by Q!Q "Q!Q "Dλ[R!(x!y* )/(y* )]. (28) The scope for reflux modification targeted by the proposed approach with FSC can be calculated from equation (24) and exactly equals the energy reduction possible for the column (equation (28)) for the case of a total condenser [where Q "Dλ(R#1) and " ] as well as a partial condenser [where Q "DλR and " ]. However, this is not the case for the top-down and bottom-up approaches as shown next. From equations (6), (13) (15), the scope for reflux modification targeted by the top-down approach can be obtained as Q!Q "Q!Q "Dλ[R!(x!y*)/(y*!x*)!(F/D) 1!q!(z!x*)/(y*!x*) ]. (29) Similarly, the reflux modification target predicted by the bottom-up approach as calculated from equations (12) (15) is Q!Q "Q!Q "Dλ[R!(x!y*)/(y*!x*)]. (30) Using the x* and y* values at the feed stage from a converged simulation, the scope for reflux modification predicted by equations (29) and (30) will never agree with those from equation (28). The top-down approach will underpredict the scope for reflux modification (R!R ) and the bottom-up approach will overpredict it for x*'x* [because the slope ( /» ) for the top-down approach in Fig. 4b is higher and the R predicted is therefore higher], and vice-versa for x*(x*. Equations (29) and (30) coincide with equation (28) whenever x* and y* are replaced by x*. As an aside, it may be noted that equation (28) may be rearranged by employing the definition of relative volatility between the light and heavy keys to obtain the reflux modification scope predicted by the Underwood (1948) equation for Class 1 separations of multicomponent systems where the pinch occurs at the feed stage (Shiras et al. 1950). Thus, on assuming constant relative volatility and constant molar overflow, the FSC allows reduction to the Underwood (1948) equation whereas the other two approaches do not Effect of FSC on feed conditioning and side exchanger targets The thermal condition of the feed influences the energy requirements for the distillation column. The slope of the CGCC near the feed stage, which determines the scope for feed conditioning (Dhole and Linnhoff, 1993; Ognisty, 1995), differs in the top-down and bottom-up approaches as does the value of H at the feed stage. The FSC defines the slope of the CGCC near the feed stage explicitly by determining the H value unambiguously at the feed stage. Therefore, the targets for feed preheating and cooling determined using the FSC are more accurate. The targets for placement of side reboilers/condensers at any given temperature are determined based on the horizontal distance of the CGCC from the temperature axis (Dhole and Linnhoff, 1993; Ognisty, 1995). For columns with a single feed, the scope for

7 1739 placing side exchangers (away from the feed stage) does not depend on the top-down or the bottom-up procedure. However, for complex columns with more than one feed, the targets for placement of side exchangers between the feed stages can differ significantly in the top-down and bottom-up approaches. When the FSC is used during the generation of the CGCC for a complex column, the ambiguity in the targets for side exchangers on stages in between the feed stages is eliminated Generalization and implementation of FSC In binary distillation, one of the components is heavy and the other is obviously light. However, this is not so obvious for multicomponent reversible distillation as the sharpness of separation is generally limited (Fonyo, 1974). The difficulty may be overcome with the pseudo-binary concept of a light and heavy key model (Fonyó, 1974; Dhole and Linnhoff, 1993), in which case the equations with the FSC proposed here provide a reliable methodology for CGCC generation. The key components are usually specified by the designer. Light non-key components are clubbed with the light key, and heavy non-key components with the heavy key. Distributed components can be clubbed with the light or heavy key depending on their K-values. In the case of crude distillation, the key definition varies from stage-tostage and keys can be defined according to the K- values of the pseudo-components or by comparing stage compositions (Dhole and Buckingham, 1994). It must be noted that the CGCC shape and the reflux modification targets depend on the key definition. Except for strongly non-ideal mixtures, the minimum reflux separation of multicomponent mixtures exhibits a pinch point in each half of the column. When the column products do not contain one or more of the components present in the feed, the pinch point is closer to the product outlet for that half of the column and does not coincide with the feed stage (Koehler et al., 1995). In general, the pinch point determining the minimum reflux is not known a priori. However, only the pinch point controlling the minimum reflux is detected by pseudo-binarization, and hence the minimum energy consumption predicted is close to that calculated through a rigorous calculation (Koehler et al., 1991). While implementing the FSC for a multicomponent distillation column, the pseudo-relative volatility is determined from the pseudo-heavy and light keys. Thus, x* and y* are calculated by summation over the light key components defined at a particular stage. The FSC is then applied in a manner