Improving Agility of Cryogenic Air Separation Plants

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-integrateddistillation columns and a side rectifier. The dynamics of the side rectifier are very slow because of threefactors: the large number of separation stages, the small amount of argon in the air feed, and the high productpurity. 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 timecan be reduced significantly by using storage vessels to collect the liquid that drains from the argon columnupon shutdown and reintroducing the liquid during the subsequent start-up. Compared to a 10 h start-up timewith no collection points, the time required to achieve argon product purity is reduced to 3.35 h by using 2collection points and is reduced to 2.23 h by using 6 collection points.

1. Introduction

Historically, the ability of a process to reject load disturbanceswas the main criterion on which its dynamic performance wasjudged. The ability to quickly transition between operatingconditions was of little importance because the operating condi-tions were changed rather infrequently. However, in recent years,there has been more emphasis placed on the ability of a processto rapidly transition between different operating conditions.

There are two paths that can be taken in improving processagility. The first path involves making improvements to thecontrol structure. The other path consists of the addition of, orthe modification of, process equipment. In most cases, improve-ments to the control structure is the method preferred becauseit is not capital-intensive and can be accomplished withoutshutting down the process. Unfortunately, this approach islimited by the dynamics of the present process equipment.

The ability to start up plants and transition between operatingstates efficiently is of particular interest in the area of cryogenicair separation. The only real costs encountered in the processare capital equipment costs and energy costs since the rawmaterial (air) is taken directly from the atmosphere. Thus, if aplant were capable of producing product in a more efficientmanner, energy cost and thus total costs could be reducedsignificantly. Also, the faster a plant can be started up, the moretime existing manpower will have to take care of other tasks.In an ideal scenario (instantaneous start-up), the process couldbe started up and shut down in response to fluctuating powerprices. The economic incentive for intermittent operation ofcryogenic air separation plants has been discussed previouslyby the authors.1

Typically, a significant amount of time is required to restarta cryogenic air separation plant (Figure 1) after an interruptionin operation or a scheduled shutdown. The shutdown orinterruption may be brought about by a power failure or byeconomic concerns over high power rates. If the interruption isnot planned, the time required to re-establish the desired productpurities can be quite costly. For example, product demands by

customers have to be satisfied by other means. During currentplant shutdown, liquid drains from the column trays or packingsections and collects in the upper (low-pressure) and lower(high-pressure) column sumps. Many times the collected liquidis drained before the next start-up, causing a loss of refrigerationto the plant. In a plant producing argon, a large amount of argoncan be lost in this draining process, and as argon makes up lessthan 1% of air, this loss can be significant. Thus, it has beenproposed that the collection of descending column liquid (frompacking sections or trays) upon shutdown and the reintroductionof the collected liquid during the subsequent start-up can helpreduce the time required to reach the desired product composi-tions in the plant. Although the methodology can be applied toall three distillation columns, the current investigation hasfocused on collection and redistribution from/to the argoncolumns only.

A number of patents have been issued that involve thecollection and re-distribution of process liquid for rapid start-up of air separation plants.2-6 A range of implementations arediscussed including the use of single or multiple storagelocations, internal or external liquid storage, recirculation ofliquid during start-up or one-way introduction, and collectionof liquid from the argon column only or collection of liquidfrom the upper (low-pressure) and lower (high-pressure) col-umns also. Methods for reintroducing the collected materialinclude pumping the stored liquid, pressurizing the storage vesselwith vapor from another portion of the plant, or including aheat exchanger in the storage vessel and vaporizing the collectedliquid. In the last scenario, some or all of the collected materialis returned to the column in the vapor phase.

A simplified schematic of the implementation that involvesthe use of a single, external storage vessel with the pressuredriving force provided by a vapor stream from another portionof the plant is shown in Figure 2. During normal operation, thevalve on the argon return would be open and that to the storagetank closed. Upon plant shutdown, the valve on the argon returnwould 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 provideenough driving force to transfer the liquid from the storage tankto the argon column. Once all the collected liquid is introduced

* To whom correspondence should be addressed. Tel.: 610-758-4256. Fax: 610-758-5297. E-mail: [email protected].

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

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

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

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

Figure 1. Simplified schematic of cryogenic air separation plant.

