Improving Agility of Cryogenic Air Separation Plants - ACS Publications

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Ind. Eng. Chem. Res. 2008, 47, 394-404

Improving Agility of Cryogenic Air Separation Plants Jason Miller and William L. Luyben* Department of Chemical Engineering, Lehigh UniVersity, Bethlehem, PennsylVania 18015

Paul Belanger, Stephane Blouin, and Larry Megan Process and Systems R&D, Praxair Inc., Tonawanda, New York 14151

Cryogenic air separation plants that produce argon in addition to oxygen and nitrogen use two heat-integrated distillation columns and a side rectifier. The dynamics of the side rectifier are very slow because of three factors: the large number of separation stages, the small amount of argon in the air feed, and the high product purity. Currently, when the plant shuts down, the liquid inventory in the argon column drains into the upper (low-pressure) column. A normal start-up takes about 10 h to achieve argon product purity. The start-up time can be reduced significantly by using storage vessels to collect the liquid that drains from the argon column upon shutdown and reintroducing the liquid during the subsequent start-up. Compared to a 10 h start-up time with no collection points, the time required to achieve argon product purity is reduced to 3.35 h by using 2 collection points and is reduced to 2.23 h by using 6 collection points. 1. Introduction Historically, the ability of a process to reject load disturbances was the main criterion on which its dynamic performance was judged. The ability to quickly transition between operating conditions was of little importance because the operating conditions were changed rather infrequently. However, in recent years, there has been more emphasis placed on the ability of a process to rapidly transition between different operating conditions. There are two paths that can be taken in improving process agility. The first path involves making improvements to the control structure. The other path consists of the addition of, or the modification of, process equipment. In most cases, improvements to the control structure is the method preferred because it is not capital-intensive and can be accomplished without shutting down the process. Unfortunately, this approach is limited by the dynamics of the present process equipment. The ability to start up plants and transition between operating states efficiently is of particular interest in the area of cryogenic air separation. The only real costs encountered in the process are capital equipment costs and energy costs since the raw material (air) is taken directly from the atmosphere. Thus, if a plant were capable of producing product in a more efficient manner, energy cost and thus total costs could be reduced significantly. Also, the faster a plant can be started up, the more time existing manpower will have to take care of other tasks. In an ideal scenario (instantaneous start-up), the process could be started up and shut down in response to fluctuating power prices. The economic incentive for intermittent operation of cryogenic air separation plants has been discussed previously by the authors.1 Typically, a significant amount of time is required to restart a cryogenic air separation plant (Figure 1) after an interruption in operation or a scheduled shutdown. The shutdown or interruption may be brought about by a power failure or by economic concerns over high power rates. If the interruption is not planned, the time required to re-establish the desired product purities can be quite costly. For example, product demands by * To whom correspondence should be addressed. Tel.: 610-7584256. Fax: 610-758-5297. E-mail: [email protected].

customers have to be satisfied by other means. During current plant shutdown, liquid drains from the column trays or packing sections and collects in the upper (low-pressure) and lower (high-pressure) column sumps. Many times the collected liquid is drained before the next start-up, causing a loss of refrigeration to the plant. In a plant producing argon, a large amount of argon can be lost in this draining process, and as argon makes up less than 1% of air, this loss can be significant. Thus, it has been proposed that the collection of descending column liquid (from packing sections or trays) upon shutdown and the reintroduction of the collected liquid during the subsequent start-up can help reduce the time required to reach the desired product compositions in the plant. Although the methodology can be applied to all three distillation columns, the current investigation has focused on collection and redistribution from/to the argon columns only. A number of patents have been issued that involve the collection and re-distribution of process liquid for rapid startup of air separation plants.2-6 A range of implementations are discussed including the use of single or multiple storage locations, internal or external liquid storage, recirculation of liquid during start-up or one-way introduction, and collection of liquid from the argon column only or collection of liquid from the upper (low-pressure) and lower (high-pressure) columns also. Methods for reintroducing the collected material include pumping the stored liquid, pressurizing the storage vessel with vapor from another portion of the plant, or including a heat exchanger in the storage vessel and vaporizing the collected liquid. In the last scenario, some or all of the collected material is returned to the column in the vapor phase. A simplified schematic of the implementation that involves the use of a single, external storage vessel with the pressure driving force provided by a vapor stream from another portion of the plant is shown in Figure 2. During normal operation, the valve on the argon return would be open and that to the storage tank closed. Upon plant shutdown, the valve on the argon return would be closed and the valve to the storage tank opened. During the next start-up, vapor from the lower (high-pressure) column could be used to pressurize the storage tank to provide enough driving force to transfer the liquid from the storage tank to the argon column. Once all the collected liquid is introduced

10.1021/ie070975t CCC: $40.75 © 2008 American Chemical Society Published on Web 12/13/2007

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Figure 1. Simplified schematic of cryogenic air separation plant.

