Note: Descriptions are shown in the official language in which they were submitted.
File 913,~24
CATA1YTIC REACTOR FOR ISOT~ERM~L REACTIONS
This invention relates to a catalytic
reactor for substantially isothermal reactions
having cocurrent heat exchange.
There are many catalytic reactions which
release or absorb large quantities of heat.
Important reactions include hydrogenation of carbon
monoxide to methane and water over nickel catalyst ~ ~
and hydrogenation of nitrogen to give ammonia over ~-
an iron catalyst. Reactions involving large
quantities of heat are relatively difficult to
control. Lack of control may result in high tempera-
tures which may lead to damage to the reaction vessel,
production of undesirable by-products, deterioration
of the catalyst or shift of thermodynamic equilibrium
away from most favorable yields. Optimally it is ~ -.
desirable to avoid a temperature rise and to main~ ~'
tain substantially uniform or isothermal temperature ~'
or to permit a slight drop in temperature.
- 20 There have been at least four procedures
which have been used in the design of equipment to
; control extremely exothe,rmic reactions, viz.,
1) dilution of reactants with inert medium; ;~
2) reacting in stages with cooling
between stages,
; ~ 3) surrounding with a boiling heat ex-
change medium and
4) using incoming reactant to partially
cool the reaction.
Each of these offers disadvantages such as repeated
' ' ' ' ' .~ .
recycling and complexity of' equipment although
actually employed in production. It would be consi-
derably more convenient if reactors could be con-
structed in wh~ch even a highly exothermic reaction
5 would proceed smoothly under substantially isothermal
conditions. The specification of operable parameters
for such reactors is a principal aim of this inven-
tion.
As materials flow through a reactor re-
quiring cooling it is usual practice to consider
;~ countercurrent flow of coolant as being most effi-
cient. However, it can be shown mathematically that
i~ is not possible to achieve substantially isothermal
conditions by using countercurrent heat exchange~
- 15 e.g. cooling.
There has been some consideration of the
use of cocurrent flow in reactors although not
necessarily to attain isothermality.
Surprisingly, it has been found that
substantially isothermal conditions can be maintained
using cocurrent heat exchange, e.g. cooling, and
that the parameters of the reactor for a hetero-
geneous or homogeneous reaction having cocurrent or
pseudococurrent flow of coolant (or heating medium)
through passages in heat exchange relationships are
expressed by the mathematical relationship for exo-
thermic or endothermic reaction:
(-~H)Co PCCpCVCUH~HSH (1-1)
where
TH = inlet temperature of reactants (C)
TC = inlet temperature of coolant (C)
-~H = heat of reaction (cal/g. mole)
5 CO = inlet concentration of reactant(s)
; (g. moles/cm3)
H = overall heat transfer coefficient on
reaction side (cal/(sec)(cm2)(C))
UC = overall heat transfer coefficient on
coolant side (cal/(sec)(cm2)(C))
TH = space-time on reaction side (sec)
= space-time on coolant side (sec) ` ~
H = heat transfer area on reaction side (cm2) ~ ~;
C = heat transfer area on coolant side (cm2)
VH = free volume on reaction side (excluding
~ particulate catalyst) (cm3)
:'~ V a free volume on coo]ant side (cm3)
C : ~
- pcCpc = product of density by heat capacity of
coolant gas in cal/(cm3)(C)
when the chemical reaction is carried out over a
;~ catalyst under conditions such that the rate of heat
liberation is in substantially direct relationship to
concentration of reactant which relationship is a
function of Uc and the ratio Tc/TH.
By "space-time" is meant the time for the
gas in question to transit the passageways free from
any included particulate substances such as catalyst
pellets. The heat transfer area on each side is
defined as including surfaces which are common to the
streams on the respective sides and surfaces intruding
3 -
8~
between the common surface such as corrugations.
Those of skil~l in engineering practice
will readily perceive that these relationships de-
f-lne an entire family of reactors from which
specific selection is made by setting certain
values for the particular reaction being contem-
plated, such as inlet temperatures, concentrations
and other factors. Selection of the reaction
will normally determine heat of reaction and
usually also density and heat capacity. The re-
maining terms will be affected by the scale of the
reaction and by details of construction. It is
found that the specified conditions are conveniently
fulfilled using reactors which may be a sequence of
cross-flow reactors or heat exchangers each~one of
which has passageways for reactant and coolant
running at right angles and separated by heat ex-
changing layers. Preferably each cross-flow reactor
is a unit or monolith~ which for very elevated
temperatures or corrosive materials is preferably of
ceramic. The precise dimensions and variations in
~ such cross-flow reactors will be dictated by the
; requirements of the above mathematical relationship
as will be apparent to those of skill in the art and
will be readily calculated by usual methods of
engineering practice. Somewhat surprisingly it is
; found that only a relatively narrow range of certain
parameters is possible to maintain isothermality of a
reaction. This range of parameters is somewhat
analogous to the "windows" of calculations for extra-
terrestrial flight and may be similarly termed.
321~
The portion of a reactor in which reacsion
is carried out is herein sometimes termed reaction
situs. It will be recognized that various configura-
tions are possible within the scope of the invention
although cross-flow reactors are particularly pre-
ferred.
Illustrative reactions which are either
first order or can be made to simulate first order
and therefore can be carried out by processes and
in apparatus according to the invention include:
Exothermic reactions
1. Methanation, i.e., CO + 3H2 -~ CH4 ~ H20.
2. Oxidation, 2CH2 = CH2 + 02 -~ 2C\ ~CH2.
3. Formation of hydrocarbons from methanol.
4. Oxidation of naphthalene to phthalic
anhydride.
5. Chlorination of hydrocarbons.
6. Hydrodesulfurization, e.g. removal of
thiophene by reaction with H2 to give
~3 butadiene plus H2S.
7. Formation of methanol: CO + 2H2 -~ CH30H. ~ -
Endothermic reactions
1. Dehydrocyclization, e.g. n heptane
toluene.
2. Catalytic cracking of petroleum.
In order that the invention may be more
clearly understood it is also described in ter~s of
the accompanying drawings wherein
Figure 1 shows diagrammatically one cross-
flow heat exchanger about 7 cm on a side with catalyst
impregnatecl pellets abou-t 2 mrn in diameter and 3 mm
high in one set of passageways.
Figure 2 shows an arrangernent of four of
the heat exchangers of Figure 1 mounted in a casing
to provicle a pseudococurrent flow reactor in
accordance with the invention.
Figure 3 is a flow sheet showing diagram-
matically the sequence of calculations which can be
used in calculating the parameters of a reactor of
the invention.
Figure l~ shows diagrammatically a small
scale reactor and adJunct controls and supply sour~es,
The reactor is discussed in connection with ~xample 1.
Figures 5 through 10 show graphi~ally
variations in isothermality and conversion at
specified reaction conditions.
Figure ll,appearing on the first sheet of
drawings,shows kemperature c~nditions progressively/
~ through a reactor of the inve~tion with pseudococurrent
; 20 flow.
Figure 12 shows diagrammatically a plant
design for methanol synthesis from CO and H2 with
stacked heat exchangers in the reactor.
Figure 13 shows graphs comparing the catalyst
loading employed in the apparatus of Figure 12 as
compared to that of the same isothermal reaction of
the prior art.