Figure 2. Simplified schematic of design modification.

Ind. Eng. Chem. Res., Vol. 47, No. 2, 2008395

Although there are several patents describing the collectionand redistribution of liquid from/to argon columns, there is verylittle mention of quantitative improvements in start-up achievedby implementing such designs. Smith and Espie6 discusssimulation results for an argon column that is split into twoshells because of height considerations in the cold box. Theirresults suggest that collecting liquid in the sump of the secondargon column and recirculating liquid in the column during start-up can reduce the time required to achieve product purity by50% over the base case where no liquid is collected orrecirculated. By collection and recirculation of liquid in bothargon columns, the time required to achieve argon purity isreduced by 64% over the base case. However, until now, therehas not been a study published that provides insights into theimpact of the number of collection vessels and liquid introduc-tion policy on the start-up of cryogenic air separation plants.

In this study, we have assumed a “semi-cold” start-up. Thismeans that the plant will have been shutdown for a brief periodof time, at most a few days, before the next start-up. Thus, liquidis present in the column sumps prior to the introduction of airto the plant. As the plant remains idle. heat will be transferredto the cold box, which contains the distillation columns, fromthe atmosphere and the liquid in the system will eventuallyevaporate. When a plant is started with essentially zero liquid,this is characterized as a “warm” start. The “warm” start scenariois 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 siderectifier to recover high-purity liquid argon. Feed air (from theatmosphere) is compressed and passed through an adsorbentbed of molecular sieves to remove water, carbon dioxide,acetylene, ethylene, butane, and other heavier hydrocarbons.This helps alleviate the potential dangers of hydrocarbon-oxygen mixtures and prevents the freezing of material in thesystem.

The feed air stream is split, with a good portion beingexpanded in the lower column turbine, after being cooled inthe primary heat exchanger against returning cold oxygen andnitrogen 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 heatexchanger and provides liquid air for both the high-pressureand low-pressure columns.

The lower column (high-pressure column) operates at ap-proximately 85 psia (0.586 MPa) and separates the air into ahigh-purity nitrogen stream (top) and oxygen-enriched liquidstream (bottom). Nitrogen vapor at the top of the lower columnis condensed against boiling liquid oxygen in the bottom of theupper column by heat exchange in a reboiler-condenser. Thenitrogen stream from the top of the lower column is referred toas the “shelf transfer” and the enriched oxygen stream is calledthe “kettle transfer”. The upper (low-pressure) column operatesat approximately 20 psia (0.138 MPa) and produces high-puritynitrogen (top) and oxygen (bottom) product streams. The oxygenliquid product stream is pumped to a higher pressure. A portionis vaporized in the primary heat exchanger and provides high-pressure gaseous oxygen product, while the remainder goes tothe product oxygen liquid storage tank. Reflux for both columnsis generated at the top of the lower column (i.e., shelf transferacts as reflux for the upper column). Additional reflux for theupper column is provided by a liquid “nitrogen-add” stream,

which is combined with the shelf transfer. The liquid nitrogen-add stream is provided by drawing from the liquid nitrogenstorage tank or by recycling liquid from a nitrogen liquefier. Anitrogen liquefier includes a series of compression, expansion,and heat-exchange equipment.7

Argon boils between oxygen and nitrogen, which results ina peak argon composition in the lower portion of the uppercolumn. A vapor side stream is drawn from the upper columnnear the argon peak and is fed to the super-staged argon column.Physically, the super-staged argon column consists of twoseparate shells due to height restrictions in the cold box. Thevapor stream from the top of the first argon column is feddirectly to the bottom of the second argon column. A pump isutilized to produce the driving force for liquid transfer fromthe sump of the second argon column to the top of the first.The argon columns produce a liquid argon product that containsparts-per-million level impurities of oxygen and nitrogen. Theproduct stream is drawn several stages from the top of thecolumn to prevent too much nitrogen from entering the productargon stream. Reflux for the argon column is provided by heatexchange in the argon condenser between the vapor at the topof the argon column and the oxygen-enriched liquid (kettletransfer) from the lower column. This stream, after expansionto the lower pressure, has a lower boiling point than the argon.The liquid from the bottom of the first argon column is fed tothe upper column. The oxygen-enriched liquid and vapor fromthe cold (boiling) side of the argon condenser are also fed tothe upper column. The oxygen product from the bottom of theupper column typically contains 99.5% or greater oxygen withthe remainder being argon. The nitrogen product from the uppercolumn typically contains parts-per-million level impurities ofoxygen.