analogous to that described in Section 3.2. In what follows, equations for computer implementation are provided that readily allow the generation of a CGCC for the general case of a distillation column with a feed, a liquid product, a vapor product and a side exchanger (side condenser or side reboiler) on every stage (Fig. 5). Equations (1), (2) and (5) can be Fig. 5. Distillation column with feed, liquid product, vapor product and side exchanger on every stage. generalized for the Nth stage as given below.» # F # " (D #D ), (31)» y* # (F z x* )" # (D x* #D y* ), (32)» H # (F H )#H " # (D H #D H ), (33) where JL" j if jth component is light key on stage N and stage numbering starts from the top of the column. The subscripts i and j denote the ith stage and jth component, respectively. As in Section 2.1, and» can be obtained from equations (31) and (32). Then, can be calculated from equation (33) and can be determined from H " Q # " Q # (D H #D H ) # (! ) (D x* #D y* )

8 1740 # x*! y* (D #D ) (y*!x* )! (F H )! (! ) # x*! y* (F z ) F (y*!x* ). (34) On viewing side reboilers as negative side condensers, equation (34) may be utilized for side reboilers with merely a change of sign for Q (i.e., the first term on the right-hand side). To incorporate the FSC, equation (23) and the local quadratic approximation to the equilibrium curve at the feed stage can also be generalized as follows. q "(! )/(! ), (35) α " y* 1! x* x* 1! y*. (36) The FSC calculations are now performed in the following stepwise manner. The enthalpy and composition values from the converged simulation at the feed stage are used to determine q and α from equations (35) and (36), respectively. Then, equation (26) is solved with q"q, α"α, and other appropriate substitutions such as z " z to obtain the corrected value of x* (" x* ), which must lie between zero and unity. Next, a corrected value of y* is determined from equation (36) by assuming constant α. Finally, is computed from equation (34), and this value from the FSC must lie between those based on the top-down and bottom-up approaches. The CGCC will be identical irrespective of whether equation (34) based on top-down envelopes or its analogue based on bottom-up envelopes is used provided the FSC is applied. Equations (26), (34) (36) form the basis of a computer program used for generation of the CGCC in the various case studies discussed in the next section. The input data to this computer program are extracted from the output of a base-case distillation column simulation. 4. Case studies To demonstrate the differences in the energy targets from the top-down and bottom-up calculation procedures and the proposed approach based on the FSC, various case studies are presented below. Simulations, wherever required to generate the data for the CGCC, are performed with the PRO/II ( ) software with SRK as the thermodynamic method. The values of H obtained at the feed stage and the scope for energy reduction by reflux modification from the three methods are summarized in Tables 1 and 2, respectively. Stage numbering starts from the top of the column with 1 denoting the condenser Binary distillation A simple example of a binary (benzene-toluene) distillation column operating at 1 kg/sq cm pressure Table 1. Comparison of H values at feed stage calculated by three approaches Case study Top-down Bottom-up Proposed FSC Binary distillation kcal/h kcal/h kcal/h Seven-stage stripping tower kcal/h! kcal/h kcal/h 40-stage distillation column kcal/h kcal/h kcal/h Five-component distillation MMBtu/h MMBtu/h MMBtu/h Complex column Stage 6: kbtu/h kbtu/h kbtu/h Stage 9: kbtu/h kbtu/h kbtu/h Table 2. Comparison of energy targets for reflux modification by three approaches Case Study Top-down Bottom-up Proposed FSC Binary distillation kcal/h kcal/h kcal/h Seven-stage stripping tower kcal/h! kcal/h kcal/h 40-stage distillation column kcal/h kcal/h kcal/h Five-component distillation MMBtu/h MMBtu/h MMBtu/h Complex column kbtu/h kbtu/h kbtu/h

9 1741 and comprising 20 stages (including total condenser and reboiler) is presented first to demonstrate the ambiguity of the top-down and bottom-up approaches at the feed stage. The column is simulated with the feed (100 kg mol/h at 92 C and 1 kg/sq cm containing 50% benzene) at the 10th stage, and 99% product purity desired both at the top and the bottom. The scope for reduction in energy consumption by reflux modification is directly given by the H value at the feed stage for the bottom-up and FSC approaches (Fig. 6). For the top-down approach, feed stage H value is kcal/h; but, the CGCC pinch is improperly located at the 9th stage (Fig. 6a). The targets predicted by the top-down and bottom-up approaches are and kcal/h, respectively. When the FSC is applied, the target is kcal/h from a rigorous flash calculation and kcal/h based on the quadratic approximation at the feed stage [equation (26)]. Here, the target is overpredicted by the top-down approach and underpredicted by the bottom-up approach. Furthermore, it may be observed that the quadratic approximation is accurate enough for targeting purposes and the additional simulation may be unnecessary. The target for energy-savings potential by reflux modification can be validated by rigorous simulation of a column