Referring to Figure 1 there is shown a
cross-flow heat exchanger useful for apparatus of
the invention when several are used in series to pro-
vide pseudococurrent flow. As noted above this is
diagrammatical. It will be seen there are four sets
of passageways (10) and (12) bounded and separated
by flat sheets (14) and sinusoidal corrugated sheets
(16) or (18) and closed along the sides by sheets
(20) or (22). It will be seen that passageways (10)
; and (12) are not of equal height and it will be
recognized that variations may be made in the relative
heights as desired. It will further be seen that
~ i
the passageways (12) are filled with catalysk im~
pregnated pellets (30) with some omitted to show
inner portions of passageways. In referring to such
structures hereinaf'ter it is convenient to designate
two axes for each segment including a corrugate be-
tween two flats. The axes are designated q in the
direction of the corrugations and x at right angles
thereto and in the direction of flow through the
corrugations. Corners (34) are plugs fi]led with
ceramic plugging marginal passageways in each
direction.
In Figure 2 there are shown how f~ur of the
heat exchangers (40) of Figure 1 are positioned in ~ ~ ,
series in casing (42) with inlets (44) for reactant
and (46) for coolant arid outlets (50) and (52) for
reactant and coolant respectively. Details of
insulation and sealing of heat exchangers are not
shown as they will be readily apparent. Mounting
may be by lugs or brackets (54) within the casing
or other means for sealing between inlet and outlet
sides of heat exchangers and at points where the
heat exchangers come to walls of casing (42). Paths
.
-- 7 --
32~
of flow of reactant are shown by solid lines and of
coolant by broken lines~ Ends of the casing are
held together diagrammatically by bolts (56) and
catalyst is retained in passageways of heat exchangers
(40) by screens (58) suitably of stainless steel.
Referring now to Figure 3 there is provided
a flow diagram for one method of calculating the
dimensions of an apparatus of the invention as shown
in Figure 2 for a specific gaseous reaction. It
will be seen that the several boxes are indicated by
numbers. In the following description the mathe-
matical or mental operations needed for each box are
indicated in some detail. It will be recognized that
the operations may be performed by any suitable means
using normal computing aids such as longhand
numerical calculations, computers, slide rules or
sophisticated computer programs. The selection of a
~; particular method for arriving at the desired result
is well within the skill o~ the art as are other
sequences o~ operations to arrive at the same or
similar results.
In making the following calculations cer-
tain simplifying assumptions are made to avoid
unnecessary complications. ~hus, it is assumed that
- 25 neither reactants nor products diffuse forward or
backward along the flow path and there is no conduction
of heat along the flow path, i.e., axially. It is
further assumed that the only resistance to radial
heat transfer is at the walls. Further, it is
` 30 assumed that no heat transfer occurs by radiation in
.
-- 8 --
any direction within the reactor. It is assumed that
khe front of reactant or coolant moves forward at
the same speed across the entire front, i.e., plug
flow.
The most important assumption, which is
generally valid when two or more cross-flow reactors
are in series is that there is cocurrent flow. In
the case of cross-flow units this means that conver-
sion should not occur abruptly in the first unit but
must be only fractional in each cross-flow unit. Al-
though such an assumption may not appear significant
at first glance it is necessary because if excessive
reaction occurs in a portion of the cross-flow
reactor there may be a deviation from isothermality
reaction which can resulk in inactivation of catalyst
or undesirable side reactions in a portion of the
reactor and gradual degradation and deterioration
of overall performance.
Boxes 120, 1303 lLlO and 150 require
specifying3 respectively, inlet values, kinetic
parameters, properties of gases (reactants, products
and coolants) and certain predetermined physical
dimensions of the reactor's internal structures. For
convenience in the following treatment the necessary
quantities are syrnbolized as follows and are expressed
in units as noted for metric system usage.
I. For box 120 specify:
j~ CO Inlet concentration of reactant
(in g moles of reactant/cm3 of total
feed). Determined on basis of need
for dilution to avoid hot spot~ing,
_ g _
explodability, etc.
C Outlet concentration of reactant
(in same units as CO)-
z=l-Cc Conversion (as a fraction) selected
on basis of value of product and
feed cost, difficulty of separation,
~- etc. and governed by temperature
selected in V (box 160) below.
- F Catalyst-side inlet feed rate, of
reactant (kg mole per day). Deter-
mined by production requirements.
MH Average molecular weight of gases
on reactant side (daltons, i.e., gm.
per gm.-mole).
-~H Heat of reaction per mole of
reactant or reactants (cal/gm-mole).
This is characteristic of the reac-
~;~ 20 tion and the numerical value is
positive for an exothermic reaction,
the term~ however, is negative. Heat
~; , .
;~ losses are estimated as portion of
.
heat of reaction, e.g., reducing it
by one third or other amount. Heat
losses are generally less for larger
reactors.
II. For Box 130 specify kinetic and catalyst
parameters.
3 PT Density of catalyst (g/cm3) deter
mined experimentally on solid.
- 1 0 -
. ~ ,
Void fraction of bed (dimension-
less) calculated from bulk density
of catalyst compared to solid density
of catalyst~ Pr.
k~ Pre-exponentia] factor from `i
Arrhenius (rate) equation for the
reaction system and catalyst being
used. (Reciprocal seconds.)
Dp Diameter of catalyst pellet (as-
suming spherical shape) determined ,;
by measurement of a statistical
sample. (cm.)
E/R Energy of activation divided by
gas constant. Determined from rate
equation as slope of ln(k) (reaction -
velocity constant) versus reciprocal ~;
absolute temperature (degrees Kelvin). ~ -
III. ~or box 140 specify properties of gases. ; ~
' ::
CpH Heat capacity of gaseous reaction
mixture (on catalyst side) assuming
constant temperature and average
; composition. (cal/(g)(C)).
pC Heat capacity of coolant gas
assuming average temperature.
(cal/(g)(C)).
~iscosity of gas. Use average of
reactant and coolant gases. (g/cm-
- sec).
K Thermal conductivity Or gas. Use
average of reactant and coolant
gases. (cal/(sec)(cm2)(C/cm)).
MC Molecular weight of coolant gas
(daltons).
PH Density of reactant gases.
`' (g/cm3 ),
Density of coolant gas (g/cm3).
I~. For box 150 certain characteristics of the
heat exchangers or reactors without load of catalyst
pellets must be speci~ied. The present reactors are
cross-flow heat exchangers in which in actual use
one set of passageways is filled with catalyst-
impregnated pellets. The calculation of the heat
exchange area will vary slightly depending on the
geometry of the passageways. The following applies
to passageways formed between flat plates separated
by corrugations~ ~ins or other means and without
catalyst pellets present. It is illustrative and not
limiting. The geometrical terms which are directly
- measurable or are calculated are listed below. All
` terms which are lengths or distances are in centi
meters. The use of subscript letters C or H permits
the use of each term for coolant side or reactant
(hot) side, respectively~ as shown in Example l below.
= ratio of height of block heat exchanger to
distance along flow path.
25 J = length along sinusoid over one wavelength. ~;
~ = wave~Length along q axis.
a - amplitude = 1/2 height of corrugations.
b = 2~
f = overlap factor = fraction of sinusoid
length bonded to flats.
2j = height between flats.
= thickness of sinusoids (cm.).
~ - thickness of flats (cm.)
K' = thermal conductivity of material of reactors, ;
including flats and corrugations. -~
J is calculated from the relationship~
J= ~Jl+(ab cos bq)~ dq (IV~
10 using, if desired, a computer program where q is the ;
distance along the q axis defined as above for Figure
1. Certain ~unctions of the above terms are conven-
iently adapted to computer programming.
The heat transfer area S for unit area (x
by q) passageways (including surface common to
reactant and coolant side) is calculated as the sum
of the area of sinusoids (two faces) plus the area of
flats less the overlap factor "f".
,
S=2~ -~2- 2fJ = (l-f) 2J -~2 (I~ 2)
The heat transfer area on the reactant
side, SH, and on the coolant side, Sc~ are calculated
per unit area for surface common to reactant and
coolant sides using appropriate values of J, ~ and f.