3. Plant Start-Up Model

3.1. Introduction. To analyze a variety of design modifica-tions and liquid feed trajectories, a detailed start-up model ofan 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 wasdeveloped in gPROMS version 3.0 (Process Systems EnterpriseLimited, London, UK). The model has proven to be quiteefficient, with 17 h of plant operation being simulated in about20-30 min. This 17 h span follows one particular period ofplant operation from the initial introduction of air to the plant,through the start-up phase, followed by a period of steady-stateoperation, right up to the point of shutdown. The simulationswere run on a Dell OPTIPLEX GX620 with an Intel Pentium4HT processor.

3.2. General Modeling Equations.The model is based ona first-principles approach utilizing traditional component moleand stage energy balances as given by eqs 1 and 2.8 Note thatthe terms must be added for each feed and product stream,

whereM is the total liquid molar holdup (lb‚mol), N is the stagenumber,i is the component number (1) argon, 2) oxygen,and 3) nitrogen),x is the liquid mole fraction,y is the vapormole fraction,L is the liquid molar flow rate (lb‚mol/h), V is

d(MNxi,N)

dt) LN+1xi,N+1 - LNxi,N + VN-1yi,N-1 - VNyN (1)

d(MNhN)

dt) LN+1hn+1 - LNhN + VN-1HN-1 - VNHN (2)

396 Ind. Eng. Chem. Res., Vol. 47, No. 2, 2008

the vapor molar flow rate (lb‚mol/h), h is the liquid molarenthalpy (Btu/lb‚mol), andH is the vapor molar enthalpy (Btu/lb‚mol).

For all column sections containing trays, a Francis-weirrelationship was utilized to determine the liquid flow rates fromeach stage as shown in eqs 3 and 4.9 For all packing sections,the liquid flow rates leaving a given stage were determined asa function of the overall stage liquid holdup as described by eq5,

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 isthe available area on the tray (ft2), andhw is the weir height(ft).

Vapor flows in the columns were determined by solving thefull energy balance under a steady-state assumption. Both theenergy and mole balances were assumed to be at steady state.This allows one to calculate the vapor molar flow rate from agiven stage based on the liquid (L) and vapor (V) flows to thatstage along with the liquid (h) and vapor (H) enthalpies aroundthat stage as shown in eq 6.8 Note that the terms must be addedto the energy balance for each product and feed stream.

The rate of change of the pressure at the top of each column,along with the boiling side of the argon condenser, wasdetermined by performing a mole balance at the top of thecolumns as shown in eq 7.9 In general, the equation includes aterm 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 necessarilyinclude all three vapor flow terms. For example, the lower (high-pressure) column does not have a vapor product being drawnfrom the top of the column and thus only hasVtop andLc termsin the equation determining the rate of change of the pressure.The condensation rate is a function of the heat-transfer ratebetween the fluids on the hot and cold sides of the respectivecondensers, as described below,

wherePtop is the pressure at the top of the column (psia),R isthe gas constant, 10.73 ft3‚psia/lb‚mol‚R, Tavg is the averagesteady-state column temperature (R), Vcolumnis the total columnvolume (ft3), Vtop is the vapor flow rate from the top stage ofthe column (lb‚mol/h), Lc is the condensation rate at the top ofthe column (lb‚mol/h), andVdraw is the product vapor draw ratefrom the top of the column (lb‚mol/h).

The pressure on the top stage of each column was determinedby integrating eq 7 at each time step. The remaining stagepressures at each time step were obtained by assuming a constantstage pressure drop for each column.

