Invariant rectifying-stripping curves for targeting minimum energy and feed location in distillation

Transcription

1 Invariant rectifying-stripping curves for targeting minimum energy and feed location in distillation Santanu Bandyopadhyay a, Ranjan K. Malik b, Uday V. Shenoy c, * a Energy Systems Engineering, Department of Mechanical Engineering, Indian Institute of Technology, Powai, Bombay , India b Computer Aided Design Centre and Department of Chemical Engineering, Indian Institute of Technology, Powai, Bombay , India c Department of Chemical Engineering and Computer Aided Design Centre, Indian Institute of Technology, Powai, Bombay , India Abstract Invariant rectifying-stripping (IRS) curves are proposed that are independent of the feed location and operating reflux of the distillation column for a given separation problem. IRS curves represent the enthalpy surpluses and deficits in the rectifying and stripping sections, respectively, as a function of temperature for all possible values of reflux and reboil. The IRS curves provide a new representation on the temperature-enthalpy diagram to set distillation column targets prior to detailed design for minimum energy requirement, feed location, feed preconditioning, and side-exchanger loads. The application of the proposed concepts to two binary distillation examples (one featuring a tangent pinch) and a multicomponent distillation example illustrates the usefulness of the IRS curves in properly locating the feed, determining the minimum utility requirements, and reducing the tedium of repeated simulations. The IRS curves are rigorously invariant and provide the absolute minimum utility requirements for binary systems (ideal as well as non-ideal); however, they are near-invariant and predict the near-minimum utility requirements for multicomponent systems (where the pseudo-binary concept of alight and heavy key is employed). Keywords: Distillation; Thermodynamic minimum; Temperature enthalpy diagram; Feed location; Energy targeting; Pinch analysis 1. Introduction The temperature-enthalpy (T H) curve for a binary distillation column at the minimum thermodynamic condition (MTC) can be generated by solving the coupled heat and mass balance equations for the reversible separation scheme (Benedict, 1947; Fonyó, 1974; Fitzmorris & Mah, 1980; King, 1980; Naka et al., 1980; Ho & Keller, 1987). The limitations in the sharpness of reversible multicomponent separations (Fonyó, 1974; Franklin & Wilkinson, 1982) can be overcome by using the pseudo-binary concept of a light and heavy key model (Fonyó, 1974; Dhole & Linnhoff, 1993). Dhole and Linnhoff (1993) described a procedure for generating a T H curve (which they called the column grand composite curve or the CGCC) from a converged simulation of a distillation column. The calculation procedure 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 they do not consider the enthalpy balances at the feed stages. A feed stage correction (FSC) that rigorously considers the mass and enthalpy balances at feed stages has been recently proposed by Bandyopadhyay, Malik and Shenoy (1998) to resolve the discrepancy. The invariant rectifying-stripping (IRS) curves proposed here have the FSC built-in, and consequently have the advantage of not requiring a separate correction procedure to the CGCC. The CGCC is a T H curve at the practical near-minimum thermodynamic condition, which inherently accounts for the inevitable feed loss, pressure loss, sharp-separation loss, and loss due to chosen configuration. The energy-saving potential for different column

2 1110 modifications like reflux reduction, feed conditioning, and scope for side reboiler/condenser can be addressed on such a T H diagram (Naka et al., 1980; Terranova & Westerberg, 1989; Dhole & Linnhoff, 1993; Ognisty, 1995; Hall, Ognisty and Northup, 1995; Trivedi et al., 1996). The horizontal enthalpy gaps at the top and bottom of the CGCC denote the reboiler and condenser loads, respectively. These gaps may be decreased by reducing the reflux (i.e. by increasing the number of stages). Dhole and Linnhoff (1993) discuss reflux modification and target its scope in terms of the utility reduction in the reboiler/condenser. The CGCC depends not only on the operating reflux, but also on the feed location in the column. Dhole and Linnhoff (1993) assumed the feed stage location for the column had been appropriately chosen beforehand. Although they indicated that appropriate feed stage location should be identified before targeting for any column modification, no methodology for locating the feed was suggested by them. It must be emphasized that improper feed location leads to energy penalties in the reboiler and condenser, as well as an erroneous reflux modification target. The feed stage location is an important parameter for column optimization, and may be determined through several simulation runs. Different methods for the optimal location of the feed stage and their shortcomings are reviewed by King (1980) and Kister (1992). Though the empirical correlation proposed by Kirkbride (1944) can be utilized to find the approximate feed location, it is not very reliable and satisfactory for asymmetric feeds (Henley & Seader, 1981). Hengstebeck (1968) proposed a graphical approach to correct the feed location from the base case simulation result. The separation parameter plot of Hengstebeck used for this purpose is essentially based on compositions (key ratio) and does not consider enthalpies. A poor feed location causes relatively sharp breaks on the separation parameter plot, which may be corrected by relocating the feed using a slope criterion on an extrapolated curve as discussed by Hengstebeck (1968). The approach proposed here for feed location overcomes the deficiencies in previous methods and captures composition as well as temperature dependencies. It is reliable for all types of feeds and accurate as it does not involve extrapolation or slope calculations. In this paper, targeting procedures for minimum utility consumption and feed location are established. Invariant rectifying-stripping (IRS) curves, that primarily depend on the separation problem and not on the column configuration, are proposed for this purpose. These curves are invariant to the operating reflux and the feed location in the column. They depend only on the separation and the operating pressure. The invariant property of the curves is rigorously proved for binary and reversible multicomponent separations. The invariance approximately holds for general multicomponent systems, and is demonstrated through a case study where the pseudo-binary concept of a light and heavy key is used. The IRS curves provide the feed location target in terms of temperature, which may be then converted to a stage number by a simple methodology. Thus, a systematic procedure, free from heuristics, for locating the feed in a column through pinch analysis is presented. The work extends the energy targeting concepts (Linnhoff, Townsend & Boland, 1982) originally developed for heat exchanger networks (HENs) to distillation columns. The analogs of hot utility load, cold utility load, and T min in HENs are reboiler duty, condenser duty, and reflux ratio in distillation. Just as energy targets for HENs are established in pinch analysis (Linnhoff, 1993) ahead of network design based only on stream specifications, energy targets for distillation are developed here from IRS curves prior to column design based purely on feed/products specifications. The targeting procedures aim at reducing the potentially large space of design alternatives to a small set of promising designs that merit more detailed attention. Targets provide the direction in which the base-case design should be evolved to ensure the optimal solution. 2. Motivation Dhole and Linnhoff (1993) suggested that the scope for reduction in energy requirement by decreasing the reflux ratio may be targeted in terms of the enthalpy gap (horizontal distance) of the CGCC pinch from the temperature axis. The pinch is defined as the point on the CGCC with the minimum enthalpy value (i.e. closest to the temperature axis). The CGCC pinch typically occurs close to the feed stage except for some non-ideal binary systems (where it occurs in either the stripping section or the rectifying section depending on the vapor liquid equilibrium). Mathematically speaking, the scope for energy conservation (in terms of reboiler/condenser loads) by reflux modification as well as the minimum reflux (for a specified separation with a given column configuration) can be estimated from Q r Q r,min =Q c Q c,min =H CGCC,min D (R R min ) (1) 2.1. Proper location of feed Unless the feed is appropriately located in the column, the reflux modification scope predicted by Eq. (1) in terms of H CGCC, min is erroneous. If the feed is located too high or too low in the column, the CGCC pinch at the feed stage will usually show a reduced