with a large number of stages. When a 300-stage column was simulated with the feed at the 150th stage, the energy reduction was observed to be kcal/h which compares well with the FSC targets (given the approximations made and other computational tolerances) Seven-stage stripping tower The simulation results for a four-component, seven-stage stripping tower with the feed ( kmol/h) at the 6th stage are provided as an example problem in ColumnTarget (1994). The vapor product at kmol/h is collected at the top and the reboiler duty is reported as kcal/h. Also, 83.8% of component-3 is recovered at the bottom. The light key is defined by lumping components 1 and 2, whereas the heavy key is defined by lumping components 3 and 4. The CGCC generated by the top-down calculation procedure shows a pinch at the fifth stage with the scope for reflux modification yielding an energy savings of kcal/h. The H value at the feed stage is kcal/h. The bottom-up calculation shows the pinch at the feed stage with an H value of! kcal/h. The negative value of the scope for energy reduction by reflux modification questions the very operation of the column. It is obviously erroneous as the column has been simulated. The CGCC when calculated with the FSC shows the H value at the feed stage to be kcal/h. The pinch is at the fifth stage and the scope for energy reduction by reflux modification is kcal/h as Fig. 6(a). CGCC by top-down calculation procedure for the binary distillation column example (see Section 4.1). (b) CGCC by bottom-up calculation procedure for the binary distillation column example (see Section 4.1). (c) CGCC by FSC calculation procedure for the binary distillation column example (see Section 4.1). obtained in the top-down approach. It may be noted that the details of the column and the simulation are not available; so, the quadratic approximation is used to perform the FSC calculations.

10 stage distillation column The simulation results for a five-component, 40- stage distillation column with the feed ( kmol/h) at the 22nd stage are also given as an example problem in ColumnTarget (1994). The liquid product at kmol/h is collected at the top and the reboiler duty is reported as kcal/h. Further, % of component-2 is recovered at the top and % of component-3 at the bottom. Component-2 is defined as the light key and component-3 is defined as the heavy key. However, the mole fractions of components 1, 4, and 5 are insignificant; therefore, component-1 may be lumped with component-2 as the light key, whereas components 4 and 5 may be lumped with component-3 as the heavy key. The CGCC generated by the top-down approach shows the pinch at the feed stage and the energysavings potential through reflux modification to be kcal/h. The bottom-up approach results in an H value at the feed stage of kcal/h with the pinch just below the feed stage yielding a energysavings target by reflux modification of kcal/h. The CGCC obtained through the FSC shows the H value at the feed stage to be kcal/h; however, the pinch at the 23rd stage establishes the energy-savings scope to be kcal/h as obtained in the bottom-up approach. As in the previous case study, the quadratic approximation is used for the FSC in the absence of details for the column and simulation Five-component distillation The example problem with the feed and product specifications is described by Dhole and Linnhoff (1993). The feed stage location, the thermodynamic method and the two specifications used in the column simulation are, however, not explicitly reported. As a first step, the simulation of the five-component distillation with 18 stages (including partial condenser and reboiler) is performed with PRO/II ( ) using SRK as the thermodynamic method and the feed located on the ninth stage. The mole fractions of nonane in the top product and octane in the bottom product are both specified to be The condenser and reboiler duties (in MMBtu/h) from the simulation are and 82.52, respectively. These compare reasonably with the values of 39.6 and 83.3 reported by Dhole and Linnhoff (1993). The simulation shows the condenser and reboiler temperatures to be and C, respectively. Although the condenser temperature compares well with the value of C given by Dhole and Linnhoff (1993), the reboiler temperature is about 3.6 C higher than their reported value of C. Here, heptane and octane are grouped as the light keys. Nonane, decane and C15 are grouped as the heavy keys. In comparison with the H values at the feed stage from the top-down (34.08 MMBtu/h) and bottom-up (20.97 MMBtu/h) calculation procedures, the FSC approach gives a value of MMBtu/h. The distance of the CGCC pinch (which occurs at the eighth stage) from the temperature axis represents the scope for energy conservation and is observed to be MMBtu/h. Dhole and Linnhoff (1993) observed that the CGCC shows scope for improvement in the reflux ratio by about MMBtu/h. It may be noted that the feed in this case is subcooled, and the column is therefore potentially irreversible Complex column A complex multicomponent distillation column (16 stages including partial condenser and reboiler) with two feeds (on the sixth and ninth stages), two sidestreams (liquid product from third stage and vapor product from 13th