-
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 corresponds to one input sample;
each input sample consists of 12 temperatures and 2 ma-
nipulated variables
X, = lower dimensional data set obtained from the projection o
fXonW
y = measured concentration yn = nominal concentration defined in
(28) 6 j = deviation for the variable j A" = uncertainty matrix Ai*
= individual uncertainty elements A = IMC filter constant p =
structured singular value (SSV) Z = matrix of the singular values
of X T~ = controller integral reset time in (46)
Literature Cited
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Harris, T.; MacGregor, J.; Wright, J. Optimal sensor location
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Hoskuldsson, A. Partial least squares regression methods. J.
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1991,27 (3), 519-527.
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Soft-sensors for process estimation and inferential control. J.
Process Control. 1991,l (3).
Van Herwijnen, T.; Van Doesburg, H.; De Jong, W. Kinetics of the
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-
actor. Ph.D. Thesis, California Institute of Technology, 1990.
Webb, C.; Budman, H.; Morari, M. Identifying frequency domain
uncertainty bounds for robust controller design-theory with ap-
plication to a fixed-bed reactor. Proc. Am. Control Conf. 1989,
Wold, S.; Ruhe, A.; Wold, H.; Dunn, W. The collinearity problem
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753-743.
Received for review March 24, 1992 Accepted April 13, 1992
1528-1533.
Separation System Synthesis: A Knowledge-Based Approach. 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 synthesis advisor (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 system for the syntheais of 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 1992 American Chemical Society
-
1680 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
THE SEPARATION SYNTHESIS HIERARCHY
Split
!wuamQQ mass
RmiQDQu
Condensation
THE SEPARATION SYNTHESIS HIERARCHY
Distiilatbn Azeototropic Zeotropic
Simpb Distillation Azeotrapic Disliilatlon Extractive
Distillation Liquid-Liquid
Earaction Equilibrium-Limited
Adsorption Mokcular Sieve
Adsorption Melt Cystalliutbn Si ripping Membrane Penneation
Figure 1. Separation synethesis hierarchy, showing each
manager
The separation of 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 systematic approach 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 synthesis problem involves method selection and
sequencing subproblems. However, beyond these super- ficial
similarities the specifics of the synthesis problem for gas/vapor
mixtures are fundamentally different from the corresponding problem
for liquids. Whereas liquid method selection is clearly biased
toward simple distillation, no such dominant method exists for
gases. Several methods 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 characteristics of the
components to be separated are often the dominant factors (Barnicki
and Fair, 1990).
This paper addresses the complexities of separation method
selection and sequencing for gas/vapor mixtures. The design experts
knowledge is organized as an auton- omous problem-solving entity,
called the gas split manager (GSM). The purpose of the GSM is to
provide control over 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 gas mixture
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 process engineer follows. The
overall sep-
siwa9mm Bulk, Sharp Enrichment Purification
l2wiamM Phyaicai Abrorptbn Chemical Absorption
Equiibuhn-Limited
Adsorption Mokcular Sbvo
Adsorption Cryogenk DlSlltrtbn Membrana Permeation Condensation
Catalytic Comembn
with its complement of selectors and designers.
aration problem for fluid mixtures can be divided into four
distinct synthesis phases composed of unique selection, sequencing,
and design subproblems, but all with parallel problem-solving
structure. The four managers which comprise the SSH are 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 overall separation synthesis
activity. The first three of these (the PSM, DSM, and LSM) have
been described previously (Barnicki and Fair, 1990). This paper
concentrates on 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 1 of 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
categorize gas/vapor separations are 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
several industrially significant gas/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
Manager rslectlon
t Split gonemion
+
Split sequencing
Seprratlon design
Figure 2. Overview of the problem-solving strategy of the
separa- tion synthesis hierarchy.
For each mixture accessed from the agenda, one must select the
appropriate manager. This choice is trivialized here, as all
example separations described here require only the GSM. However,
more complicated examples requiring 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 components in the resulting submixtures.