The volume of the space per unit length and
width (x by q) is the area by the height between flat
sheets, i.e.~ "2j".
The unit open volume "v" is the total
volume minus the volume of the ceramic sinusoid:
v=2j- ~ (IV-3)
- 1 3-
This is calculated for coolant side, vc, and reactant
side VH.
The relation of heat transf'er area to
empty volume S/v is calculated in reciprocal centi
meters f'or the reactant side and for the coolant side.
It is found that the hydraulic diameter of
the passageways Dh (in cm.) is given by the expression
D = 4S (IV-4)
The fraction of open face area, that is
the portion of the surface of unit length of' passage-
ways for flow "G", including one blank row and one
open row, is
2j~ 2
2jH+2iC+2~ +iC+a (I~-5)
This quantity is calculated for GH and GC using
appropriate terms in the numerator.
The fraction of the total heat transfer
area Q due to the area of the sinusoids is
f~ (IV-6)
(l-f) ~+2 l-f'-~
The ratio of' heat transfer area on
reactant side to that on coolant side is
SH
SC. ~:
and the ratio of volumes of' reactant side to coolant
side is
V
- 1 11 -
V. The isothermal temperature TH (in degrees
centigrade) at which it is intended to run
the reaction is selected in accordance with
: j :
box (160) based on known or experimental
data on the catalyst system. This tempera-
ture very strongly influences the conversion
"z" above. In general the highest tempera-
ture is chosen at which
a. the catalyst will not sinter, ~ ;
b. the ca-talyst is not rapidly poisoned,
d. undesirable side reactions do not
occur,
e. the reaction will not proceed so
-~ rapidly as to result in damaging
the reactor.
VI. For box (170) the space-time on the reactant
side TH is calculated for a first order
reaction, or reaction simulating first order,
from the relationship
~`~ 20 - = exp(-r) (VI~
where r ls the catalytic activity:
r - k~THexp(-RTH) (VI-2)
so that the expression becomes:
-lnc = k~THeXp( E ) (V1-3)
in which all quantities are known from above
; except for TH. Thè space-time is expressed
in seconds.
- 1 5-
313
VII. For box (180) the total amount of catalyst
required (in kg), also referred to as
catalyst loading, W, is determined from the
relationship
F ~ r (VII-l)
O '~ ~:
where F is flow rate of reactant to catalyst
side determined by production requirements
. ::, .. ...
as kg. per year, z is the conversion as de~
fined in I, zO: is numerically zero and z is
the final converslon, and r is the rate o~
reaction defined~by~
r = k;~exp ~ C (VII-2) ;:
~ for a first order reaction.
~. VIII. The total volume of space occupied by all
the eatalyst needed~when the~passageways on
the reactant side are filled in:accordance : ;~
:with~the above conditions is vH and is
determined ~or box ~(l90)~rom the . ~:
:~ : relationship
. :1 : : :~
: 20 VH ~ ~ (VIII-l)
where~p~ lS defined as above~as the solid : .::~
density of the catalyst and W was calculated -;~
in VII above.
IX. The number of transfer units on the coolant
~` side, Nc, is calculated for box (200) from
the relationship:
NC = -ln(l-z) (IX-l)
: - l 6-
~.
The number of transfer units, N~ is a
nondimensional expression of the "heat transfer
size" of a heat exchanger. When N is small the
exchanger effectiveness is low and when N is large ;
- 5 the effectiveness approaches asymptotically the
limit imposed by flow arrangement and thermodynamic
considerations (Kays and London, Compact Heat
Exchangers, 2nd ed (1964) pp 15-16).
X. For box (210) an assumption of temperature
(TC in degrees centigrade) of entering
coolant gas is made. This determines the
driving force for heat transfer from the
~ reactant side to the coolant side. Some -~
; factors which are particularly important
to consider are~
A. Ambient temperature.
B. Temperature of some available gas
` stream.
C. A temperature such that the reactant
gases are first used as coolant gases
.~
and leave the coolant side at the
desired temperature for entering the
reactant side.
XI. ~or box (220) the ~alue of r ls calculated
from the relationship
r = k~THeXp( RTH) (XI-l)
~ All of the terms of which are known from
- previous sections, e.g., sect. VI. The
value is dimensionless.
- 17 -
XII. For box (230) the number of transfer units
on the catalyst side, NH, is calculated f'rom
~' NH = Q (XII-l)
where r is f`rom step XI and
(TH-TC)PHC H (XII-2)
and all terms are previously known.
'~ XIII. For box (240) the overall heat transfer
coefficient on the catalyst side in cal/-
(,sec)(C) designated UH is calculated
(NH)(PH)( p~)( H (XIII~
in which all terms are known from above, e.g.,
the ratio SH/vH from IV.
XIV. For box (250) the ratio of number of transfer ~-
units on catalyst side to the number on
coolant side is designated Y. It can be shown
' and is known that Y = Q. This fact is used ~'
'-, in calculating the ratio of gas velocity ;~
(in cm/sec) on the coolant side to that on
catalytic side. The ratio is designated a.
This is shown to be
C ~ c c p c ( x Iv~
in which all terms are known except for ~.
From the relationships established in
Sections I to XIV above it is also shown that the
relation between rate of liberation of heat and
- 18 -
concentration of reactant, designated kR, is a
function of Uc and the ratio Tc/~I. By establishing
a heat balance for an incremental or differential
. volume, dvH, the following equation is formulated
..:,
- 5 where QL is the rate of evo].ution of heat over tlhe
. entire path (cal/sec) and Cx is the
:; concentration in volume dvH.
dQL = (-QH)cxkRdVH (XIV-2)
which is integrated to :
QL (-~H)kRIo CxdVH (XIV-3)
k~ is the proportionality constant, i.e., reaction
~:~ velocity constant, which, in terms of previously
defined terms, is
. kR = k~ exp(-RE ) (XIV-4)
and -~H is a characteristic of the reaction. There
;:~ is clearly a relation between rate of liberation of .~.
heat and concen~ration of reactant at the positi.on of
:~ voIumn dvH. Then, because of the equality f NC
. and r
,,~ UCSC'lC
r = kR~H = pCc cvC NC (XIV-5)
Sc
kR = T (UC ) ( p C V ) (XIV-6)
S
The values of the term (pCc ~ ) depend upon the
nature of the cooling medium which is selected and
geometry of the apparatus and may be considered a
constant insofar as reactant is concerned so that kR
is a function of Uc and rc/TH.
-- 19 --
32~
XV. For box (260) the length of flow path on
the coolant side is (X) for one individual
; reactor as described in IV. The value of
X can be selected on the basis of the
scale of operation, commercially available
shapes etc. It is generally efficient to
use a multiplicity Or cubical reactors as
described elsewhere but it is fully possible
,:
to employ reactors in which the ~low path
~ 10 on the coolant side is X, on the reaction
;~ side ~X and the reactor is I~X perpendicular
to the directions of flow. In the present
discussion it is assumed that catalyst is
~; deposited on pellets, but the catalyst may
be deposited on the walls with~or without
impregnated pellets.~ Pellets without
- ~ catalyst may be used in coolant passageways.
; XVI. ~or box (2~70) the velocity of flow on each
side is càlculated whi;ch is necessary to
give the overall heat ~transfer coefficlent
UH as calculated in XIII above. ~he cal-
culation proceeds stepwise by calculating
, ~ : :
heat transfer coefficients on coolant and
,: : : .
reaction sides and combining them in conven-
~; 25 tional fashion. A value for velocity on ~ ~;
coolant side, Vc, is assumed which is prac~
- tical, e.g., 80 cm/sec.
A. The average film coefficient for laminar
flow on coolant side hC in cal/(sec)(cm2)-
~; 30 (C) is given by the relationship
- 2~
,
.
