GB1604980A - Catalytic reactor for isothermal reactions - Google Patents

Description

(54) CATALYTIC REACTOR FOR ISOTHERMAL REACTIONS (71) We, MINNESOTA MINING AND MANUFACTURING COMPANY, a corporation organised and existing under the laws of the State of Delaware, United States of America, of 3M Center, Saint Paul, Minnesota 55101, United States of America, do hereby declare the invention, for which we pray that a patent may be granted to us, and the method by which it is to be performed, to be particularly described in and by the following statement:- This invention relates to a catalytic reactor for substantially isothermal reactions having cocurrent heat exchange and to a process for establishing substantial isothermality in a catalytic reaction.

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 temperatures 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 maintain substantially uniform or isothermal temperature or to permit a slight drop in temperature.

There have been at least four procedures which have been used in the design of equipment to control extremely exothermic reactions, viz., 1) dilution of reactants with inert medium; 2) reacting in stages with cooling between stages; 3) surrounding with a boiling heat exchange 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 considerably more convenient if reactors could be constructed in which even a highly exothermic reaction would proceed smoothly under substantially isothermal conditions. The specification of operable parameters for such reactors is a principal aim of this invention.

As materials flow through a reactor requiring cooling it is usual practice to consider countercurrent flow of coolant as being most efficient. However, it can be shown mathematically that it is not possible to achieve substantially isothermal conditions by using countercurrent heat exchange, 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 heterogeneous 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 exothermic or endothermic reaction: (TH-TC) UC#CSC#H (1-1) (-#H)Co #CCpC#cUH#HSH where TH=inlet temperature of reactants (OC) Tinlet temperature of coolant (OC) -H=heat of reaction (caVg. mole) CO-inlet concentration of reactant(s) (g. moles/cm3) UH=overall heat transfer coefficient on reaction side (cal/(sec)(cm2)(0C)) Uc=overall heat transfer coefficient on coolant side (caV(secXcmz)("C)) TH=space-time on reaction side (sec) Th=space-time on coolant side (sec) Heat transfer area on reaction side (cm2) Sc=heat transfer area on coolant side (cm2) v,=free volume on reaction side (excluding particulate catalyst) (cm3) vfree volume on coolant side (cm3) pcCpc=product of density by heat capacity of coolant gas in cal/(cm3)(0C) 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 TJTH.

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 between the common surface such as corrugations.

Those of skill in engineering practice will readily perceive that these relationships define an entire family of reactors from which specific selection is made by setting certain values for the particular reaction being contemplated, 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 remaining terms will be effected 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 exchanging 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.

The portion of a reactor in which reaction is carried out is herein sometimes termed reaction situs. It will be recognized that various configurations are possible within the scope of the invention although cross-flow reactors are particularly preferred.

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+H2O. 2. Oxidation,

3. Formation of hydrocarbons from methanol.

4. Oxidation of naphthalene to phthalic anhydride.

5. Chlorination of hydrocarbons.

6. Hydrosulfurization, e.g. removal of thiophene by reaction with H2 to give butadiene plus H2S.

7. Formation of methanol: CO+2H2+CH3OH.

Endothermic reactions 1. Dehydrocyclization. e.g. n heptaneotoluene.

2. Catalytic cracking of petroleum.

In order that the invention may be more clearly understood it is also described in terms of the accompanying drawings wherein Figure 1 shows diagrammatically one cross-flow heat exchanger about 7 cm on a side with catalyst impregnated pellets about 2 mm in diameter and 3 mm high in one set of passageways.

Figure 2 shows an arrangement of four of the heat exchangers of Figure 1 mounted in a casing to provide a pseudococurrent flow reactor in accordance with the invention.

Figure 3 is a flow sheet showing diagrammatically the sequence of calculations which can be used in calculating the parameters of a reactor of the invention.

Figure 4 shows diagrammatically a small scale reactor and adjunct controls and supply sources. The reactor is discussed in connection with Example 1.

Figures 5 through 10 show graphically variations in isothermality and conversion at specified reaction conditions.

Figure 11 shows temperature conditions progressively through a reactor of the invention with pseudococurrent 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 provide 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 the passageways (12) are filled with catalyst impregnated pellets (30) with some omitted to show inner portions of passageways. In referring to such structures hereinafter it is convenient to designate two axes for each segment including a corrugate between 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 filled with ceramic plugging marginal passageways in each direction.

In Figure 2 there are shown how four of the heat exchangers (40) of Figure 1 are positioned in series in casing (42) with inlets (44) for reactant and (46) for coolant and 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 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 mathematical 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 of the art as are other sequences of operations to arrive at the same or similar results.