5. Submixture analysis: The submixtures generated by each
separation must be analyzed to determine if 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 ranked lists for a11 pertinent propertks
IdeMlfy possible splits In ranked lists
appropriate #elector
(-) (-1 (-) Split selector Spilt selector Split selector
heuristics lo determln
I 1 * * * CONSULT
rpproprhte j
Analyze all 11 submixtures ANALYSIS COMPLETE. PROCEED TO NEXT
MIXTURE ON 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 components the keys of the separation. For a
large multicomponent mixture the number of possible pairs of keys
clearly precludes a de- tailed examination of all options. A
workable approach requires a compromise between thoroughness and
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 components for 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 (especially those requiring mass
separating agents, MSA) are well-characterized by a single,
easily-calculable property. For example, once the mass separation
agent is known, the distribution of com- ponents can be determined
readily, and from this the possible splits. However, the selection
of the MSA, which
-
1682 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
Table I. Separation Methods and Their Corresponding
Characteristic Properties
seDaration method properties cryogenic distillation 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 entirely dependent 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 processes ex-
cept distillation), ranked property lists are still used to
generate the possible splits. Although these characteri- zations
are not perfect, they are generally accurate enough in a
qualitative sense for a preliminary analysis. The selection of the
appropriate property (or properties) which can reliably predict the
component distribution for 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 serious
consideration in the literature. This effort has resulted in some
relatively simple, reliable heuristic methods of generating
near-optimal distillation sequences (Kelly, 1987; Liu, 1987;
Nishida et al., 1981). These methods generally make use of a series
of 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 magnitudes of the
desired products and the ratio of the expected distillate to
bottoms flow rates. Since simple distillation typically haa been
the only separation method 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- lecular sieve adsorption and
cryogenic distillation processes yield similar product
distributions (and would thus trigger the same process
characteristic heuristics), how does one compare the relative
volatility and the difference in kinetic diameters to determine
which separation method results in a more efficient separation?
The sequencing of 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 Components
should be removed as early as practical. Many gas-phase separation
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 cryogenic
units. High gas humidity or moisture content reduces the
effectiveness of many adsorption processes (particularly the
adsorption of low molecular weight com- pounds). Other components,
high boilers and polymeriz- able compounds, may permanently foul an
adsorbent. Such components should be removed first, downstream of
any important, larger-scale separations.
It is obviously advantageous to perform a separation which
removes a component directly as a product. This generally will
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 conditions are especially favorable for certain
separation methods. These special circumstances may override the
more general sequencing and selection heuristics. A list of some
typical special processing con- ditions is given in Table III. See
also the sections Physical Absorption, Adsorption, and
Condensation.
The sequencing procedure presented above does not guarantee that
only one potential separation will be found in all cases. Because
of their highly qualitative nature, 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 competing separation system 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 YEUBRANE PERLlEITlON
z Elifdm
MOLECULAR SIEVE hlnow fouling conponrmr err(
A d 8 O ~ l . f O u i n g bN (h C O n l p W W I l 8 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.
synthesis process, only one final separation system design will
result.
Separation Method Selection for Gas Mixtures Separation Spes.
Gas-phase separations are classified
into three categories based on the purity, recovery, and
magnitude of the pertinent Separation. Each category is the basis
for a dietinct separation selector in the SSH (1) enrichment
separation; (2) sharp separation; (3) purifica- tion
separation.
The classification system allows for 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
membrane permeation. 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 considered to 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
n ADSORPTION \ 4 VES
EuIdma EQUIUBRUYUYTED
ADSORPTION i Figure 5. Logic diagram for the selection of
separation methods for gas-phase sharp separations, sharp split
selector.
splita are greater than 9.0-9.5 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 componenta which
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.
