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Title:
CATALYST FOR AMMONIA SYNTHESIS
Document Type and Number:
WIPO Patent Application WO/2018/215202
Kind Code:
A1
Abstract:
A catalyst for catalysing the synthesis of ammonia from hydrogen gas and nitrogen gas, comprising ruthenium, wherein lithium metal is incorporated into the catalyst as a promoter of the catalytic activity of the ruthenium.

Inventors:
HUGHES TIMOTHY (GB)
LIAO FENGLIN (CN)
TSANG SHIK CHI (GB)
WILKINSON IAN (GB)
WU SHUN SHING SIMSON (CN)
Application Number:
PCT/EP2018/061907
Publication Date:
November 29, 2018
Filing Date:
May 08, 2018
Export Citation:
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Assignee:
SIEMENS AG (DE)
International Classes:
B01J21/18; B01J23/58; B01J35/00; C01C1/00; C01C1/04
Foreign References:
US4250057A1981-02-10
EP0036939A11981-10-07
Other References:
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Claims:
CLAIMS :

1. A catalyst for catalysing the synthesis of ammonia from hydrogen gas and nitrogen gas, comprising ruthenium,

characterised in that lithium metal is incorporated into the catalyst as a promoter of the catalytic activity of the ruthenium .

2. A catalyst according to claim 1, further comprising a barium promoter.

3. A catalyst according to claim 1 or claim 2, comprising a support of carbon. 4. A catalyst of claim 3 wherein the support of carbon is of activated carbon.

5. A catalyst of claim 3 wherein the support of carbon is of activated carbon nanotubes.

6. A catalyst of claim 3 wherein the support of carbon is of activated graphene .

7. A catalyst according to any preceding claim wherein a ratio of added lithium to ruthenium is above 15:1.

8. A method of synthesising ammonia from nitrogen gas and hydrogen gas, comprising the step of passing nitrogen gas and hydrogen gas over a catalyst according to any of claims 1-7.

9. A method according to claim 8, wherein the recited step is performed at a temperature in the range of 300-700°C and a pressure in the range of 0.1-50 MPa.

10. A method according to claim 9, wherein the recited step is performed at a pressure in the range of 0.1-5 MPa.

11. A method according to claim 10, wherein the recited step is performed at a temperature in the range of 400-470°C.

12. A method according to any of claims 8 to 11, wherein the hydrogen gas is prepared by hydrolysis of water using electricity obtained from a renewable energy source.

13. Apparatus for synthesising ammonia from nitrogen gas and hydrogen gas, comprising

- an electrical generator for generating electricity from a renewable energy source;

- an electrolyser for electrolysing water using electricity generated by the generator from the renewable energy source to generate the hydrogen gas,

- an air separator for separating air to provide the nitrogen gas ,

- a catalyst according to any one of claims 1-7,

- a heater and a compressor for heating and pressurizing the hydrogen gas and the nitrogen gas and passing the hydrogen gas and nitrogen gas over the catalyst.

Description:
CATALYST FOR AMMONIA SYNTHESIS

The present invention relates to a catalyst for catalysing the synthesis of ammonia N¾ from hydrogen gas H 2 and nitrogen gas N 2 . It also relates to methods and apparatus for synthesis of ammonia N¾ from nitrogen N 2 and hydrogen H 2 .

Fig. 1 represents an outline schematic of the well-known Haber-Bosch method for ammonia synthesis. A 3:1 ratio of hydrogen (H 2 ) 10 and nitrogen (N 2 ) 12 gases are supplied to a heat process 14. The heated mixture of H 2 and N 2 gases 16 is passed over a hot iron catalyst 18, which catalyses synthesis of a portion of the heated mixture of H 2 and N 2 gases into ammonia (NH 3 ) . Typically, a ratio of 20% NH 3 to 80% unreacted N 2 and H 2 is achieved. The resultant ammonia- containing mixture 20 is cooled in a condenser 22, such that the synthesised ammonia 24 liquefies and is removed from the process . The process is usually operated continuously for maximum efficiency. The hot iron catalyst 18 requires to be maintained at high temperatures, around 400°C - 500°C, to favour the formation of ammonia and at high pressure, around 15-30 MPa, to achieve an acceptable rate of synthesis. Ruthenium (Ru) catalysts are also known for use in such processes. Maintenance of such a high-temperature, high pressure environment means that the process consumes a large amount of energy, typically derived from fossil fuels. In a conventional Haber-Bosch process, fossil-fuelled hydrogen generation is employed, which is also a high- temperature process, and waste heat from hydrogen generation may be used to heat the catalyst and the H 2 and N 2 mixture. Current research examines ammonia generation and combustion as a manner for storage of renewable energy, and as a carbon- free fuel. However, renewable energy sources may provide intermittent power, for example from solar or wind power. For this reason, it has sometimes been considered inappropriate to run a Haber-Bosch process from renewable energy sources, as use of an intermittent energy source will compromise the efficiency and/or cost of a standard synthesis process. Ammonia production plants are currently powered by energy derived from fossil fuel.

