Separation system synthesis gas vapor mixtures

Ind. Eng. Chem.Res. 1992,31, 1679-1694 1679
T,= sampling time
U = matrix derived from the SVD of X
V = matrix derived from the SVD of X
W = projection matrix of X
W,+ = weights used for SSV analysis described in Figure 4b;
Wd = disturbance weight
W, = performance weight
X = input data, each row correspondsto one input sample;
each input sample consists of 12 temperatures and 2 ma-
nipulated variables
X,= lower dimensionaldata set obtained from the projection
ofXonW
y = measured concentration
yn = nominal concentration defined in (28)
6j = deviation for the variable j
A" = uncertainty matrix
Ai*= individual uncertainty elements
A = IMCfilter constant
p = structured singular value (SSV)
Z = matrix of the singular values of X
T~ = controller integral reset time in (46)
Literature Cited
1 = 1 , 2
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through the use of secondary measurements: Inferential and in-
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lication.
Lee, J.; Morari, M. Robust measurement selection. Automatica
1991,27(3),519-527.
Luyben, W. L. Parallel cascade control. Znd. Eng. Chem.Fundam.
1973,12 (41,463-467.
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methanation of carbon monoxide and carbon dioxide on a nickel
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Webb, C. Robust Control Strategies for a Fixed Bed Chemical Re-
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Received for review March 24,1992
Accepted April 13,1992
1528-1533.
SeparationSystem Synthesis: A Knowledge-BasedApproach. 2.
Gas/Vapor Mixtures
Scott D.Barnicki and James R.Fair*
Separations Research Program, Department of Chemical Engineering, The University of Texas at Austin,
Austin, Teras 78712-1062
A description is given for a prototype knowledgebased expert system, the separation synthesisadvisor
(SSAD),for synthesis of separation sequences for gas/vapor mixtures. The core of the SSAD is
the separation synthesis hierarchy (SSH),a highly structured, taak-oriented framework for repre-
senting separation knowledge. The hierarchy, based on interviews and information from the literature,
emulates the approach that an expert process engineer follows. In ita current implementation, the
SSH is limited to the preliminary sequencing of multicomponent gas/vapor mixtures using the
following separation methods: (1)physical absorption; (2) chemical absorption; (3)cryogenic dis-
tillation; (4) membrane permeation;(5)molecular sieve adsorption; (6) equilibrium-limited absorption.
Several examples of practical industrial separation problems are included.
Introduction
This paper is the second of a series on the development
of a prototype expert systemfor the syntheaisof separation
sequences for fluid mixtures; the system is called the
separation synthesis advisor (SSAD).Part 1 concentrates
on separation system synthesis for liquid mixtures (Bar-
nicki and Fair, 1990). Part 2 focuses on the parallel
0888-5885/92/2631-1679$03.00/0
problem for gaslvapor mixtures. The SSAD is a prelim-
inary process design tool. Ita purpose is to formulate a
limited number of feasible separation systems for a given
multicomponent mixture. Final comparisons and opti-
mization must be carried out with the aid of a process
simulator, as the SSAD currently does not have the ca-
pability to perform a detailed economic analysis.
0 1992American Chemical Society

1680 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
THE SEPARATION
SYNTHESISHIERARCHY
Split
!wuamQQ
mass
RmiQDQu
Condensation
THE SEPARATION
SYNTHESISHIERARCHY
Distiilatbn Azeototropic
Zeotropic
Simpb Distillation
Azeotrapic Disliilatlon
Extractive Distillation
Liquid-Liquid
Earaction
Equilibrium-Limited
Adsorption
Mokcular Sieve
Adsorption
Melt Cystalliutbn
Siripping
MembranePenneation
Figure 1. Separationsynethesis hierarchy,showing each manager
The separationof gas and vapor mixtures is a significant
part of many key activities in the chemical process in-
dustries, ranging from the recovery of carbon dioxide in
enhanced oil recovery to environmental concerns over the
removal of solvents and acid gases from exhaust and
process streams. In spite of its obvious importance, the
synthesis of separation sequences for gas/vapor mixtures
has been completely neglected in the process design lit-
erature. In the 23 years since the first proposals of Rudd
and Masso advocating a systematicapproach to separation
system synthesis(Rudd, 1968;Masso and Rudd, 1969),not
one article has appeared on any aspects of gas/vapor
separation system synthesis.
As with liquid mixture separation synthesis,the general
gas/vapor synthesisproblem involvesmethod selectionand
sequencing subproblems. However, beyond these super-
ficial similaritiesthe specifics of the synthesisproblem for
gas/vapor mixtures are fundamentally different from the
correspondingproblem for liquids. Whereas liquidmethod
selection is clearly biased toward simple distillation, no
such dominant method exists for gases. Severalmethods
can often compete favorably. Moreover, the appropri-
ateness of a given method depends to a large extent on
specific process requirements, such as the quantity and
extent of the desired separation. The situation contrasts
markedly with liquid mixtures in which the chemical
characteristicsof the componentsto be separated are often
the dominant factors (Barnicki and Fair, 1990).
This paper addresses the complexities of separation
method selectionand sequencing for gas/vapor mixtures.
The design expert’s knowledge is organized as an auton-
omous problem-solvingentity, called the gas split manager
(GSM). The purpose of the GSM is to provide controlover
the overall synthesis activity. The GSM is further sub-
divided into three essentially independent subproblems,
referred to as separation method selectors. Each selector
pertains to a distinct aspect of the gasmixture separation
method problem.
The GSM and its complement of selectors are part of
a larger, highly structured framework for representing
separation knowledge, the separation synthesis hierarchy
(SSH)(Figure 1). The hierarchy emulates the approach
that an expert processengineer follows. The overall sep-
siwa9mm
Bulk, Sharp
Enrichment
Purification
l2wiamM
PhyaicaiAbrorptbn
Chemical Absorption
Equiibuhn-Limited
Adsorption
Mokcular Sbvo
Adsorption
Cryogenk DlSlltrtbn
Membrana Permeation
Condensation
Catalytic Comembn
with its complement of selectorsand designers.
aration problem for fluid mixtures can be dividedinto four
distinct synthesis phases composed of unique selection,
sequencing, and design subproblems, but all with parallel
problem-solving structure. The four managers which
comprisethe SSHare the phase split manager (PSM),the
distillation split manager (DSM),the liquid split manager
(LSM),and the gas split manager (GSM). Each manager,
selector, and designer represents a clearly defined and
essentially independent subtask of the overallseparation
synthesis activity. The first three of these (the PSM,
DSM,and LSM) have been describedpreviously (Barnicki
and Fair, 1990). This paper concentrateson the manager
and selector subtasks for gas/vapor mixtures.
The paper is organized into three sections. The first
summarizes briefly the structure of the manager subtasks,
concentrating on the particulars of the gas split manager.
The basic task-oriented problem-solving philosophy of the
SSH and the SSAD has been described in part 1of this
series of papers; it will be outlined only briefly here to
orient the reader. The second section presents the con-
cepts involved in separation method selection for gas/va-
por mixtures. The process attributes which can be used
to categorizegas/vapor separationsare described,together
with a discussion of the conditions under which the in-
dividual separation methods are feasible. Emphasis is
placed on identifying the component properties and pro-
cess attributes which determine the utility of a particular
technique. The final section presents severalindustrially
significantgas/vapor separation examples which illustrate
the capabilities of the SSH.
The Gas Split Manager
Structure of the Gas Split Manager (GSM). A
schematic overview of the problem-solving strategy em-
ployed by the SSH is shown in Figure 2. An initial sep-
aration problem (Le., a fluid mixture) is formulated from
the problem specifications pertaining to the feed compo-
nents and desired products. This first mixture is placed
on an “agenda”,which is initially empty. The agenda is
expanded as separations of the initial and succeeding
submixtures are specified. Only those submixtures that
require further separation (Le., those that do not match
a desired product directly) are added to the agenda.