Purification Separations. A purification separa-
tion involves the removal of one or more low concentration
impurities from a feed stream. A low concentration im- purity is
arbitrarily defined here as a component or 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
concentrations of the impurity (characteristic of a purification
separation), physical ab- sorption processes are typically not able
to achieve ex- tremely high purities (Tennyson and Schaaf, 1977).
One notable exception to this rule is the absorption of water vapor
by glycol solutions. Glycol dehydration processes are able to
achieve dew point depreasiom of 200 OF or more (Valerius, 1974).
However, adsorptive desiccation is gen- erally more economical when
dew point depreasions of 80 OF or more are neceesary (Kohl and
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 achieve the 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 purification split selector
(PSS) appears in Figure 6.
Separation Methods. A. Membrane Permeation. The ease of
separation of two gaseous components by membrane permeation is
characterized by the ratio of their permeabilities in the membrane
material. This permse- lectivity is often represented in the
literature as consisting of solubility and diffusivity
contributions:
The ability of a polymer membrane to act as a selective
separating agent 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 diffusivity
ratio is dependent on the size and shape of the molecules, while
the solubility ratio 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 (Stookey et al., 1986).
Permeability data are readily available for many com- mon
gaseous systems, such as C02/CH4 and 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 is possible by examining
the 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 (effective
kinetic diameter or van
der Waals volume) and a solubility-related parameter (effective
Lennard-Jones well depth or critical tempera- ture) of the
components in question.
B. Catalytic Conversion. Catalytic conversion is not a
separation method in the conventional sense. Impurities or other
objectionable Components are not removed, but rather chemically
transformed on the surface of a solid catalyst into less
objectionable species. The new compo- nent(s) may then require
further separation.
Because of its destructive nature, catalytic conversion can be
eliminated from further consideration i f the im- purities are a
desired product.
Catalytic conversion is especially favorable for separa- tions
in which extremely high purity is needed. In fact, almost complete
removal of the objectionable components 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 gases and purges (Kohl and Riesenfeld,
1985; McInnea et al., 1990). The removal of small amounta of the
leas volatile components (i.e., liquid-type compounds 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 specific to 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,
depending on the composition of the impurities:
impurities + O2 + heat - H20 + N2 + COP + SO2 Typical industrial
applications of this technique involve
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1686 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
Table IV. Hydrogenation Reactivity 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 than 10% 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 oxidation is difficult to predict.
Reaction temperatures are usually between 250 and 700 "C, assuming
an impurity composition of approximately 10% of the lower explosive
limit (Suter, 1955).
From the standpoint of preliminary process analysis catalytic
combustion is feasible for purification processes only when the
impurities are at concentration levels below 10% of the lower
flammability limit 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 reactivity
of various functional groups as well 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 feasible purification op- eration
only when the impurities contain functional groups listed in Table
IV. Moreover, the reactivity of the functional groups in the
impurities must be higher than that of the bulk stream species, i f
the bulk stream is to be unaltered by hydrogenation. Hydrogenation
is espe- cially favorable for processes 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 characterizsd by
specific nonchemical interactions between the absorbent liquid and
the solute gas. These interactions are t y p i d y a linear
function of the solute partial pressure in the gas phase and the
solute concentration in the liquid phase. Consequently, a physical
solvent maintains its absorptive properties even when the partial
pressure of 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
(Tennyson and Schaaf, 1977). Thus the best applications of physical
absorption involve sharp and enrichment separations.
One exception to this rule is the widespread use of glycol
absorption for the dehydration of natural gas and other process
streams. For large-scale operations with dew point depression
requirements of 50 O F or less, glycol absorption is generally the
most economical alternative. When dew point depressions of 50-80 O
F are necessary, glycol ab- sorption and adsorption are competitive
technologies (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' dipole
moments 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-phase mole 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 coefficient ratio 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 correlations for
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 Molecules Table V.