In a renewable-fuelled ammonia generation plant, such waste heat is not available and the iron catalyst is of low efficiency at lower temperatures.

There is a possibility to decentralize synthesis of H 3 by manufacturing with ¾ obtained from renewable energy sources such as wind and solar in smaller units and at low pressure. No suitable catalyst has yet been developed for such operation. Ru based catalysts are found to operate at lower pressure than Fe catalysts. Unexpectedly, amongst the alkali promotors studied, the inventors found that Li gives the highest rate albeit its poorest electron donating ability in accordance with electronegativity.

The inventors have unexpectedly found that exceptional promotion by Li renders Li-Ru catalysts suitable for ammonia synthesis at low pressure (0.1-5.0 MPa) but effective over a range of 0.1-40.0 MPa. The Li-promoted Ru catalysts of the invention have been found to outclass conventional commercial Fe counterparts by 350 fold; and also to outclass other conventional catalytic systems many fold. The role of Li in 2 activation over a catalytic Ru surface are elucidated below . Electric power generated from renewable energy sources such as wind or solar power at smaller units provide for local grid use but can also be used to produce hydrogen via electrolysis of water for ammonia synthesis without carbon emission 5 . Momentary unbalance of electrical generation and consumption into and from a grid system due to fluctuations in supply and load may be smoothed by synthesising H 3 as an operating reserve capacity.

¾ manufactured by electrolysis at low pressure would require an efficient catalyst for high production rate of NH 3 in such smaller units. Wind energy may be used to make electricity and then to perform the Haber-Bosch process to make NH 3 locally by electricity derived from wind energy. An outline schematic of an example "eHB" (electrolysis-Haber-Bosch) system is shown in Fig. 2. Wind energy from wind farms is transferred into electricity which supports the demand profiles such as the electricity grid. Surplus electricity, for example generated when strong wind is encountered may be employed for the energy storage system (ESS) . Water is electrolyzed using surplus electricity into ¾ . As electrolysers have a stringently high water purity requirement, a mechanical vapour compression unit (MVC) is applied prior to the electrolysis unit. The plant-formed ¾, and 2 from air separation, are then condensed as a stock of supply gases for ammonia synthesis.

Fig. 2 shows a schematic view of an eHB process integrating the ammonia synthesis energy storage system (ESS) and electricity produced by wind energy. Fig. 2 illustrates such a system driven by an intermittent electrical power input from a wind farm which is provided to satisfy a given electricity demand (demand profile) . Surplus power from the wind farm is used to operate an Energy Storage System (ESS) consisting of ¾, 2 and N¾ production modules. Excess electrical power is stored by electrolysing water to generate ¾, by extracting 2 from air and synthesising NH 3 from these gases. Power deficits are overcome by converting NH 3 from NH 3 storage back to electricity. This ensures that (a) the demand profile is satisfied, and (b) a minimum level of operation of the ESS is maintained.

Storage of ¾ and N¾ is considered to ensure that (a) the minimum operation loads of the ESS components are met, and (b) the NH 3 production process operates with minimal load variations to maximise the lifetime of the catalyst. A condition for a feasible system is that no cumulative deficits in any of the intermediate products (¾, 2 and N¾) occur and that the demand profile is satisfied. This contrasts with the Haber-Bosch catalytic process for industrial N¾ production where non-renewable natural gas is used as the energy and ¾ source with a concomitant release of large CO 2 emissions. In order to obtain the optimal productivity of NH 3 , the reaction conditions are usually set at a temperature regime of 400-500 °C, and pressures of 15-30 MPa under a maximal flow of reactant gases. Under these conditions, catalyst selection can be less critical since slightly less active, or deactivated, catalysts such as Fe- based catalysts can reach the same conversion rates at smaller reactant flows. NH 3 generation in a small-scale eHB plant requires that catalysts show significant activity at a lower pressure to minimise the cost of investment and mitigate safety risks. It is thus of great significance to reduce the reaction pressure below the typical pressures employed in the Haber-Bosch process to reduce operational cost and energy requirements and achieve the eHB process.