Figure 2. Simplified schematic of design modification.

into the column, the tank vent could be opened to remove the vapor that was used to pressurize the tank. Because the vapor

contains a large quantity of nitrogen, it is undesirable for the vapor to enter the argon column.

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Although there are several patents describing the collection and redistribution of liquid from/to argon columns, there is very little mention of quantitative improvements in start-up achieved by implementing such designs. Smith and Espie6 discuss simulation results for an argon column that is split into two shells because of height considerations in the cold box. Their results suggest that collecting liquid in the sump of the second argon column and recirculating liquid in the column during startup can reduce the time required to achieve product purity by 50% over the base case where no liquid is collected or recirculated. By collection and recirculation of liquid in both argon columns, the time required to achieve argon purity is reduced by 64% over the base case. However, until now, there has not been a study published that provides insights into the impact of the number of collection vessels and liquid introduction policy on the start-up of cryogenic air separation plants. In this study, we have assumed a “semi-cold” start-up. This means that the plant will have been shutdown for a brief period of time, at most a few days, before the next start-up. Thus, liquid is present in the column sumps prior to the introduction of air to the plant. As the plant remains idle. heat will be transferred to the cold box, which contains the distillation columns, from the atmosphere and the liquid in the system will eventually evaporate. When a plant is started with essentially zero liquid, this is characterized as a “warm” start. The “warm” start scenario is not considered in this study. 2. Process Description A typical super-staged argon cryogenic air separation plant (Figure 1) includes a double distillation column with a side rectifier to recover high-purity liquid argon. Feed air (from the atmosphere) is compressed and passed through an adsorbent bed of molecular sieves to remove water, carbon dioxide, acetylene, ethylene, butane, and other heavier hydrocarbons. This helps alleviate the potential dangers of hydrocarbonoxygen mixtures and prevents the freezing of material in the system. The feed air stream is split, with a good portion being expanded in the lower column turbine, after being cooled in the primary heat exchanger against returning cold oxygen and nitrogen product streams, along with the waste nitrogen stream. The expansion of the air provides refrigeration for the plant. This stream provides vapor air feed to the high-pressure column. The air that is not expanded is also cooled in the primary heat exchanger and provides liquid air for both the high-pressure and low-pressure columns. The lower column (high-pressure column) operates at approximately 85 psia (0.586 MPa) and separates the air into a high-purity nitrogen stream (top) and oxygen-enriched liquid stream (bottom). Nitrogen vapor at the top of the lower column is condensed against boiling liquid oxygen in the bottom of the upper column by heat exchange in a reboiler-condenser. The nitrogen stream from the top of the lower column is referred to as the “shelf transfer” and the enriched oxygen stream is called the “kettle transfer”. The upper (low-pressure) column operates at approximately 20 psia (0.138 MPa) and produces high-purity nitrogen (top) and oxygen (bottom) product streams. The oxygen liquid product stream is pumped to a higher pressure. A portion is vaporized in the primary heat exchanger and provides highpressure gaseous oxygen product, while the remainder goes to the product oxygen liquid storage tank. Reflux for both columns is generated at the top of the lower column (i.e., shelf transfer acts as reflux for the upper column). Additional reflux for the upper column is provided by a liquid “nitrogen-add” stream,