Estimated H2S/C02 Selectivities method Selectivity
vapor pressure extrapolation 6.56 Shair correlation 4.15 ideal
solubility 2.59 Henrys constants 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 coefficient is given by the
Scatchard-Hildebrand-Flory-Huggins equation as (Walas, 1985)
vi vi Vi 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
desirable solvent for selective physical absorption will form an
ideal solution with some of the solutes and not the others. AB a
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 solvent is
similar to component i , then 6, = (si and V , = Vi. Component i
will be preferentially absorbed:
f.01 .* Vj vj vj f.01 .* RT vi vi In = In - I + - ( ( s i - + In
- - - + 1 (8)
1 PI One can now estimate the selectivity of 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 calculating the stand- ard-state liquid fugacity and on
how different the chosen solvent is from the solutes. The
selectivity achievable with a physical solvent that is not an exact
analog of one of the solutes will rarely exceed a value of 10 and
is generally in the range of 3-8 (Astarita et al., 1983).
Taking into consideration the inaccuracies of the above analysis
one can formulate a general heuristic on the fea- sibility of
physical absorption for a given separation:
If the selectivity calculated from eq 8 is 3 or greater for an
enrichment process or 4 or greater for a sharp sepa- ration, then
physical absorption should 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- tivities obtained by
each of the four methods of correlating the standard-state liquid
fugacity are shown in Table V. The solvent is assumed to 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 absorption is a feasible separation option for these two
gases. The ideal solubility method, however, does not
basic ~TOUDS ammonia amines water alcohols aromatic amines
heteronitrogen aromatics thiols
acid groups carbon dioxide sulfur dioxide hydrogen sulfide
thiols hydrogen bond donors (see Kaliszan, 1987)
indicate a favorable selectivity. This method is probably
inappropriate, as the system temperature is close to the critical
temperatures of both components. Astarita et al. (1983) report an
experimental H2S/C02 selectivity 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)
(Astarita et al., 1983; Tennyson and Schaaf, 1977).
Although results have been published for selected sys- tems
(Astarita et al., 1983; Kohl and Riesenfeld, 1985), a generalized
predictive method for chemical absorption equilibrium is not
currently available. Without selectivity information, determining
the feasibility of chemical ab- sorption is difficult but not
hopeless. Chemical absorption often involves the 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 i f the species to be separated contain different acid-base
functional groups (or i f 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 categorically ensure that an appropriate chemical
solvent can be found.
E. Cryogenic Distillation. The feasibility of a cryo- genic
distillation can be determined from the relative volatility, a, of
the key components in much the same way as high-temperature
distillation. The relative volatilities of condensed gaseous
systems tend 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 (Timmerhaus and
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
cryogenic distillation separations, 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 economics of a cryogenic separation are
dominated by the scale of the process as well as the
thermodynamics. Cryogenic distillation is rarely cost-efficient for
small-scale separations or purification operations which produce
less than 10-20 tons/day of product gas. For example, energy
consumption for 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.
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1688 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
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 adsorption bed depends to a
large extent on the types of components that are processed.
High-boiling organics (those with 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 sensitive to
acid solutions, while silica gels 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 (Ullmanns,
1988).
When possible, 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
eapecially dramatic when using zeolites 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. A number of
industrially important vapor-phase (and liquid-phase) adsorptive
separations are based on this molecular sieving effect, notably
Union Carbides 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 characteristics of a molecule
(see Barnicki (1991) for methods of estimating kinetic diameter).
Commercially available molecular sieves fall into five distinct
categories according to their nominal aperture sizes (Le., pore
size distribution). Thus gaseous species can only be separated by
molecular sieving effects when their kinetic diameters fall into
different zeolite aperture size categories.