3.65KC ~ 0 ~78 XRePr)
h = - ~ x ~ dx
(XVI-l)
where KC is thermal conduetivity of
coolant gas in eal/(sec)(cm2)(C/em).
DH is the hydraulic diameter;
Re is Reynolds number for an assumed
veloeity;
~` Pr is Prandtl number of the coolant;
X is the length of the flow path on the
` 10 coolant side of one reactor;
3.65 is adopted as the Nusselt number ,~
~: for fully developed lamlnar flow in the
~ effective passageways of convenient
`,-; commercial ceramie shapes shown in ;~
` 15 Figure 1. The average value is used
: i :
;~ because laminar flow is not established
until after the coolant gas has passed
through a portion of the passageways.
-~ This is known as the "end effect.l'
The integration of the above equation
~;~ is conveniently performed by computer
methods, e.g., by Simpson's rule.
B. The film coefficient on the reaction side
filled with catalyst pellets is calcu-
lated from
KH ~ 75 (XVI-2)
- 21
2~
:;
where the term in parentheses is the
Reynold's number for flow where Dp is - ~-
the particle diameter. The above
expression is applicable when Dp ranges ~ -
from about 0.2 to o.8 times the
~.,
hydraulic diameter of the passageways
(cf. calculation above in IV) :
KH is thermal conductivity of reactant- :
side gases in cal/(sec)(cm2)(0C/cm).
~ .
:~. 10 PH is density of reactant-side gas,
~` ~H is bulk viscosity of reactant-side
gas
~; VH is the linear velocity of the reactant- ~;
side gas based on passageways containing
no particulate material given by the :
expression~
VC ~ :
~;~ VH = ~ (XVI-3)
: from XIV above
~ C. In order to combine the two film coeffi-
- 20 cients of A and B above it is necessary ::
to determine total surface temperature
effectiveness of the flat heat transfer .-~ ~.
surfaces on coolant and reactant side
because of the diminishment in effect1ve- ~ .
ness caused by the sinusoidal corruga-
:~ tions. ~ .
' A term m is defined~
:~ m = ~ (XVI-4)
- 2~
, - , :: :
:
2~3~
where h = film coef`ficient for respec-
tive side as in A or B above
K' = thermal conductivlty of
material of corrugation
0 = thickness of corrugation.
When 2j is the distance between flats,
i.e. amplitude o~ corrugations, the sur-
` face effectiveness of the intrudlng sur- ;
faces, e.g., corrugations, n~,, is given
by the relationship
nF mJ (XVI-5) ~;
and thus is employed in the calculation of
total surface temperature effectiveness nO
for the respective sides, nc coolant, nH
reactant.
nO = 1 ~ S (l-nF) ~XVI-6) ~ ;
where S is total~heat transfer area on one
: .
side (Sc, on coolant side or SH, on reaction
side) as given in IV above and S~ is total
i
area of corrugations on the side being cal-
culated.~
D. The two film coefficients of A and B
above car now be combined where UH is
the overall heat transfer coefficient
based on reactant side and underlying
` area of corrugations, and is given by;~
the relationship:
S~l C C SH
- 23~
:~
-
In this expression Sw is the area of
the surface common to both reactant
and coolant streams. This expression
can be simplified because the middle
term representing heat transfer through ~;
the walls is relatively very small for
thin walls and can be ignored. The
relationship is thus
UH ~HhH ~ S (XVI-8)
in which all terms except UH have been
- calculated or are known from above.
,: .
The value of UH calculated above is
compared with the value calculated in XIII
above. If agreement is not within about
0.1% changes are made in the assumed veloci-
ties made initially to effect proper agree-
ment, e.g., by increasing velocities for
box (280).
XVII. For box (290) the length of the reactor L is
calcula-ted on the basis of parameters calcu-
lated above:
L = THVH (XVII-l)
where TH was calculated in VI and VH was
the linear velocity on the reaction side
assumed and confirmed in XVI above.
`
XVIII. ~'or box (300) the cross sectional area of
passages on the reaction side~ AXH, is
calculated from the relation
- 24 -
'
AXH L (XVIII~
where L is from step XVII and v~l is from
`~ step VIII.
XIX. The total facial area of the reaction side,
ATH, is calculated for box (310) from the
relation:
ATH GH (XIX~l)
where AXH is from step XVIII and GH is from
step IV.
XX. For box (320) parameters of the coolant side ~ .
are calculated
H :
VC ~ ~ (X~
the ratio of vH/vc is known f`rom step IV and
: VH was calculated in step VIII.
The average cross-sectional area of
~; passages on the coolant side, AXc, is given
.
by the relation
~ ~ AXc L (XX-2)
:~ and the total facial area on the coolant
side, ATC, by the relation ~:
: A ~:
ATC GC (XX-3) : :~
where GC was calculated in Step IV.
XXI. For box (330) the length of the flow path,
X, is calculated. Assuming that the base
is square, either a cube with side X or
- 25 -
:
:
prism with base X by X and ~X perpendi-
cular to the passages of flow, i.e., high,
the relationship is, respectively~
X = ~ or X = ~ ~H (XXI~
XXII. Comparîson of values of X from XV and XXI
are made for box (340). If the length just
calculated is different from that assumed
in step XV, steps XVI to XXI are repeated
via box (350) to box (260) using the calcu-
lated value of X, and repeating until agree-
- ment is reached. When agreement is reached
proceed to step XXIII.
XXIII~ For box (360) the outlet~temperature Or
coolant gas, T~,, is calculated. For this ~
adiabatic reaction temperature, ~T, is ~ .
first calculated from the relation
~T = ~ ~ (XXIII-1)
in which C p C and -~H were specified
under I or III above. The value of ~T is
employed in calculating the outlet tempera-
ture in degrees centigrade from the rela-
tionship
T~ = T - N w H exp {-(k~H) exp-
(T +273) ~ T +273} (XXIII-2)
` 5 where ~T is known from above, TH was ;
`:
' ' ` :'
:,
:
::: .
selected in step V and A is the ratio of
E/R in appropriate units as determined in
: step II.
'
XXIV. For box (370) the molar flow rate of coolant
gas in rnoles per day, ~C' is calculated from
the relation
86400VCAxcp
C (XXIV-l)
-. where 86400 is seconds per day, MC and PC
are from step III, Vc from step XVI and AXc
from step XX.
XXV. For box (380) the number, Nn, of individual
reactors of the dimensions assumed above are
calculated from the relation:
L
Nn = X (XXV~
where L is the length of reactor from step
~` XVII and X is the flow pa-th per individual
~; reactor calculated in step XXI.
.,
The isothermal condition on the ca-talyst
side can be maintained only if the rate of liberation
of heat is in a substantially direct relationship to
the concentration of reactant. It will be recogni~ed
that the rate of liberation or evolution of heat as
described herein includes the cases where the rate is
either positive (e~othermic reactions) or negative
(endothermic reactions). If the reaction kinetics
are anything other than first order and irreversible~
the physical characteristics of the system must be
- 27
modified such that a direct relationship between
rate of liberation of heat and concentration of
reactant holds. For a second order reaction between
A and B the rate, r", is given
r" = k~ exp(-RE )CA.CB (S-1)
where the last two terms are concentrations. Modi-
fication of the reaction conditions effectively makes
the reaction conform to first order kinetics for which
the pseudo first order equations are
10 r" = (k~CB)exp(-RE )CA and r" = (k~CA)exp(-RT )CB ~
(S-2) ~;
for which rate constants are (k~CB) and (k~CA)
respectively. Similar considerations can be
applied to reactions of other orders and the rate
constants thus assumed are used in the above
calculations, e.g. Sections VI, VII, XI, XIV.