Ind. Eng. Chem. Res., Vol. 31,No. 7,1992 1681
Pmbkm spsclflution:
creme inltbl midun. rwnda
S S H
I . -
I
top 01 the agonda
NO
Managerrslectlon
t
Split gonemion
+
Split sequencing
Seprratlon design
Figure2. Overviewof the problem-solvingstrategyof the separa-
tion synthesis hierarchy.
For each mixture accessed from the agenda, one must
select the appropriate manager. This choice is trivialized
here, asall example separationsdescribedhere require only
the GSM. However, more complicatedexamplesrequiring
manager selection are given in Barnicki and Fair (1990)
and Barnicki (1991). A manager oversees five problem-
solving activities:
1. Split generation: Possible separation points (splits)
are identified. The possible splits of a given mixture de-
pend on product specifications and on the order of the
components in ranked property lists.
2. Selector Analysis: The appropriate separation
methods (if any) for each possible split are determined.
A potential split is defined as a split which may be ac-
complished by at least one separation method.
3. Split sequencing: The potential splits are compared
to determine which are the most appropriate to perform
next. This analysis is guided by well-known design heu-
ristics.
4. Separation design: Each potential split chosen in
step 3 is subjected to a shortcut separation design proce-
dure to find the distribution of componentsin the resulting
submixtures.
5. Submixture analysis: The submixtures generated
by each separation must be analyzed to determineif they
meet product specifications. Those that require further
separation are added to the agenda.
The procedure is repeated for each mixture on the
agenda and continues until the agenda is empty (i.e., all
product specifications are met).
GAS MIXTURE
Generate rankedlistsfor
a11pertinentpropertks
IdeMlfy possiblesplits In ranked lists
appropriate#elector
(-) (-1 (-)Split selector
Spilt selectorSplit selector
heuristicslo determln
I ” 1 * * * ”
CONSULT ’
rpproprhte ‘ j
Analyze all
11submixtures
ANALYSIS COMPLETE. PROCEED
TO NEXT MIXTUREON AGENDA
Figure 3. Logic diagram for the gas split manager.
The gas split manager (GSM) is the only split manager
of the SSH devoted exclusively to predominantly gaseous
mixtures. No clearly dominant separation method exists
for gas separations. However, the problem-solving ap-
proach of the GSM still follows the general strategy out-
lined above. The logic diagram for the GSM is presented
in Figure 3.
Split Generation. Every separation method is based
on a difference between one or more physical or chemical
properties of the components in a mixture (King, 1980,
Rudd et al., 1973). A given method can achieve a sepa-
ration between any components in which these charac-
teristic properties differ significantly. Since the term
“differ significantly” is difficult to quantify, one could
conceivably separate between any two components of a
mixture. We will call these two componentsthe keys of
the separation. For a large multicomponentmixture the
number of possible pairs of keys clearly precludes a de-
tailed examination of all options. A workable approach
requires a compromisebetween thoroughnessand the need
to eliminate infeasible splits with minimal effort.
The strategy adopted in the SSH utilizes ranked prop-
erty lists. A ranked property list orders the components
by the magnitude of the characteristic property of the
separation method (e.g., relative volatility for cryogenic
distillation). Thus, a ranked list determines, in a quali-
tative sense, the possible distribution of componentsfor
a given separation method. The possible separation points
are further restricted by product specifications. Splits
between components appearing in the same product are
prohibited.
Not all separation methods (especiallythose requiring
mass separating agents, MSA) are well-characterized by
a single,easily-calculableproperty. For example, once the
mass separation agent is known, the distribution of com-
ponents can be determined readily, and from this the
possiblesplits. However, the selection of the MSA, which

1682 Ind. Eng. Chem. Res., Vol. 31, No. 7,1992
Table I. Separation Methods and Their Corresponding
CharacteristicProperties
seDarationmethod properties
cryogenicdistillation
physical absorption
chemical absorption
catalytic conversion
membrane permeation
molecular sieve adsorption
equilibrium-limited adsorption
condensation
relative volatility
chemical family
chemical family
chemical family
critical temperature,
kinetic diameter
equilibrium loading
relative volatility
van der Waals volume
itself is nontrivial,is entirelydependent on the separation
method chosen. One cannot determine definitely the
proper separation method until the possible separation
points are known.
In these situations (i.e., for essentially all processesex-
cept distillation), ranked property lists are still used to
generate the possible splits. Although these characteri-
zationsare not perfect,they are generallyaccurate enough
in a qualitative sense for a preliminary analysis. The
selectionof the appropriateproperty (or properties) which
canreliably predict the componentdistributionfor a given
separation method is open to some debate. Table I
presents a list of the gas/vapor separation methods cur-
rently implemented in the SSH along with their corre-
sponding characteristic property or properties.
Split Sequencing. Separation sequencing is a critical
step in the generation of optimal to near-optimal separa-
tion system designs. Limited aspects of the topic have
received seriousconsiderationin the literature. Thiseffort
has resulted in some relatively simple, reliable heuristic
methods of generatingnear-optimal distillationsequences
(Kelly, 1987; Liu, 1987; Nishida et al., 1981). These
methodsgenerally make use of a seriesof ranked heuristics,
which are applied sequentially. If a heuristic is not ap-
plicable, the next one on the list is considered.
For these techniques,sequencing is based primarily on
process characteristics,such as the relative magnitudesof
the desired productsand the ratio of the expecteddistillate
to bottoms flow rates. Since simple distillation typically
haa been the only separationmethod dealt with in previous
studies, relative volatility is an adequate measure of how
easy it is to accomplish a particular separation method.
Thus, there is no need to consider separation method
characteristics as well as process characteristics; the se-
quencing and separation method selection problems be-
come decoupled.
When a variety of separation methods are available,
however,one must now compare the relative ease of sep-
aration of competitive techniques. For example, if mo-
lecularsieve adsorptionand cryogenicdistillationprocesses
yield similarproduct distributions (and would thus trigger
the same process characteristic heuristics), how does one
comparethe relative volatility and the differencein kinetic
diameters to determine which separation method results
in a more efficient separation?
The sequencingof gas separations does not lend itself
as readily to the highly qualitative approach used for
distillation sequencing. However, several of the general
separation sequencing heuristics formalized in previous
studies are still applicable to gas separations, albeit in
rather weak forms. Table I1 shows the sequencing heu-
ristics as modified for gas separations.
The presence of corrosive or hazardous materials tends
to increase the expense of equipment. Therefore these
Componentsshould be removed as earlyaspractical. Many
gas-phaseseparation processes are affected adversely by
the presence of trace impurities. Small amounts of
Table 11. Sequencing Heuristics for the Gas Split Manager
1. Remove corrosive and hazardow materials first.
2. Remove troublesome trace impurities first.
3. Favor separations which match the desired products
directly. If a separation resulta in a substream which
requires no further separation, and is a desired product,
and if that product is the most plentiful in the mixture,
remove it next.
4. Favor separations which give equimolar splits. When ease
of separation and compositions are similar, perform the
separation which divides the feed as equally as possible.
Table 111. Typical Special Processing Conditions for the
Gas Split Manager
1. Favor condensation for the removal of high boilers from
noncondensable gases when cooling water can be used as
the condensing medium. Condensation is one of the
simplest and cheapest unit operations.
2. Favor catalytic conversion when the impurities can be
converted into 4 desired product. Further purification
and/or separation steps may be unnecessary.
3. Favor adsorption for small-scale desiccation operations.
Solid-phase desiccant systems are relatively simple to
design and operate. They are generally the lowest cost
alternative for processing small quantities of gas.
4. Favor adsorption for processes which require essentially
complete removal of water vapor. Adsorptive dehydration
is capable of achieving dew point depressions of 80 O F or
more.
5. Favor glycol absorption for large-scale desiccation operations
required dew point depressions of 50 O F or less. The
initial and operating costa of high-volume glycol absorbers
are typically much lower for small to medium dew point
depressions than the corresponding costa of solid-phase
desiccation.
freezable components (water, carbon dioxide) may foul
cryogenicunits. High gas humidity or moisture content
reduces the effectivenessof many adsorption processes
(particularlythe adsorption of low molecular weight com-
pounds). Other components,high boilers and polymeriz-
able compounds, may permanently foul an adsorbent.
Such componentsshould be removed first,downstreamof
any important, larger-scale separations.
It is obviously advantageous to perform a separation
which removes a component directly as a product. This
generallywill improve overall recovery and purity. The
specification of equimolar splits tends to reduce the
downstream separation load more effectively. In terms of
energy usage, two smaller separation units are generally
more efficient than one very large unit.
Some processing conditionsare especially favorable for
certain separation methods. These special circumstances
may override the more general sequencingand selection
heuristics. A list of some typical specialprocessing con-
ditionsis given in Table III. See alsothe sectionsPhysical
Absorption, Adsorption, and Condensation.
The sequencing procedure presented above does not
guarantee that only one potential separationwill be found
in all cases. Because of their highlyqualitativenature, the
heuristics often cannot differentiate between several al-
ternatives. When such a situation arises, all alternatives
are considered to be equally feasible at this stage of the
process design;a detailed economic analysis is often nec-
essary to determine which method is actually preferred.
The qualitatively equivalent separations are propagated
through the remainder of the manager activity and lead
to unique submixtures. If such branching does occur, the
final output of the gas split manager will contain several
competingseparationsystem designs. On the other hand,
if no equivalent separations are found at any stage of the