Table VI1 presents 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 diameters of gas molecules. Breck (1974)
presents one set of values, whereas several other authors report
considerably different figures (Barrer and Brook, 1959; Collins,
1968, Ullmanns, 1988). Barnicki (1991) describes methods of
estimating kinetic diameters 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 sieves are extremely effective desiccants 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 i f 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-Limited Adsorption. As stated in the section
Separation Types, the primary uses of equi- librium-limited
adsorption are restricted to purifications and the separation of
dilute components from 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, i f the de- sired
separation or purification requires an adsorber that is longer than
20 f t , then equilibrium-limited adsorption
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Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 1689
Table VIII. Favorable Components and Chemical Families for
Desiccation by Equilibrium-Limited Adsorption
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
organics from air, oxygen, nitrogen, helium, etc). In thia case,
the equilibrium loading of the inert ~ 8 9 on the adsorbent is
negligible and can be ignored.
The second application of equilibrium-limited adsorp- 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 breakthrough of the more ahorbed component should be less
than 20 f t . 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 preferably higher (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 enrichment separations (i.e., adsorbed
components consist of 10 mol % 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 use of equilibrium-limited adsorption for desiccation
operations has been notably successful. Silica gels, 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):
I f 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 separation techniques requiring mass
separating agents, the appropriate adsorbent for a given separation
is 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 experimental isotherm data 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.
Condensation should 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 difference is greater than 40 "C.
Condensation is most favorable for the separation of
high-boiling organic vapors from noncondensable gases, 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 generally greater than 95% removal is possible.
Example Separations Mixed Solvent Recovery from a n Air Stream.
In
order to comply with strict environmental regulations on the
extent of toxic emissions, many chemical synthesis processes
include one or more steps involving the removal of trace amounts of
organics from 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 organics are to be
separated and recovered, rather than removed and possibly
destroyed. Air is considered to be 71 mol % nitrogen and 29 mol %
oxygen for this problem.
The separation analysis starts with the phase split manager
(PSM) as described in part 1 of this series (Barnicki and 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
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1690 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
Table X. Ranked Property Lists for Mixed Solvent Recovery ranked
Property
method DroDertv components values chemical absorption chemical
family oxygen catalytic oxidation nitrogen
ethyl
toluene molecular sieve kinetic diameter oxygen
acetate
adsorption nitrogen ethyl
toluene equilibriumlimited equilibrium loading toluene
adsorption (mol/g of ads) ethyl
acetate
acetate oxygen nitrogen
inorganic gas inorganic gas acetate
alkylbenzene
-
Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 1691
benzene chloroethane carbon dioxide mhane
- - - - - Separation by EOUILIBRIUM-LIMITED ADSORPnON ntLpea
f'' methane Oxygen Separation by
MOL SIEVE ADSORPTlON
izmfmmu Methane \- methane Product nitrogen
oxygen methane
methane nitrogen Sanaratinn hv oxygen carbon dioxide G171EM'' -
- - - Separationby
methane CRYOGENIC DlSTlLLATlON
Carbon Dioxide \ Product
Figure 7. Summary of landfill gas separation process
alternatives.
Table XII. ReDremntative Landfill Gas Com~osit ion~ 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 99.985 mol % methane 99.98 mol % total sulfur 0.3
ppm max chlorides 0.25 g/100 SCF'
total hydrocarbons 5 ppm max sulfur 1.25 g/100 SCFc
OBlakely (1983). bStockmann and Zollner (1987). 'SCF p
standard
compounds
compounds
ft.3
use of chemical absorption to remove hydrogen sulfide followed
by a second separation step to remove the chlo- roethane and the
benzene. The second process would be necessity (see analysis
above), involve equilibrium-limited adsorption. Therefore, the best
initial separation for the feed mixture is equilibrium-limited
adsorption 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 47.4 mol % 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
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1692 Ind. Eng. Chem. Res., Vol. 31, No. 7,1992
the landfill gas separation is a large-scale process, pro-
ducing approximately 21 tons/day of methane. However, the presence
of large amounts of carbon dioxide precludes its use; the carbon
dioxide will freeze and foul condenser surfaces (see Cryogenic
Distillation). Oxygen and nitrogen can be separated from methane
and carbon dioxide by 3A molecular sieves, with the oxygen and
nitrogen as the ad- sorbed components (see Table VII). Equilibrium
loadings on activated carbon are favorable for the preferential ad-
sorption of carbon dioxide over methane. However, as the problem is
stated, almost 50% of the stream would be adsorbed (carbon dioxide
as well 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 298 K using the Shair correlation. Thus, physical
absorption is a feasible alter- native (a common solvent, Selexol,
gives a selectivity of approximately 6.5 (Kohl and Riesenfeld,
1985)). Since high purity is required, the physical absorption
process should 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 selector analysis 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 91
mol ?% methane, 1.9 mol ?% oxygen, and 7.1 mol % nitrogen.