Experimental evidence points to that the 2 dissociative adsorption to be the rate determining step in NH 3 synthesis 6 . Therefore, a more efficient catalyst for N¾ synthesis should have a suitable surface potential for more favourable adsorption and dissociation of 2 under the kinetic controlled conditions.

The eHB process requires that the catalyst works under a relatively low reaction pressure. Compared with the conventional commercial Fe, Ru is a better candidate for the eHB process as it is relatively active at low pressure 7 .

Ru catalyst is not presently applied in the Haber-Bosch NH 3 synthesis industry, partly because the practicality of such catalyst may be limited by its vulnerability to be poisoned by carbon deposition from CH 4 decomposition, and the high cost of Ru catalysts. In the eHB system, since the ¾ is generated from electrolysis of water, there is no risk that the ¾ may contain CH 4 , so the poisoning risk is avoided. This makes Ru a potential candidate for low pressure synthesis .

Even so, on consideration of its high cost, it is necessary to improve the activity of Ru-based catalyst, to operate the eHB process at a higher yield. Considering the high energy barrier of dissociation of N 2 , alkali metals with strong electron donation ability (Na, K, and Cs) are generally employed to improve traditional Fe- or Ru- based catalysts

— 1 Ω

for ammonia synthesis According to the present invention, a lithium-promoted ruthenium catalyst is provided. Such catalyst may provide higher activity for ammonia synthesis than the conventional standard iron catalyst. Use of a lithium-promoted ruthenium catalyst allows ammonia production rates to be achieved comparable with the conventional fossil-fuelled Haber-Bosch process, but at reduced temperature and/or pressure. The production rate may be ramped up and down according to availability of energy, without such a large loss in efficiency as would be observed by applying intermittent energy supply to the conventional Haber-Bosch process.

The present invention accordingly provides methods and apparatus as defined in the appended claims.

The above, and further, objects, characteristics and advantages of the present invention may be better understood from the following description of certain embodiments thereof, given by way of examples only, in conjunction with the appended drawings wherein:

Fig. 1 represents an outline schematic of the Haber-Bosch method for ammonia synthesis;

Fig. 2 an outline schematic of an electrolysis-Haber-Bosch (eHB) method for ammonia synthesis;

Figs. 3a - 3e represent physicochemical properties and catalytic performance of catalysts according to embodiments of the present invention;

Fig. 4 illustrates an effect of increasing lithium (Li) concentration in the preparation of a Ru catalyst for ammonia synthesis; and

Fig. 5 illustrates a comparison of the catalytic activity of certain catalysts of the present invention against a conventional Fe and Ru catalysts at various pressures. η

The present invention provides a catalyst for ammonia synthesis. The catalyst of the present invention is a lithium (Li ) -promoted barium-ruthenium (Ba-Ru) catalyst on a carbon support. An activated carbon support is employed.

Lithium (Li) is rarely considered for use to improve conventional Fe- or Ru- based catalysts for ammonia synthesis, because of the anticipated inferior electron donation capacity of Li compared to other alkali metals. The present invention however provides superior activity of Ru catalysts when promoted by Li.

The present inventors have found that Li-enhanced Ru catalysts outclass those of all reported catalytic systems at low pressure (0.1-5.0 MPa) , yet provides catalytic activity comparable to conventional Fe based catalysts at much higher pressures and similar temperatures: up to 40.0 MPa and 700°C. The regenerative electron donation of Li-Ru and surface stabilization to lower the energy barrier for dissociation of nitrogen triple bonds are noted in this efficient catalyst.

