Hydrogenation Of Thiophene Research Articles

Синтез и свойства каталитических хемосорбентов на основе оксида титана

In this work, we studied the synthesis and properties of catalytic chemisorbents based on titanium dioxide with additions of ZnO and γ-Al2O3. The goal was to obtain chemisorbents with desired performance characteristics and evaluate their potential in destructive hydrogenation of organo-sulfur compounds. Their sulfur capacity and hydrogenating capacity were measured by the static method with carbon disulfide absorption. Textural and morphological characteristics were deter-mined with the use of X-ray phase analysis, low-temperature nitrogen adsorption/desorption, and scanning electron microscopy. It was also found that addition of alumina did not give additional reflections on the X-ray pattern, in contrast to introduction of zinc oxide. It was found that addi-tion of zinc oxide significantly increased the values of the specific surface area, many times more than expected, according to additivity principle. Conversely, addition of alumina did not give the expected increase in surface area. The one and the other were explained through active interaction of phases. The ratios of components for obtaining chemisorbents with optimal strength properties were established. It was found that a composite consisting of titanium and aluminum oxides was more resistant to sulfurization than one with additions of zinc oxide. SEM and low-temperature ni-trogen adsorption/desorption methods confirmed the mesoporous structure of the studied samples, while the sample containing gamma alumina showed a more pronounced desorption branch to-gether with the surface consisting of spherical formations arranged in a regular order. The sample with zinc oxide had slit-like pores in its volume. Hydrogenation of thiophene with gaseous hydro-gen was carried out for the studied composites. Chromatographic analysis of the resulting product was performed. It was proven that composites based on titanium, zinc, and aluminum oxides not only had sorption properties with respect to organosulfur compounds, but also catalyzed their de-structive hydrogenation. Thus, it was established that the studied samples were chemisorbents. The study provides insight into synthesis and properties of catalytic titania-based chemisorbents, high-lighting the influence of additives and their potential for organosulfur reduction reactions.

Appropriate active-site in [Mo3S(S2)6]2− or [Mo2(S2)6]2− clusters for catalysis of thiophene hydrodesulfurization

Through a facial immersion method, thiomolybdates [Mo3S(S2)6]2 − and [Mo2(S2)6]2 − clusters have been successfully anchored on SBA-15, and the loaded catalyst was characterized by various methods. The terminal/bridging sulfur atoms on the sulfide cluster have a strong tendency to combine with H atom and then transferred to the S atom of thiophene for hydrodesulfurization. The catalytic activity and desulfurization selectivity of the supported catalysts Mo3S13/SBA-15 and Mo2S12/SBA-15 were investigated at different temperature and different time. Direct hydrogenation of thiophene occurs presumably with the participation of –SH groups, produced from the opening of S–S bridges by hydrogen. And the desulfurization of thiophene occurs presumably with the breaking of C–S bond and formation of C-OH bond for the product is butanol. Mo3S13/SBA-15 and Mo2S12/SBA-15 display excellent catalytic performance. The conversion rate of thiophene is about 97% for Mo3S13/SBA-15 and 94% for Mo2S12/SBA-15, while the desulfurization selectivity is about 97% (Mo2S12/SBA-15) and 82% (Mo3S13/SBA-15).

Hydrogenation and C[sbnd]S bond activation pathways in thiophene and tetrahydrothiophene reactions on sulfur-passivated surfaces of Ru, Pt, and Re nanoparticles