stage), and one intercooler (on stage 3) is simulated with the SRK thermodynamic method using the PRO/II ( ) simulator. The detailed description of the problem is given by Henley and Seader (1981, p. 568). Here, ethane and propane are grouped together as light keys and the rest are taken as heavy keys. The reflux rate is specified in this case study as it is provided in the original problem. Two feeds cause two pinches in the column. The energy-conservation potential is determined by the controlling pinch, that is, the one with the minimum horizontal distance for the CGCC from the temperature axis. In the case of the top-down approach (Fig. 7a), the controlling pinch is on stage 9 and the scope for energy reduction by changing reflux is kbtu/h. Interestingly, by the bottom-up approach (Fig. 7b), the pinch that controls the energyconservation potential is on stage 6 and the corresponding scope is kbtu/h. The CGCC, when calculated with the FSC (Fig. 7c), shows the controlling pinch to be on stage 9. The pinch on stage 6 is very close to the one on stage 9 in terms of H values as observed in Table 1. The scope for energy reduction predicted by the FSC approach (782.1 kbtu/h) is higher than the values predicted by both the top-down and the bottom-up approaches. It is worth noting that the shape of the lower portion for the three CGCCs (in Fig. 7) varies significantly due to changes in the enthalpy values of only two data points (corresponding to the two feed stages). The pocket observed in the CGCCs is due to the presence of the intercooler. 5. Conclusion The enthalpy cascade (H ) value at the pinch point denotes the scope for energy conservation by reflux modification and thus provides an energy target on the CGCC. In many distillation columns, the pinch occurs at or near the feed stage. The top-down and bottom-up calculation procedures predict two different H values at the feed stage, and therefore introduce an ambiguity in the energy targets for reflux modification and feed conditioning. The ambiguity

11 1743 Fig. 7(a). CGCC by top-down calculation procedure for the complex column example (see Section 4.5). (b) CGCC by bottom-up calculation procedure for the complex column example (see Section 4.5). (c) CGCC by proposed FSC procedure for the complex column example (see Section 4.5). manifests itself as two available options in targeting software like ColumnTarget (1994); however, neither of the CGCCs generated is strictly correct. The ambiguity has been fundamentally analyzed in this paper and resolved through a feed stage correction (FSC) procedure. It has been demonstrated that the existing topdown and bottom-up approaches are both fundamentally in error at feed stages even in the case of binary distillation, and may lead to inaccurate energy targets especially for the reflux modification scope. It has been further observed from Table 1 that the two approaches may overpredict or underpredict the targets depending on the case study, and this adds to the uncertainty in the column targets at feed stage(s). The FSC ensures that the ¹ H curve of a column at the practical near-minimum thermodynamic condition (PNMTC) is independent of the direction of calculation. As the proposed method properly accounts for the mass and enthalpy balance equations at each stage, especially the feed stage(s), it does not matter from which direction the envelopes are generated for the computation of the CGCC. Instead of assuming that the compositions obtained from the converged simulation will remain the compositions for the feed stage at PNMTC, the FSC suggests that feed stage compositions may be calculated assuming the same relative volatility as that obtained from the simulation. The H values at the feed stage from the proposed FSC lie between those based on the top-down and bottom-up approaches for the various case studies in Table 1, as should be the case. When this value is the minimum amongst the H values for all the stages, then the pinch is at a feed stage and it directly provides the energy target for reflux modification. However, the pinch (given by the minimum H value) may not always occur at a feed stage as demonstrated in the case studies involving the 7-stage stripping tower, the 40-stage distillation column and the 5-component distillation. The FSC is especially significant in columns involving multiple feeds as discussed in the complex column case study in the previous section. The FSC is also of prime importance in refinery columns with several pumparounds (where each pumparound is treated as a feed and a product), notably where the pumparound draw and return are on different stages. Finally, the CGCC computation (even for a complex column with a feed, liquid/vapor product and side exchanger at every stage) is shown to involve the mere substitution of values outputted by a process simulator into equation (34). In other words, an important contribution of this work is the derivation of a single equation (rather than a stepwise procedure) for the calculation of the net enthalpy deficits during the generation of the CGCC. Acknowledgements The authors wish to thank Dr Hiren K. Shethna for valuable discussions that helped clarify several issues related to the minimum thermodynamic condition for distillation.