which is combined with the shelf transfer. The liquid nitrogenadd stream is provided by drawing from the liquid nitrogen storage tank or by recycling liquid from a nitrogen liquefier. A nitrogen liquefier includes a series of compression, expansion, and heat-exchange equipment.7 Argon boils between oxygen and nitrogen, which results in a peak argon composition in the lower portion of the upper column. A vapor side stream is drawn from the upper column near the argon peak and is fed to the super-staged argon column. Physically, the super-staged argon column consists of two separate shells due to height restrictions in the cold box. The vapor stream from the top of the first argon column is fed directly to the bottom of the second argon column. A pump is utilized to produce the driving force for liquid transfer from the sump of the second argon column to the top of the first. The argon columns produce a liquid argon product that contains parts-per-million level impurities of oxygen and nitrogen. The product stream is drawn several stages from the top of the column to prevent too much nitrogen from entering the product argon stream. Reflux for the argon column is provided by heat exchange in the argon condenser between the vapor at the top of the argon column and the oxygen-enriched liquid (kettle transfer) from the lower column. This stream, after expansion to the lower pressure, has a lower boiling point than the argon. The liquid from the bottom of the first argon column is fed to the upper column. The oxygen-enriched liquid and vapor from the cold (boiling) side of the argon condenser are also fed to the upper column. The oxygen product from the bottom of the upper column typically contains 99.5% or greater oxygen with the remainder being argon. The nitrogen product from the upper column typically contains parts-per-million level impurities of oxygen. 3. Plant Start-Up Model 3.1. Introduction. To analyze a variety of design modifications and liquid feed trajectories, a detailed start-up model of an existing cryogenic air separation plant has been developed, which is capable of reproducing historical plant start-up data. This model is based on a first-principles approach8 and was developed in gPROMS version 3.0 (Process Systems Enterprise Limited, London, UK). The model has proven to be quite efficient, with 17 h of plant operation being simulated in about 20-30 min. This 17 h span follows one particular period of plant operation from the initial introduction of air to the plant, through the start-up phase, followed by a period of steady-state operation, right up to the point of shutdown. The simulations were run on a Dell OPTIPLEX GX620 with an Intel Pentium 4HT processor. 3.2. General Modeling Equations. The model is based on a first-principles approach utilizing traditional component mole and stage energy balances as given by eqs 1 and 2.8 Note that the terms must be added for each feed and product stream,

d(MNxi,N) ) LN+1xi,N+1 - LNxi,N + VN-1yi,N-1 - VNyN (1) dt d(MNhN) ) LN+1hn+1 - LNhN + VN-1HN-1 - VNHN (2) dt where M is the total liquid molar holdup (lb‚mol), N is the stage number, i is the component number (1 ) argon, 2 ) oxygen, and 3 ) nitrogen), x is the liquid mole fraction, y is the vapor mole fraction, L is the liquid molar flow rate (lb‚mol/h), V is


the vapor molar flow rate (lb‚mol/h), h is the liquid molar enthalpy (Btu/lb‚mol), and H is the vapor molar enthalpy (Btu/ lb‚mol). For all column sections containing trays, a Francis-weir relationship was utilized to determine the liquid flow rates from each stage as shown in eqs 3 and 4.9 For all packing sections, the liquid flow rates leaving a given stage were determined as a function of the overall stage liquid holdup as described by eq 5,

LN ) 11988lw,NFl,N(how,N)1.5 how,N )

(3)

MN - hw,N Fl,NAact,N

(4)

LN ) f(MN)

(5)

where lw is the weir length (ft), Fl is the liquid molar density (lb‚mol/ft3), how is the height of the liquid over weir (ft), Aact is the available area on the tray (ft2), and hw is the weir height (ft). Vapor flows in the columns were determined by solving the full energy balance under a steady-state assumption. Both the energy and mole balances were assumed to be at steady state. This allows one to calculate the vapor molar flow rate from a given stage based on the liquid (L) and vapor (V) flows to that stage along with the liquid (h) and vapor (H) enthalpies around that stage as shown in eq 6.8 Note that the terms must be added to the energy balance for each product and feed stream.

VN ) LN+1

(

)

(

)

hN+1 - hN HN-1 - hN + VN-1 HN - hN HN - hN

RTavg dPtop [V - Lc - Vdraw] ) dt Vcolumn top

Q ) UA∆T

(8)

A ) fcAss

(9)

where Q is the heat-transfer rate (Btu/h), A is the heat-transfer area (ft2), ∆T is the temperature difference between fluids on the hot/cold sides of the condenser (R), fc is the level factor (between 0 and 1), Ass is the heat-transfer area representing full condenser coverage (ft2), and U is the overall heat-transfer coefficient (Btu/h‚ft2‚R). The rates of condensation in the lower and argon columns are determined as functions of the overall rate of heat transfer (Q), the molar enthalpy of the condensed liquid (h), and the molar enthalpy of the vapor entering the condenser (H) as shown in eq 10:

Lc )

Q (H - h)

(10)

(6)

The rate of change of the pressure at the top of each column, along with the boiling side of the argon condenser, was determined by performing a mole balance at the top of the columns as shown in eq 7.9 In general, the equation includes a term for the vapor flow rate from the top stage of each column (Vtop), the product vapor flow rate from the top of the column (Vdraw), and the condensation rate at the top of the column (Lc). The equation also includes a proportionality constant (RTavg/ Vcolumn). One should note that each balance does not necessarily include all three vapor flow terms. For example, the lower (highpressure) column does not have a vapor product being drawn from the top of the column and thus only has Vtop and Lc terms in the equation determining the rate of change of the pressure. The condensation rate is a function of the heat-transfer rate between the fluids on the hot and cold sides of the respective condensers, as described below,