3 1111 Fig. 1. Effect of feed location on CGCC: (a) feed is located too low in the column; (b) feed is located too high in the column. For comparison, dashed line shows the CGCC when feed is properly located in the column. potential for reflux modification in terms of the enthalpy gap. In such cases, the utility consumption may be significantly decreased by simply relocating the feed as explained graphically in Fig. 1. Fig. 1a shows a typical CGCC for the case where the feed is located too low in the column. A sharp change in enthalpy is observed at the feed stage (at a relatively high temperature closer to the reboiler). This is due to the sudden jump in the driving forces in the column as may be seen on the x y diagram (King, 1980). If the feed is located too high in the column, the CGCC (Fig. 1b) shows a behavior similar to that in Fig. 1a but it is flipped vertically in a sense. Fig. 1 includes the CGCC (as a dashed line) for the case where the feed is properly located maintaining the same number of stages in the column. On comparing the CGCCs for the properly-located and improperly-located feed, it is observed that a significant reduction in the utility consumption is possible due to the alteration in the feed location without changing the number of stages. Furthermore, proper location of the feed enhances the scope for reduction in energy requirement by increasing the number of stages (often referred to as the scope for reflux modification). It is appropriate to target the reflux modification scope from the CGCC only after deciding where the feed is to be introduced into the column. Thus, the primary goal of this paper is to establish a proper feed location target that will minimize the utility consumption for a fixed number of stages and maximize the scope for energy conservation through reflux modification Reduction in simulation effort Several simulation runs are usually required to study the effect of reflux (or number of stages) and feed location, as well as determine their optimum values. Furthermore, the generation of a CGCC requires a simulation run, when the number of stages and/or feed location are altered. For illustration, consider a binary (benzene toluene) distillation column operating at 1.1 kg cm 2 pressure with a feed of 100 kg-mol h 1 (at dew point and 1.2 kg cm 2 containing 50% benzene), and 99% product purity desired at both the top and the bottom. Fig. 2 shows three CGCCs for this binary separation generated from the following three simulations: (a) 20 total stages (including total condenser and reboiler) with the feed at the eighth stage (from the top of the column); (b) 20 total stages with the feed at the 18th stage; and (c) 70 total stages with the feed at the 25th stage. The three CGCCs are substantially different in their appearance. However, Fig. 3 shows the data points from the three CGCCs (Fig. 2) unified into simply two curves. In fact, it is possible to coalesce all the CGCCs for this binary separation problem (corresponding to different feed stage locations and total number of stages in the distillation column) into a pair of master curves (which may be called invariant rectifying-stripping (IRS) curves). Therefore, an important motive of this work is to establish the IRS curves and consequently reduce the tedium involved in performing repeated simulations. 3. Invariant rectifying-stripping curves The invariant rectifying-stripping (IRS) curves are defined below based on a derivation for a simple distillation column (with a single feed and two products) at the minimum thermodynamic condition (MTC). The MTC is defined as reversible operation for a column with no entropy generation. It corresponds to a column with infinite stages having a side exchanger at every stage [as discussed in detail by Bandyopadhyay et al. (1998)]. Furthermore, the operating curve coincides with the equilibrium curve at MTC (King, 1980).