Ind. Eng. Chem. Res., Vol. 31, No. 7,1992 1683
uimlm
PHYSCAL ABSORPTION
No
EfinUMW YEUBRANEPERLlEITlON
z
Elifdm
MOLECULAR SIEVEhlnow fouling
conponrmr err(
A d 8 O ~ l . f O u i n g bN (hCOnlpWWIl8
c#rpornn(r p v n l 7 of oimilr aim/- 7
Efimim
EOUIUBRIUU-UYTED
ADSORPTION
Rwnow f#lltng
conpomnla err(
*d.orb.nl.lorling EWIUBMUY
cOnlpommtmpvn17 --C
rrcuvlry Mol 7
EfifdMW!
CONDEHSAllON
Figure 4. Logic diagram for the selection of separation methods for gas-phase enrichment separations, enrichment split selector.
synthesisprocess, only one finalseparation system design
will result.
Separation Method Selection for Gas Mixtures
SeparationSpes. Gas-phaseseparationsare classified
into three categories based on the purity, recovery, and
magnitude of the pertinent Separation. Each category is
the basis for a dietinctseparationselector in the SSH (1)
enrichment separation; (2)sharp separation; (3)purifica-
tion separation.
The classificationsystem allowsfor a certain amount of
synergy,as several separation methods may be combined
in order to achieve the desired result. Each separation
category is organized as a distinct selector, with its own
favored separation methods. The applicable separation
techniques for gas mixtures are shown in Table I.
A. Enrichment Separations. An enrichment is de-
fined as a separation process that results in the increase
in concentration of one or more species in one of the
product streams and the depletion of the same species in
the other product stream. Neither high purity nor high
recovery of any components is achieved.
Because of a lack of stringent purity and recovery
specifications,enrichments are the most general gas sep-
aration type. They can be accomplished with a wide va-
riety of separation methods: physical absorption, molec-
ular sieve adsorption, equilibrium adsorption, cryogenic
distillation,condeneation,and membranepermeation. The
logic diagram for the enrichment split selector (ESS) is
shown in Figure 4.
B. Sharp Separations. A sharp separation results in
two high-purity, high-recovery product streams. No re-
strictions are placed on the mole fraction(s) of the com-
ponent(s) to be separated. A separation is consideredto
be sharp in the present work when the key component

1684 Ind. Eng. Chem. Res., Vol. 31,No. 7, 1992
mimi- CaJbr PHVS ABS.
PMVSlCAL ABSORPTION + CHEYCAL ABS
nADSORPTION

4VES
EuIdma
EQUIUBRUYUYTED
ADSORPTION
iFigure 5. Logic diagram for the selection of separation methods for gas-phase sharp separations, sharp split selector.
splita are greater than9.0-9.5 or less than 0.111-0.105.A
key component split is defined as:
Skey = c1/c2 1 9.0-9.5 for c1 > c2 (1)
Skey cl/c2 5 0.105-0.111 for c2 > c1 (2)
where Shy= split of light or heavy key, c1 = flow rate of
key component in product 1, and c2 = flow rate of key
component in product 2.
The separation methods that can potentially obtain a
sharp separation in a single step are physical absorption,
molecular sieve adsorption, equilibrium adsorption (for
componentawhich comprise less than 10% of feed mix-
ture), and cryogenic distillation. The sharp split selector
(SSS)is illustrated in Figure 5.
Chemical absorption is often used to achieve sharp
separations, but is generally limited to situations in which
the componenta to be removed are present in low con-
centrations. These special cases of low mole fraction,
high-recovery, high-purity separations are treated as a
distinct separation type, purification separation.
C. PurificationSeparations. A purification separa-
tion involvesthe removal of one or more low concentration
impurities from a feed stream. A low concentration im-
purity is arbitrarily defined here as a componentor group
of componenta which comprise less than 2 mol 9% of the
parent mixture. A purification separation typically resulta
in a product of very high purity (e.g., >99% impurity
removal, depending on the separation method used). It
may or may not be desirable to recover the impurities.
The separation methods considered here as applicable
to purifications are limited to equilibrium adsorption,
molecular sieve adsorption, chemical absorption, and
catalytic conversion. Physical absorption is not included
in this list. With low inlet concentrationsof the impurity
(characteristic of a purification separation), physical ab-
sorption processes are typically not able to achieve ex-
tremely high purities (Tennysonand Schaaf, 1977). One
notable exception to this rule is the absorption of water
vapor by glycol solutions. Glycol dehydration processes
are able to achievedew point depreasiomof 200 OF or more
(Valerius,1974). However, adsorptive desiccation is gen-
erally more economicalwhen dew point depreasionsof 80
OF or more are neceesary (Kohland Riesenfield, 1986)
(refer also to sections Physical Absorption and Adsorp-
tion).
In some cases an enrichment may be coupled with a
purification step in order to achievethe desired separation
sharpness (e.g., physical absorption followed by chemical
absorption, condensation followed by a purification op-

Ind. Eng. Chem. Res., Vol. 31, NO.7, 1992 1685
Figure 6. Logic diagram for the selection of separation methods for gas-phase purification separations, purification split selector.
eration). A logic diagram for the purificationsplit selector
(PSS) appears in Figure 6.
Separation Methods. A. Membrane Permeation.
The ease of separation of two gaseous components by
membrane permeationis characterized by the ratio of their
permeabilities in the membrane material. This permse-
lectivity is often represented in the literature asconsisting
of solubility and diffusivity contributions:
The abilityof a polymer membrane to act as a selective
separatingagent for a particular mixture of gaseous species
is a function of the physical properties of the polymer as
well as those of the components to be separated. The
magnitude of the diffusivityratio is dependent on the size
and shape of the molecules,while the solubilityratio is an
expression of their relative condensability (Koros and
Hellums, 1989).
In general, an aij* 2 15 is required for a membrane
permeation process to be commercially feasible (Hogsett
and Mazur, 1983). Moreover, permeate purity is rela-
tively unaffected by an aij* > 20 (Stookeyet al., 1986).
Permeability data are readily available for many com-
mon gaseous systems, such as C02/CH4and 02/N2(Koros
et al., 1988; Walker and Koros, 1991; Teplyakov and
Meares, 1990). However, when experimental data are
nonexistent or unavailable, a preliminary screening of
potential membrane processes ispossible by examiningthe
combination of component properties which would result
in a permselectivity of 15 or greater. Barnicki (1991)
presents a generalized method for predicting whether a
favorable permselectivity (e.g., aij*2 15)can be obtained
for a given gaseous separation using any of 51 glassy or
rubbery polymers. One needs only a knowledge of a dif-
fusion-related property (effectivekinetic diameter or van
der Waals volume) and a solubility-related parameter
(effectiveLennard-Jones well depth or critical tempera-
ture) of the components in question.
B. CatalyticConversion. Catalyticconversion is not
a separationmethod in the conventionalsense. Impurities
or other objectionable Components are not removed, but
rather chemically transformed on the surface of a solid
catalyst into less objectionablespecies. The new compo-
nent(s) may then require further separation.
Because of its destructive nature, catalytic conversion
can be eliminated from further consideration if the im-
purities are a desired product.
Catalytic conversion is especially favorablefor separa-
tions in which extremely high purity is needed. In fact,
almost completeremoval of the objectionablecomponents
is possible (down to 1-10 ppm). Conversion is best for a
stream with a low concentration of impurities (less than
about 5000 ppm), for high temperature, and for low
pressure, e.g., flue gasesand purges (Kohl and Riesenfeld,
1985;McInnea et al., 1990). The removal of small amounta
of the leas volatile components (i.e., liquid-typecompounds
is also a favored situation. The utility of catalytic con-
version hinges on a difference in reactivity of impurities
and bulk stream components. Industrially significant
purification conversions can be classified as either com-
bustion or hydrogenation reactions. Other conversion
methods specificto particular compounds, (e.g., the cata-
lytic reduction of nitrogen oxides with ammonia) are not
considered in this work.
Combustion (an oxidation-reduction reaction) entails
the addition of oxygen and heat, often over a precious
metal catalyst, to yield water, carbon dioxide, and some-
times sulfur dioxide,dependingon the compositionof the
impurities:
impurities + O2+ heat -H20+ N2+ COP+ SO2
Typical industrialapplicationsof this techniqueinvolve