Table 1 shows a comparison of reactivity in the reduction of 2 to NH 3 over Ru, Fe, Co-based catalysts, along with others from the literature. Commercial Fe catalyst with multi promotors composed of Fe30 4 or Fe 2 <03, AI 2 O 3 , K 2 0, CaO, MgO and S1O 2 is evaluated, which displays a good reaction rate of 95, 600 ymol g C at ~1 h ~1 under operating pressure of 15 MPa (entry 12) . However, the reaction rate dramatically attenuates to 3, 600 ymol g C at ~1 h ~1 when reducing the pressure to 1 MPa (entry 13) . Fe catalyst is thus not a good candidate for the ESS system since it is too sensitive to the reduced pressure. Ru with higher electron density of d-orbitals can donate electrons into the anti-bonding orbital of adsorbed N 2 , facilitating its dissociation and hence can work under a lower pressure as compared to Fe based catalysts.

This can be seen from Table 1 that all Ru based catalysts display a consistently higher rate than that of Fe based catalysts. In accordance with the literature data, the ammonia production rate of a barium-enhanced ruthenium catalyst on an activated carbon support (Ba-Ru/AC) shows 2.3 times the catalytic conversion rate as that of a commercial Fe catalyst (entries 3, 13). 14

A caesium-enhanced ruthenium (Cs-Ru) - based catalyst (entries 4, 7) is one of the most active Ru catalysts claimed for N¾ synthesis with an enhanced reaction rate. 15 ' 16

Ru/Ci 2 A7:e ~ and Co-LiH catalysts may be used as NH 3 -synthesis catalysts due to effective electron back donation from metal to N 2 . 17,18

In contrast, the results shown in Table 1 clearly indicate that the Ba-Ru-Li catalyst of the present invention significantly outclasses these catalytic systems. The ammonia production rate of the Ba-Ru-Li catalyst of the present invention is 12.9 folds than that of commercial Fe and 5.6 folds than that of Ba-Ru/AC at 1 MPa (entries 9, 13 and 3) . In addition, the Ba-Ru-Li catalyst of the present invention is 5 folds more active than (entries 5, 6, 9 and 10) Ru/Pr 2 <0 3 which regarded as effective under low pressure 19 .

The superiority of Ba-Ru-Li catalyst of the present invention is more apparent when the activity is compared in term of moles N¾ ammonia per mole of alkali metal used. Its activity is almost 348.3 fold than that of commercial Fe at 1 MPa and is much better than all systems reported in literature. Interestingly, the Ba-Ru-Li catalyst of the present invention shows a rate comparable to that of the commercial Fe catalysts at 15 MPa but under a significantly reduced pressure of 3 MPa. Even evaluated at 1 MPa, the Ba-Ru-Li catalyst of the present invention also gives a considerable activity (entry 10). In order to reduce the high cost of working catalyst, a catalyst with lower metal contents of 0.5 wt% Ru and 0.76 wt% Li (entry 11) was tested, which shows the highest ratio of moles N¾ produced per mole of Ru metal (251.1 mol NH 3 / mol Ru) . Thus, this exceptional high rate at low alkali metal loading renders the Ba-Ru-Li/AC catalysts of the present invention more applicable for the eHB process under low applied pressure.

Figs. 3a - 3e represent physicochemical properties and catalytic performance of catalysts according to embodiments of the present invention.

Fig. 3a represents width angle x-ray diffusion patterns of reduced Ru-Li/AC (4.8 wt% Ru, 7.6 wt% Li) samples. Vertical lines indicate the reference signal of Ru cluster. No obvious peak shift of Ru and Ru-Li samples is observed.

Fig. 3b represents a typical TEM image of reduced Ba-Ru-Li sample (4.8 wt% Ru, 7.6 wt% Li) showing the homogeneous distribution of Ru nanoparticles with average particle size of 2.9 nm.

Fig. 3c represents a typical high resolution TEM image of reduced Ru nanoparticle in Ru-Li/AC sample. Highlighted points represent the stepped atoms in the nanoparticle as B5 sites (which consist of an arrangement of three Ru atoms in one layer and two further Ru atoms in an internal layer) . The inset image is the Fourier transition of the 2-nm nanoparticle showing the majority lattice face of hep (101) .

Fig. 3d represents carbon monoxide (CO) chemical sorption on the reduced Ba-Ru/AC and Ba-Ru-Li/AC samples. Note that the Ba-Ru-Li/AC sample shows a reduced amount of CO chemical sorption, indicating that the surface of Ru nanoparticles is at least partially covered by Li species.