4 1112 Fig. 2. CGCC for benzene toluene system at different reflux ratios (number of stages) and feed locations: (a) 20-stage column with feed at stage 8; (b) 20-stage column with feed at stage 18; (c) 70-stage column with feed at stage In ariant rectifying cur e (T s. H R ) For the envelope in Fig. 4a, the overall mass balance and component balance are V min =L min +D (2) V min y*=l min x*+dx D (3) Eqs. (2) and (3) yield the minimum flows for liquid (L min ) and vapor (V min )tobe L min =D(x D y*)/(y* x*) (4) V min =D(x D x*)/(y* x*) (5) The enthalpy balance for the envelope is used to evaluate the enthalpy surplus (H R ) from V min H V =L min H L +DH D +H R (6) Eqs. (4) (6) may be combined to yield the following: H R =D[H V (x D x*)/(y* x*) H L (x D y*)/(y* x*) H D ] (7) Eq. (7) may be rewritten in terms of the slope of the (rectifying) line joining a point on the operating curve with the distillate point (x D, x D ) as shown in Fig. 4b. Thus, H R =D[(H V H L S R )/(1 S R ) H D ] (8) where S R =slope of the rectifying line=(x D y*)/ (x D x*)=l min /V min. The quantity H R signifies the minimum condenser load required to carry out a separation from x* tox D. By rotating the rectifying line from y*=x D to x*=x B with the distillate point (x D, x D ) as the pivot, its slope is continuously varied and the enthalpy surplus (H R ) calculated from Eq. (7) or Eq. (8) (for all possible values of reflux). This enthalpy surplus is then plotted as a function of temperature to give a T versus H R curve which may be termed the invariant rectifying curve. A typical invariant rectifying curve is shown in Fig. 4c In ariant stripping cur e (T s. H S ) For the envelope in Fig. 5a, the analogs for Eqs. (2) (5) are L min =V min +B (9) L min x*=v min y*+bx B (10) L min =B(y* x B )/(y* x*) (11) V min =B(x* x B )/(y* x*) (12) The enthalpy deficit (H S ) for the envelope in Fig. 5a may be determined from L min H L +H S =V min H V +BH B (13) On combining Eqs. (11) (13), the following expression for H S is obtained. H S =B[H V (x* x B )/(y* x*) H L (y* x B )/(y* x*) +H B ] (14) An alternative form of Eq. (14) may be obtained in terms of the slope of the (stripping) line joining a point Fig. 3. Invariant rectifying-stripping (IRS) curves based on coalescing the CGCCs from Fig. 2.

5 1113 Fig. 4. Generation of invariant rectifying curve: (a) rectifying section of a column for determination of enthalpy surplus; (b) rectifying line on x y diagram; (c) typical invariant rectifying curve. on the operating curve with the bottoms point (x B, x B ) as shown in Fig. 5b. On denoting the slope of the stripping line by S S =(y* x B )/(x* x B )=L min /V min, H S =B[(H V H L S S )/(S S 1)+H B ] (15) The quantity H S signifies the minimum reboiler load necessary to carry out a separation from x* tox B.As before, the stripping line may be rotated from x*=x B to y*=x D with the bottoms point (x B, x B ) as the pivot and the enthalpy deficit (H S ) continuously computed from Eq. (14) or Eq. (15) (for all possible values of reboil). This enthalpy deficit is then plotted as a function of temperature to yield a T versus H S curve which may be termed the invariant stripping curve. Fig. 5c shows a typical invariant stripping curve IRS cur es When the invariant rectifying curve (Fig. 4c) and the invariant stripping curve (Fig. 5c) are plotted on the same T H axis, the invariant rectifying-stripping (IRS) curves (T H R H S ) are obtained (see Fig. 3). Details of the procedure for actually generating such IRS curves are provided in the application examples discussed later. Physically, the IRS curves correspond to the enthalpy surpluses and deficits for the rectifying and stripping sections, respectively, for all possible values of reflux and reboil. It must be emphasized that the enthalpy surpluses and deficits are calculated on the basis of the minimum flows by neglecting the effect of the feed. The curves extend from T B to T D on the temperature scale. They correspond to the MTC (rather than merely the minimum reflux or infinite stages) and consequently represent heat cascades based on an infinite number of side exchangers. The invariance property of these curves is discussed next. A binary two-phase system has exactly two degrees of freedom as per Gibb s phase rule. On specifying the operating pressure and the separation, the distillation problem becomes deterministic. Therefore, H R and H S are functions of temperature only. In other words, the IRS curves are invariant to the feed location and the operating reflux for a distillation system whose operating pressure and separation are specified. The IRS curves may be used to target the feed location and the minimum energy requirement for the distillation system as described next. 4. Feed location target The material, component, and enthalpy balances for the overall column (Fig. 6) are F=D+B (16) Fz F =Dx D +Bx B (17) DH D +BH B FH F =Q r Q c (18) Eq. (18) shows that the parameter (which is the constant enthalpy difference for the utility requirements of the column from the first law of thermodynamics) really depends on the separation problem (i.e. D, H D, B, H B, F and H F ) and not on the column operation (i.e. Q r and Q c ). Eqs. (16) (18) may be combined with Eqs. (7) and (14) to determine the following relationship between H R and H S : H S =H R +F[H L (z F y*)/(y* x*) H V (z F x*)/(y* x*)+h F ]+ (19) The above relation may be employed to target the feed location. For this purpose, a fundamental analysis needs to be performed at the feed stage.

