CA1098288A - Catalytic reactor for isothermal reactions - Google Patents

Abstract

ABSTRACT

A catalytic reactor for isothermal reactions is specified by mathematical rela-tionships of parameters for cocurrent heat exchange between reactant gas stream and coolant gas stream. The reactions are preferably first order or substantially first order.
Heterogeneous reactions are considered parti-cularly but the apparatus can be employed for homogeneous reactions.

Description

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 .

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 .

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.

. ~ , 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) 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

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.

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.

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 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.

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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) 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 ' 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 :

:

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 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.

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 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 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.

III. Cp~ 0.254 cal/(gm)(C) CpC 0.256 cal/(gm)(C) 2.38 x 10-4 gm/cm sec ~ :

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

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 ~. ~

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 %~

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 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 :` :
.

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~

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-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).

,:. .

~-~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.
. ~

~ ';

: ~, .:

.

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) .,~ .

', ' ": ', , 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~

~ 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 ~

Claims (15)

File 913,824 The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. A process for establishing sub-stantial isothermality in a heterogeneous catalytic reaction which process comprises passing a reaction medium susceptible to said heterogeneous catalytic chemical reaction over suitable catalyst under conditions such that heat is liberated at a rate which is substanti-ally in direct relationship to concentration of reactant in a first set of passageways while coolant is passed through a second set of passageways in a cocurrent or pseudococurrent relationship to said first set of passageways, said first and second sets of passageways being in heat-exchange relationship and being thermally connected but separate, the rate of flow and inlet temperatures at which said reaction medium and coolant are passed through said passageways, and the geometry of said passageways being summarized by the relationship:

wherein all terms are in consistent units and wherein TH = inlet temperature of reactants;
TC = inlet temperature of coolant;
-.DELTA.H = heat of reaction;

CO = inlet concentration of reactant(s);
UH = overall heat transfer coefficient on reaction side;
UC = overall heat transfer coefficient on coolant side;
TH = space-time on reaction side;
TC = space-time on coolant side;
SH = heat transfer area on reaction side;
SC = heat transfer area on coolant side;

VH = free volume on reaction side (ex-cluding particulate catalyst);
VC = free volume on coolant side;
pCCpc = product of density by heat capacity of coolant gas;
and the relationship between rate of liberation of heat and concentration of reactant being a direct function of UC and the ratio TC/TH.

2. An apparatus for catalytic conversion of at least one reactant to a product under approximately isothermal conditions and under conditions such that heat is liberated at a rate which is substantlally in direct relationship to concentration of reactant and having means for introducing reactants and temperature controlling fluid at predetermined temperatures and means for removal thereof, said apparatus being characterized by comprising a reaction situs com-prising first and second sets of passageways wherein said reactants and temperature controlling fluid flow without intermingling in cocurrent to pseudococurrent relation under controlled heat exchanging relationship, the rate of flow and inlet temperatures at which said reactants and coolant are passed through said passageways and the geometry of said situs being summarized by the relationship wherein all terms are in consistent units and wherein TH = inlet temperature of reactants;
TC = inlet temperature of coolant;
-.DELTA.H = heat of reaction;

CO = inlet concentration of reactant(s);
UH = overall heat transfer coefficient on reaction side;
UC = overall heat transfer coefficient on coolant side;
TH = space-time on reaction side;
IC = space-time on coolant side;
SH = heat transfer area on reaction side;
SC = heat transfer area on coolant side;

VH = free volume on reaction side (ex-cluding particulate catalyst);
VC = free volume on coolant side; and pCCpC = product of density by heat capacity of coolant gas and the relationship of rate of liberation of heat to concentration of reactant being a direct function of UC and TC/TH.

3. Apparatus according to Claim 2 wherein the reaction situs comprises at least one series of at least two cross-flow heat exchanger units having first passageways through which reactants flow and containing catalyst and second passageways at right angles to said first passageways through which coolant flows, said first passageways being interconnected through first chambers and said second passageways through second chambers and said apparatus comprising means preventing passage of reactants or coolants between said first and second chambers and said first and second passageways, said first passageways having a free volume excluding particulate catalyst of VH, a heat transfer area of SH, said reactants being at an initial concentration of CO and temperature TH and having an overall heat transfer coefficient of UH for space time of TH and being susceptible to a reaction having heat of reaction of -.DELTA.H liberating heat at a rate which is in direct relationship to concentration of reactant, said second passageways having a free volume of VC and heat transfer area of SC
said coolant having initial temperature of TC
and product of density by heat capacity pCCpC
and being in said second passageways for a space time TC and then having overall heat transfer coefficient UC, the relationships between passageways, temperatures and flow rates being expressed by wherein all terms are in consistent units and the relationship of rate of liberation of heat to concentration of reactant being a direct function of UC and TC/TH.