In making the following calculations certain simplifying assumptions are made to avoid unnecessary complications. Thus, it is assumed that 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 assumed that no heat transfer occurs by radiation in any direction within the reactor. It is assumed that the 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 crossflow units this means that conversion should not occur abruptly in the first unit but must be only fractional in each cross-flow unit. Although 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 which can result in inactivation of catalyst or undesirable side reactions in a portion of the reactor and gradual degradation and deterioration of overall performance.

Boxes 120, 130, 140 and 150 require specifying, 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 symbolized as follows and are expressed in units as noted for metric system usage.

I. For box 120 specify: CO Inlet concentration of reactant (in g moles of reactant/cm3 of total feed).

Determined on bases of need for dilution to avoid hot spotting, explodability, etc.

C Outlet concentration of reactant (in same units as CO)- C z=l C Conversion (as a fraction) selected on basis of C0 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). Determined by production requirements.

MH Average molecular weight of gases on reactant side (daltons, i.e., gm. per gm.-mole).

-AH Heat of reaction per mole of reactant or reactants (cal/gm)mole.

This is characteristic of the reaction 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.

PT Density of catalyst (g/cm3) determined experimentally on solid.

E Void fraction of bed (dimensionless)calculated from bulk density of catalyst compared to solid density of catalyst, PT. k, Pre-exponential factor from Arrhenius (rate) equation for the reaction system and catalyst being used. (Reciprocal seconds).

Dp Diameter of catalyst pellet (assuming 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 In(k) (reaction velocity constant) versus reciprocal absolute temperature (degrees Kelvin).

III. For box 140 specify properties of gases.

COH Heat capacity of gaseous reaction mixture (on catalyst side) assuming constant temperature and average composition. (cal/(g)( C)).

C Heat capacity of coolant gas assuming average temperature. (caW(g)(0C)). p Viscosity of gas. Use average of reactant and coolant gases. (g/cm-sec).

K Thermal conductivity of gas. Use average of reactant and coolant gases.

(caV(sec)(cm2X0C/cm)).

Mc Molecular weight of coolant gas (daltons).

PH Density of reactant gases. (g/cm3).

Pc Density of coolant gas (g/cm3).

IV. For box 150 certain characteristics of the heat exchangers or reactors without load of catalyst pellets must be specified. The present reactors are crossflow 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, fins or other means and without catalyst pellets present. It is illustrative and not limiting. The geometrical terms which are directly measureable or are calculated are listed below.

All terms which are lengths of distances are in centimeters. 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 I below.

=ratio of height of block heat exchanger to distance along flow path.

J=length along sinusoid over one wavelength.

A=wavelength along q axis. a=amplitude=l/2 height of corrugations. b=27rlA. f=overlap factor=fraction of sinusoid length bonded to flats.

2j=height between flats.

0=thickness of sinusoids (cm.). a=thickness of flats (cm.).

K'=thermal conductivity of material of reactors, including flats and corrugations.

J is calculated from the relationship:

using, if desired, a computer program where q is the distance along the q axis defined as above for Figure 1. Certain functions of the above terms are conveniently 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".

2J 2fJ 2J S= +2- =(1-f) +2 (IV-2) A A 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, A 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 "u" is the total volume minus the volume of the ceramic sinusoid: j#J #=2-J (IV-3) # This is calculated for coolant side, #c, and reactant side #H.

The relation of heat transfer area to empty volume S/# is calculated in reciprocal centimeters for 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 4v Dh= (IV-4) S The fraction of open face area, that is the portion of the surface of unit length of passageways for flow "G", include one blank row and one open row, is #J #J 2j A 2A G= = (IV-5) 2jH+2jC+2# JH+JC+# this quantity is calculated for GH and GC using appropriate terms in the numerator.

The fraction of the total heat transfer area # due to the area of the sinusoids is

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 #H #C V. The isothermal temperature TH (in degrees centigrade) at which it is intended to run the reaction is selected in accordance with box (160) based on known or experimental data on the catalyst system. This temperature very strongly influences the conversion "z" above. In general the highest temperature is chosen at which a. the catalyst will not sinter, b. the catalyst 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 C exp(-I') (Vl-1) CO where r is the catalytic activity:

so that the expression becomes:

in which all quantities are known- from above except for rH. The 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

where F is flow rate of reactant to catalyst side determined by production requirements as kg. per year, z is the conversion as defined in I, z0 is numerically zero and z is the final conversion, and r is the rate of reaction defined by

for a first order reaction.

VIII. The total volume of space occupied by all the catalyst needed when the passageways on the reactant side are filled in accordance with the above conditions is #H and is determined for box (190) from the relationship W #H= (VIII-1) (1-#)p# where p# is 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) 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 the effectiveness approaches asymptotically the limit imposed by flow arrangement and thermodynamic considerations (Kays and London, Compact Heat Exchangers, 2nd ed (1964) pp 1516).