6 1114 Fig. 5. Generation of invariant stripping curve: (a) stripping section of a column for determination of enthalpy deficit; (b) stripping line on x y diagram; (c) typical invariant stripping curve Feed location criterion The material balance, component balance and enthalpy balance at a feed stage (Fig. 6) are as follows: L in +V in +F=L out +V out (20) L in x F * +V in y F * +Fz F =L out x F * +V out y F * (21) L in H L +V in H V +FH F =L out H L +V out H V (22) Eqs. (21) and (22) assume the composition and molar enthalpy changes of the saturated liquids and vapors over the feed stage are negligible. This assumption holds when the feed stage is pinched or the column is operating at the MTC. After some algebraic manipulations, Eqs. (20) (22) give (a) If =0 (i.e. Q r =Q c ), then the invariant rectifying as well as stripping curve need not be translated (Fig. 7a). (b) If 0 (i.e. Q r Q c ), then the invariant rectifying curve is translated to the right by, with no shift in the invariant stripping curve (Fig. 7b). (c) If 0 (i.e. Q r Q c ), then the invariant stripping curve is translated to the right by with no shift in the invariant rectifying curve (Fig. 7c). H L (z F y* F )/(y* F x* F ) H V (z F x* F )/(y* F x* F )+H F =0 (23) On substituting Eq. (23) into Eq. (19), the following relation is obtained: H S =H R + at the feed stage (24) Eq. (24) defines the criterion for the proper location of the feed at MTC. The next step is to work out the implications of this criterion on the IRS curves Translated IRS cur es Given the fact that enthalpies are relative (i.e. the enthalpy difference is important rather than the absolute enthalpy), the IRS curves can be horizontally flipped. Moreover, the invariant rectifying curve and/or the invariant stripping curve may be translated horizontally. The following convention may be adopted to translate the IRS curves in accordance with Eq. (24). Depending on the sign of (as defined in Eq. (18)), the translations may be conveniently classified into three cases: Fig. 6. Feed stage analysis of an MTC column.

7 1115 Fig. 7. Translated IRS curves: (a) =0 (Q r =Q c ); (b) 0 (Q r Q c ); (c) 0 (Q r Q c ). Note that the condenser and reboiler loads are approximately equal [case (a)] when the feed and products are saturated liquids (Terranova & Westerberg, 1989), which is not an uncommon situation. The other two cases occur depending on the thermal condition of the feed and products, e.g. case (b) can occur when the feed is a subcooled liquid and case (c) when the feed is a saturated vapor with the products being saturated liquids. Mathematically, the horizontal translations of the IRS curves may be represented as: H RT =H R + /2+ /2 (25) H ST =H S /2+ /2 (26) Eqs. (24) (26) may be combined to obtain H ST =H RT at the feed stage. Thus, the important conclusion is that the point of intersection of the translated IRS curves (as shown in Fig. 7) defines the target temperature for locating the feed (T F ) Feed stage location methodology Eq. (24) defines the feed location target in terms of temperature. Note that this feed location target is independent of the operating reflux (in contrast to the graphical McCabe Thiele and Ponchon Savarit methods). The target may be converted from temperature to stage number using the following methodology. The first step is to calculate H RT and H ST from Eqs. (7), (14), (25) and (26) using stage-by-stage values outputted by a converged simulation of a distillation column. Having generated H RT and H ST as functions of both stage number N and temperature T, the second step is to superpose the data points on the IRS curves (as shown in Fig. 8, where each open circle corresponds to a stage in the column). The feed stage in the column simulation is shown by a filled-in circle. If the feed is properly located (Fig. 8a), then the feed stage will be very close to the intersection point of the translated IRS curves. Furthermore, the rectifying and stripping sections of the simulated column will correspond to the portion of the invariant rectifying curve below T F and the portion of the invariant stripping curve above T F, respectively. When the feed is not properly located (Fig. 8b), then the stage number corresponding to the intersection point of the translated IRS curves (denoted by N I ) will not coincide with the feed stage number in the column simulation (denoted by N F ). Then, the feed stage relocation may be performed using N F =mean(n F, N I ). Here, N F denotes the stage to which the feed needs to be relocated in the next simulation and therefore requires to be rounded off to the nearest integer. Clearly, convergence to the proper feed stage location is achieved when N F =N F. Experience shows that the correction for the feed location based on the geometric mean leads to fast convergence (typically, within about three iterations). Conceptually, the above methodology attempts to systematically redistribute the open circles (corresponding to the column stages) over the IRS curves such that the filled-in circle (representing the feed stage) is either just above or just below the intersection point of the translated IRS curves. It must be noted that the methodology may be implemented directly with the simulation output (without plotting the circles on the IRS curves) by ensuring that the feed stage temperature from the simulation matches the target temperature T F. 5. Minimum energy target If the feed is properly located at T F, then the absolute minimum energy requirements for a binary distillation process may be established as follows. The portion of the invariant rectifying curve below T F and the portion of the invariant stripping curve above T F may be circumscribed by a right-angled trapezium. Then, the pinch on the IRS curves is defined as the point touching the vertical side of the trapezium. The widths of the parallel sides of the trapezium at the top and bottom