Thiophene-H2 reactions proceed via sulfur removal and hydrogenation routes on dispersed metal nanoparticles that become decorated by refractory S adlayers during catalysis. The identity and kinetic relevance of the required elementary steps are described here based on rates measured at S-chemical potentials set by H2S/H2 ratios similar to those prevalent during practical catalysis on Re, ReSx, Ru, and Pt catalysts. The free energies of formation of S adatoms from H2S/H2 reactants are large and negative at low coverages (< −50 kJ mol−1 on Pt(111) and < −150 kJ mol−1 on Re(0001) and Ru(0001)), but strong repulsion among adatoms prevents full saturation, leading to sub-monolayer coverages and to passivated surfaces that expose uncovered interstices. The residual interstitial spaces (*) within adlayers of unreactive S-atoms (S′) bind intermediates and transition states reversibly, thus allowing these passivated surfaces to carry out catalytic turnovers. These interstices are larger on Pt than on Ru or Re surfaces, leading to concomitantly higher turnover rates for thiophene hydrogenation and desulfurization routes. The identity and kinetic relevance of elementary steps for desulfurization (to form C4 hydrocarbons) and hydrogenation (to form tetrahydrothiophene; THT) are similar among these catalysts; they involve kinetically-relevant H-addition steps of thiophene-derived intermediates that cleave their CS bonds or “over-hydrogenate” to THT in one surface sojourn. THT undergoes CS bond cleavage in secondary reactions that correct this over-hydrogenation to form the more unsaturated species that cleave CS bonds. THT/C4 product ratios are insensitive to H2S/H2 ratios and thiophene pressure, even though active interstitial spaces are covered by kinetically-detectable S* and bound thiophene; therefore, primary and secondary reactions must occur on the same active ensembles. The observed increase in THT/C4 ratios with H2 pressure shows that THT formation transition states involve a larger number of H-atoms than for CS cleavage. CS bonds cleave in species with partial unsaturation (H-contents between those in THT and thiophene), in processes that are reminiscent of the requirement to add or remove H-atoms from C and O atoms in cleaving CC and CO bonds in alkanes and alkanols, as well as CO bonds in CO hydrogenation reactions. The rate and selectivity data and the mechanistic conclusions described here show that thiophene hydrogenation and desulfurization routes require similar binding interstices within refractory S adlayers and that metal-sulfur bond energies act as indirect descriptors of reactivity because they determine the number, size, and binding properties of the exposed weakly-binding ensembles that stabilize the relevant transition states and enable catalytic turnovers.

Novel application of MgH2/MoS2 hydrogen storage materials to thiophene hydrodesulfurization: A combined experimental and theoretical case study

In addition to serving as an important energy carrier, hydrogen storage material also has the potential to be used as an effective solid reducing agent. This paper is concerned with the application of MgH2/MoS2 hydrogen storage materials to thiophene desulfurization through catalytic transfer hydrogenation. The hydrogen content of the as-prepared MgH2/MoS2 composites is determined to be 6.15 wt% with a dehydrogenation peak temperature of 402 °C. Taking MgH2 as hydrogen donor, thiophene hydrodesulfurization has taken place at atmospheric pressure and at the temperature lower than the onset desorption temperature, indicating that a coupling effect occurs between MgH2 decomposition and thiophene hydrogenation. It is further revealed that sulfur removal in thiophene under the studied condition preferentially proceeds via direct desulfurization (DDS) route. Our density functional theory (DFT) calculations manifest that energy barriers of the minimum energy path for thiophene hydrodesulfurization are all <1.35 eV. This exploratory case study demonstrates the feasibility of catalytic transfer hydrogenation using solid-state hydrogen storage materials.

DSA Preparation of Pt NPs @MIL-53(Fe) and Its Catalytic Behaviors

In this work, the effects of preparation methods such as CE oven, microwave irradiation, and ultrasound on the morphology, particle size and crystallinity of MIL-53(Fe) are firstly investigated. Furthermore, the methods are utilized to prepare Pt NPs@MIL-53(Fe). As a result, well-defined Pt NPs@MIL-53(Fe) prepared by microwave irradiation exhibits uniformed morphology, high crystallinity, and high-disperse Pt NPs, which has been confirmed by FT-IR, TG, N2 adsorption at 77K, TEM and PXRD. Pt NPs@MIL-53(Fe) composite can selectively catalyze the thiophene hydrogenation over nitrobenzene and benzothiophene hydrogenation. The result shows that the sulfur amount can rapidly be reduced to less than 10 ppm and the crystallinity of reacted Pt NPs@MIL-53(Fe) is unchangeable.