The heat duty (Q) in the main and argon condensers is afunction of the overall heat-transfer coefficient (U), the heat-transfer area (A), and the temperature difference (∆T) betweenthe condensing vapor on the hot side of the condenser and theboiling liquid on the cold side as shown in eq 8. It was assumedthat the overall heat-transfer area will vary linearly with thelevel on the boiling sides of the respective condensers betweensome maximum level corresponding to full heat transfer and aminimum level corresponding to zero heat transfer. Thus, theoverall heat-transfer area (A) is a function of a level factor (fc)and the steady-state heat-transfer area (Ass), which representsfull condenser coverage and thus full heat-transfer area (see eq9),

whereQ is the heat-transfer rate (Btu/h),A is the heat-transferarea (ft2), ∆T is the temperature difference between fluids onthe hot/cold sides of the condenser (R), fc is the level factor(between 0 and 1),Ass is the heat-transfer area representing fullcondenser coverage (ft2), and U is the overall heat-transfercoefficient (Btu/h‚ft2‚R).

The rates of condensation in the lower and argon columnsare determined as functions of the overall rate of heat transfer(Q), the molar enthalpy of the condensed liquid (h), and themolar enthalpy of the vapor entering the condenser (H) as shownin eq 10:

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

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

whereF is the liquid or vapor molar flow rate (lb‚mol/h), κ isthe valve coefficient (lb‚mol/%‚h‚psia0.5), γ is the valve position(%), Pin is the inlet pressure (psia), andPout is the outlet pressure(psia).

The primary heat exchanger is modeled as three countercur-rent heat exchangers in series with a single pseudo cold stream,consisting of the product and waste nitrogen along with theproduct oxygen, contacting each incoming hot stream. Eachcountercurrent heat exchanger was broken up into a number ofsegments (NHX ) 20), with a cold stream temperature (Tc), hotstream temperature (Th), and metal mass temperature (Tm) ineach section (see Figure 3). The metal mass temperature in eachsection is determined by integrating the energy balance for themetal mass in each section at each time step as shown in eq

LN ) 11988lw,NFl,N(how,N)1.5 (3)

how,N )MN

Fl,NAact,N- hw,N (4)

LN ) f(MN) (5)

VN ) LN+1(hN+1 - hN

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

HN - hN) (6)

dPtop

dt) ( RTavg

Vcolumn)[Vtop - Lc - Vdraw] (7)

Q ) UA∆T (8)

A ) fcAss (9)

Lc ) Q(H - h)

(10)

VN ) Q(HN - hN)

+ LN+1(hN+1 - hN

HN - hN) (11)

F ) κγ(Pin - Pout)0.5 (12)


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

where Tm is the metal mass temperature (R), z is the nodenumber,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 heat-transfer rate between the metal and hot fluid (Btu/h),Qc is theheat-transfer rate between the metal and cold fluid (Btu/h),Tc

is the temperature of the cold fluid (R), Th is the temperature ofthe hot fluid (R), (UA)HX is the product of the heat-transfercoefficient and heat-exchange area (Btu/h‚R), mc is the molarflow rate of the cold fluid (lb‚mol/h),mh is the molar flow rateof the hot fluid (lb‚mol/h), Cp,c is the heat capacity of the coldfluid (Btu/lb‚mol‚R), and Cp,h is the heat capacity of the hotfluid (Btu/lb‚mol‚R).

It was assumed that the product of the heat-transfer coefficientand heat-exchange area, (UA)HX, between the metal and fluidis 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 temperaturesfor the heat exchangers would match the plant data at steadystate for the given number of heat-exchanger sections. Thus, atsteady state the metal mass temperature in each section is simplythe average of the hot and cold temperatures in each section.

All thermodynamic properties (liquid and vapor enthalpies,liquid molar volumes, etc.) and equilibrium compositions andtemperatures are determined using Multiflash (Infochem Com-puter Services Ltd., London, UK), which is directly linked withgPROMS. The Peng-Robinson equation of state,10 withparameters regressed for cryogenic conditions, is utilized forall thermodynamic computations. Liquid-vapor equilibrium isassumed throughout the entire start-up phase. Each packingsection height is converted into a given number of theoreticaltrays using an in-house correlation provided by the sponsor ofthe project (Praxair, Inc.).

3.3. Special Start-up Equations.In addition to the generalmodeling equations discussed in section 3.2, there are a numberof equations geared directly toward plant start-up. First, the start-up control logic for the plant was implemented in the model.The logic is used to automate the start-up of the plant byperforming control moves that would typically be implementedmanually by the plant operators. Several valves in the plant aremoved according to this logic during start-up and neglectingthe logic in the model makes it very difficult to capture thedynamic behavior of the plant during start-up.