Table IV. HydrogenationReactivity
reacting chemical family" hydrogenation products
alkynes
olefins
acyl fluorides
acyl chlorides
nitriles-aromatic nitros-oximes
aliphatic nitros
aldehydes
ketones
aromatic rings
heterooxygen aromatics
heteronitrogen aromatics
anhydrides
esters
organic acids
amides
thiole-sulfides
heterosulfur aromatics
olefins
paraffins
aldehydes, hydrogen fluoride
aldehydes, hydrogen chloride
primary, secondary amines
primary, secondary amines
alcohols
alcohols
cycloalkanes
cyclic ethers, n-alkanes
nitrogen cyclics
polyesters
alcohols, acids, ethers
alcohols
primary amines
hydrogen sulfide, hydrocarbons
hydrogen sulfide, n-alkanes
a Ease of hydrogenation decreases from top to bottom of table.
the removal of species that are environmentally objec-
tionable or detrimental to downstream processes, (e.g.,
hydrogen, elemental sulfur, hydrogen sulfide, and organ-
ics). Combustion is not recommended for halogenated
organics,as the reaction products are generally as objec-
tionable as the original compounds.
For safety reasons the concentration of the impurities
should be no more than10% of their lower explosive limit.
The selectivity of the combustion reaction is generally
poor; almost all organic compounds will catalytically ox-
idize. Close control of the reaction temperature generally
improves selectivity,but the most favorable temperature
for oxidationis difficultto predict. Reaction temperatures
are usually between 250 and 700 "C, assumingan impurity
composition of approximately 10% of the lower explosive
limit (Suter, 1955).
From the standpoint of preliminary process analysis
catalytic combustion isfeasibleforpurification processes
only when the impurities are at concentrationlevels below
10% of the lowerflammabilitylimit and when the bulk
stream already consists of oxidation products, e.g., air
stream, off-gases,and other inerts. In addition,catalytic
oxidation should not be used when the process stream
contains halogenated organics.
The hydrogenation reaction involves the addition of
hydrogen to specific functional groups. Conversions of
9599% are typical for the reaction
impurities + H, -addition products
Hydrogenation requires much milder conditions than
combustion, typically at temperatures lower than 100"C.
High selectivity is possible by a controlled addition of
hydrogen, depending on the functional groups present.
The order of reactivityof variousfunctionalgroups aswell
as their hydrogenation products is listed in Table IV
(Rylander, 1985; Streitwieser and Heathcock, 1981).
Groups higher in the table hydrogenate more easily than
those lower down.
Catalytic hydrogenation is a feasiblepurification op-
eration only when the impurities contain functional
groups listed in TableIV. Moreover, the reactivity of the
functionalgroups in the impurities must be higher than
that of the bulk stream species, if the bulk stream is to
be unaltered by hydrogenation. Hydrogenation is espe-
cially favorableforprocesses in which the impurities can
be converted into desired products.
The conversion of acetylene to ethylene during the
production of ethylene is an excellent industrial example
of the use of hydrogenation for product purification
(Reitmeier and Fleming, 1958).
C. Physical Absorption. Physical absorption is
characterizsdby specificnonchemical interactionsbetween
the absorbent liquidand the solutegas. Theseinteractions
aret y p i d y a linear functionof the solutepartial pressure
in the gas phase and the solute concentration in the liquid
phase. Consequently, a physical solvent maintains its
absorptivepropertieseven when the partial pressureof the
solute in the feed is high (England, 1986). This contrasts
markedly to a chemical solvent which typically loses its
effectiveness as the solubility limit of the solute is ap-
proached. However, unless the solute-solvent solubility
is extremely large,the product stream concentration gen-
erally cannot be reduced much below 100 ppm with a
physical solvent (Tennysonand Schaaf, 1977). Thus the
best applications ofphysical absorption involve sharp and
enrichment separations.
One exceptionto this rule is the widespread use of glycol
absorption for the dehydration of natural gas and other
process streams. For large-scaleoperationswith dew point
depressionrequirements of 50 O F or less, glycolabsorption
is generally the most economical alternative. When dew
point depressions of 50-80 O F are necessary, glycol ab-
sorptionand adsorptionare competitivetechnologies (Kohl
and Riesenfeld, 1985).
Selective physical absorption is based on a difference
in solubility resulting from the intermolecular forces be-
tween the gaseous solutes and the absorptive liquid.
Fundamental intermolecular force calculations,involving
the species' dipolemoments and polarizabilities(Kaliszan,
1987),are not accurate enough to be even qualitative in-
dicators of the feasibility of physical absorption. There-
fore, one is forced to turn to bulk thermodynamic mea-
surements of the solubility selectivity.
The selectivity exhibited by a particular absorbent can
be expressed in terms of the ratio of the liquid-phasemole
fractions of two gaseous solutes in the liquid solvent.
(4)
For purely physical absorption at low to moderate
pressures, gas-phase solute-solute interactions are gener-
ally small and tend to cancel (Le., = 4).Moreover, as
a first approximation the activity coefficientratio can be
replaced with infinite dilution values. Upon substitution
eq 4 becomes
(5)
The standard-state liquid fugacity of a component can
be determined by any of the commonly used methods
listed below:
1. Extrapolation of the vapor pressure curve to a hy-
pothetical liquid state. This is the simplest approach, but
it can be extremely unreliable for temperatures much
above the critical temperature (Prausnitz et al., 1986).
2. Use of semiempirical fugacity correlations. Praus-
nitz and Shair(1961)and Yen and McKetta (1962)present
correlationsfor nonpolar and polar solvent systems. Ac-
curacy is varied.
3. Use of the 'ideal" solubility concept (Gjalbaek,1952,
England, 1986). The expression for ideal solubility is
derived form the Clausius-Clapeyron equation and
Raoult's law. Results are best for simple non-polar gases
well above their critical temperatures.
4. Use of Henry's constants. Sander et al. (1983) de-
scribe the use of a modified version of the UNIFAC group
contribution method for calculating Henry's constants.

Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 1687
Table VI. Acid-Base Functional Groups and MoleculesTable V. Estimated H2S/C02Selectivities
method Selectivity
vapor pressureextrapolation 6.56
Shair correlation 4.15
ideal solubility 2.59
Henry’sconstants 4.87
Only the activity coefficients in eq 5 are solvent-de-
pendent; the standard-state liquid fugacities depend only
on the properties of the individual solutes. For regular
solutions,the infinite dilution activity coefficientis given
by the Scatchard-Hildebrand-Flory-Huggins equation as
(Walas, 1985)
vi viVi
RT v, v, (6)In T~~= -(a, - (si)2 +In -- - + 1
Note that eq 6 is a function only of the properties of
component i and the solvent, not those of component j .
This is consistent with the assumption of negligible so-
lute-solute interactions. Substitution of eq 6 into eq 5
yields
v: (V:- V:)I’
(7)
At the preliminary process design stage, the choice of
the “best” solvent cannot be known a priori (Barnicki,
1991). In general,a desirablesolventfor selectivephysical
absorption will form an ideal solution with some of the
solutesand not the others. ABa rough approximation,one
can assume that this yet unknown solvent will have
properties very similar to one or more of the solutes (and
therefore form an ideal solution with these species). For
the binary case of components i and j in solvent s, if the
solventis similarto component i, then 6, =(si and V,= Vi.
Component i will be preferentially absorbed:
f.01 .* Vj vj vj
f.01 .* RT vi viIn = In -I + -((si - +In - - - + 1 (8)
1 PI
One can now estimate the selectivityof a potential ab-
sorption separaton solely from the properties of the two
competing solutes. The selectivity calculated from eq 8
tends to be within 20-40% of experimental values, de-
pending on the method chosen for calculatingthe stand-
ard-state liquid fugacity and on how different the chosen
solventisfrom the solutes. The selectivityachievablewith
a physical solventthat is not an exact analog of one of the
soluteswill rarely exceed a value of 10and is generally in
the range of 3-8 (Astarita et al., 1983).
Taking into considerationthe inaccuraciesof the above
analysis one can formulate a general heuristic on the fea-
sibility of physical absorption for a given separation:
Ifthe selectivity calculated from eq 8 is 3 orgreater for
an enrichment process or 4 or greater for a sharp sepa-
ration, thenphysical absorptionshould be considered as
a feasible separation method.
The utility of eq 8 is illustrated by predicting the se-
lectivity for a mixture of hydrogen sulfide and carbon
dioxide,common industrial gas components. The selec-
tivitiesobtained by each of the four methods of correlating
the standard-state liquid fugacity are shown in Table V.
The solventis assumedto be similar to H2S,and the partial
pressures of the gases are assumed to be equal. The
magnitudes of the estimated selectivities indicate that
physical absorptionis a feasibleseparation option for these
two gases. The ideal solubilitymethod, however, does not
basic ~TOUDS
ammonia
amines
water
alcohols
aromaticamines
heteronitrogenaromatics
thiols
acid groups
carbon dioxide
sulfur dioxide
hydrogensulfide
thiols
hydrogenbond donors
(see Kaliszan, 1987)
indicate a favorable selectivity. This method is probably
inappropriate, as the system temperature is close to the
criticaltemperatures of both components. Astarita et al.
(1983) report an experimental H2S/C02selectivity in
methanol of 5.50 for the commercial Rectisol process.
D. Chemical Absorption. Chemical absorption is
characterized by nonlinear interactions that are particu-
larly strong at low concentrations or partial pressures.
These interactions tend to weaken considerably as one
approaches the solubility limit of the solute; the solvent
loses ita absorptive properties. In general, chemical ab-
sorption is favored when the partial pressure in the feed
of the components to be removed is low and when the
desired removal is high (purities at the ppm level are not
uncommon)(Astaritaet al., 1983; Tennysonand Schaaf,
1977).
Although results have been published for selected sys-
tems (Astarita et al., 1983;Kohland Riesenfeld, 1985),a
generalized predictive method for chemical absorption
equilibrium is not currentlyavailable. Without selectivity
information, determining the feasibility of chemical ab-
sorption is difficultbut not hopeless. Chemicalabsorption
often involvesthe complexing of the acid-base functional
groups of the solvent and solute. Table VI lists common
acid-base functional groups (Ho, 1977). Note that only
a limited number of functional groups exhibit acid-base
behavior. Thus if the species to be separated contain
differentacid-base functional groups (or if one contains
neither),then chemical absorption (based on an acid-base
reaction) may be a feasible alternative.
The above rule is a crude indication of potential utility
only; it does not categoricallyensure that an appropriate
chemical solvent can be found.
E. Cryogenic Distillation. The feasibilityof a cryo-
genic distillation can be determined from the relative
volatility,a,of the key componentsin much the same way
as high-temperature distillation. The relative volatilities
of condensedgaseoussystemstend to be larger than those
of liquid systems because of the wide boiling point ranges
of the gases normally encountered. For typical industrial
applications 2.0 I CY I 5.0 (Timmerhausand Flynn, 1989),
and in general cryogenic distillation can be considered
as a feasible bulk separation alternative when CY 12.0.
Although comparatively high relative volatilities are
common for cryogenicdistillationseparations,one cannot
categorically state that such a process will be the clearly
favored separation method as is the case for high-tem-
perature distillation (see Barnicki and Fair (1990)). The
economicsof a cryogenicseparation are dominated by the
scale of the process as well as the thermodynamics.
Cryogenicdistillation is rarely cost-efficientfor small-scale
separations or purification operationswhich produce less
than 10-20 tons/day of product gas. For example,energy
consumptionfor air separations drops from approximately
500 kW-h/ton of gas to less than 300 kW-h/ton of gas as
the process scale increases from 10 tons/day to 100
tons/day (Springmann, 1985).
Cryogenic distillation is feasible only for bulk,sharp,
or enrichment separations involving high throughput.