The above modification of the apparent
order of the reactions can be accomplished by the
-~following methods:
First: The catalyst concentration can be
varied over the reaction path.
Second: The space time on the reaction
side can be controlled by varying
the size and/or the number of
passages in the reactor structure
on the reaction side.
The first of these is the more practical because
this can be done by diluting the catalyst with inert
material.
- 28-
It has been shown that
P = exp~(n~ C L] (S~3)
where
P = ratio of catalyst loading Wx (gm
catalyst/cm3) at any point x in the
reactor to the catalyst loading W0 at
x = O.
n = order of reaction ~ ;
NC = number of transfer units on the
coolant side = -ln(l-z)
~; x = specific length down reaction path
L - total length of reaction path
If severa], i.e., four or more, individual reactor
heat exchangers are in series, as shown, for example,
:.: .
in Figures2 and 12 and on the assumption that the rate
of any catalytic reaction per unit volume is
directly proportional to the amount of catalyst
present, the dilution of catalyst described above
~' can be closely approximated by filling the catalyst
.~ :
~ 20 passages in each reactor heat exchanger or stage ~
: . ~
~; with catalyst of the correct concentration to give
the average P ratio over the length of that block.
These concentratlons can be calculated by calculating
the values of P at values of x corresponding to in-
lets and outlets of successlve reactor heat exchangers,
i.e., for four exchangers, calculations are for ratios
L of , 0.25, 0.50, 0.75 and 1Ø From those values
of P the average in each reactor heat exchanger is
calculated and the amount of dilution on a volume
basis is readily calculated assuming that the highest
_ 29 _
, `
8~3 ~
concentration of catalyst will be used in the last
stage and that this will be diluted with greater
amounts of` inert material in earlier stages. The
inert material will preferably be the same e.g. as
to particle size and shape, thermal eapacity, etc.
as the substrate for the catalyst but without
catalyst thereon.
Analogous methods are readily derived for
correcting the catalyst loading for adsorption-
inhibited kinetics and reversible reactions.
Although the discussion in the specifi-
cation and examples is coneerned primarily with
` heterogenous reactions, particularly catalyzed
reaetions, it is eontemplated that homogeneous
, . . .
reaetions ean also be earried out under isothermal
- eonditions in eoeurrent or pseudo-eoeurrent
i
apparatus as described herein by making relatively
simple engineering modifications which will be
evident to those skilled in the art. It will be
reeognized that it is very dif`fieult to design
~- equipment in whieh there is exelusively eocurrent
flow because of the problems of manifolding.
Pseudococurrent flow as discussed herein is more
readily aehieved. Beeause of the straight
~ 25 passageways in eross-flow heat exehangers, loading
- with eatalyst is relatively simple.
Example 1
A model reactor is set up for conversion
of earbon monoxide to earbon dioxide as shown
diagrammatieally in Figure 4 with eover removed to
.
.
show four cross-flow heat exchangers (400) approxi-
mately as shown in ~igure 1 but of specific dimen-
sions as described elsewhere herein ancl bolts (418).
Heat exchangers (400) of cordierite are mounked in
casing (402) between brackets (414) having insulating
covering (404) shown in section. High temperature
gasketing material (not shown) as described in U.S.
Patent 3,916,057 is interposed between heat exchangers -
(400) and all areas of contact as at brackets (414)
and covers (not shown). Bolts (not shown) are
employed to retain the cover (not shown) in position.
The passageways of each heat exchanger are as in
Figure 1 with passageways in one direction filled
with "AeroBan~" copper chrome catalyst (not shown;
available in pelleted form, cylinders about 2mm in
diameter and 3 mm high from American Cyanamid Co.
and containing 1.44% Cu and 0.97% Cr) to within about
6 mm of surface and then further filled with chips
of ~uartz (of approximately fiame size as catalyst
pellets) to the face. The chips and catalyst are
retained in position by stainless steel screens (416).
A stream of air (410) ~o provide oxygen and coolant
and a stream of carbon monoxide (412) are provided
from suitable supply means not shown. The part of
the air stream used for coolant passes through valve
(406) and rotameter (408) and enters the reactor at
(420) and is exhausted at (422). The portion of the
stream used as a source of oxygen passes through
throttling valve (430), air filter (432), rotameter
(434), heating means (436) in which a small amount
- 31 -
2~
:
of copper chrome catalyst (438) is provided. The
carbon monoxide stream (412) is controlled parti-
cularly by valve means on the supply source (not
shown). The main stream passes through rotameter
(440) and mixes with the air stream emerging from
heater means (436). In order to heat the air
stream to higher temperatures than convenient with
- heating means (436) a small amount of the carbon
monoxide stream may be bled through valve (442) to
enter the air stream at (444) and is then oxidized
exothermically on catalyst (438). The combined
: stream of air and carbon monoxide enters the reactor
~` at (450) and after passing in pseudococurrent
... .
` relation to the coolant stream through the sequence
of reactors and oxidation over the copper chrome
catalyst ("AeroBan~" available from American
Cyanamid Co.) in the passages, the air stream car-
rying carbon dioxide emerges at (452). In order to
be able to determine experimentally isothermality
~-~ and degree of conversion in the reactant stream,
means (470) are provided for measuring temperatures in
~ ., .
chambers (474) and means (472) for sampling the gas
stream from chambers (474). In addition means (476)
are provided for measurement of temperatures of
reactant stream in reactor heat exchanger units (400).
25 Additionally means (460) are provided for measuring
temperatures in chambers (464) and means (462) for ~ ~.
sampling the coolant gas stream from chambers ( 464)
to detect diffusion through reactor walls or leakage
from one stream to the other. Means (466) are pro-
30 vided for measurement of temperatures of coolant
32
s~
stream :in reactor heat exchanger units (400).
Temperatures are conveniently measured by thermo-
couples and gas samples analyzed by gas chromato-
graphy.
The measurable parameters for the system
as designated in I, II, III and IV above are speci-
:~ fied as following in Table 1 in which the numerical
values are in the units indicated and the terms are
symbolized as set forth above. The symbol (-)
: 10 indicates dimensionless quantities.
Table 1
: Section Term Value in Units
:~ I. CO 5.19 x 10 7 gm moles/cm3
C 7.21 x 10- 8 gm moles/cm3
~: 15 z o.86 (-) ;
~ 20.6 gm moles/day ~ ;
MH 29.0 gms/gm mole
: -~H 45,600 cal/gm mole
II. p~ 1.19 gm/cm3
E 0 . 564 (-)
k~ 1.75 x 10 8 sec
Dp 0.317 cm.
E/R 8944K
III. Cp~ 0.254 cal/(gm)(C)
CpC 0.256 cal/(gm)(C)
2.38 x 10-4 gm/cm sec
~ :
- 33 -
2~3
Table 1 continued
~ Section Term Value in Units
'.- K 8.39 x 10 5 cal/(sec)(cm2~(C/cm)
C 29.0 gm/gm mole
. 5 PH 7-53 x 10 4 gm/cm3
:~ Pc 7.93 x 10 4 gm/cm3 . - :
IV. ~ 1.0 (~
: JH 1.93 cm
C ~99 cm
~H -95 cm
~C 0.71 cm
aH 4 0 cm
,.~, .
; aC 0.16 cm
:~: bH 6.60 cm
bC 8.80 cm
~, f 0.10 (-)
2jH 0.83 cm :~
2jc 348 cm
; a 0. 0305 cm
' J ~ ' 20 K' 3.44 x 10 3 cal/(sec)(cm2)(0C/cm~
. ~ 0.061 cm
~; It should be noted that F is glven above for
-~ carbon monoxlde at 2% concentration initially in
air. The actual gm moles per day of C0 plus carrier
air will be substantially 50 times 'che amount glven
;~ above for F.