4. Apparatus according to Claim 3 wherein catalyst is contained in first passage-ways on impregnated pellets.

5. Apparatus according to Claim 3 wherein catalyst is on the walls of the first passageways.

6. Apparatus according to Claim 3 wherein catalyst in first passageways is at varied concentrations to modify reaction kinetics to being of substantially first order.

7. Apparatus according to Claim 6 wherein concentrations of catalyst increases along the length of the first passageways.

8. Apparatus according to Claim 7 where there are at least four cross-flow heat exhanger units successively containing catalyst at increasing concentrations.

9. Apparatus for homogeneous conver-sion of one reactant product under approximately isothermal conditions and under conditions such that heat is liberated at a rate which is substantially a direct relationship to concen-tration of reactant said apparatus having means for introducing reactant and temperature con-trolling fluid at predetermined temperatures and means for removal thereof, said apparatus being characterized by comprsing a reaction situs comprising first and second sets of pas-sageways wherein said reactant and temperature controlling fluid flow without intermingling in cocurrent to pseudococurrent relation under controlled temperature exchanging relationship, the rate of flow and inlet temperatures at which said reactant and coolant are passed through said passageways and the geometry of said situs being summarized by the relationship wherein all terms are in consistent units and wherein TH = inlet temperature of reactants;
TC = inlet temperature of coolant;
-.DELTA.H = heat of reaction;

CO = inlet concentration of reactant(s);
UH = overall heat transfer coefficient on reaction side;
UC = overall heat transfer coefficient on coolant side;
TH = space-time on reaction side;
TC = space-time on coolant side;
SH = heat transfer area on reaction side;

SC = heat transfer area on coolant side;
VH = free volume on reaction side (excluding particulate catalyst);
VC = free volume on coolant side; and pCCpC = product of density by heat capacity of coolant gas and the relationship of rate of liberation of heat to concentration of reactant being a direct function of UC and TC/TH.

10. Apparatus for catalytic conversion of at least one reactant to a product under approximately isothermal conditions with reaction velocity constant kR having means for introducing reactants and temperature controlling fluid at predetermined temperatures and means for removal thereof, said apparatus being characterized by comprising a reaction situs comprising at least one series of at least two cross-flow heat exchanger units having first passageways through which reactants flow and containing catalyst and second passageways at right angles to said first passageways through which coolant flows, said first passageways being interconnected through first chambers and said second passageways through second chambers and said apparatus comprising means preventing passage of reactants or coolants between said first and second chambers and said first and second passageways, said first passage-ways having a free volume excluding particulate catalyst of VH, a heat transfer area of SH, said reactants being at an initial concentra-tion of CO and temperature TH and having an overall heat transfer coefficient of UH for space time of TH and being susceptible to a reaction having heat of reaction of -.DELTA.H
liberating heat, said second passageways having a free volume of VC and heat transfer area of SC said coolant having initial temperature of TC and product of density by heat capacity pCCpC and being in said second passageways for a space time TC and then having overall heat transfer coefficient UC, the relationships between passageways, temperatures, flow rates and reaction kinetics being expressed by wherein all terms are in consistent units.

11. Apparatus according to Claim 2 for converting carbon monoxide and hydrogen to methanol wherein CO is the inlet concentration of carbon monoxide as the rate controlling reactant.

12. Apparatus according to Claim 10 for converting carbon monoxide and hydrogen to methanol wherein CO is the inlet concentration of carbon monoxide as the rate controlling reactant and the catalyst loading in the first passageways of the series of at least two cross-flow heat exchanger units is increased in succes-sive downstream units.

13. Apparatus according to Claim 12 wherein the catalyst is pellets of ZnO-Cr2O3 or ZnO-CuO-Gr2O3 containing inert diluent in at least first passageways of the first cross-flow heat exchanger units and successively less diluent in first passageways of downstream heat exchanger units.

14. Apparatus according to Claim 13 wherein cooling through second passageways is provided at least in part by reactant gases before said reactant gases are introduced into the first passageways containing catalyst.

15. Apparatus according to Claim 10 wherein the at least two heat exchanger units are superimposed one on the other with all first passageways running at right angles to all second passageways and with baffle means between successive heat exchanger units directing flow from first and second passageways of a lower unit to first and second passageways, respectively, of the next higher unit.