12 1744 Nomenclature B bottom product molar flow CGCC column grand composite curve D distillate molar flow F feed molar flow FSC feed stage correction H enthalpy J light key components set K vapor liquid equilibrium ratio liquid molar flow N stage number PNMTC practical near-minimum thermodynamic condition q quantity (related to feed condition) defined in Section 3.1 Q heat duty R reflux SRK Soave Redlich Kwong ¹ temperature» vapor molar flow x mole fraction in liquid y mole fraction in vapor z mole fraction in feed α relative volatility difference in values calculated from top-down and bottom-up procedures λ heat of vaporization Subscript B C CGCC D def F i in j L min N out R V bottom product condenser column grand composite curve distillate deficit feed stage index in to (entering) a stage component index liquid minimum stage number out of (leaving) a stage reboiler vapor Superscript * equilibrium condition References Benedict, M. (1947) Multistage separation processes. ¹rans A.I.Ch.E. 43, 41. ColumnTarget (1994) Super ¹arget for ¼indows,»ersion 3.0 ºser Guide, Linnhoff March, Cheshire, England. Dhole, V.R. and Buckingham, P.R. (1994) Refinery column integration for de-bottlenecking and energy saving. Presented at ESCAPE I» Conf., Dublin, March. Dhole, V.R. and Linnhoff, B. (1993) Distillation column targets. Comput. Chem. Engng 17(5/6), Fitzmorris, R.E. and Mah, R.S.H. (1980) Improving distillation column design using thermodynamic availability analysis. A.I.Ch.E. J. 26, Fonyó Z. (1974) Thermodynamic analysis of rectification. I. Reversible model of rectification. Int. Chem. Engng 14, Franklin, N.L. and Wilkinson, M.B. (1982) Reversibility in the separation of multicomponent mixtures. ¹rans I. Chem. E. 60, Hall, S.G., Ognisty, T.P. and Northup, A.H. (1995) Use process integration to improve FCC/VRU design. Part 1. Hydrocarbon Process Henley, E.J. and Seader, J.D., (1981) Equilibrium-Stage Separation Operations in Chemical Engineering. Wiley, New York. Ho, F.G. and Keller, G.E. (1987) Process integration. In Recent Developments in Chemical Process and Plant Design, Y.A. Liu, H.A. McGee and W.G. Epperly, Eds. Wiley, New York. King, C.J. (1980) Separation Processes. McGraw-Hill, New York. Koehler J., Aguirre, P. and Blass, E. (1991) Minimum reflux calculations for nonideal mixtures using the reversible distillation model. Chem. Engng Sci. 46(12), Koehler, J., Poellmann, P. and Blass, E. (1995) A review on minimum energy calculations for ideal and nonideal distillations. Ind. Engng Chem. Res. 34, Naka, Y., Terashita, M., Hayashiguchi, S. and Takamatsu, T. (1980) An intermediate heating and cooling method for a distillation column. J. Chem. Engng Japan, 13, Ognisty T.P. (1995) Analyze distillation columns with thermodynamics. Chem. Engng Prog PRO/II, ( )»ersion 4.1, Simulation Sciences, Inc., California, U.S.A. Rachford, H.H., Jr. and Rice, J.D. (1952) J. Pet. ¹ech. 4(10), sections 1, 19 and 2, 3. Shenoy, U.V. (1995) Heat Exchanger Network Synthesis: Process Optimization by Energy and Resource Analysis. Gulf Publishing Co., Houston. Shiras, R.N., Hanson, D.N. and Gibson, C.H. (1950) Calculation of minimum reflux in distillation columns. Ind. Engng Chem. 42, Terranova, B.E. and Westerberg, A.W. (1989) Temperatureheat diagrams for complex columns. 1. Intercooled/interheated distillation columns. Ind. Engng Chem. Res. 28(9), Treybal, R.E. (1981) Mass-¹ransfer Operations. McGraw- Hill, New York. Trivedi, K.K., Pang, K.H., O Young, D.L., Klavers H.W. and Linnhoff, B. (1996) Optimize a licensor s design using pinch technology. Hydrocarbon Process Underwood, A.J.V. (1948) Fractional distillation of multicomponent mixtures. Chem. Engng Prog