( )

The heat duty (Q) in the main and argon condensers is a function of the overall heat-transfer coefficient (U), the heattransfer area (A), and the temperature difference (∆T) between the condensing vapor on the hot side of the condenser and the boiling liquid on the cold side as shown in eq 8. It was assumed that the overall heat-transfer area will vary linearly with the level on the boiling sides of the respective condensers between some maximum level corresponding to full heat transfer and a minimum level corresponding to zero heat transfer. Thus, the overall heat-transfer area (A) is a function of a level factor (fc) and the steady-state heat-transfer area (Ass), which represents full condenser coverage and thus full heat-transfer area (see eq 9),

(7)

where Ptop is the pressure at the top of the column (psia), R is the gas constant, 10.73 ft3‚psia/lb‚mol‚R, Tavg is the average steady-state column temperature (R), Vcolumn is the total column volume (ft3), Vtop is the vapor flow rate from the top stage of the column (lb‚mol/h), Lc is the condensation rate at the top of the column (lb‚mol/h), and Vdraw is the product vapor draw rate from the top of the column (lb‚mol/h). The pressure on the top stage of each column was determined by integrating eq 7 at each time step. The remaining stage pressures at each time step were obtained by assuming a constant stage pressure drop for each column.

Similarly, the vapor boilups in the main and argon condensers are calculated from energy balances. For example, the rate of boiling (V) on the cold side of the main condenser is a function of the overall heat-transfer rate (Q), the liquid (h) and vapor (H) enthalpies around the stage, and the liquid flow rate (L) to the stage as described in eq 11:

VN )

(

)

hN+1 - hN Q + LN+1 HN - hN (HN - hN)

(11)

All external flow rates in the model are calculated using the simple pressure drop relation described by eq 12. Thus, the flow rate is a function of the inlet pressure (Pin), the outlet pressure (Pout), a valve coefficient (κ), and the valve position (γ). The valve position (γ) is either a constant value, follows a specified time trajectory, or is set by a controller output signal,

F ) κγ(Pin - Pout)0.5

(12)

where F is the liquid or vapor molar flow rate (lb‚mol/h), κ is the valve coefficient (lb‚mol/%‚h‚psia0.5), γ is the valve position (%), Pin is the inlet pressure (psia), and Pout is the outlet pressure (psia). The primary heat exchanger is modeled as three countercurrent heat exchangers in series with a single pseudo cold stream, consisting of the product and waste nitrogen along with the product oxygen, contacting each incoming hot stream. Each countercurrent heat exchanger was broken up into a number of segments (NHX ) 20), with a cold stream temperature (Tc), hot stream temperature (Th), and metal mass temperature (Tm) in each section (see Figure 3). The metal mass temperature in each section is determined by integrating the energy balance for the metal mass in each section at each time step as shown in eq

398


Figure 3. Simplified schematic of heat-exchanger model.

13. The rate of change of the metal temperature is a function of the mass of the metal (mm), the heat capacity of the metal (Cp,m), the heat-transfer rate between the metal and the cold fluid (Qc), and the heat-transfer rate between the metal and the hot fluid (Qh). This metal mass temperature is then used to solve the steady-state energy balance on the cold (see eq 14) and hot (see eq 15) sides of the heat exchanger and to provide the temperatures of the hot and cold streams in each section of the heat exchanger. An average temperature between adjacent nodes is used to calculate the heat-transfer rate between the metal and fluids in each heat-exchanger section in eqs 14 and 15,

dTm 1 ) (Q - Qc) dt mmCp,m h

(13)