The logic involves a sequence of steps to transfer the givenplant measurements into a particular control move. First, theinputs 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 baseis then consulted to determine how to manipulate the controlleroutputs in a qualitative sense based on one or more linguisticdescriptions (ramp open valve, ramp close valve, etc.). Last,the outputs are transformed from their linguistic descriptionsinto actual numbers that a computer can process. This sequenceof steps is captured in the model by a hierarchy of “if/then”logic.

Next, several of the inlet conditions for the plant are specifiedfunctions of time. These include the compressor dischargepressure and temperature, which represent the inlet of the systembeing modeled. The compressors themselves are not modeledin detail. These variables are given as specified time trajectoriesby connecting small linear segments that represent the trajec-tories of the plant data. All of the individual linear segmentscan be grouped into a single equation using the “SGN” functionin gPROMS. This function returns the sign of the argument. Ifthe argument in the “SGN” function is greater than or equal to0, 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 linearsegments. Thus, if “t” is less than “t1”, then “y” is equal to thefirst linear segment “f1(t)”. If “ t” is greater than “t1”, then “y”is equal to the second linear segment “f2(t)”. This same approachcan be extended to any number of linear segments,

wheret is the current time (h),t1 is the time at which the firstlinear segment ends and the second begins (h), f1(t) is the firstlinear segment, f2(t) is the second linear segment, andy is theprocess variable.

Last, a number of equations in section 3.2 were modifiedslightly to help maintain numerical stability. By its very nature,start-up modeling involves taking a plant from an idle statewhere very little, if any, liquid is inventoried on the trays andpacking sections of the distillation columns, through a somewhatturbulent start-up phase, all the way to steady-state operation.The rapid swings in process variables that occur early in thestart-up result in the models being highly susceptible tosimulation failures due to numerical instability. To avoid anynumerical difficulties, it was first assumed that liquid wouldnot flow from a packing stage unless a sufficient amount ofliquid (Msmall) was inventoried on that stage. The full flowequation described by eq 5 was not used until the liquid molarholdup (M) reached another specified critical value (Mlarge) asgiven by eqs 17 and 18. These critical values were chosen in asomewhat arbitrary manner and were used solely to maintainnumerical stability. In the model, “MAX” and “MIN” functions

Figure 3. Simplified schematic of heat-exchanger model.

dTm

dt) 1

mmCp,m(Qh - Qc) (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)

y )1 - SGN(t - t1)

2f1(t) +

1 + SGN(t - t1)

2f2(t) (16)


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

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

3.4. Simulation Results: Model vs Plant Data.A com-parison of the simulation results obtained with the modeldescribed above against the actual plant data for several keyprocess variables can be observed in Figures 4-7. All flow ratesare presented as a percentage of the steady-state plant flow ratefor each stream. Thus, each plant flow rate has a value of 100%at steady state. One can note that several of the stream flowrates, 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 steadystate. However, the deviations are not large enough to causeconcern. One should note that liquid flow measurements inchemical plants, including air separation plants, are particularlyprone 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-stateplant measurement, are captured very well by the model. Thiscan also be said of the pressures in the lower (Figure 4a), upper(Figure 6a), and argon (Figure 7a) columns along with that inthe argon condenser (Figure 7b). Overall, it was decided thatthe model captures the dynamic behavior of the plant adequatelyenough to validate any simulation results obtained in the designmodification 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 imple-mentations of the primary design modification discussed in thepatent literature. In this paper, we discuss four different designs.The “A” in each design name refers to liquid being collectedfrom the argon columns only, while the number refers to thetotal number of collection vessels. The first design, A6, involvescollecting liquid from three separate points in each argon columnfor a total of six collection vessels. Designs A4, A2 (Figure 8),and A1 have also been studied. One should note that designA1 involves collection of liquid from the second argon columnonly, not collection of liquid from both argon columns in onevessel. There are more than six packed sections in the argoncolumn, which means that the number of collection vessels canbe extended beyond six. However, as the total number of packedsections in the column is proprietary, designs involving morethan six collection vessels are not discussed in this paper.