Moreover, when cryogenic distillation is considered as an
alternative,one must ensure that components with high
melting points are removed before the distillation is
carried out (i.e,,species that may freeze at processing
conditions).
Any solids formed may foul reboilers, condensers, and
other piping. The nitrogen-oxygen distillation of air is a
good example of a separation in which freezable com-
pounds cause problems. The inlet air typically contains
carbon dioxide and water that freeze at the temperature
and pressure at which nitrogen and oxygen liquify. Isalski
(1989)lists other freezable impurities that are commonly
present in cryogenic plant feed gases.
F. Adsorption. F.1. Adsorbent Fouling and
Chemical Damage. The ultimate lifetime and capacity
of an adsorptionbed depends to a large extent on the types
of components that are processed. High-boiling organics
(thosewith normal boiling points above 150-180 “C)tend
to be preferentially adsorbed and are extremely difficult
to remove during the regeneration cycle. Under favorable
conditions,low molecular weight organics may polymerize
on the surface of the adsorbent. Dialkenes, 1-alkenes,
alkynes, and epoxides are especially susceptible to this
behavior.
Highly acidic or alkaline moieties may also cause per-
manent chemical alterations in the adsorbent. Aluminas
are sensitiveto acid solutions,while silicagels are strongly
attacked by alkalies and hydrogen fluoride. Zeolites are
generally resistant to chemical attack when the pH is kept
in the range of 5-12 (Ullmann’s, 1988).
Whenpossible, adsorbent-fouling and adsorbent-dam-
aging components should be removed upstream of the
adsorber inlet.
F.2. Molecular sieve Adsorption. The effect of dif-
ferences in adsorbate molecular structure and size on se-
lectivity can be eapeciallydramatic when usingzeolites and
carbon molecular sieves. Certain sizes and shapes of
molecules may be excluded completely from the micro-
pores of the adsorbent due to the extremely narrow dis-
tribution of pore sizes. Anumber of industriallyimportant
vapor-phase (and liquid-phase)adsorptive separations are
based on this molecular sieving effect, notably Union
Carbide’s IsoSiv processes (Cusher, 1986) and certain
Sorbex processes of UOP (Mowry, 1986; Johnson and
Kabza, 1990).
The molecular dimension of importance in sieve-baaed
adsorption processes is the minimum kinetic diameter. It
is a combined measure of the cross-sectional area and
shape characteristicsof a molecule (seeBarnicki (1991)for
methods of estimating kinetic diameter). Commercially
availablemolecular sieves fall into five distinct categories
according to their nominal aperture sizes (Le., pore size
distribution). Thusgaseous species can only be separated
by molecular sieving effects when their kinetic diameters
fall into different zeolite aperture size categories.
Table VI1presents the nominal aperture size and cor-
responding zeolite types for each category. This classifi-
cation system was developed by Barrer (1959) and is re-
peated in modified form in many other references (e.g.,
Collins, 1968;Yang, 1987; Kovach, 1988). There is con-
siderable disagreement in the literature on the subject of
kinetic diametersof gas molecules. Breck (1974)presents
one set of values, whereas several other authors report
considerably different figures (Barrer and Brook, 1959;
Collins,1968,Ullmann’s, 1988). Barnicki (1991)describes
methods of estimating kineticdiameters for limited classes
of compounds when no experimental data are available.
These estimates are consistent with the results of Barrer
Table VII. Aperture Size Categories for Major
Commercial Zeolites
category nomind aperture size (A) zeolite type
5 3 3A Linde
3A Davison
4 4 4A Linde
4A Davison
3 5 5A Linde
5A Daviaon
2 a 1OX Linde
1 10 13X Linde
13X Daviaon
and Brook (1959). In spite of the inconsistencies in the
reported values of kinetic diameters of individual mole-
cules, there is general agreement on which molecules are
excluded from the pores of a given zeolite type.
Recent advances in the understanding of zeolite mor-
phology have enabled the fabrication of molecular sieves
with aperture sizes tailor-made for a specific separation
application(Vaughan, 1988;Ruthven, 1988). However, the
use of custom-made sieves adds considerably to the cost
of the adsorption process and is not considered as an op-
tion here.
Molecular sievesare extremely effectivedesiccants be-
cause of their highly polar surface environment. Because
of this high affinity for water, molecular sieve drying
processes can achieve essentially complete dehumidifica-
tion of gas streams. Dew point depressions of 80 O F or
more are readily obtainable (Kohl and Risenfeld, 1985).
If water vapor is present in a gas stream, it typically will
be the most strongly adsorbed species. Thus if the ob-
jective is to recover adsorbed components which are free
of water vapor, then the inlet gas stream should be dried
before the molecular sieve adsorption process occurs.
F.3. Equilibrium-LimitedAdsorption. As stated in
the section Separation Types, the primary uses of equi-
librium-limitedadsorption are restricted to purifications
and the separationof dilute componentsfrom bulk streams
(i-e.,for components consisting of less than 10% of the
feed). In order to limit the necessary size of the adsorbent
bed and to facilitate the subsequent regeneration steps,
it follows that equilibrium-limited adsorption will be a
favorable alternative only when the adsorbent affinity is
greater for the impurities or dilute components than for
the bulk stream. The mutual affinity of a given adsor-
bate-adsorbent pair is typically reported in terms of
equilibrium loading on the adsorbent. The equilibrium
loading is expressed as a function of adsorbate partial
pressure at a single temperature (i.e., an isotherm ex-
pression (Yang, 1987;Ruthven, 1984)). Once the isotherm
expression is known, the design of an adsorber is a rela-
tively simple task (Fair, 1969; Kovach, 1988; Wankat,
1990).
The ultimate utility and cost of an adsorption process
is closely related to the interrelation between the amount
of time that the product gaa(es)can be collected (i.e., the
cycle time) and the size of the required adsorption unit.
As the cycle time increases, the adsorber length (and
separation cost) increases correspondingly. For a large-
scale industrial process a cycle time of 2 h is typical.
Depending on the magnitude of the equilibrium loading
of the preferentially adsorbed components, the length of
the adsorber needed to achieve such a cycle time may
result in an uneconomical process. Thus, the required
adsorber length is a criterion of the feasibility of an ad-
sorption separation.
In general,for a standard cycle time of 2 h, if the de-
sired separation or purification requires an adsorber that
is longer than 20 ft,then equilibrium-limited adsorption