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. For box (220) the value of # is calculated from the relationship

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 from F NH= (Xll-l) Q where r is from step XI and (TH-TC)#HCpH Q= (XII-2) (-AH)C0 and all terms are previously known.

XIII. For box (240) the overall heat transfer coefficient on the catalyst side in caV(sec)( C) designated UH is calculated (NH)(PH)(CPHXLH) UH= (XIII-l) THSH in which all terms are known from above, e.g., the ratio SH/rH 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 1 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 VHPHCpHY α= (XIV-1) #C#CCpC in which all terms are known except for a.

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 mm By establishing a heat balance for an incremental or differential volume, d#H, the following equation is formulated where QL is the rate of evolution of heat over the entire path (cal/sec) and Cx is the concentration in volume d#H. dQ,=(AH)CxkRdvH (XIV-2) which is integrated to

KR is the proportionality constant, i.e., reaction velocity constant, which, in terms of previously defined terms, is E kR=k#exp( ) (XIV-4) RTH and -AH is a characteristic of the reaction. There is clearly a relation between rate of liberation of heat and concentration of reactant at the position of volume d#H.

Then, because of the equality of Nc and # UCSCTC r=kRTH= Nc (XIV-5) #CCpC#C Tc Sc kR= (UC)( ) (XIV-6) #N #CCpC#C The values of the term Sc ( ) #CCpC#C 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 TJTH.

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 bases of the scale of operation, commercially available shapes etc. It is generally efficient to use a multiplicity of cubical reactors as described elsewhere but it is fully possible to employ reactors in which the flow path on the coolant side is X, on the reaction side #X and the reactor is #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. For box (270) the velocity of flow on each side is calculated which is necessary to give the overall heat transfer coefficient UH as calculated in XIII above. The calculation proceeds stepwise by calculating heat transfer coefficients on coolant and reaction sides and combining them in conventional fashion. A value for velocity on coolant side1 Vc, is assumed which is practical, e.g., 80 cm/sec.

A. The average film coefficient for laminar flow on coolant side hc in cal/(sec)(cm2)(0C) is given by the relationship

where Kc is thermal conductivity of coolant gas in caV(sec)(cm2)(0C/cm).

DH is the hydraulic diameter; Re is Raynolds number for an assumed velocity; P, is Prandtl number of the coolant; X is the length of the flow path on the coolant side of one reactor; 3.65 is adopted as the Nusselt number for fully developed laminar flow in the effective passageways of convenient commercial ceramic shapes shown in Figure 1. The average value is used 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". 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 calculated from

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 0.8 times the hydraulic diameter of the passageways (cf. calculation above in IV) KN is thermal conductivity of reactant-side gases in caV(sec)(cm2)(0C/cm).

PH is density of reactant-side gas, PH 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 V, (XVI-3) a from XIV above C. In order to combine the two film coefficients 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 of ineffectiveness caused by the sinusoidal corrugations.

A term m is defined:

where h=film coefficient for respective side as in A or B above K'=thermal conductivity of material of corrugation 0=thickness of corrugation.

When 2j is the distance between flats, i.e. amplitude of corrugations, the surface effectiveness of the intruding surfaces, e.g., corrugations, t7F, is given by the relationship tan h(mj) (XVl-5) (XVI-5) mJ and thus is employed in the calculation of total surface temperature effectiveness #o for the respective sides, rl, coolant, #H reactant SF #o=1 (1-#F) (XVI-6) S 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 SF is total area of corrugations on the side being calculated.

D. The two film coefficients of A and B above can 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: 1 1 # 1 = + + (XVI-7) UH #HhH SW SC K'

The average cross-sectional area of passages on the coolant side, Axc, is given by the relation #c Axc= (XX-2) L and the total facial area on the coolant side. ATC, by the relation AxC ATC= (XX-3) GC 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 perpendicular to the passages of flow, i.e., high, the relationship is, respectively,

XXII. Comparison of values of X from XV and XXI are made for box (340). If the length just calculated is different from that assumed in ste XV, steps XVI to XXI are repeated via box (350) to box (260) using the calculated value of X, and repeating until agreement is reached. When agreement is reached proceed to step XXIII.