8 1116 Fig. 8. Locating the feed stage on translated IRS curves: (a) feed is located appropriately; (b) feed is located too high in the column. define the minimum energy targets for the reboiler and condenser, respectively (see Fig. 7). These minimum energy targets are related to and, in a sense, define the minimum reflux target. As an aside, it may be noted that the operating reflux target (for grassroots cases) and the reflux modification target (for retrofit cases) involve a cost optimization where the tradeoff between utility cost (based on the reboiler and condenser loads) and capital cost (based on the column diameter and number of stages) needs to be explored. Fig. 7 illustrates the case where the intersection point of the translated IRS curves determines the pinch. This is often the case; mathematically, it requires the IRS curves to be monotonic in nature. However, exceptions exist as demonstrated in the example later (on the non-ideal acetic acid water system) Relation between IRS cur es and CGCC The invariant property of the IRS curves allows the CGCC to be readily constructed from a knowledge of the stage temperatures. Fig. 9 shows how the CGCCs in Fig. 2 may be derived from the IRS curves in Fig. 3 after appropriate translation as per Eqs. (25) and (26). The CGCCs (horizontally flipped with respect to those in Fig. 2) are shown by heavy lines and the IRS curves by dashed lines in Fig. 9. To visualize the CGCCs as shown in Fig. 2, it is convenient to reflect the heavy lines on Fig. 9 in mirrors represented by vertical lines at a distance (on the abscissa) corresponding to the actual condenser or reboiler load (whichever is larger). This ensures consistency with the convention (Dhole & Linnhoff, 1993; Shenoy, 1995) where the enthalpy gaps at the top and bottom on the CGCCs denote the actual heat duties of the reboiler and condenser, respectively. The mathematical relation to obtain the CGCCs (without additional enthalpy calculations) by exploiting the invariant property of the IRS curves is given by H CGCC =Q C +H def (27) where H def = H R in the rectifying section, and H def = H S + in the stripping section of the column. The maximum scope for decrease in utility consumption by reflux reduction (i.e. by increasing the number of stages) is given by the enthalpy gap (horizontal distance) of the pinch point from the vertical mirror. The pinch is defined as the point closest to the vertical mirror. For the IRS curves, only the portion of the invariant rectifying curve below T F and the portion of the invariant stripping curve above T F must be considered while determining this enthalpy gap. As expected, Fig. 10 (which is a magnified view of Fig. 9a) shows the scope for reflux reduction according to the pinch based on the IRS curves (on appropriately locating the feed) to be higher than that based on the CGCC. Accordingly, Eq. (1) may be written more accurately as Q r Q r,min =Q c Q c,min =Q r H S,TF =Q c H R,TF D (R R min ) (28) where H R,TF and H S,TF are the enthalpy values at T F on the (not translated) invariant rectifying and stripping curves, respectively. 6. Application to binary distillation The enthalpy surplus (H R ) and the enthalpy deficit (H S ) may be directly evaluated from Eqs. (7) and (14) provided the enthalpies and compositions on the stage as well as for the feed and products are known. For binary systems, thermodynamic models for enthalpy and vapor liquid equilibrium may be readily used for this purpose. In general, the right-hand-sides of Eqs. (7) and (14) may be conveniently calculated for each stage of a distillation column from the output of a converged

9 1117 Fig. 9. CGCCs and their relation to IRS curves for benzene toluene system: (a) 20-stage column with feed at stage 8; (b) 20-stage column with feed at stage 18; (c) 70-stage column with feed at stage 25. simulation. In the examples that follow, the simulations are performed using the PRO/II ( ) software based on the problem data given in Table 1. Stage numbering starts from the top of the column with 1 denoting the condenser. The IRS curves are generated using the DISTARG (1998) software, which is primarily based on Eqs. (7) and (14). The results for all the examples are summarized in Table 2 for ready comparison Benzene toluene example Fig. 11a shows the CGCC for this binary distillation problem based on a simulation of a column comprising 20 total stages (including total condenser and reboiler) with the feed at the 15th stage. The simulated column has an operating reflux ratio of with reboiler and condenser duties of and kcal h 1, respectively. The CGCC pinch shows the energy savings potential by reflux reduction to be kcal h 1. Consequently, the minimum reflux ratio from Eq. (1) is Fig. 11b shows the translated IRS curves (on noting that = kcal h 1 ). Their point of intersection provides the target temperature for locating the feed as C. The parallel sides of the right-angled trapezium (that appropriately circumscribes the curves) establish the minimum load targets for the reboiler and condenser to be and kcal h 1, respectively. The corresponding minimum reflux ratio is As the IRS curves are monotonic, their intersection point also denotes the pinch. On superposing the circles corresponding to the stage temperatures (not shown), it is observed that the feed at the 15th stage is located too low in the column. Then, on using the feed stage location methodology (discussed earlier) and relocating the feed based on the geometric mean correction, the circles redistribute themselves such that the feed stage (filled-in circle) approximately coincides with the intersection point of the translated IRS curves (Fig. 11b) when the column is re-simulated with the feed on the tenth stage. The feed at the tenth stage yields reboiler and condenser loads of and kcal h 1, respectively. These are the minimum duties for a 20-staged column as may be verified through a simulator by varying the feed location. Simulation of a 100-stage column with the feed at the 50th stage yields an operating reflux ratio of with a feed stage temperature of C and thereby validates the targets (as shown in Table 2) Acetic acid water example Fig. 12a shows the CGCC for this non-ideal binary distillation problem generated from a simulation of a column consisting of 30 total stages (including total condenser and reboiler) with the feed at the 29th stage. The column simulation gives an operating reflux ratio of with reboiler and condenser duties of and kcal h 1, respectively. The CGCC pinch shows the scope for energy savings by reflux reduction to be kcal h 1 and the corresponding minimum reflux ratio to be The translated IRS curves (Fig. 12b) show an intersection point at 99 C, which defines the target temperature for locating the feed in this problem. The trapezium (which appears more of a rectangle because of kcal h 1 is practically insignificant) appropriately circumscribes only the portion of the invariant rectifying curve below 99 C and the portion of the invariant stripping curve above 99 C. The invariant rectifying curve is not monotonic and consequently, the pinch does not coincide with the intersection point of the IRS curves. Rather, there is a tangent pinch in the rectifying section. The trapezium shown in Fig. 12b has its vertical side just touching this pinch with the parallel sides defining the targets for the minimum reboiler load and minimum condenser load to be and kcal h 1, respectively. The corresponding minimum reflux ratio as per Eq. (1) is