Fig. 3e represents catalytic results of Ba-Ru/AC promoted by a series of compositional Li. As shown, a volcano relationship between activity and Li loading is exhibited, indicating an optimization in lithiation before excessive coverage is evident. The reaction conditions used for the test in question were: 5 MPa; 743 K; 62, 400 ml g cat ~1 h ~1 . As shown in Figs. 3b, 3c the Ru nanoparticles in Ba-Ru-Li/AC are homogeneously distributed on the carbon support with average particle size of 2 nm.

DFT calculations indicated the active site on Ru nanoparticle is likely to be so called , B5-type' for the 2 activation, which offers exposed three-fold hollow sites at a proximity to bridge metal sites. This can ensure two nitrogen atoms are not bonded to the same Ru atom. Jacobsen et al. showed the optimal Ru size of 1.8-2.5 nm which contained the maximum number of B5-type sites; this number decreased for larger particle sizes. Interestingly, our particle size appears to match the range of optimal Ru nanoparticle size for the ammonia synthesis. With the lithiation of Ru nanoparticles, the particle size only slightly increases to 2.5 nm, as illustrated in Fig. 3c. Intriguingly, the activity is significantly improved with almost 13.7 folds TOF (Turn over frequency: TOF = Moles of desired product formed/moles of catalyst/time) of Ru despite its severe surface coverage with Li + (Table 1) .

Fig. 3c clearly shows that the Ru nanoparticle having a size of 2 nm in the Ba-Ru-Li/AC is covered with high density of stepped sites for B5 type, which benefits for the catalytic reduction of N 2 . The present inventors have found that Li + may preferentially take residence on the surface of Ru nanoparticles rather than penetrating into interstitial of Ru lattices. From the width angle x-ray diffusion patterns in Fig. 3a, the diffraction peaks of metallic Ru show no obvious shift upon the addition of Li + into the system, indicating no expansion of Ru lattice. This can also be directly observed from the high resolution TEM image of Fig. 3c. The number of exposed Ru metallic sites may be determined by carbon monoxide (CO) chemical sorption. The values are 78.1 ymol.g -1 and 19.5 ymol.g -1 for Ba-Ru/AC and Ba-Ru-Li/Ac, respectively, suggesting the partial coverage or decoration of Li + on the Ru (Fig. 3d) .

The present inventors anticipate that surface Ru atoms promoted by Li + instead of Li° to provide active sites for 2 activation to N¾ . Indeed, a volcano relationship is obtained when NH 3 production rate is plotted against Li + loading with an optimum value reaching at around 15 wt% (Fig. 3e) . Excessive loading of Li + could reduce the number of exposed Ru active sites despite the beneficial promotion effect. Unlike the case of Li + promotion to Ru, Li + does not seem to offer much significant promotion to Fe for the ammonia synthesis (Table 1, entries 14 and 15) . Alkali promotors or supports Na , K and Cs to Ru nanoparticles have been proposed to boost catalytic activity m converting 2 to N¾ m ¾ . Electrons are thought to transfer from the alkali metals to the Ru nanoparticles and thus promoting the electron density of Ru into the pi star anti-bonding orbital of 2 to facilitate the dissociation of the N≡N nitrogen-nitrogen triple bonds N≡N. According to the electronegativity values of the geometric mean of the electronegativity of the constituent elements 28 , the promotion ranking should follow: Cs + > K + > Na + > Li + . Unexpectedly, however, the present inventors have found that Li + with the highest electronegativity displays higher electronic promotion than all other alkali ions especially in low pressure.

The combination of the Haber-Bosch process at low pressure and the wind energy (referred to here as eHB) supports a great opportunity for the current energy-urgent society. The present invention may enable efficient NH 3 synthesis in small unit plants at relatively low pressure by use of simple Ba- Ru-Li/AC catalysts.

In an embodiment of the invention, a catalyst is prepared by impregnating Ru particles into a carbon support. The carbon support may have previously been prepared by heating a carbon support to 950°C in a gas mixture comprising 5% ¾ in argon, to perform a chemical reduction and to provide an activated carbon with a high surface area. Li metal is then incorporated into the Ru nanoparticles. The incorporation of lithium metal may be achieved by preparation with lithium acetate dehydrate. The catalyst is promoted by introducing barium. Promotion by barium may be achieved by use of barium nitrate solution. Promotion to a catalyst is achieved by adding a small quantity of chemical - barium, in this example - to greatly enhance its catalytic performance. It is thought that barium carbonate is formed as a structural promotor such that its presence on a catalyst particle as high melting compound can prevent the aggregation of small metal particles. The lithium role is thought to be as an electronic promotor which enhances electron richness of Ru for the activation of N 2 . Barium and lithium are accordingly thought to work as two independent promotors to Ru metal .