XXIII. For box (360) the outlet temperature of coolant gas, T'c, is calculated.

For this adiabatic reaction temperature, AT, is first calculated from the relation (-#H)(Co) #T= (XXIII-1) (PM)(CPH) in which Co, #H, CpH and -#H were specified under I or III above. The value of #T is employed in calculating the outlet temperature in degrees centigrade from the relationship (#T)(k##H) -A A TC'=TH- exp{-(k##H) exp- ( ) - NH TH+273 TH+273 (XXIII-2) where AT is known from above, TM 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 moles per day, #C, is calculated from the relation 86400VcAxcPc #C= (XXIV-1) MC where 86400 is seconds per day, MC and #c 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 N@= (XXV-1) X where L is the length of reactor from step XVII and X is the flow path per individual reactor calculated in step XXI.

The isothermal condition on the catalyst 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 recognized that the rate of liberation or evolution of heat as described herein includes the cases where the rate is either positive (exothermic 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 E r''=k#exp(- )CA . CB (S-1) RTM where the last two terms are concentrations. Modification of the reaction conditions effectively makes the reaction conform to first order kinetics for which the pseudo first order equations are E r"=(kC8)exp(- )CA and RTM E r"=(kOOCA)eXP(- )CB (S-2) RTM for which rate constants are (kOOC5) and (kOOCA) 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 modificatlon 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 (S-3) P=exp[(n-1)NC ] L where P=ratio of catalyst loading Wx (gm catalyst/cm3) at any point x in the reactor to the catalyst loading WO at x-A). n=order of reaction Number of transfer units on the coolant side=-ln(l-z) x=specific length down reaction path L=total length of reaction path If several, i.e., four or more, individual reactor heat exchangers are in series, as shown, for example, in Figures 2 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 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 concentrations can be calculated by calculating the values of Pat values of x corresponding to inlets and outlets of successive reactor heat exchangers, i.e., for four exchangers, calculations are for ratios x L of 0, 0.25, 0.50, 0.75 and 1.0 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 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 capacity, 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 specification and examples is concerned primarily with heterogenous reactions, particularly catalyzed reactions, it is contemplated that homogeneous reactions can also be carried out under isothermal conditions in cocurrent or pseudo-cocurrent apparatus as described herein by making relatively simple engineering modifications which will be evident to those skilled in the art. It will be recognized that it is very difficult to design equipment in which there is exclusively cocurrent flow because of the problems of manifolding. Pseudococurrent flow as discussed herein is more readily achieved.

Because of the straight passageways in cross-flow heat exchangers, loading with catalyst is relatively simple.

Example I A model reactor is set up for conversion of carbon monoxide to carbon dioxide as shown diagrammatically in Figure 4 with cover removed to show four cross-flow heat exchangers (400) approximately as shown in Figure 1 but of specific dimensions as described elsewhere herein and bolts (418). Heat exchangers (400) of cordierite are mounted 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 2 mm in diameter and 3 mm high from American Cyanamid Co. and containing 1.44% Cu and 0 97V Cr) to within about 6 mm of surface and then further filled with chips of quartz (ot approximately same 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) to provide oxygen and coolant and a stream of carbon monoxide (412) are provided from suitable supply means not shown. The art 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 word "Rotameter" is a Registered Trade Mark). 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 of copper chrome catalyst (438) is provided.

The carbon monoxide stream (412) is controlled particularly 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 carrying 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). 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 provided for measurement of temperatures of coolant stream in reactor heat exchanger units (400). Temperatures are conveniently measured by thermocouples and gas samples analyzed by gas chromatography.

The measurable parameters for the system as designed in 1, II, III and IV above are specified 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 (-) indicates dimensionless quantities.

TABLE 1 Section Term Value in Units I. Co 5.19 x 10-7 gm moles/cm C 7.21 x 10-8 gm moles/cm z 0.86 (-) F 20.6 gm moles/day MH 29.0 gms/gm mole -#H 45.600 cal/gm mole II. ## 1.19 gm/cm # 0.564 (-) k# 1.75 x 10-8 sec-1 Dp 0.317 cm.

E/R 8944 K III. CpH 0.254 cal/(gm)( C) CpC 0.256 cal/(gm)( C) 2.38x 10-4 gm/cm sec K 8.39x10-5 cal/(sec)(cm)( C/cm) MC 29.0 gm/gm mole #H 7.53 x 10-4 gm/cm #C 7.93 x 10-4 gm/cm IV. # 1.0 (-) JH 1.93 cm JC 0.99 cm #H 0.95 cm #C 0.71 cm aH 0.40 cm aC 0.16 cm bH 6.60 cm-1 bC 8.80 cm-1 f 0.10(-) 2jH 0.83 cm 2jc 0.348 cm 8 0.0305 cm K' 3.44x 10-3 caV(sec)(cm2X0C/cm) a 0.061cm It should be noted that F is given above for carbon monoxide at 2% concentration initially in air. The actual gm moles per day of CO plus carrier air will be substantially 50 times the amount given 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 expression TH-TC UC#CSC#H = (1-1) (-#H)(Co) #CCpC#CUH#HSH where #CCpC may also be written as (#Cp)C. The terms in Table 2 are calculated from the above data. It will be noted that certain terms are calculated as ratios.