10 1118 Fig. 10. Minimum energy targets and scope for reflux modification from (a) CGCC and (b) IRS curves. On superposing the circles corresponding to the stages on the IRS curves (not shown), it is observed that the feed at the 29th stage is located too low in the column. Use of the feed stage location methodology and re-simulation of the column with the feed on the 25th stage results in the filled-in circle (feed stage) relocating itself in the immediate neighborhood of the intersection point on the translated IRS curves (Fig. 12b). As in the benzene toluene example, it can be proven through simulations that this feed stage location yields the minimum reboiler and condenser duties for the given number of stages. Simulation of a 300-stage column with the feed appropriately located at the 276th stage results in an operating reflux ratio of with a feed stage temperature of 99.1 C thereby validating the targets (Table 2). Note that the ratio of the feed stage number to the total number of stages is not constant for a non-ideal system. Finally, it may be noted that the minimum energy targets in Table 2 based on the IRS curves differ considerably from those based on the CGCC because the feeds are grossly mislocated. The difference would not be dramatic had the feed been properly located during the CGCC generation. Importantly, the IRS curves (being independent of feed location) not only provide the true minimum energy target even with a grossly mislocated feed, but also provide a target for properly locating the feed. 7. Application to multicomponent distillation For multicomponent distillation, many methods exist to approximately predict the minimum energy requirements through plate-to-plate calculations (i.e. simulation). Koehler, Aguirre and Blass (1995) have reviewed the most important methods for calculating minimum energy requirement for ideal and nonideal distillation including the work of Doherty and co-workers (Levy, VanDongen and Doherty, 1985; Knight & Doherty, 1986; Julka & Doherty, 1993). Koehler et al. (1995) observed that most methods are based on the simulation of a portion or of an entire column, and a universal method which finds minimum energy consumption for nonideal and multicomponent distillation, at the touch of a button, has not yet been developed. The IRS-based method, discussed below, is a simulation-based approximate method to predict minimum energy requirement for general multicomponent distillation. However, in addition to minimum energy, targets for feed location, feed conditioning and side-exchangers can be simultaneously set through the IRS curves as discussed in the following sections. For reversible multicomponent distillation, the degrees of freedom are still two (Koehler, Aguirre & Blass, 1991). By arguments analogous to those for the binary case, the system becomes deterministic. The IRS curves are invariant to the feed location and the operating reflux on specifying the operating pressure and the separation. But, the sharpness of separation is generally limited in reversible multicomponent distillation (Fonyó, 1974; Franklin & Wilkinson, 1982). However, this limitation can be overcome during the generation of IRS curves using the pseudo-binary concept of a light and heavy key (Fonyó, 1974) that defines a practical near-minimum thermodynamic condition (Dhole & Linnhoff, 1993). For illustration, consider a multicomponent (heptane-octane-nonane-decane-c15 example in Table 1) distillation column operating at 200 kpa pressure with a feed of 1000 kg-mol h 1 (at 100 C and 200 kpa containing 20% of each component), and 0.9% octane desired at the bottom and 0.9% nonane at the top. For this multicomponent separation (more details of which are available in the next sub-section), Fig. 13 shows data for rectifying (T vs. H R ) and stripping (T vs. H S )

11 1119 Table 1 Data for various examples System Benzene toluene Acetic acid water Heptane-octane-nonane-decane-C15 Thermodynamic method SRK NRTL with enthalpy from LK SRK Operating pressure 1.1 kg cm 2 1kgcm kpa Feed data Flow-rate 100 kg mol h kg mol h kg mol h 1 Composition 50% each 69% water 20% each Pressure 1.2 kg cm 2 1kgcm kpa Temperature Dew point Bubble point 100 C Specifications Top 99% benzene 86.1% water 0.9% nonane Bottom 99% toluene 99% acetic-acid 0.9% octane Table 2 Comparison of targets from IRS curves with CGCC targets and simulation results a Benzene toluene Acetic acid water Multicomponent IRS CGCC SIMULATION N t =100, N F = 50 IRS CGCC SIMULATION IRS CGCC SIMULATION N t =300, N F =276 N t =180, N F =80 Q c,min Q r,min R min T F ( C) N.A N.A N.A T P ( C) and and a Q c,min and Q r,min in 10 6 kcal h 1 for benzene toluene and acetic acid water systems. Q c,min and Q r,min in MMBtu h 1 for multicomponent system. curves generated from five different simulations on varying the feed stage (N F ) and the total number of stages (N t ). The three data sets corresponding to relatively low reflux ratios (R=1.462, 1.315, and 1.305, i.e. close to the minimum reflux R min 1.173) practically define unique rectifying and stripping curves; however, as the reflux ratio increases, the data sets (for R=3.404 and 5.190) show a certain degree of deviation. Thus, the curves show near-invariance, to the total number of stages and feed location, close to the minimum reflux. The invariant property of the IRS curves does not hold rigorously for multicomponent systems because the distribution of the mole fractions of the components depends on the operating reflux of the column. Stupin and Lockhart (1968) noted that this distribution bears a non-linear relationship for any finite operating reflux. The separation of the extreme components improves with decreasing reflux and the other way around for intermediate components. From the Gilliland (1940) stage-reflux correlation, it may be noted that the change in reflux with stages is insignificant for a high number of stages (typically, if N 3N min ). The temperature vs. composition (T x y) and the enthalpy vs. composition (H x y) behaviors of pseudo-binary systems do not change significantly (Johnson & Morgan, 1985; Campagne, 1993) near the minimum reflux for the column. Therefore, the IRS curves for any pseudo-binary system can be taken to be invariant of the number of stages and the feed location for targeting purposes. Essentially, IRS curves for establishing targets in multicomponent systems must be generated through a simulation with a high number of stages (i.e. at a low reflux ratio). The targets need to be finally verified through rigorous column simulation Fi e components example The feed and product specifications for this example problem are 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. The 5-component distillation problem is simulated using the PRO/II ( ) software for a column with 18 total stages (including partial condenser and reboiler) and feed at the ninth stage. The mole fractions of nonane in the top product and octane in the bottom product are both specified to be The thermodynamic method is