Table VIII. Favorable Components and Chemical Families
for Desiccation by Equilibrium-LimitedAdsorption
gases chemical families
argon aliphatics
helium hydrocarbon aromatics
hydrogen chlorides
chlorine fluorides
hydrogen chloride oxygenated compounds
sulfur dioxide
ammonia
air
can be eliminated as a potential separation method.
Two distinct applications for equilibrium-limited ad-
sorption are possible. The first entails the removal of
adsorbable components from an inert carrier gas (e.g.,
removal of organicsfrom air, oxygen,nitrogen,helium, etc).
In thia case,the equilibrium loading of the inert ~ 8 9on the
adsorbent is negligible and can be ignored.
The second application of equilibrium-limitedadsorp-
tion involves the separation between adsorbable compo-
nents. The objective here is to collect the less adsorbed
component in pure form for a period of time (typically
about 2 h) until the adsorber bed is exhausted. At that
point the more adsorbed component will break through
and will begin to contaminate the product. Such a process
will be feasible only under the following conditions:
1. The more adsorbed component must be in the mi-
nority in the feed (less than 10 mol %). If the majority
feed component(s) were to be adsorbed, the adsorber bed
would fill rapidly or would be impractically long.
2. For a cycle time of 2 h, the adsorber length required
to achieve breakthroughof the more ahorbed component
should be less than 20 ft. The length of an adsorber can
be found by several methods such as those given by Fair
(1969)or by Wankat (1990).
3. The ratio of the equilibrium loadings of the two
components should be at least 2, and preferablyhigher
(Chu, 1991). A high loading ratio ensures that simulta-
neous adsorption will be minimal. Because of its high
concentration in the feed, the less adsorbed component
may displace the more adsorbed component if the loading
ratio is too low.
A limited number of bulk enrichmentseparations (i.e.,
adsorbed components consist of 10mol % of more of the
process stream)are now routinely performed with pressure
swing adsorption cycles. Examples include hydrogen re-
covery, methane enrichment from biogases, oxygen en-
richment, carbon dioxide recovery, and natural gas re-
covery. Further details are available in Richter (1987).
These cases currently are not covered by the SSAD.
The useof equilibrium-limitedadsorption for desiccation
operationshasbeen notably successful. Silicagels, zeolite
molecular sieves, and activated aluminas have high affin-
ities for water. The following heuristic reflects current
industrial applications (Keller et al., 1987;Yang, 1987):
If the process stream to be dried contains less than 3
wt % water and is composed of gases or organic species
which are members of the chemical families listed in
Table VIII,then equilibrium-limited adsorption will be
a feasible (and probably the best) alternative. The ap-
propriate adsorbent (some type of silica gel, zeolite mo-
lecular sieve, or activated alumina) for the particular
application in question cannot be determined at this
stage.
As is the case with other separationtechniques requiring
mass separating agents, the appropriate adsorbent for a
given separationis not known in the early stages of process
development. With hundreds of commercial adsorbents
available, the examination of each potential adsorbate-
Table IX. Mixed Solvent Recovery Specifications
mol mol boiling point component
component % wt (K) type
nitrogen 70.645 28.0 77.4 gas
oxygen 28.855 32.0 90.2 gas
ethyl acetate 0.256 88.1 350.3 liquid
toluene 0.244 92.1 383.6 liquid
adsorbent pair would be prohibitively time-consuming.
Moreover, even if an exhaustive search could be done
quickly, the available isotherm data are relatively limited
(Valenzuela and Myers, 1989).
When experimentalisothermdata are unavailable, ad-
sorption affinity can be estimated for activated carbon
adsorbents from a generalized Dubinin-Polanyi charac-
teristic curve developed by Barnicki (1991).The method
described by Barnicki requires only molar volume and
fugacity data.
G. Condensation. Condensation is a basic separation
technique in which a gas stream is brought to its saturation
(dew) point where the low volatility components begin to
liquefy. As these Components condense out, the dew point
rises and the temperature must be lowered further to
continue the process. A condenser is typically equivalent
to only one or two theoretical equilibrium separation
stages. Consequently, condensation processes exhibit poor
selectivity unless the relative volatility or boiling point
temperature difference of the components is extremely
large.
Condensationshould be explored as a potential sepa-
ration method for enrichment operations when the rela-
tive volatility between key components is greater than
approximately 7 or the boiling point differenceisgreater
than 40 "C.
Condensation is most favorable for the separation of
high-boiling organic vapors from noncondensablegases,
especially when cooling water can be used as the con-
densing medium. In such situations, extreme purity (e.g.,
ppm levels)cannot be achieved,but generallygreater than
95% removal is possible.
Example Separations
Mixed Solvent Recovery from an Air Stream. In
order to comply with strict environmentalregulations on
the extent of toxic emissions, many chemical synthesis
processes include one or more steps involvingthe removal
of trace amounts of organicsfrom process off-streams. Fair
(1967)presented a detailed study of such a process for the
removal of toluene and ethyl acetate from an air stream.
Table IX gives the input specifications for the solvent
recovery problem. The objective is to recover 99% of the
ethyl acetate and essentially all of the toluene. Note that
the organicsare to be separated and recovered,rather than
removed and possibly destroyed. Air is considered to be
71 mol % nitrogen and 29mol % oxygen for this problem.
The separation analysis starts with the phase split
manager (PSM) as described in part 1 of this series
(Barnickiand Fair, 1990).The input stream includes both
gas and liquid compounds. However, due to the extremely
low concentration of liquids (0.5 mol %), no phase sepa-
ration is required. The analysis proceeds directly to the
purification split selector (PSS)of the gas split manager
(GSM).
For purification operations, the possible separation
methods are chemical absorption, catalytic conversion,
molecular sieve adsorption, and equilibrium-limited ad-
sorption. The ranked component property lists are given
in Table X. Examining the ranked lists,the possible key
component pairs are nitrogen-ethyl acetate using chemical