TABLE 2 TH 249 C TC 199 C UC 3.37x10-4 cal/(sec)(cm)( C) UH 4.28x10-4 cal/(sec)(cm)( C) #H 0.308 sec #C 0.0476 sec SJSH 0.787 (-) #H/#C 2.68 (-) There are several methods for showing that the reaction site and conditions thus described are in fact accurately defined. In one method temperatures are measured by each of the temperature measuring 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 1.0. 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, respectively, x, triangle, + and circle. It will be seen that the temperature of the coolant rises from 199 C to about 251 C and of the reactant, introduced at 249 C to about 255 C at the maximum. The range is therefore 252 #3 C which is excellent confirmation of isothermality. The conversion is measured as 85.4% as compared to 86% employed in calculations (z=0.86).

Further confirmation 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 above are given in Table 3.

TABLE 3 305.8 cm3 #C 113.3 cm L 20.32 cm X 5.08 cm AxH 15.05 cm AXC 5.593 cm2 #C 5,670 gm moles/day Nn 4 W 158 gm Terms employed in calculations derived from the above are set forth in Table 4 to three significant figures.

TABLE 4 NH 5.04 (-) NC 1.97 (-) # 1.97 (-) a 2.56 (-) Q 0.390 (-) TH 0.308 sec UH 4.28x10-4 cal/(sec)/(cm)( C) VC 434 cm/sec VH 67.1 cm/sec Rec 375(-) ReH 67.4(-) 'Ic 0.867 (-) #H 0.695 (-) hH 7.77x10-4 cal/(sec)(cm)( C) hC 1.88x10-3 cal/(sec)(cm)( C) 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 % VH 311.5 cm3 1.85 116.1cm3 2.50 L 20.69cm 1.75 X 5.188 cm 1.92 AxH 15.143 cm2 0.62 AXC 5.574 cm2 0.0 6,014 gm moles/day 0.08 #c Nn 4 0 W 162.7 gm 3.07 It will be seen that in all cases agreement is very good. It should also be noted that figures above are sometimes rounded off to three or four significant figures from numbers arising from computer calculations. It is accordingly considered that the deviations calculated above are insignificant in all instances.

Example 2 Using mathematical relations given above the computer calculations for convenience, graphs showing maximum deviation from isothermalitv 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 TM. For simplicity, NH=NX for the calculations and the quantitiy EPHCPH =11.11 (2-1) R(-AH)C0 in all cases, Coolant gas is introduced at OOC. The reactant gas contains 5.48{" CO.

Deviations above isothermality are designated as +ATH and below as ATM.

The term km is convenient for tabulation in Table 6 which shows variables in Figures 5 through 10.

TABLE 6 Figure kooTH NM=Nc 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 variations 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 +ATM and ATM curves must show 0 deviation at the same time. This occurs at their intersection in Figure 5 at a temperature of about 550"C.

It will be evident that changes to slightly higher inlet temperatures will favor higher conversions because of the steep negative slope of the conversion 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 + l000C of isothermality.

The range can also be set as --00 and +100"C 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.

The person of skill in the art will recognize that factors other than conversion may be 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 particular system the temperature rise on the reaction side is 1000 C. 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 conditions. These calculations are made on the assumptions that the reaction occurs only fractionally in each part of the reactor and that the flow is behaving as cocurrent flow.

Example 3 The invention is further illustrated in a reactor for the production of 231 kg per hr of CH3OH by the reaction CO+2H2=CH30H 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 COk#Ka(1-Z) E r= exp(- ) (3-1) 1 Ka(1-Z)+ RTH CO where CO is the inlet concentration of rate-controlling reactants and K" is the adsorption equilibrium constant at temperature TM for adsorption of rate controlling reactant on the catalyst.

Following mathematical procedures analogous to those above and assuming that NH=NC the following relationship is derived:

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

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 dZ P#H L = . (r) (3-4) dx CO Further the heat balances on reaction side and coolant side of the heat exchanger are dTH (-#H)P#H L =-NH(TH-TC)+ . (r) (3-5) dx #HCpH dTC L =NC(TH-TC) (3-6) dx Solving these three equations simultaneously provides the equations (-#H)C0 (-#H)P#H NH[TH-TC-Z( )] = . (r) (3-7) #HCpH #HCpH and

from which P, the ratio of catlyst concentration as defined above, can be calculated as a function of length from values of NH, NC, CO#H 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 discharged (518) to scrub CO3 and other soluble impurities. If desired portions of the gaseous mixture can be returned to stage 1(512) of compressor (510) by connection (514). The gas to pass to the reactor passes through stage 2 (517) of 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 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 embrittlement by H2. Particularly at elevated temperatures copper-lined equipment may be advantageous as for 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 accommodated utilizing the teachings of the present invention.