The analysis of the separation of methane from oxygen and
nitrogen is quite similar to the previous exposition for carbon
dioxide. Cryogenic distillation is feasible this time because the
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 as the adsorbed components
(see Table VII). Methane is preferentially adsorbed on activated
carbon. However, again, this would require the adsorption of the
majority of the feed. It is worth noting that this separation may
be accomplished with incomplete recovery 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 sieve adsorp- 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 pointed out that a proceas stream 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 dioxide are 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 streams were the
desired products, then the selector analysis would have followed
the 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
synthesis of separation sequences for gas/vapor mixtures has
been presented. The architecture of the SSAD is based on a
combination of rule analysis and task-oriented methods. The
cornerstone of the task-oriented problem- solving methods used in
the SSAD is the separation syn- thesis hierarchy (SSH). The
separation synthesis hierarchy (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
industrially significant separation problems 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 f j o l = 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 x i = liquid-phase mole fraction yi
= vapor-phase mole fraction a = relative volatility aij* = membrane
permselectivity 6i = solubility parameter yi = activity coefficient
yijm = infinite dilution activity coefficient 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
-
Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 1693
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 controllers ability to reject
disturbances is introduced. Next, a new robust control framework of
characterizing model uncertainty descriptions by probability
distributions is developed. 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. Several simulation 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 control system is then designed to
minimize the effects of a worst-case situation. 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 existing design techniques for robustness
include the following: (1) closed-loop stability is guaranteed over
the entire range of model uncertainty (robust stability); (2) an
upper bound on a given perform- ance measure is guaranteed (robust
performance). Because the controllers are generally designed for
worst-case situ- ations that may have a low probability of
occurring, the resulting robust controllers may be very
conservative for more typical operating conditions that have a much
higher probability of occurring.
In this paper, a new approach to robust process control design
is developed in which model uncertainty is char- acterized by
probability distributions. This approach allows closed-loop
performance tradeoffs to be analyzed as a function of the
likelihood of controller performance; that is, performance can be
characterized by a probability measure for all situations between
nominal and worst-case conditions. The result is a more complete
analysis strategy 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. Modeling error 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 developed from a wide
variety of sources, including statistical information on
phenomenological model parameters, empirical model parameters, or
fre- quency response (Cloud and Kouvaritakis, 1987; Correa, 1989;
Goodwin and Salgado, 1989; Stengel and Ryan, 1989). Also, process
knowledge is usually available in the form of engineering
heuristics 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 to the development of a general probabilistic
framework, a statistical measure of closed-loop disturbance
rejection capabilities is introduced for process control
applications. A disturbance rejection 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
specifications for outputs or inputs can be formulated in terms of
statistical moments. For ex- ample, a typical product specification
is expressed in terms of a mean and standard deviation (also
referred to as root mean square). Well-known control design
strategies have 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 as robust linear quadratic Gaussian (LQG) control
strategiea (Stengel, 1986; Bernstein and Haddad, 1990) and
constrained minimum variance control (Makila et al., 1984; Hotz and
Skelton,
0 1992 American Chemical Society