12 1120 Fig. 11. Minimum energy targets for benzene toluene system from (a) CGCC and (b) IRS curves. Fig. 12. Minimum energy targets for acetic acid water system from (a) CGCC and (b) IRS curves. based on the SRK (Soave Redlich Kwong) equation of state. The condenser and reboiler duties (in MMBtu h 1 ) from the simulation are and 82.52, respectively. These compare reasonably well 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. For the purpose of generating the CGCC and the IRS curves (Fig. 14), heptane and octane are grouped as the light keys whereas the rest are grouped as the heavy keys in a manner similar to that adopted by Dhole and Linnhoff (1993). The distance of the CGCC pinch (which occurs at the eighth stage on Fig. 14a) from the temperature axis represents the scope for energy conservation and is observed to be MMBtu h 1 (corresponding to a minimum reflux ratio of in contrast to an operating reflux ratio of ). Dhole and Linnhoff (1993) observed that the CGCC shows scope for energy savings by about MMBtu h 1 through reduction in the reflux ratio. Fig. 14b shows the translated IRS curves ( =42.8 MMBtu h 1 ) based on a simulation of a 50-stage column with the feed at the 20th stage. The point of intersection of these curves provides the target temperature for locating the feed as C. The invariant rectifying and stripping curves are both not monotonic and consequently, two pinches are observed at and C. The parallel sides of the circumscribing trapezium establish the minimum reboiler and condenser load targets to be and MMBtu h 1, respectively. The corresponding minimum reflux ratio is On superposing the circles corresponding to the stage temperatures (not shown on Fig. 14b, but can be visualized from Fig. 14a), the feed at the eighth stage is observed to be the appropriate location. Simulation of a 180-stage column with the feed between the 80th and 90th stage yields the feed stage temperature to be C with reboiler and condenser duties of and MMBtu h 1, respectively. The pinch zones from the simulation are found to be at and C. These values compare well with the targets. The reflux ratio target (1.2727) differs from the operating reflux ratio (1.1734) based on the

13 1121 Fig. 13. Near-invariant property of (a) rectifying and (b) stripping curves for multicomponent system at different operating conditions. Fig. 14. Minimum energy targets for multicomponent system from (a) CGCC and (b) IRS curves. simulation because of the approximate value of used in Eq. (28). 8. IRS curves for feed preconditioning and side-exchanger targets Although the focus in this paper has been on minimum energy and feed location targets, the IRS curves have the potential to provide targets for feed preconditioning and side-exchangers. Feed preconditioning causes a change in the feed enthalpy. If Q F is the amount of heat exchanged with the feed, then Eq. (18) shows that the parameter will be changed by the same amount. For the sake of concreteness, consider preheating the feed by Q F for the case ( 0) depicted by the translated IRS curves in Fig. 7c. Then, the invariant stripping curve will further move to the right by an amount Q F according to Eq. (26) as shown by the dashed curve in Fig. 15a. The new intersection point defines the target temperature for the feed stage (denoted by T FP ). The important conclusion from Fig. 15a is that the difference between the translated IRS curves at a certain temperature T FP specifies the amount of heat required to change the feed stage temperature from T F to T FP. Mathematically, (H RT H ST ) TFP =Q F. Since either Q F or T FP may be arbitrarily varied, the equation defines the feed preconditioning target through a continuous mapping between Q F and T FP. Clearly, Q F may be computed if T FP is specified and vice versa. The feed preconditioning target based on the IRS curves is precise, in contrast to the fuzzy target (ColumnTarget, 1994) based on the CGCC. The target from the CGCC is approximate because visual inspection is required to estimate the extent of the sharp enthalpy change in the CGCC profile near the feed location (Dhole & Linnhoff, 1993; Ognisty, 1995). In fact, such sharp enthalpy changes in the CGCC may be caused by an inappropriate feed condition or position as observed by Dhole and Linnhoff (1993). Importantly, the IRS curves simultaneously target feed condition and position, allowing the feed to be properly located after feed preconditioning using the methodology discussed in Section 4.3 Side exchangers provide increased opportunities for heat integration and reduction in utility costs. As the IRS curves are fundamentally based on the MTC, they define the maximum heat load that can be placed on side exchangers at specified temperature levels. Fig. 15b