Cocurrent reactor (530) is essentially a cylindrical tower containing a series of six superimposed crossflow heat exchanger units of the type shown in Figure 1 having corrugations (540 and 542) 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 of parameters) as in the previous examples but with relatively thinner walls which are, however, sufficient for mechanical strength. It will be recognized 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 they touch the reactor vessel to prevent leakage and baffles (537 and 538) are placed between successive units as will be more completely described below. Cocurrent reactor (530) is provided with inlets for coolant (532) and reaction mixture (534) and outlet for coolant (533) is connected to reaction mixture inlet (534) through auxiliary heater. By-pass line (539) through valve (541) provides means for adding more reactants at (534) 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 (538) respectively above unit I and the respective streams pass upward to unit II where further baffles (537) and (538) respectively force passage through unit II. This is continued until the streams have passed through the uppermost unit, unit VI of the diagram. The coolant stream, which has absorbed a considerable amount of heat as a result of the reaction on the reactant side when the process is operating, is passed to the reaction side where, under the influence of the catalyst in passages (544) it commences reacting. In order to initiate reaction at start up, heat is supplied from auxiliary heater 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.

The reaction mixture comprises principally CO, H2 and CH2OH leaves cocurrent reactor (530) and (531) and enters condensor (560) where it is cooled by coil (565) in which cold water flows from (564) to (562). After entering at (566) the 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) is 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 (576) and pressure is released in tank (580). Gaseous components leave 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 fractionated with reflux condensor (600) passing upward at (596) and return reflux at (594). Pure methanol (608) is removed through valve (602) and residual impurities, e.g., water, are removed at (595).

The cocurrent reactor (530) is packed with ZnO-Cr2O3 or ZnO-CuO-Cr2O3 catalyst in units 1-VI of varying concentrations calculated as described above using kinetic and thermodynamic data for ZnO-Cr2O3 catalyst of Natta (in "Catalysis", P. H. Emmett, ed., Vol. 3, Page 345 et seq. (1955)) and for that and ZnO-CuO-Cr2O3 Pasquon and Dente (J. Catal. Vol. 1, pages 508 ff (1962)). The optimum conditions are 395 C and 280 atmospheres.

Pasquon and Dente provide the relationship: aCOAH2-aCH3OH/KP r=# (3-10) (A+BaCO+CaH2+DaCH3OH) where r=reaction rate, kg moles CH3OH per kg per hour #=catalyst efficiency=0.67 aCO=thermodynamic activity of CO=γCOpCO aH2=thermodynamic activity of H2=γH2pH2 aCH3OH=thermodynamic activity of CH3OH=γCH3OHpCH3OH γCO=activity coefficient of CO=1.0 γH=activity coefficient of H2=1 .0 γCH3OH=activity coefficient of CH3OH=0.52 p=partial pressure (product of mole fraction of components and 280 atmospheres).

Kp=equilibrium constant for homogeneous reaction of methanol synthesis=2.67xlO-s atm-2 AH=-24.45 kca1/g.mole AT=3860C Cp=7.6 cal/(g.mole)( C) A=125 B=l.0 empirical constants determined by C=0.125 @ Natta (supra).

D=4.63 Assuming #H=0.011 hr, and coolant temperature TC, of 9 C entering unit I equations 3-7, 3-8 and 3-9 above can be solved for the case where NC=NH=0.357.

Equation 3-7 can be rearranged to solve for the ratio of catalyst loading, P, at any point in the reactor:

where P0 is ratio of catalyst loading entering unit I and is numerically unity, and r0 is rate of reaction and Z0 is conversion entering unit 1. 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 of 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 unit in gm moles CH3OH per (gm catalyst)-(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 Unit Z P rx 102 R1 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 0.076 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 N 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 Figure 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 6.12x10-4 gm moles/cm C 4.61x10-4 gm moles/cm .30 (-) F 5.77x 105 gm moles/day MH 7.52 gm/gm mole -#H 24,450 cal/gm mole ## 1.31 gm/cm # 0.50 (-) Do 0.95 cm kR 0.129 sec-1 CpH 7.60 cal/(gm)( C) CpC 7.60 cal/(gm)( C) H 3.46x10-4 gm/cm sec C 2.18x10- Proceeding as described in Example I 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 N H 0.357(-) Nc 0.357(-) # 0.357 (-) α 1.031 (-) Q l.0(-) 39.6 sec UH 6.37x 10-4 caV(sec)(cm2)(0C) Vc 4.75 cm/sec V H 4.63 cm/sec 2062 (-) RBH 361 (-) 7c 0.68 (-) #H 0.41 (-) hH 6.50x10-3 cal/(sec)(cm)( C) hC 1.82x10-3 cal/(sec)(cm)( C) Using the data of Tables 9, 10 and 11 calculations are made verifying 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 8.67x 105 cm3 #C 3.32x105 cm L 365 cm X 60.9 cm AxH 2369 cm AxC 907 cm 2.00x 105 gm moles/day 6(-) W 569 kg It Is evident that the unit described provides methanol from carbon monoxide and hydrogen at the desired rate.