4.1.2. Liquid Feed Trajectories.Similar to the wide rangeof potential implementations of the design modification, thereare innumerable potential policies for reintroducing the collectedliquid to the argon columns during start-up. In this study, onegeneral policy has been tested. The policy involves feeding thecollected liquid between two times, “tinit” and “tfinal”. Prior totinit, the flow rate of liquid to the column is 0. Attinit, the flowrate of liquid is ramped to a maximum value over a 0.1 h period.

Figure 4. Simulation results: base model.

ε ) ( M - Msmall

Mlarge- Msmall) (17)

L ) ε[f(M)] (18)

VN ) ε(LN+1(hN+1 - hN

HN - hN) +

VN-1(HN-1 - hN

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


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

collection vessel was fed during the same time period. Thus, inthe case of multiple collection points, the liquid begins to befed from each vessel at the sametinit and the introduction fromeach vessel ceases at the sametfinal. The collected liquid wasfed back to the top of the column section from which it wascollected. It was assumed that sufficient pressure driving force




is available to transport the collected liquid to the argon columns.Last, it was assumed that the liquid fed to the columns duringstart-up is saturated and at an enthalpy close to that of the liquidon the stage to which it is fed. Thus, a term for the liquid fedto the argon columns during start-up is not included in theenergy balance used to calculate the vapor flow rates in thecolumns.

4.1.3. Holdup and Composition of Collected Liquid.Thesteady-state simulation results for the base case were used todetermine the holdup and composition of liquid collected for

each design. The total amount of liquid collected from thesecond argon column is approximately equivalent to 3.5 h ofholdup of product argon at its steady-state flow rate, while thatcollected from the first column represents about 3 h of holdup.The holdup of liquid in each packing section of the argoncolumns at steady state is approximately the same. For designA2, the composition of the collected liquid in each vessel isequal to the average steady-state composition of liquid in therespective columns from which it was collected. As more vesselsare used, the composition of the collected liquid will be closerto the steady-state compositions on the separation stage to whichthe liquid is reintroduced.

4.2. Trial-and-Error Optimization Approach. 4.2.1. In-troduction. A trial-and-error simulation approach was used todetermine the “optimal” liquid feed trajectories for each design.The minimum initial time chosen for the liquid introduction is0.5 h. As one can observe from Figure 6c, this is prior to vaporfeed being introduced into the argon column. The minimumfinal time is 0.75 h. Holding the initial time constant, the finaltime was increased by 0.25 h intervals (i.e., 0.75, 1.0, 1.25,etc.) until decreasing performance was observed. The initial timeat which liquid is introduced was then shifted by 0.25 h andthe same approach to adjusting the final time was utilized. Thisshifting of the initial and final times was continued until clearreductions in performance were observed.

4.2.2. Simulation Results.A summary of the simulationresults obtained for designs A2 and A6 can be observed inFigures 9 and 10, respectively. A shift to the right in data pointscorresponds to a 0.25 h increase intfinal. Thus, the first datapoint corresponds to feeding the collected liquid between 0.5and 0.75 h. The second data point corresponds to feeding thecollected liquid between 0.5 and 1.0 h. As one can observefrom Figure 9, the fastest start-up for design A2 is 3.35 h.This is obtained by feeding the collected liquid between 0.75and 1.5 h.


Figure 8. Simplified schematic design A2.


As one can observe from Figure 10, the fastest start-upobtained for design A6 is 2.23 h. This corresponds to feedingthe liquid between 0.75 and 1.5 h. There is a significant dropin performance once an initial time for liquid introduction of1.0 h is reached. Also, after 1.0 h, there is much less variabilityin the start-up time astfinal is changed. This is caused by thecolumn being sufficiently inventoried with liquid, from con-densation of feed vapor, prior to the liquid introduction takingplace. Thus, any potential advantage from segregating the liquid

by composition is lost if the liquid is introduced after the columnis inventoried with liquid from condensation. The behavior ofdesign A4 is quite similar to that of A6. A summary of theoptimal trajectories for each design is provided in section 4.3below.