14 1122 Fig. 15. Application of invariant rectifying-stripping curves for: (a) feed preconditioning targets; (b) side-exchanger targets. shows corners truncated out of the trapezium (in Fig. 7c). The upper corner depicts the maximum scope to supply a portion (Q sr,max ) of the required heat through a side reboiler at a temperature (T sr ) below that of the main reboiler. The lower corner shows the maximum potential to remove a portion (Q sc,max ) of the excess heat through a side condenser at a temperature (T sc ) above that of the main condenser. The side exchanger targets from the IRS curves are conceptually equivalent to those defined by earlier workers (Naka et al., 1980; Ho & Keller, 1987). 9. Conclusions This work provides targets for distillation in terms of the minimum reboiler/condenser duties, feed location and pinch. These targets (with the exception of feed location) are analogous to those discussed by Linnhoff et al. (1982) for heat exchanger networks (HENs). The energy targets for distillation from the IRS curves are based purely on feed/products specifications and are established prior to column design. In a similar fashion, the energy targets for HENs from pinch analysis (composite and grand composite curves) are based purely on streams specifications and are established prior to network design. The analogs of hot utility load, cold utility load, and T min in HENs are reboiler duty, condenser duty, and reflux ratio in distillation. The problem of deciding loads amongst multiple utilities in HENs is equivalent to the case of distributing duties between side-reboilers and side-condensers in distillation. The IRS curves have the potential of providing targets for side exchangers on recognizing that the portion of the IRS curves within the circumscribed trapezium corresponds to the grand composite curve in HENs at T min =0. The significance of the pinch, in the context of distillation, may be stated as follows: no (side- )reboiling below the pinch and no (side-)condensing above the pinch. This is consistent with the observations of Naka et al. (1980) and Agrawal and Fidkowski (1996). It may be noted that the minimum energy target from the IRS curves is exact for any binary system, irrespective of its chemical nature. This is superior to the prediction from the minimum reflux equation of Underwood (1948), which assumes constant relative volatility and constant molar overflow. However, IRS curves for multicomponent systems are based on a pseudo-binary approach and this limitation does not exist in Underwood s method. As discussed earlier, the limitation may be overcome by generating IRS curves from a simulation of a column with a large number of stages (i.e. close to the minimum reflux). The key representation proposed in this work is the IRS curves. Earlier studies had generated only portions of such T H curves and, consequently, failed to recognize their invariance to feed location. Thus, IRS curves allow targets to be established for feed location. In fact, IRS curves simultaneously target feed location and minimum energy (which is equivalent to the scope for reflux modification) ahead of configuring the column. It is inappropriate to locate feed and reduce reflux sequentially as recommended by earlier works. Multiple simulations are not required to generate the IRS curves and establish targets from them. On the other hand, multiple simulations are required to set targets based on the CGCC because a new CGCC needs to be generated after each column modification. Thus, the simulation work is reduced (i.e. no simulation is necessary for binary systems and a single simulation is required for multicomponent systems) during targeting by IRS curves. Multiple simulations are necessary only for configuring the column (i.e. to locate the feed stage appropriately in a column with finite number of stages). A preliminary design procedure (Kister, 1992) involves four typical steps to determine: (1) minimum number of stages (e.g. by Fenske equation); (2) minimum reflux (e.g. by Underwood s equation); (3) actual

15 number of stages for a given reflux (e.g. by Gilliland s plot or a stage-reflux correlation); and (4) feed location (e.g. by Kirkbride s equation). This work provides an improved methodology for steps (2) and (4). In other words, steps (1) and (3) are done as before. The optimum reflux could be established by minimizing the total annual cost target starting with the IRS curves (Bandyopadhyay, 1999). Thus, the IRS-based method provides a systematic energy analysis tool to generate a thermodynamically efficient configuration of a distillation column while using some of the existing methods of preliminary design. Further, the possibility for integration (Ho & Keller, 1987) of the distillation column with the background process can be conveniently explored on a temperature enthalpy diagram since the behavior of the column is depicted by a set of invariant curves. It may be noted that for retrofit cases, feed relocation is easier to implement and has no major cost implication when compared to reflux modification. Appropriately relocating the feed may also help in debottlenecking. Furthermore, IRS curves are independent of the enthalpy of the feed and allow targeting for feed preconditioning (preheating/cooling). Current work is directed towards targeting the efficiency of feed preconditioning in terms of impact on reboiler/condenser loads. c CGCC D def F FP I in L max min out p r R RT sc sr S ST t TF V Superscript * 1123 condenser column grand composite curve distillate deficit feed preconditioned feed intersection point on translated IRS curves in to (entering) a stage liquid maximum minimum out of (leaving) a stage pinch reboiler rectifying curve rectifying curve (translated) side condenser side reboiler stripping curve stripping curve (translated) total (stages) at temperature T F vapor equilibrium condition 10. Notation B CGCC D F H IRS L LK MTC N NRTL Q R SRK S T V x y z Subscript B bottom product molar flow column grand composite curve distillate molar flow feed molar flow enthalpy invariant rectifying-stripping (curves) liquid molar flow Lee Kesler minimum thermodynamic condition stage number non-random two-liquid heat duty reflux ratio (L/D) Soave Redlich Kwong slope of rectifying/stripping line temperature vapor molar flow mole fraction in liquid mole fraction in vapor mole fraction in feed enthalpy difference defined in Eq. (18) heat of vaporization bottom product. References Agrawal, R., & Fidkowski, Z. T. (1996). On the use of intermediate reboilers in the rectifying section and condensers in the stripping section of a distillation column. Industrial & Chemistry Engineering Research, 35, Bandyopadhyay, S. (1999). Energy targeting for optimisation of distillation processes, Ph.D. thesis, Indian Institute of Technology, Bombay. Bandyopadhyay, S., Malik, R. K., & Shenoy, U. V. (1998). Temperature enthalpy curve for energy targeting of distillation columns. Computers & Chemical Engineering, 22(12), Benedict, M. (1947). Multistage separation processes. Transactions of the American Institute of Chemical Engineers, 43, 41. Campagne, W. v. L. (1993). Use Ponchon Savarit in your process simulation, Hydrocarbon Processing, 41, September. ColumnTarget (1994). SuperTarget for Windows, Version 3.0 User Guide, Linnhoff March, Cheshire, England. Dhole, V. R., & Linnhoff, B. (1993). Distillation column targets. Computers & Chemical Engineering, 17(5/6), DISTARG (1998). Version 2.0, Indian Institute of Technology, Bombay, India. Fitzmorris, R. E., & Mah, R. S. H. (1980). Improving distillation column design using thermodynamic availability analysis. American Institute of Chemical Engineers Journal, 26, Fonyó, Z. (1974). Thermodynamic analysis of rectification. I. Reversible model of rectification. International Chemical Engineering, 14, Franklin, N. L., & Wilkinson, M. B. (1982). Reversibility in the separation of multicomponent mixtures. Transactions of the Institution of Chemical Engineers, 60,