Table X. Ranked Property Lists for Mixed Solvent Recovery
ranked Property
method DroDertv components values
chemical absorption chemical family oxygen
catalyticoxidation nitrogen
ethyl
toluene
molecularsieve kinetic diameter oxygen
acetate
adsorption nitrogen
ethyl
toluene
equilibriumlimited equilibrium loading toluene
adsorption (mol/g of ads) ethyl
acetate
acetate
oxygen
nitrogen
inorganic gas
inorganicgas
acetate
alkylbenzene
<3 A
<3 A
<8 A
<a A
0.00202
0.00132
=o.o
=o.o
absorption, catalytic oxidation, or molecular sieve ad-
sorption and ethyl acetateoxygen using equilibrium-lim-
ited adsorption. One must now refer to Figure 6, the
purification split selector (PSS),to determine which of
these separations are feasible.
Looking at the firstbranch of the PSS,one can eliminate
immediately chemical absorption as a possibleseparation
method because neither nitrogennor ethyl acetate contains
acid-base functionalgroups (seeTable VI). Although ethyl
acetate and toluene are oxidizable impurities, catalytic
oxidation cannot be used because these two components
are desired products. They would be destroyed in the
oxidation process.
The kineticdiameters of nitrogenand oxygen are clearly
much smaller than those of the organics;the Components
can be separated by molecular sieves. However, in this
case, the oxygen and nitrogen would be adsorbed and the
ethyl acetate and toluene would be excluded from the
molecular sieve pores. Adsorption of 99.5 mol ?% of the
feed stream is obviously impractical. Therefore,molecular
sieve adsorption is also eliminated.
The final potential separation method is gas-phase
equilibrium-limited adsorption. From the generalized
characteristic adsorbent curve for activated carbons
(Barnicki,1991),the equilibrium loadingsof ethyl acetate
and toluene are found to be 0.00132 and 0.00202mol/g of
adsorbent, respectively. The adsorption of oxygen and
nitrogen is negligible. In addition, no adsorbent-fouling
componentsare present,and the amountadsorbed is small.
Thus, equilibrium adsorption is the favored separation
method. These results are summarized in Table XI.
Separationand Purificationof Landfill Gases. One
ton of municipal waste contains approximately 200 kg of
organic material. In the anaerobic environment of a
landfill, the organicrefuse is decomposed by microorgan-
isms into a gaseous product consisting of 40-60 mol 5%
methane, 40-50 mol ?% carbon dioxide, and 5000ppm or
more of impurities (various hydrocarbons, halogenated
compounds, and sulfur compounds). Large municipal
landfiiare capable of producing (0.2-8.0) X 106standard
ft3/day of gas for up to 20 years. Thus, landfill gas rep-
resents a significant potential sourceof carbon dioxide and
methane (Ruf and Egli, 1988;Malik et al., 1987). For this
exercise, the landfill is assumed to be of moderate size,
producing 2 X lo6standard ft3/day of gas.
The key to the economic viabilityof such a reclamation
process centerson the effective separationand purification
of the methane and carbon dioxide components. A rep-
resentativegas compositionconsistingof sevencomponents
is given in Table XI1 (simplified slightly from the com-
positions given by Magnani (1984) and Schumacher
(1983)). Blakely (1985)reports typical specifications for
salable carbon dioxide. Stockmann and Zollner (1987)
indicate typical chemical synthesis methane gas specifi-
cations. These are repeated in Table XIII. For merchant
gas applications, the carbon dioxide product must be es-
sentially free of all impurities, including methane.
Methane synthesis gas also must be essentially free of
impurities (ppm levels permissible).
Separationsynthesisfor the landfillgasproceeds directly
to the split manager rather than the phase split
manager. The low concentration of liquid-phase compo-
nents (~0.81mol ?% combined aromatics and halohydro-
carbons) precludes the need for both gas and liquid sep-
aration systems. The GSM analysis begins with the gen-
eration of ranked property lists and the identification of
possible separationpoints. Because of the presence of the
trace impurities benzene, chloroethane, and hydrogen
sulfide, the initial separation step will involve the removal
of these components (see sequencing heuristics in Table
11). The separation of trace impurities is a purification
process (refer to the section Separation Types and Figure
6). Therefore, the potential separation techniques are
limited to chemical absorption, catalytic conversion,and
adsorption. Ranked property lists for these separation
methods are shown in Table XIV.
Looking first at chemical absorption, one finds that the
process stream contains acid-base functional groups,
namely hydrogen sulfide and carbon dioxide (see Figure
6). Moreover,it is known that amine solventsare available
which can selectivelyremove hydrogen sulfide (Kohl and
Riesenfeld, 1985). Since chemical absorption is capable
of removing one of the impurities,it is kept for the moment
as a feasible separation alternative.
Again referring to Figure 6, catalytic conversion is ex-
amined next. Catalytic oxidation is eliminated from fur-
ther consideration because the methane oxidizes more
readily than the impurities themselves. Hydrogenation
is also inappropriate. Only benzene is amenable to hy-
drogenation and the saturated hydrocarbon product from
this reaction must still be separated from the mixture.
Thus, all forms of catalytic conversion can be eliminated.
Adsorption based on molecular sieving effects (using
1OX sieves)theoreticallycould be employed to remove the
chloroethaneand benzene from the rest of the feed stream,
However, as chloroethane and benzene are the larger
molecules (and are thus excluded from the zeolitepores),
it is clearly infeasibleto adsorb 99.7% of the feed stream.
Molecular sieving adsorption also can be eliminated from
further consideration.
As indicated by the ranked list of equilibriumadsorbent
loadings (seeTable XIV), equilibrium-limited adsorption
is favorable for the removal of all three impurities si-
multaneously. This alternative is clearly superior to the
Table XI. Summary of Mixed Solvent Recovery Separations
separation method logic
RejectedMethods
nitrogen/ethyl acetate chemical absorption no acid/base functionalgroups
nitrogen/ethyl acetate catalytic oxidation oxidizableComponentsare desiredproduct
nitrogen/ethyl acetate mol sieve adsorption
oxygen/ethyl acetate
adsorbedcomponents (02,Nz)are majorityof feed
selectivity for toluene, ethyl acetateadsorbates high
Selected Method
equilibrium-limitedadsorption

Ind.Eng.Chem. Res., Vol. 31,No. 7, 1992 1691
benzene
chloroethane
carbondioxide
mhane
- - - - - Separationby
EOUILIBRIUM-LIMITED
ADSORPnON ntLpea
f'' methane
Oxygen Separationby
MOL SIEVE ADSORPTlON
izmfmmu
Methane
-methane Productnitrogen
oxygen
methane
methane
nitrogen Sanaratinn hv
oxygen
carbon dioxide G171EM''
- - - - Separationby
methane CRYOGENICDlSTlLLATlON
CarbonDioxide
Product
Figure 7. Summary of landfill gas separation process alternatives.
Table XII. ReDremntativeLandfill Gas Com~osition~
component mol %
methane 47.50
carbon dioxide 47.00
nitrogen 3.70
oxygen 0.99
hydrogen sulfide 0.01
aromatics (benzene) 0.30
halohydrocarbons (chloroethane) 0.50
a Magnani (1984);Schumacher (1983).
Table XIII. Methane and Carbon Dioxide Product
Swcifications
merchant carbon dioxide' synthesis methane gasb
carbon dioxide 99.985mol % methane 99.98mol %
total sulfur 0.3ppm max chlorides 0.25 g/100 SCF'
total hydrocarbons 5 ppm max sulfur 1.25g/100 SCFc
OBlakely (1983).bStockmannand Zollner (1987).'SCF p standard
compounds
compounds
ft.3
use of chemical absorption to remove hydrogen sulfide
followedby a second separation step to remove the chlo-
roethane and the benzene. The second process would be
necessity (see analysisabove),involve equilibrium-limited
adsorption. Therefore, the best initial separation for the
feed mixture is equilibrium-limitedadsorption to remove
the chlorobenzene, hydrogen sulfide,and benzene in one
step.
For the preliminary process analysis it is assumed that
the chlorobenzene, hydrogen sulfide, and benzene are
completely removed, leaving only oxygen, nitrogen,
methane, and carbon dioxide (3.7, 1.0,47.9,and 47.4mol
% respectively). Because of the product specifications,the
next separation is required to be sharp. The potential
separation methods are limited to physical absorption,
cryogenic distillation, and adsorption (see the section
Separation Types and Figure 5). Ranked property lists
and split points for these separation methods are shown
in Table XV. One must now refer to Figure 5 to deter-
mine the feasibility of the indicated splits.
The relative volatility between methane and oxygen is
favorable for cryogenic distillation (a= 2.7). Moreover,
Table XIV. Ranked Property Lists for Purification Separations of Landfill Gas
chem absorption
component chem family
carbon dioxide acid gas
hydrogen sulfide acid gas
nitrogen inorg gas
oxygen inorg gas
chloroethane chloride
benzene alkylbenzene
methane n-alkane
mol sieve adsorption
component diam (A)
nominal kinet
oxygen <3
nitrogen <3
hydrogen sulfiide <4
carbon dioxide <4
methane <4
chloroethane <5
benzene <8
equilib adsorption
equilib loading
component (mol/g of ads)
oxygen =o.o
nitrogen so.0
methane 0.0005
carbon dioxide 0.0035
benzene 0.0046
chloroethane 0.0070
hydrogen sulfide 0.0069
Table XV. Ranked Property Lists for Sharp Separations of Landfill Gas
cryogenic distillation equilib adsorption mol sieve adsorption
re1 equilib loading nominal kinetphysical absorption
componenta chem family component volatility component , (mol/a of ads) Component diam (A)
-oyxgen inorg gas nitrogen 1.13 nitrogen so.0 oxygen <3
nitrogen inorg gas oxygen 2.73 oxygen =o.o nitrogen <3
carbon dioxide acid gas methane methane 0.0005 carbon dioxide <4
methane n-alkane carbon dioxide freezes carbon dioxide 0.0035 methane <4