By calculations as set forth above using ~:
the above data and calculating for the unknown factors
it is possible to complete all terms in the expres-
30 sion
/
_ 34 _
, ~'
T~l-TC UC'r CS CVH ( 1~
where pcCpc may also be written as (pCp)c. The
` terms in Table 2 are calculated from the above data.
It will be noted that certain terms are calculated
5 as ratiosO -
, ~ ,.
Table 2
; T~ 249C
TC 199C
3.37 x 10-4 cal/(sec)tcm2)(C)
: ,
UH 4.28 x 10 4 cal/(sec)(cm2)(C)
~` T~ 0.308 sec ~ -~
C 0.0476 sec
Sc/SH o.787 (~
; v /v 2.68 (-)
~` 15 There are several methods for showing that
~ the reaction situs and conditions thus described are
;; in fact accurately defined. In one method tempera~
tures are measured by each of the temperature mea-
suring means 460, 466, 470 and 476 in the path of the
respective flow and plotted in sequence as a function
~- of total path, i.e. 0 to 1Ø The results of an
experimental run as described by the above parameters
are plotted in Figure 11. Symbols used for points
- determined by means 460, 466~ 470, and 476 are, respec-
; 25 tively, x, triangle, -~ and circle. It will be seen ~ !
that the temperature of the coolant rises from 199C
to about 251C and of the reactant, introduced at
249C to about 255C at the maximum. The range
.
:,
is therefor 252 + 3C which is excellent confima-
~ , .
tion of isothermality. The conversion is measured
as 85.4% as compared to 86% employed in calculations
` ~ (z = o.86).
Further conflrmation of the relationships
herein disclosed is possible by calculating the
,;
sequence of heat exchangers needed, their dimensions
~ and coolant flow needed to reproduce the results
-~ actually obtained. Additional pertinent data as
regards the experimental arrangement described abo~e
are given in Table 3,
~,
Table 3
VH 305.8 cm 3
`-' VC 113.3 cm3
L 20.32 cm
X 5.08 cm
A H 15.05 cm2
~ x
5.593 cm
~C 5,670 gm moles/day
~. ~
N 4
W 158 gm
~` Terms employed in calculations deri~ed
from the above are set forth in Table 4 to three
significant figures.
.~ ,
,
.. ~, . ~
'.' ~ '
:~,
: ~
~ 36 -
:
Table 4
N~i 5'4 (~)
NC 1.97 (-)
r 1.97 (-)
~ 2.56 (-)
Q 0.390 (-)
~H 0.308 sec ~-~
: UH 4.28 x 10 4 cal/~sec)(cm2)(C)
VC 434 cm/sec
. 10 V 67.1 cm/sec
H
: ReC 375 (~
ReH 67.4 (-)
; nC o.867 (-)
H 0.695 (-~ ~ .
~` hH 7.77 x 10 4 cal/(sec)(cm2)(C)
C 1.88 x 10 3 cal/(sec)(cm2)(0C) : h
Using data of Tables 1, 2 and 4 the terms of ~:
Table 3 (which are experimental) are calculated as
shown in Table 5 together with approximate deviation ~ :
in % from the values of Table 3.
Table 5
Deviation %
H 311.5 cm3 1.85
~: VC 116.1 cm3 2.50
L 20.69 cm . 1.75
X 5.188 cm 1.92 : :
. . :.
`~ ~xH 15.143 cm2 0.62
AxC 5.574 cm2 o.o .
~C 6~014 gm moles/day 6.o8
Nn 4 0
W 162.7 gm 3.07
- 37 -
%~
It will be seen that in all cases agree-
ment is very good. It shou1d also be noted that
figures above are sometirnes rounded off to three or
four significant figures from numbers arising from
computer calculations. It is accordingly considered
that the deviations calculated above are insignifi-
` cant in all instances.
; Example 2
Using mathematical relations given above
and computer calculations for convenience, graphsshowing maximum deviation from isothermality in C
and C/CO as left and right ordinates respectively
with inlet temperature of reactants in C as
abscissae are computed for variations in ~H. For
simplicity~ N~I = NC for the calculations and the
quantity ;
in all cases. Coolant gas is introduced at 0C. The
reactant gas contains 5.4a% CO.
Deviations above isothermality are desig-
nated as +~TH and below as -~TH. The term k rH ~:
is convenient for tabulation in Table 6 which shows
variables in Figures 5 through 10. -~
' ~
"'' :
- 38 _
Table 6
; Figure k ~ N = N
~ H H C
~, ,
~;~ 5 1620 0.983
6 2500 0.983
7 1000 0.983
8 1620 0.000
9 1620 2.00
`~ 10 1620 25.00
It will be seen that the above vari-
ations in TH and NH cover rather wide ranges on
either side of the optimal values shown in Figure
5. In order that conditions be exactly isothermal
~-~ both +~TH and ~TH curves must show 0 deviation
~:~ at the same time. This occurs at their inter- ;
section in Figure 5 at a temperature of about 550C.
It will be evident that changes to slightly higher
inlet temperatures will favor higher conversions
because o~' the steep negative slope of the conver-
-~ sion curve at this temperature. The range of
operability can be selected on either side of
~;~ isothermality, e.g.~ as shown by the arrows which -~
indicate + 100C of isothermality. The range can
also be set as -0 and +100C or such other amounts
as may be desired and the graphs then show the
effects on conversion. It will be seen that
isothermality within ~ 3 as shown in Example 1 ;
permits of a relatively small range of' operating
conditions.
he person of skill in the art will
recognize that factors other than conversion may be
_ ~9 -
, ~':
, . ' ':' , ' . ~ . '' :
. :
significant such as coking in a methanation reaction
at excessive temperatures. For any given reaction a
family of such curves can be generated to serve as a
guide to manual control or a computer can be
programmed to correct for variations which are
monitored automatically and continuously.
Figures 6 through 10 show that no other
conditions provide isothermality or permit deviation
of' small amounts at as good conversions as do the
conditions of Figure 5. Figure 8 shows that with
no cooling the reaction temperature only rises and
although good conversion is attained in this parti-
cular system the temperature rise on the reaction side ~ -
is 1000C. Such a large temperature rise is only
possible because this selected model system is
relatively free from side reactions, catalyst poisoning
and other untoward results. In other systems such as
.~ methanation this is not necessarily the case. Figures
:
9 and 10 show great fluctuations in temperature condi-
; 20 tions. These calculations are made on the assump-
tions that the reaction occurs only fractionally in
each part of the reactor and that the flow is be-
having as cocurrent flow.
; Example 3
The invention is further illustrated in a
; reactor for the production of 231 kg per hr of CH30H
by the reaction
~- CO + 2H2= CH3OH
for which so-called Langmuir adsorption kinetics are
applicable (F. Daniels and R. Alberty, Physical
- 40 -
Chemistry, 3rd ed., 288 (1966, John Wiley)). For
such reactions generally and using, insofar as
possible, terms defined above, the rate, r, is given
by
(l-z) E (3-1)
K (l-Z)+ 1 R H
where C0 is the inlet concentration of rate-control- ~ ;
ling reactants and Ka is the adsorption equilibrium
constant at temperature TH for adsorption of rate- ~;
controlling reactant on the catalyst. ~;
Following mathematical procedures analo- ?
: gous to those above and assuming that NH ~ NC the
following relationship is derived:
NHexP(- L +RT-)~ C 1 ;~
k~lH =~ Ncx ~~ [Kaexp(- L )+C0] (3-2)
Kaexp(- L )C~
For Langmuir adsorption kinetics the ratio
of catalyst loading, P, at any point in the reactor
to the loading at the beginning of the reactor is
~; given by ~ ;~
Ncx
(~ L ) + C
P = K + 1 (3-3)
- Assuming that the rate of any catalytic
reaction per unit volume the reaction pass is directly
proportional to the amount of catalyst present, then
very generally the material balance in the reaction - `~
pass is
, :~, ,- :
4 1_
~ .