Qc,z ) mcCp,c(Tc,z - Tc,z-1) ) (UA)HX[Tm,z - 0.5(Tc,z + Tc,z-1)] (14) Qh,z ) mhCp,h(Th,z - Th,z-1) ) (UA)HX[0.5(Th,z + Th,z-1) - Tm,z] (15) where Tm is the metal mass temperature (R), z is the node number, mm is the mass of the metal in each section (lb), Cp,m is the heat capacity of the metal (Btu/lb‚R), Qh is the heattransfer rate between the metal and hot fluid (Btu/h), Qc is the heat-transfer rate between the metal and cold fluid (Btu/h), Tc is the temperature of the cold fluid (R), Th is the temperature of the hot fluid (R), (UA)HX is the product of the heat-transfer coefficient and heat-exchange area (Btu/h‚R), mc is the molar flow rate of the cold fluid (lb‚mol/h), mh is the molar flow rate of the hot fluid (lb‚mol/h), Cp,c is the heat capacity of the cold fluid (Btu/lb‚mol‚R), and Cp,h is the heat capacity of the hot fluid (Btu/lb‚mol‚R). It was assumed that the product of the heat-transfer coefficient and heat-exchange area, (UA)HX, between the metal and fluid is the same on both the hot and cold sides. The value of (UA)HX was chosen in such a way that the inlet and outlet temperatures for the heat exchangers would match the plant data at steady state for the given number of heat-exchanger sections. Thus, at steady state the metal mass temperature in each section is simply the average of the hot and cold temperatures in each section. All thermodynamic properties (liquid and vapor enthalpies, liquid molar volumes, etc.) and equilibrium compositions and temperatures are determined using Multiflash (Infochem Computer Services Ltd., London, UK), which is directly linked with gPROMS. The Peng-Robinson equation of state,10 with parameters regressed for cryogenic conditions, is utilized for all thermodynamic computations. Liquid-vapor equilibrium is assumed throughout the entire start-up phase. Each packing section height is converted into a given number of theoretical trays using an in-house correlation provided by the sponsor of the project (Praxair, Inc.).

3.3. Special Start-up Equations. In addition to the general modeling equations discussed in section 3.2, there are a number of equations geared directly toward plant start-up. First, the startup control logic for the plant was implemented in the model. The logic is used to automate the start-up of the plant by performing control moves that would typically be implemented manually by the plant operators. Several valves in the plant are moved according to this logic during start-up and neglecting the logic in the model makes it very difficult to capture the dynamic behavior of the plant during start-up. The logic involves a sequence of steps to transfer the given plant measurements into a particular control move. First, the inputs of the controllers (errors, rate of change of errors, etc.) are classified in terms of linguistic descriptions. For example, an error might be described as “high”, “low”, etc. A rule base is then consulted to determine how to manipulate the controller outputs in a qualitative sense based on one or more linguistic descriptions (ramp open valve, ramp close valve, etc.). Last, the outputs are transformed from their linguistic descriptions into actual numbers that a computer can process. This sequence of steps is captured in the model by a hierarchy of “if/then” logic. Next, several of the inlet conditions for the plant are specified functions of time. These include the compressor discharge pressure and temperature, which represent the inlet of the system being modeled. The compressors themselves are not modeled in detail. These variables are given as specified time trajectories by connecting small linear segments that represent the trajectories of the plant data. All of the individual linear segments can be grouped into a single equation using the “SGN” function in gPROMS. This function returns the sign of the argument. If the argument in the “SGN” function is greater than or equal to 0, the function returns a value of +1. If the argument in the “SGN” function is less than 0, the function returns a value of -1. For example, eq 16 shows a forcing function with two linear segments. Thus, if “t” is less than “t1”, then “y” is equal to the first linear segment “f1(t)”. If “t” is greater than “t1”, then “y” is equal to the second linear segment “f2(t)”. This same approach can be extended to any number of linear segments,

y)

1 + SGN(t - t1) 1 - SGN(t - t1) f1(t) + f2(t) (16) 2 2

where t is the current time (h), t1 is the time at which the first linear segment ends and the second begins (h), f1(t) is the first linear segment, f2(t) is the second linear segment, and y is the process variable. Last, a number of equations in section 3.2 were modified slightly to help maintain numerical stability. By its very nature, start-up modeling involves taking a plant from an idle state where very little, if any, liquid is inventoried on the trays and packing sections of the distillation columns, through a somewhat turbulent start-up phase, all the way to steady-state operation. The rapid swings in process variables that occur early in the start-up result in the models being highly susceptible to simulation failures due to numerical instability. To avoid any numerical difficulties, it was first assumed that liquid would not flow from a packing stage unless a sufficient amount of liquid (Msmall) was inventoried on that stage. The full flow equation described by eq 5 was not used until the liquid molar holdup (M) reached another specified critical value (Mlarge) as given by eqs 17 and 18. These critical values were chosen in a somewhat arbitrary manner and were used solely to maintain numerical stability. In the model, “MAX” and “MIN” functions


Figure 4. Simulation results: base model.

were used to restrict the parameter “” between a value of 0 and 1.