The advantages of the apparatus of this invention are made evident by comparison with the apparatus with varying catalyst concentration using 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, Vol. 101, Pages 215-230 (1969). (The word "Dowtherm" is a Registered Trade Mark). Comparison can be made on the total catalyst volume employed which is the volume of catalyst plus volume of diluent employed. The larger the total, i.e. the more dilute the catalyst, the greater the volume necessary to provide the same through-put. The results of Calderbank et al. are expressed in terms of a catalyst dilution factor, R' which bears a relationship to the values of P used above, namely, PL R= (3-12) P where P, is the value of P at the exit end of the reactor. Values of R' 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 the Figure 13 where the abscissae indicate units of the present example, or the dimensionless distance which is I at the end of unit VI and ordinates are values of R'. Curve A is shown as stepwise change of dilution factor R1 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 sufficient 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.

Claims (29)

1. WHAT WE CLAIM IS:- 1. A process for establishing substantial isothermality in a heterogeneous or homogeneous catalytic reaction for the conversion of at least one reactant to a product, which process comprises passing a reaction medium 'susceptible to the heterogeneous or homogeneous catalytic chemical reaction over suitable catalyst under conditions such that heat is liberated or absorbed at a rate which is substantially 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 the first set of passageways, the 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 the reaction medium and coolant are passed through the passageways, and the geometry of the passageways being summarised by the relationship: (TH-Tc) Uc#cSc#H = (-#H)Co pcCpc#cUH#HSH wherein all terms are in consistent units and wherein TH=inlet temperature of reactants; Tc=inlet temperature of coolant; -AH=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; free volume on reaction side (excluding particulate catalyst); #c=free volume on coolant side; pcppc=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 TJTH.
2. 2. A process as claimed in Claim 1, wherein the reaction takes place in 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 the first passageways through which coolant flows, the first passageways being interconnected through first chambers and the second passageways through second chambers, passage of reactants or coolants between theist and second chambers and the first and second passageways being prevented, the first passageways having a free volume excluding particulate catalyst of #H, a heat transfer area of SH, the reactants being at an initial concentration of Co and temperature TH and having an overall heat transfer coefficient of UH for space time of #H and being susceptible to a reaction having heat of reaction of -AH liberating heat at a rate which is in direct relationship to concentration of reactant, the second passageways having a free volume of #C and heat transfer area of SC, the coolant initial temperature of TC and product of density by heat capacity #CCpC and being in the second passageways for a space time #C and then having overall heat transfer coefficient UC, the relationship between passageways, temperatures and flow rates being expressed by (TH-TC) UC#CSC#H = (-#H)Co #CCpC#CUH#HSH wherein all terms are in constant units and the relationship of rate of liberation of heat to concentration of reactant being a direct function of Uc and TJTH.
3. 3. A process as claimed in Claim 1 or 2, wherein the catalyst is contained in the first passageways on impregnated pellets.
4. 4. A process as claimed in Claim 1 or 2, wherein the catalyst is on the walls of the first passageways.
5. 5. A process as claimed in any of Claims 1 to 4, wherein the concentration of catalyst in the first passageways of each successive heat exchanger unit is greater than in the preceding unit thereby modifying reaction kinetics to being of substantially first order.
6. 6. A, process as claimed in Claim 5, wherein the concentrations of catalyst increase along the length of the first passageways.
7. 7. A process as claimed in Claim 6, wherein there are at least four cross-flow heat exchanger units successively containing catalyst at increasing concentrations.
8. 8. A process as claimed in any of Claims 1 to 7 for converting carbon monoxide and hydrogen to methanol wherein CO is the inlet concentration of carbon monoxide and is the rate controlling reactant.
9. 9. A process 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, the conversion taking place in 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 the first passageways through which coolant flows, the first passageways being interconnected through first chambers and the second passageways through second chambers and means preventing passage of reactants or coolants between the first and second chambers and the first and second passageways, the first passageways having a free volume excluding particulate catalyst of L'H' a heat transfer area of SH, the 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 -AH liberating heat, the second passageways having a free volume of Pc and heat transfer area of Sc the coolant having initial temperature of Tc and product of density by heat capacity PCCPC and being in the second passageways for a space time TC and then having overall heat transfer coefficient Us, the relationships between passageways, temperatures, flow rates and reaction kinetics being expressed by (TH TC) UCTCSCVH (-AH)C0 PcCpcPCUHTHSH and TC SC KR=(UC) ) TH PCCPCDC wherein all terms are in consistent units.