L dZ- = CH . (r) (3-4) ~.
Further the heat balances on reaction side
and coolant side of the heat exchanger are
dTH (-~H)P~H
L dx NH(TH TC) pHCpH (r)
~; 5 (3-5)
~` ~ dTC
L -dx = NC(TH TC) (3 6)
Solving these three equations simultaneously pro-
vides the equations
H)Co (-~H)P~
-~; N [TH-TC-z( C )] p C (r) (3-7)
. H PH pH H pH
'.~. 10 ,~ .
and
: c Z(-~H)Co ) :
~ L NC ~ln[l (TH TC)pHC ~]~ (3-8j :~
-: from which P, the ratio of catalyst concentration -
. ., ~.
as defined above, can be calculated as a function of
15 length from values of NH~ NC~ COIH and Z at any point
x, '~
-:~ L
~; This procedure is applied to the methanol :
synthesis system shown in Figure 12.
In this Figure a mixture of CO and H2 in
percents by volume of 12% Co, 80% H2, 8% inerts,
. sometimes known as synthesis gas, is introduced at
(500) and taken up by stage 1 ( 512) of two stage
compressor (510) and introduced into scrubber (515).
In the scrubber cold water is introduced ( 516) and
25 discharged (518) to scrub CO2 and other soluble
- 42 -
:` :
.
impurities. If desired portions o~ the gaseous
mixture can be returned to stage 1 (512) of com-
pressor (510) by connection (514). The gas to
pass to the reactor passes through stage 2 (517) of
5 compressor (510) where it is compressed to a suitable
working pressure and enters trap (520) at (522) and ?
emerges at (524) after removal of oil or other
suspended impurities that may have been picked up
from the compression cycle. It will be recognized
10 that the materials of construction to this point ;~
must be resistant to the mixture of CO and H2 being ;~
used and particularly to reaction with CO or embrit-
~ tlement by H2. Particularly at elevated temperatures
; copper-lined equipment may be advantageous as for ;~
15 cocurrent reactor (530). Although only one cocurrent
reactor is illustrated and described in some detail,
it will be readily apparent that several such can
be operated in parallel, and that variation in
dimensions can be accomodated utilizing the teachings
20 of the present invention. ~;,
Cocurrent reactor (530) is essentially a
cylindrical tower containing a series of six super~
imposed crossflow heat exchanger units of the type -~
I shown in Figure 1 having corrugations (5LIo and 542)
25 those on the reactor side (540) being packed with ` -
catalyst (not shown) as in Figure 1. For purposes -
- of the present Example it is assumed to use six
cubical units 60.8 cm on an edge in a tower 368 cm
tall. The corrugations employed in these units are
assumed to be of the same form (i.e., ratios o~
- 43 -
pararneters) as in previous examples but with
; relatively thinner walls which are, however, suf-
ficient for mechanical strength. It will be recog-
nized that a multiplicity of such towers may be
combined and suitably manifolded to provide larger
production capacity. The tower is shown as being
insulated because the following calculations assume
no heat loss.
The units are packed at the edges where
~;~ 10 they touch the reactor vessel to prevent leakage and
baffles (537 and 538) and are placed between suc-
cessive units as will be more completely described
below. Cocurrent reactor (530) is provided with
inlets for coolant (532) and reaction mixture (534)
15 and outlet for coolant (533) is connected to reaction
mixture inlet ( 534) through auxiliary heater ( 535) .
By-pass line (539) through valve (541) provides means
` for adding more reactants at (532) than are used as
;~; coolant.
When coolant enters at (532) and reaction
;~ mixture at ( 534) each is forced through passages ( 542)
and (540) respectively of the lowermost heat exchange
units I because of` baffles (537) and (53~) respective-
ly above unit I and the respective streams pass up-
25 ward to unit II where further baffles (537) and (538) ~ ::
respectively force passage through unit II. This is
cont,inued until the streams have passed through the
uppermost unit, unit VI of the diagram. The coolant
stream, which has absorbed a considerable amount of
30 heat as a result of the reaction on the reactant side
_ 1,4 -
when the process is operating, is passed to the
reaction side where, under the influence of the
catalyst in passages ( 544) it commences reactlng.
In order to initiate reaction at start up, heat is
5 supplied from auxiliary heater ( 535) to heat the
,
stream of synthesis gas to a temperature high enough
so that reaction will start on the catalyst in
passages (540) of unit I and eventually occur
throughout units I and VI.
Thereaction mixture comprising princi-
pally C0, H2 and CH30H leaves cocurrent reactor ~
(530) at (531) and enters condensor (560) where it ~;
is cooled by coil (525) in which cold water flows~;~
from (564) to (562). After entering at (566) the;~
15 cooled stream, which now is in both gaseous and
liquid phases, emerges at (568) and passes to
separator (570) at (572) where liquid and gases are
separated. The gases leave at (574) and pass to
recirculator (610) for recycling. Valve (578) i5
20 provided so that portions of the recycled gas
~ can be purged in the event there is excessive build
- up of contaminants. Condensed crude methanol is
removed from separator ~570) at (578) and pressure is
released in tank (580). Gaseous components leave
- 25 the tank at outlet ( 582) through valve ( 584) to
join purge gas from valve ( 578) and are purged at
(586) .
The crude methanol from which most of the -
dissolved gas has been removed is introduced into
still (590) heated by coil (592) where it is fraction-
- 45 -
ated with reflux condensor ( 600) passing upward
at ( 596) and return reflux at ( 594) . Pure methanol
(6083 is removed through valve (602) and residual
irnpurities, e.g. 3 water, are removed at (595) .
The cocurrent reactor (530) i3 packed
with ZnO-Cr203 or ZnO-CuO-Cr203 catalyst in units
I-VI of varying concentrations calculated as
described above using kinetic and thermodynarnic data
for ZnO-Cr203 catalyst of Natta (in "Catalysis",
P. H. Emrnett, ed., Vol. 3, page 345 et seq. (1955))
and for that and ZnO-CuO-Cr203 Pasquon and Dente (J.
Catal. Vol. 1, pages 508 ff (1962) ) . ~he optimum
conditions are 395c and 280 atmospheres.
Pasquon and Dente provide the relationship:
aCOaH2 aCH3OH/KP (3 10)
where
r = reaction rate, kg moles CH30H per
kg per hour
n = catalyst efficiency = 0.67
ac = thermodynamic activity of CO = YCoPco
= thermodynarrlic activîty of H2 = ~H2P~I2
aCH OH = thermodynamic activity of CH30H =
~CH30HPCH30H
~CO = activity coefficient of CO = 1.0 -~
~H = activity coefficient of H2 = 1.0
~CH OH = activity coefficient of CH30H =
0.52
` p = partial pressure (product of mole
fraction of components and 280
atmospheres).
- 46 -
,:. .
~-~s~
Kp = equilibrium constant for homogeneous
reaction of methanol synthesis =
2.67 x 10 5 atm 2
~H = -24.45 kcal/g.mole
s~T = 386C
Cp = 7.6 cal/(g.mole)(C)
A = 125
B = 1.0 ~ empirlcal constants determined by
~ Natta (supra).
C = 0.125
D = 4.63
Assuming ~H = 0.011 hr, and coolant tempera-
ture Tc~ of' goC entering unit I equations 3-7, 3-8
~` and 3_S~ above can be solved for the case where NC =
r .