)

(

M - Msmall Mlarge - Msmall

)

(17)

L ) [f(M)]

(18)

A similar approach is used to transition into the full energy balance, given by eq 6, used to compute the vapor flow rates in each column. If the liquid molar holdup is below “Msmall”, then the vapor flow rate from a given stage is equal to the vapor flow rate to that stage. Once the liquid molar holdup reaches “Mlarge”, the full energy balance is used as shown in eq 19:

( (

VN ) LN+1

)

hN+1 - hN + HN - hN HN-1 - hN - VN-1 + VN-1 (19) VN-1 HN - hN

(

)

)

3.4. Simulation Results: Model vs Plant Data. A comparison of the simulation results obtained with the model described above against the actual plant data for several key process variables can be observed in Figures 4-7. All flow rates are presented as a percentage of the steady-state plant flow rate for each stream. Thus, each plant flow rate has a value of 100% at steady state. One can note that several of the stream flow rates, namely, the liquid air to the upper column (Figure 4c), shelf (Figure 5a), product nitrogen (Figure 5c), and argon feed (Figure 6c), show some deviation from the plant data at steady state. However, the deviations are not large enough to cause concern. One should note that liquid flow measurements in chemical plants, including air separation plants, are particularly prone to error. Overall, the composition trajectories for the shelf (Figure 5b), product oxygen (Figure 6b), and product argon

(Figure 7d), each presented as a deviation from the steady-state plant measurement, are captured very well by the model. This can also be said of the pressures in the lower (Figure 4a), upper (Figure 6a), and argon (Figure 7a) columns along with that in the argon condenser (Figure 7b). Overall, it was decided that the model captures the dynamic behavior of the plant adequately enough to validate any simulation results obtained in the design modification analysis (section 4 below). 4. Design Modifications 4.1. Introduction. 4.1.1. Description of Designs Studied. As mentioned above, there are many different potential implementations of the primary design modification discussed in the patent literature. In this paper, we discuss four different designs. The “A” in each design name refers to liquid being collected from the argon columns only, while the number refers to the total number of collection vessels. The first design, A6, involves collecting liquid from three separate points in each argon column for a total of six collection vessels. Designs A4, A2 (Figure 8), and A1 have also been studied. One should note that design A1 involves collection of liquid from the second argon column only, not collection of liquid from both argon columns in one vessel. There are more than six packed sections in the argon column, which means that the number of collection vessels can be extended beyond six. However, as the total number of packed sections in the column is proprietary, designs involving more than six collection vessels are not discussed in this paper. 4.1.2. Liquid Feed Trajectories. Similar to the wide range of potential implementations of the design modification, there are innumerable potential policies for reintroducing the collected liquid to the argon columns during start-up. In this study, one general policy has been tested. The policy involves feeding the collected liquid between two times, “tinit” and “tfinal”. Prior to tinit, the flow rate of liquid to the column is 0. At tinit, the flow rate of liquid is ramped to a maximum value over a 0.1 h period.

400




The flow rate remains at this maximum value for a period of time and is then ramped back down to 0 over a 0.1 h period, reaching a value of 0 at tfinal. Introducing ramps in the feed trajectory helps to maintain numerical stability in the model. The maximum flow rate is chosen such that all of the collected liquid is exhausted exactly at tfinal. The liquid from each

collection vessel was fed during the same time period. Thus, in the case of multiple collection points, the liquid begins to be fed from each vessel at the same tinit and the introduction from each vessel ceases at the same tfinal. The collected liquid was fed back to the top of the column section from which it was collected. It was assumed that sufficient pressure driving force



Figure 8. Simplified schematic design A2.

is available to transport the collected liquid to the argon columns. Last, it was assumed that the liquid fed to the columns during start-up is saturated and at an enthalpy close to that of the liquid on the stage to which it is fed. Thus, a term for the liquid fed to the argon columns during start-up is not included in the energy balance used to calculate the vapor flow rates in the columns. 4.1.3. Holdup and Composition of Collected Liquid. The steady-state simulation results for the base case were used to determine the holdup and composition of liquid collected for