The lithium-barium-ruthenium (Ba-Ru-Li) catalysts so prepared have been shown to exhibit a higher activity than conventional Fe or Ru based catalysts.

Use of such catalysts allows ammonia synthesis to be carried out at lower temperatures and pressures than with conventional catalysts, enabling more efficient, cost- effective ammonia production.

According to an aspect of the present invention, catalytic activity of the Ru content of the catalyst is promoted by the incorporation of Li into the catalyst support. Further improvement in catalytic activity may be achieved through use of a Ba promoter and/or a support of high surface area, for example of activated carbon (AC) .

Fig. 4 illustrates an effect of increasing lithium (Li) concentration in the preparation of a Ru catalyst for ammonia synthesis .

The effect of increasing Li content in the preparation of the Ru catalyst of the invention may be observed. Increasing amounts of Li are seen to increase the activity of the catalyst. Significant improvement is observed for ratios of added lithium to ruthenium above 15:1. The increased catalytic activity obtained by the addition of Li allows for a reduction in temperature and/or pressure of the ammonia synthesis reaction conditions, with the associated saving in energy consumption and production costs. Fig. 5 illustrates a comparison of the catalytic activity of certain catalysts of the present invention against a conventional Fe and Ru catalysts at various pressures. The assumed reaction conditions are 470°C and weight-hourly- space-velocity (WHSV) of 835 h "1 .

Notably, significant catalytic activity is observed at a temperatures in the range of 300 - 700°C and a pressure in the range of 3-40 MPa. Catalytic activity comparable to that of conventional iron catalysts may be obtained at much higher pressures and similar temperatures, for example in the range 30-50 MPa.

Table 2 shows a comparative table of catalytic activity of example catalysts of the invention, and conventional catalysts, for illustration purposes only. Various ammonia catalysts have been developed; however, the catalyst of the present invention shows catalytic activity comparable to certain conventional catalysts but at significantly lower pressures than Fe-catalysts , for example. The reaction conditions considered include a reaction temperature of 400- 470°C. While the embodiments described above comprise a carbon support which is activated by reduction by heating in hydrogen, other embodiments employ a carbon support of carbon nanotubes. The carbon nanotubes may be activated in a similar manner. The carbon nanotubes may be found to provide a greater surface area per unit volume, and per unit mass, than other carbon supports. Yet other embodiments employ a carbon support of graphene. The graphene may be activated in a similar manner. The graphene may be found to provide a greater surface area per unit volume, and per unit mass, than other carbon supports. In other respects, embodiments of the present invention employing carbon supports of carbon nanotubes or of graphene are as the embodiments described above with a carbon support.

Embodiments of the invention provide apparatus for synthesising ammonia from nitrogen gas and hydrogen gas, comprising an electrical generator for generating electricity from a renewable energy source; an electrolyser for electrolysing water using electricity generated by the generator from the renewable energy source to generate the hydrogen gas, an air separator for separating air to provide the nitrogen gas, a catalyst as described above, and a heater and a compressor for heating and pressurizing the hydrogen gas and the nitrogen gas and passing the hydrogen gas and nitrogen gas over the catalyst.

The present invention provides lithium-promoted ruthenium catalyst compositions and equipment for ammonia synthesis. Conventionally, only two types of commercial catalysts were available for ammonia synthesis. The Cs-Ru/MgO catalyst is a lower temperature, lower pressure, higher efficiency one, and the most popular, cheaper, catalysts are based on iron promoted with one of K 2 0, CaO, Si0 2 , Al 2 03,etc. The present invention relates to a new series of catalysts: Li-Ru type catalysts. Support for such catalysts can be provided in the form of activated carbons, MgO or AI 2 O 3 .

Significant enhancement in reaction rate can be due reaction by an associative mechanism rather than dissociative mechanism. Some of the following prior art documents are referenced in the preceding text by number. They provide background discussion of the prior art.

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