10. 10. A process as claimed in Claim 9 for converting carbon monoxide and hydrogen to methanol wherein CO is the inlet concentration of carbon monoxide and is the rate controlling reactant and the catalyst loading in the first passageways of the series of at least two crossflow heat exchanger units is increased in successive downstream units.
11. 11. A process as claimed in Claim 10, wherein the catalyst is pellets of ZnO-Cr203 or ZnO^CuO-Cr203 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.
12. 12. A process as claimed in Claim 11, wherein cooling through second passageways is provided at least in part by reactant gases before the reactant gases are introduced into the first passageways containing catalyst.
13. 13. A process as claimed in any of claims 9 to 12, 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.
14. 14. An apparatus when used to carry out the process of any one of the preceding claim, the apparatus having means for introducing reactants and temperature controlling fluid at predetermined temperatures and means for removal thereof, the apparatus comprising a reaction site comprising first and second sets of passageways wherein the reactants and temperature controlling fluid flow without intermingling in cocurrent to pseudo-cocurrent relation under controlled heat exchanging relationship.
15. 15. Apparatus as claimed in Claim 14, wherein the reaction site 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 the first passageways through which coolant flows the first passageways being interconnected through first chambers and the second passageways through second chambers and the apparatus comprising means preventing passage of reactants or coolants between the first and second chambers and the first and second passageways.
16. 16. Apparatus as claimed in Claim 14 or 15, wherein catalyst is contained in first passageways on impregnated pellets.
17. 17. Apparatus as claimed in Claim 14 or 15, wherein catalyst is on the walls of the first passageways.
18. 18. Apparatus as claimed in any of claims 15 to 17, wherein the concentration of catalyst in the first passageways of each successive heat exchanger unit is greater than in the preceding unit thereby modifying reaction kinetics to being of substantially first order.
19. 19. Apparatus as claimed in Claim 18, wherein concentrations of catalyst increases along the length of the first passageways.
20. 20. Apparatus as claimed in Claim 19 where there are at least four cross-flow heat exchanger units successively containing catalyst at increasing concentrations.
21. 21. Apparatus as claimed in Claim 14 for homogeneous or heterogeneous conversion of one reactant product.
22. 22. Apparatus as claimed in any preceding claim having means for introducing carbon monoxide and hydrogen wherein CO is the inlet concentration of carbon monoxide in the means and is the rate controlling reactant.
23. 23. Apparatus for catalytic conversion of at least one reactant to a product under approximately isothermal conditions with reaction velocity constant kR when used to carry out the process of any one of Claims 1 to 13, the apparatus having means for introducing reactants and temperature controlling fluid at predetermined temperatures and means for removal thereof, the apparatus comprising a reaction site 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 the first passageways through which coolant flows, the first passageways being interconnected through first chambers and the second passageways through second chambers and the apparatus comprising means preventing passage of reactants or coolants between the first and second chambers and the first and second passageways, the first passageways having a free volume excluding particulate catalyst of H' a heat transfer area of SH, the 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 -All liberating heat, the second passageways having a free volume of Pc and heat transfer area of Sc the coolant having initial temperature of Tc and product of density by heat capacity pcC > C and being in the 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 beign expressed by (TH TC) UCTCSCPH (-AH)C0 PCCocpcUHtHSH and TC SC kR=(Uc)( TH PCCPCVC wherein all terms are in consistent units.
24. 24. Apparatus as claimed in Claim 23 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 successive downstream units.
25. 25. Apparatus as claimed in Claim 24 wherein the catalyst is pellets of ZnO Cr2O3 or ZnO-CuO-Cr2O3 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.
26. 26; Apparatus as claimed in Claim 25, wherein means are provided for introducing reactant gases through second passageways to provide at least partial cooling before the reactant gases are introduced into the first passageways containing catalyst.
27. 27. Apparatus as claimed in any of Claims 22 to 26 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.
28. 28. A process for establishing substantial isothermality in a heterogeneous or homogeneous catalytic reaction substantially as herein described.
29. 29. Apparatus according to Claim 14 or 23 for conversion of at least one reactant under approximately isothermal conditions substantially as herein described.