each design. The total amount of liquid collected from the second argon column is approximately equivalent to 3.5 h of holdup of product argon at its steady-state flow rate, while that collected from the first column represents about 3 h of holdup. The holdup of liquid in each packing section of the argon columns at steady state is approximately the same. For design A2, the composition of the collected liquid in each vessel is equal to the average steady-state composition of liquid in the respective columns from which it was collected. As more vessels are used, the composition of the collected liquid will be closer to the steady-state compositions on the separation stage to which the liquid is reintroduced. 4.2. Trial-and-Error Optimization Approach. 4.2.1. Introduction. A trial-and-error simulation approach was used to determine the “optimal” liquid feed trajectories for each design. The minimum initial time chosen for the liquid introduction is 0.5 h. As one can observe from Figure 6c, this is prior to vapor feed being introduced into the argon column. The minimum final time is 0.75 h. Holding the initial time constant, the final time was increased by 0.25 h intervals (i.e., 0.75, 1.0, 1.25, etc.) until decreasing performance was observed. The initial time at which liquid is introduced was then shifted by 0.25 h and the same approach to adjusting the final time was utilized. This shifting of the initial and final times was continued until clear reductions in performance were observed. 4.2.2. Simulation Results. A summary of the simulation results obtained for designs A2 and A6 can be observed in Figures 9 and 10, respectively. A shift to the right in data points corresponds to a 0.25 h increase in tfinal. Thus, the first data point corresponds to feeding the collected liquid between 0.5 and 0.75 h. The second data point corresponds to feeding the collected liquid between 0.5 and 1.0 h. As one can observe from Figure 9, the fastest start-up for design A2 is 3.35 h. This is obtained by feeding the collected liquid between 0.75 and 1.5 h.

402


Figure 9. Simulation results: design A2.

Figure 10. Simulation results: design A6.

As one can observe from Figure 10, the fastest start-up obtained for design A6 is 2.23 h. This corresponds to feeding the liquid between 0.75 and 1.5 h. There is a significant drop in performance once an initial time for liquid introduction of 1.0 h is reached. Also, after 1.0 h, there is much less variability in the start-up time as tfinal is changed. This is caused by the column being sufficiently inventoried with liquid, from condensation of feed vapor, prior to the liquid introduction taking place. Thus, any potential advantage from segregating the liquid

by composition is lost if the liquid is introduced after the column is inventoried with liquid from condensation. The behavior of design A4 is quite similar to that of A6. A summary of the optimal trajectories for each design is provided in section 4.3 below. 4.3. Summary of “Optimal” Trajectories. A summary of the start-up time for the “optimal” liquid feed trajectories for each design can be observed in Figure 11. As the number of collection points increases, the start-up time for the argon


Figure 11. Summary of “optimal” results.

columns decreases. In other words, product is drawn earliest with design A6 (2.23 h), followed by A4 (2.64 h), A2 (3.35 h), and finally A1 (5.2 h). This is due to the fact that the liquid being introduced to the column is closer to the steady-state composition on the separation stage to which it is fed. The reductions in start-up time achieved with designs A2 (66%) and A1 (47%) are quite close to those reported by Smith and Espie6 (64% and 50%, respectively). The optimal trajectory for designs A6, A4, and A2 involves feeding the collected liquid between 0.75 and 1.5 h. The optimal trajectory for design A1 involves feeding the collected liquid between 1.5 and 1.75 h. 5. Extensions and Future Work In the current work we have assumed that the trajectory of the liquid fed to the argon column during start-up would involve a rapid ramping of the flow rate to its maximum value, followed by a steady flow rate, and finally a ramping of the flow rate back to 0. However, there are a vast number of feed trajectories that can be utilized. It is possible that the start-up time can be further reduced by implementing alternative feed trajectories. Similarly, one can adjust the feed locations and also decouple the feed trajectories from each vessel. Also, we have utilized a trial-and-error approach to determine the optimal feed trajectories for each design. However, it is possible that one can obtain improved solutions over those discussed in the paper by employing more rigorous dynamic optimization techniques. In the current work, we have limited ourselves to collecting/ feeding liquid from/to the super-staged argon column. However, as mentioned in the patent literature,2 the methodology can also be applied to the other distillation columns. Extending the design modifications to each of the distillation columns simultaneously makes for a much more complicated optimization problem. Thus, a trial-and-error approach would be highly inefficient. Although this paper discusses the improvements in start-up that can be achieved by collecting/reintroducing liquid from/to