; 15 NH = ~357- Equation 3-7 can be rearranged to solve
for the ratio of catalyst loading, P, at any point in ~ -~
~ the reactor~
; TH _~ z _ (3~
where P0 is ratio t)f catalyst loading entering unit I
~' ~ 20 and is numerically unity, and rO is rate of reaction
`~ and Z0 is conversion entering unit I. It will, of
course, be evident that, although P0 is numerically 1,
the actual concentration of catalyst may be in terms
- of pure catalyst pellets, catalyst on a substrate or
s ~ 25 catalyst plus any substrate. The concentration of ~;
inert diluent may have any useful value. From these
relations values of Z at the exit of each unit, P, r
at exit of unir in gm moles CH30H per (gm catalyst)_
' .
~ 47 ~ ~ s
, ~ '
: .
~ .
2~3~
(hour~ are calculated for each of the six units of
(530) in Figure 12 as given in Table 7 together with
values R~ calculated as described below.
:
Table 7
5 Unit Z p r x 102 Rl
0 0 1.0 0.22 1.90
I 0.0578 1.07 0.180 1.78
II 0.112 1.21 0.150 1.57
III 0.164 1.36 0.126 1.40
IV 0.212 1.53 0.106 1.24
V 0.257 1.70 0,090 1.12
VI 0.300 1.90 O.C76 1.0
In the above description it is assumed that
six heat exchanger units having certain overall -
dimensions are employed. This effectively sets the
value of Nn in block (380) of Figure 3, as well as
certain of the dimensions and values of blocks (120) ~`
and (150) of Figure 3 and the above calculations of
Table 7 set values for block (180) of Pigure 3.
Values of the structure of the heat exchanger units,
~`~ wall thicknesses, etc. (block (150) of Figure 3)
must be calculated to satisfy the results and other
parameters imposed. The assumed data are set forth
in Table 8 with reference to symbols used herein
above, e.g., Table 1. The rate controlling reactant
is carbon monoxide and values of CO~ -~H, etc. are
based thereon.
~-
,' ,~
Table 8
CO 6,~12 x 10 ~ gm moles/cm3
C 4.61 x 10-~ gm moles/cm3
Z ~3 (~)
F 5.77 x 105 gm moles/day ;~
MH 7.52 gm/gm mole
-~H 24,450 cal/gm mole
p~ 1.31 gm/cm3 - :~
E 0 50 ( ) ~.
D 0.95 om ;~
: ~ P
kR 0~129 sec
pH 7.60 cal/(gm)~C)
pC 7.~60 cal~(gm)(C)
H 3~46 x 10 4 gm/cm sec :
~C 2,18 x 10-~ gm/cm sec
KH 5 l9/(sel)(cm~)(C~cm~
: K 2,57 x 10 4
C ~cal/(sec)(cm2)(C/cm)~
: 20 MC 7.52 gm/gm~:mole ~ : - i`~;
p 2,85 x 10-~2 gm/cm3
: H
7.22 x 10 2 gm/cm3
On the assumption noted above that the
~: wave forms of the corrugations ~of each heat exchanger
.~ ~25 : unit are in the same proportions as i.n~previous
. . ~ ,
examples~ by use o~f iterative calculations the
-dimenslons of the corrugates are calculated as glven
in Table 9.
~;
~ - 49 _ ~
';' :
2~3
Table 9
'1, O ~_~
H 9t73 cm
JC 5.05 cm
~H 4.70 cm
~ ~C 3-58 cm
"~ aH 3 93 cm
a~ 1~57 cm
bH 1.34 cm ~ ~ :
bC ~.76 cm I
fH Q.lll (_)
fc 0.163 (-)
~ 2jH 4~5 cm
`, ~ 2iC 1.68 cm
~ , 0.11 cm
.: Kl 3~44 x 10 3
~ cal/~sec)(cm2~C/cm~
`` ." G 0.16 cm
From the above data, the values given below
.: 20 in Table 10 are calculated for terms as described
~ above for Table 2.
. ~
~ ';
: ~, .:
.
- 5
8~ :
~ ~-
Table 10
~H 3~5C
:~ TC 9C
UH 6,37 x 10
~ 5 cal/(sec) (cm2 ~ (C? :
: UC 8.36 x 10 4 . ~ .
ca:L~(sec)( cm2 ) ( o C )
TH 39.6 sec
38,4 sec
Sc/SH 0.762 (~
~: VH/VC 2.61 (-)
Proceeding as described in Example 1 to
verify calculations performed in accordance with the ;~
invention~ terms corresponding to those of Table 4
are calculated or brought forward into Table 11.
Table 11
NH ~357 (~~
~, C
r 0,357 (~
~ 1.031 (~
`~: Q ~ 1 0 (~)
~H 39.6 sec
H 6.37 x 10 4 cali(sec)(cm2)(0C) ~:
VC 4~75 cm/sec
VH 4.63 cm/sec
~eC 2062 (-) .
Re~ 361 (-)
nC o.68 (~
: nH 0.41 (-~
: 30 hH 6.50 x 10 3 cal/(sec)(cm2)(C)
hC 1.82 x 10 3 cal/(sec)(cm2~(0C)
- 51 -
.,~ .
', ' ": ', ,
Using the data of` Tables 9, 10 and 1].
calculations are made veri~ying that the originally
specified dimensions as to yield, size of tower and
number of units are in fact provided by the
calculations. This is described above in Example
1 and Table 5. These data are summarized in Table
, ~ :
12.
, Table 12
VH 8,67 x 105 cm3
VC 3.3~ x 105 cm3
::~ L 36S cm .
X 6Q.9 cm
:~ AXH 2369 cm2
A C 97 cm2
: 15 ~C 2,00 x 105 gm moles/day
Nn 6 (-)
W 569 kg
:
It is evident that the unit described pro-
vides methanol from carbon monoxide and hydrogen at
: 20 the desired rate.
: :
: The advantages of the apparatus of this
invention are made evident by comparison with the
apparatus with varying ca.talyst concentration usi.ng
multiple tubes surrounded by boiling heat exchange
liquid (Dowtherm)~previously described by P, H.
Calderbank, A, Caldwell and G. Ross, Chimie et
Industrie-Genie Chimique, ~ol. 101~ pages 215-230
(1969). Cornparison ca.n be made on the total catalyst ~ ~.
volume employed which is the volurne of catalyst plus
volume of diluent employed, The l.arger the total~
- 52 -
~ tr~ rk
i.e. the more dilute the cata]yst, the greater
the volume necessary to provide the same
through-put. The results of Calderbank et al.
are expressed i-n terms of a catalyst dilution
: 5 factor, Rl which bears a relationship to the
values of P used above, namely,
p ~ .
; Rl = L (3-12)
where PL is the value of P at the exit end of the
reactor. Values of Rl for the present example
are calculated and tabulated in Table 7. The
values for Calderbank et al. are 2.6 at the
entrance, 1.8 at the midpoint and 1.0 at the exit.
The data of Table 7 are plotted as A and those of
Calderbank as B in ~igure 13 where the abscissae
;~ 15 indicate units of the present example, or the ~ .
~ dimensionless distance which is 1 at the end of
,~ ,
unit ~I and ordinates are values of Rl. Curve A
is shown as stepwise change of dilutlon factor
because in each unit it is assumed that all
the filling is of the same catalyst loading.
Curve B is shown as a straight line because it
: ;~
appears that Calderbank et al. considered a more
gradual change in catalyst loading. The lower
position of curve A shows that suffic]ent catalyst
to accomplish the desired conversion is contained
in a lesser volume than for the apparatus of
Calderbank et al. This is believed to be because
~ of the greater efficiencies of the heat exchanger
; units and control possible by the present
invention.
- 53 ~