the landfill gas separation is a large-scale process, pro-
ducing approximately 21 tons/day of methane. However,
the presence of largeamountsof carbon dioxideprecludes
its use; the carbon dioxide will freeze and foul condenser
surfaces (seeCryogenic Distillation). Oxygen and nitrogen
can be separated from methane and carbon dioxideby 3A
molecular sieves, with the oxygen and nitrogen asthe ad-
sorbed components (see Table VII). Equilibrium loadings
on activated carbon are favorable for the preferential ad-
sorption of carbon dioxideover methane. However, as the
problem is stated, almost 50% of the stream would be
adsorbed (carbondioxideaswell as some of the methane).
This is not a reasonable alternative.
The final separation method to examine is physical
absorption. The selectivity calculated from eq 8 between
carbon dioxide and methane is 4.6 at 298K usingthe Shair
correlation. Thus, physical absorption is a feasible alter-
native (a common solvent, Selexol, gives a selectivity of
approximately 6.5 (Kohland Riesenfeld, 1985)). Sincehigh
purity is required, the physical absorption processshould
be followed by a chemical absorption step (see Figures 5
and 6).
Two splits, the molecular sieve adsorption of nitrogen
and oxygen as well as the physical/chemical absorption
of carbon dioxide,have been found by the selectoranalysis
to be feasible. Comparing these two separations, one sees
that the physical absorption of carbon dioxide is the fa-
vored separation. Heuristic 3 of Table I1 indicates that
the separation which matches a desired product directly
should be done next. Assuming essentially complete re-
moval of carbon dioxide, the remaining mixture consists
of 91mol ?%methane, 1.9 mol ?% oxygen, and 7.1 mol %
nitrogen.
The analysisof the separation of methane from oxygen
and nitrogen is quitesimilarto the previousexpositionfor
carbon dioxide. Cryogenicdistillation is feasiblethistime
becausethe carbon dioxide has been removed. In addition,
oxygen and nitrogen can be separated from methane and
carbon dioxide by 3A molecular sieves, with the oxygen
and nitrogen asthe adsorbed components (see Table VII).
Methane is preferentially adsorbed on activated carbon.
However, again, this would require the adsorption of the
majorityof the feed. It is worth notingthat thisseparation
may be accomplishedwith incompleterecovery of methane
(with recycle), but the SSAD currently does not handle
such a case. Physical absorption is also infeasible.
Since both the distillation and molecular sieveadsorp-
tion proceases result in the same product distributions,one
cannot determine the “best”alternative without a detailed
economic analysis. Both separations are assumed to be
feasible at this point. A summary of two alternative sep-
aration sequences is given in Figure 7.
It should be pointedout that a proceasstream containing
carbon dioxide and methane can be treated successfully
using membrane permeation. This is a fairly common
process in the natural gas industry. However, as the
problem is stated here, both pure methane and pure car-
bon dioxideare desired products. Membrane permeation
is an enrichment process only; it is not feasible to obtain
two products of high purity and high recovery. If the
problem had been stated so that enriched carbon dioxide
and methane streamswere the desired products, then the
selectoranalysiswould have followedthe enrichment split
selector (Figure 4) rather than the sharp split selector
(Figure 5).
Conclusions
A discussion of an extension of the prototype expert
system, the separation synthesis advisor (SSAD), for the
synthesisof separation sequences for gas/vapor mixtures
has been presented. Thearchitectureof the SSAD is based
on a combination of rule analysis and task-oriented
methods. The cornerstoneof the task-oriented problem-
solvingmethods used in the SSAD is the separation syn-
thesishierarchy(SSH). The separationsynthesishierarchy
(SSH) is the first comprehensive, systematic analysis of
separation synthesis domain knowledge to appear in the
chemical engineering literature. In ita current imple-
mentation, the SSH includes all of the major separation
methods commonly encountered in industrial practice.
Two industriallysignificant separationproblems have been
presented to illustrate the capabilities of the SSAD. The
resultant separation sequences compare favorably with
actual industrial processes.
Acknowledgment
We gratefully acknowledge the partial support of this
work by a grant from the Exxon Foundation.
Nomenclature
Symbols
ci = flow rate of key component in product i
Di = diffusivity
fjol = standard-state liquid fugacity
Pi = permeability
Pisat= vapor pressure
pi* = partial pressure
R = ideal gas constant
Si = solubility
Ske= split of light or heavy key
Si# = physical absorbent selectivity
T = system temperature
Tb,i = normal boiling point
T, = critical temperature
V, = van der Waals volume
Vi= molar volume
xi = liquid-phasemole fraction
yi = vapor-phase mole fraction
a = relative volatility
aij* = membrane permselectivity
6i = solubilityparameter
yi = activity coefficient
yijm= infinitedilution activitycoefficient of component i in
+i = mixture fugacity coefficient
Superscripts
1 = liquid phase
O = standard state
Subscripts
a = adsorbate
i = component i
j = component j
s = solvent
Abbreviations
DSM = distillation split manager
ESS = enrichment split selector
GSM = gas split manager
LSM = liquid split manager
MSA = mass separating agent
PSM = phase split manager
component j

PSS = purification split selector
SSAD = separation synthesis advisor
SSH = separation synthesis hierarchy
SSS = bulk,sharp split seleotor
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Accepted April 5, 1992
Probabilistic Approach to Robust Process Control
Charles D. Schaper,*Dale E. Seborg, and Duncan A. Mellichamp
Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, California 93106
A probabilistic approach to robust process control is developed. First, a statistical measure of a
controller’s ability to reject disturbances is introduced. Next, a new robust control framework of
characterizing model uncertaintydescriptions by probability distributions isdeveloped. The statistical
measure of disturbance rejection is then incorporated within the framework. In the proposed
probabilistic approach, process knowledge can be incorporated in the design procedure and controller
performance can be analyzed by probability measures. Severalsimulation examples demonstrate
the advantages of the new approach.
Introduction
An important objective in designing a process control
system is robustness to modelling error. Previous ap-
proaches to robust process control design have generally
used bounds around the parameters or frequency response
of a nominal plant model to describe model uncertainty.
The controlsystem is then designed to minimizethe effects
of a worst-casesituation. Current design approaches for
robustness are described by Morari and Zafhiou (1989).
Process control applications of these design techniques
include those of Agamennoni et al. (1988)and Skogestad
et al. (1988).Advantages of existingdesign techniques for
robustness include the following: (1)closed-loopstability
is guaranteed over the entire range of model uncertainty
(robuststability);(2) an upper bound on a given perform-
ance measure is guaranteed (robust performance). Because
the controllers are generallydesigned for worst-casesitu-
ations that may have a low probability of occurring, the
resulting robust controllers may be very conservative for
more typicaloperatingconditionsthat have a much higher
probability of occurring.
In this paper, a new approach to robust processcontrol
design is developed in which model uncertainty is char-
acterized by probability distributions. This approach
allows closed-loopperformance tradeoffs to be analyzed
as a function of the likelihood of controller performance;
that is, performance can be characterized by a probability
measure for allsituations between nominal and worst-case
conditions. The result is a more completeanalysisstrategy
that can result in better controller design.
In the subsequent development, a general linear repre-
sentation of the plant description is used in which mod-
eling error is described by probability distributions.
Modelingerror due to both parameter uncertainty and the
linear approximation of a nonlinear plant can be included
within this probabilistic framework. It should be noted
that the error resulting from the approximation of a non-
linear system by a linear model may be greater than any
model parameter uncertainty. For example, this situation
*Present address: Department of Electrical Engineering,
Stanford University, Stanford, CA 94305.
could occur when a fundamental physical model of the
process does not exist or is too complex for controller
design, and consequently, an empirical linear model (e.g.
a transfer function model) is developed from experimental
data. In this instance, the parameters of the linear ap-
proximation can be represented by probability distribu-
tions.
Although we describe some methods and examples of
approximating this type of modeling error, it is not the
intent of this paper to provide a well-formulated descrip-
tion of how to identify model uncertainty descriptions.
However, we note that probabilistic descriptions of mod-
eling error can be developedfrom a wide varietyof sources,
including statistical information on phenomenological
model parameters, empirical model parameters, or fre-
quency response (Cloud and Kouvaritakis, 1987;Correa,
1989;Goodwinand Salgado,1989;Stengel and Ryan, 1989).
Also, process knowledge is usually available in the form
of engineeringheuristics and information about the range
of operating conditions. The probabilistic model de-
scription is sufficiently general to capture such prior
process knowledge and incorporate it within the design
procedure.
In addition tothe development of a generalprobabilistic
framework,a statisticalmeasure of closed-loop disturbance
rejection capabilities is introduced for process control
applications. A disturbancerejection measure is generally
more appropriate for process control applications because
the set-point remains constant for long periods of time.
In the development of this measure, it is important to note
that performance specificationsfor outputs or inputs can
be formulated in terms of statistical moments. For ex-
ample, a typicalproduct specification is expressed in terms
of a mean and standard deviation (also referred to as root
mean square). Well-known control design strategieshave
been developed to minimize statistical moments of the
outputa and inputs. These controller design strategies
include qlassical methods such as minimum variance
control (Astrijm, 1970;Box and Jenkins, 1976;Kucera,
1979),in addition to current methods such asrobust linear
quadratic Gaussian (LQG)controlstrategiea (Stengel, 1986;
Bernstein and Haddad, 1990)and constrained minimum
variance control (Makila et al., 1984;Hotz and Skelton,
0 1992 American Chemical Society

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