argon columns, a detailed economic analysis has not been performed. One must determine the trade-offs between the increased capital costs incurred by implementing the design modifications versus the improved plant performance. Ultimately, an analysis has to be performed to determine which implementation is most economically attractive and if the expected return on investment makes such design modifications worthwhile. Nomenclature A ) heat-transfer area (ft2) Aact ) available area on tray (ft2) Ass ) heat-transfer area representing full condenser coverage (ft2) Cp,c ) heat capacity of cold fluid (Btu/lb‚mol‚R) Cp,h ) heat capacity of hot fluid (Btu/lb‚mol‚R) Cp,m ) heat capacity of metal (Btu/lb‚R) F ) liquid or vapor molar flow rate (lb‚mol/h) f1(t) ) first linear segment f2(t) ) second linear segment fc ) level factor (between 0 and 1) h ) liquid molar enthalpy (Btu/lb‚mol) H ) vapor molar enthalpy (Btu/lb‚mol) how ) height of liquid over weir (ft) hw ) weir height (ft) L ) liquid molar flow rate (lb‚mol/h) Lc ) condensation rate at top of the column (lb‚mol/h) lw ) weir length (ft) M ) total liquid molar holdup (lb‚mol) mc ) molar flow rate of cold fluid (lb‚mol/h) mh ) molar flow rate of hot fluid (lb‚mol/h) mm ) mass of metal in each section (lb) Pin ) inlet pressure (psia) Pout ) outlet pressure (psia) Ptop ) pressure at top of column (psia)

404


Q ) heat-transfer rate (Btu/h) Qc ) heat-transfer rate between metal and cold fluid (Btu/h) Qh ) heat-transfer rate between metal and hot fluid (Btu/h) R ) gas constant, 10.73 ft3‚psia/lb‚mol‚R t ) current time (h) t1 ) time at which first linear segment ends and second begins (h) Tavg ) average steady-state column temperature (R) Tc ) temperature of cold fluid (R) Th ) temperature of hot fluid (R) Tm ) metal mass temperature (R) ∆T ) temperature difference between fluids on hot/cold sides of condenser (R) U ) overall heat-transfer coefficient (Btu/h‚ft2‚R) (UA)HX ) product of heat-transfer coefficient and heat-exchange area (Btu/h‚R) V ) vapor molar flow rate (lb‚mol/h) Vcolumn ) total column volume (ft3) Vdraw ) product vapor draw rate from top of column (lb‚mol/h) Vtop ) vapor flow rate from top stage of column (lb‚mol/h) x ) liquid mole fraction y ) vapor mole fraction y ) process variable Index Variables i ) component number (1 ) argon, 2 ) oxygen, 3 ) nitrogen) N ) stage number z ) node number Greek Letters ) liquid holdup factor γ ) valve position (%) κ ) valve coefficient (lb‚mol/%‚h‚psia0.5) Fl ) liquid molar density (lb‚mol/ft3)

gPROMS Functions MIN ) returns minimum value MAX ) returns maximum value SGN ) returns sign (i.e., +1 or -1) of argument Literature Cited (1) Miller, J.; Luyben, W. L.; Blouin, S. Economic Incentive for Intermittent Operation of Air Separation Plants with Variable Power Costs. Ind. Eng. Chem. Res., in press. (2) Billingham, J. F.; Bonaquist, D. P.; Dray, J. R.; Lockett, M. J.; Beddome, R. A. Rapid Restart System for Cryogenic Air Separation Plant. U.S. Patent No. 6272884 B1, Praxair Technology, Inc., Aug 14, 2001. (3) Darredeau, B.; Peyron, J.-M. Process for Restarting an Auxiliary Column for Argon/Oxygen Separation by Distillation and Corresponding Installation. U.S. Patent No. 5505051, L’Air Liquide, Societe Anonyme pour l’Etude et l’Exploitation des Procedes Georges Claude, April 9, 1996. (4) Moll, A.; Kunz, C. Argon-Producing Air Rectification Plant Servicing Process. Patent No. DE19734482, Linde AG, March 5, 1998. (5) Rohde, W.; Scho¨npflug, E. Process and Apparatus for Operating an Air Separation Plant. Patent No. DE3436897, Linde AG, 1986. (6) Smith, O. J., IV; Espie, D. M. Recirculation of Argon Sidearm Column for Fast Response. U.S. Patent No. 6070433, Air Products and Chemicals, Inc., June 6, 2000. (7) Olszewski, W. J. Gas liquefaction process and apparatus. U.S. Patent No. 3677019, Union Carbide Corporation, July 18, 1972. (8) Roffel, B.; Betlem, B. H. L; de Ruijter, J. A. F. First principles dynamic modeling and multivariable control of a cryogenic distillation process. Comput. Chem. Eng. 2000, 24, 111-123. (9) Luyben, W. L. Process Modeling, Simulation, and Control for Chemical Engineers, 2nd ed.; McGraw-Hill, Inc.: New York, 1990; pp 67 and 141-142. (10) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59-64.

ReceiVed for reView July 18, 2007 ReVised manuscript receiVed October 2, 2007 Accepted October 17, 2007 IE070975T

Improving Agility of Cryogenic Air Separation Plants - ACS Publications

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