4.3. Summary of “Optimal” Trajectories. A summary ofthe start-up time for the “optimal” liquid feed trajectories foreach design can be observed in Figure 11. As the number ofcollection points increases, the start-up time for the argon

Figure 9. Simulation results: design A2.

Figure 10. Simulation results: design A6.


columns decreases. In other words, product is drawn earliestwith 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 liquidbeing introduced to the column is closer to the steady-statecomposition on the separation stage to which it is fed. Thereductions in start-up time achieved with designs A2 (66%) andA1 (47%) are quite close to those reported by Smith and Espie6

(64% and 50%, respectively). The optimal trajectory for designsA6, A4, and A2 involves feeding the collected liquid between0.75 and 1.5 h. The optimal trajectory for design A1 involvesfeeding 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 ofthe liquid fed to the argon column during start-up would involvea rapid ramping of the flow rate to its maximum value, followedby a steady flow rate, and finally a ramping of the flow rateback to 0. However, there are a vast number of feed trajectoriesthat can be utilized. It is possible that the start-up time can befurther reduced by implementing alternative feed trajectories.Similarly, one can adjust the feed locations and also decouplethe feed trajectories from each vessel.

Also, we have utilized a trial-and-error approach to determinethe optimal feed trajectories for each design. However, it ispossible that one can obtain improved solutions over thosediscussed in the paper by employing more rigorous dynamicoptimization 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 alsobe applied to the other distillation columns. Extending the designmodifications to each of the distillation columns simultaneouslymakes 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-upthat can be achieved by collecting/reintroducing liquid from/to

argon columns, a detailed economic analysis has not beenperformed. One must determine the trade-offs between theincreased capital costs incurred by implementing the designmodifications versus the improved plant performance. Ulti-mately, an analysis has to be performed to determine whichimplementation is most economically attractive and if theexpected return on investment makes such design modificationsworthwhile.

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 segmentf2(t) ) second linear segmentfc ) 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)

Figure 11. Summary of “optimal” results.


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‚Rt ) 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 fractiony ) vapor mole fractiony ) process variable

Index Variables

i ) component number (1) argon, 2) oxygen, 3) nitrogen)N ) stage numberz ) node number

Greek Letters

ε ) liquid holdup factorγ ) valve position (%)κ ) valve coefficient (lb‚mol/%‚h‚psia0.5)Fl ) liquid molar density (lb‚mol/ft3)

gPROMS Functions

MIN ) returns minimum valueMAX ) returns maximum valueSGN ) returns sign (i.e.,+1 or -1) of argument

Literature Cited

(1) Miller, J.; Luyben, W. L.; Blouin, S. Economic Incentive forIntermittent 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 AuxiliaryColumn for Argon/Oxygen Separation by Distillation and CorrespondingInstallation. U.S. Patent No. 5505051, L’Air Liquide, Societe Anonymepour l’Etude et l’Exploitation des Procedes Georges Claude, April 9, 1996.

(4) Moll, A.; Kunz, C. Argon-Producing Air Rectification Plant ServicingProcess. Patent No. DE19734482, Linde AG, March 5, 1998.

(5) Rohde, W.; Scho¨npflug, E. Process and Apparatus for Operating anAir Separation Plant. Patent No. DE3436897, Linde AG, 1986.

(6) Smith, O. J., IV; Espie, D. M. Recirculation of Argon SidearmColumn for Fast Response. U.S. Patent No. 6070433, Air Products andChemicals, Inc., June 6, 2000.

(7) Olszewski, W. J. Gas liquefaction process and apparatus. U.S. PatentNo. 3677019, Union Carbide Corporation, July 18, 1972.

(8) Roffel, B.; Betlem, B. H. L; de Ruijter, J. A. F. First principlesdynamic modeling and multivariable control of a cryogenic distillationprocess.Comput. Chem. Eng.2000, 24, 111-123.

(9) Luyben, W. L. Process Modeling, Simulation, and Control forChemical Engineers, 2nd ed.; McGraw-Hill, Inc.: New York, 1990; pp 67and 141-142.

(10) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation ofState.Ind. Eng. Chem. Fundam.1976, 15, 59-64.

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

AcceptedOctober 17, 2007

IE070975T


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Improving Agility of Cryogenic Air Separation Plants