Electrochemical hydrogenation of organic sulfides

Electrochemical reduction desulfurization is a low cost, environmental friendly technology which is capable of achieving a high degree of automation. Electrochemical coupling reactions of organic sulfur hydrogenation and water electrolysis on the C/Nafion electrodes were performed. The electrochemical desulfurization was determined by cyclic voltammetry (CV), bulk electrolysis with coulometry (BEC) and electrochemical impedance spectroscopy (EIS) techniques. Thiophene and benzyl mercaptan were used as model organic sulfur compounds. The results of cyclic voltammetry showed that the electrochemical hydrogenation reduction reaction of thiophene occurred at about −0.35 V. The process included proceeding chemical reaction and electrochemical reaction. The currents generated from thiophene hydrogenation reactions increased with the reaction temperature and the H+ concentration of the electrolyte acidity of anode. Under the same reaction conditions, the desulfurization efficiency of benzyl mercaptan was significantly higher than that of thiophene. From the products of electrolytic reactions, the mechanisms of electrochemical hydrogenation of thiophene were proposed, consisting of two pathways: ring opening followed by hydrogenation and directly hydrogenation followed by ring opening. The proposed reaction mechanisms were consistent with the EIS results, indicating the predominant reactions were ring opening followed by hydrogenation. The reaction products and EIS results suggested that the reaction mechanisms of electrochemical hydrogenation of benzyl mercaptan were by breaking CS bond to form H2S and toluene.

Influence of sulfur vacancy on thiophene hydrodesulfurization mechanism at different MoS2 edges: A DFT study

The detailed hydrogenation (HYD) and direct desulfurization (DDS) pathways of thiophene over the sulfur vacancy of different MoS2 edge structures were investigated by density functional theory (DFT) calculations. The interaction energies were evaluated by dispersion corrected methods (DFT+D). Innovatively, a detailed thiophene hydrodesulfurization (HDS) reaction network over the sulfur vacancy was proposed, involving most of products which could be detected in the experiments. Taking the influence of sulfur vacancy into consideration, it could be found that the sulfur vacancy at Mo-edge was more beneficial for the formation of intermediates and products contained in DDS pathway by comparing the reaction barriers of DDS and HYD pathways. The HYD reaction pathway, which involved hydrogenation to 2-hydrothiophene followed by hydrogenation to 2,3-dihydrothiophene and 2,5-dihydrothiophene, could proceed with a mild reaction barrier at the S-edge with the creation of sulfur vacancy. The results also showed that butane could be formed at both S and Mo edges with relatively high reaction barriers of 52.60kcal/mol (Mo-edge, DDS), 53.99kcal/mol (S-edge, DDS) and 58.07kcal/mol (Mo-edge, HYD), however, the formations of 1-butene and 2-butene were much more favored with energy barriers of 33.45kcal/mol (S-edge HYD) and 35.20kcal/mol (Mo-edge DDS), respectively. These results demonstrated that the sulfur vacancy at the different edges of MoS2 catalysts had a great impact on the overall HDS reaction routes. Based on the systematic calculations, the contribution of sulfur vacancy to the formation of certain intermediates and products was clearly orientated, which provided theoretical guidance for designing highly active catalysts for HDS technology.

Electrochemical hydrogenation of thiophene on SPE electrodes

Electrochemical reduction desulfurization is a promising technology for petroleum refining which is environmental friendly, low cost and able to achieve a high degree of automation. Electrochemical hydrogenation of thiophene was performed in a three-electrode system which SPE electrode was the working electrode. The electrochemical desulfurization was studied by cyclic voltammetry and bulk electrolysis with coulometry (BEC) techniques. The results of cyclic voltammetry showed that the electrochemical hydrogenation reduction reaction occurred at -0.4V. The BEC results showed that the currents generated from thiophene hydrogenation reactions increased with temperature. According to Arrhenius equation, activation energy of thiophene electrolysis was calculated and lower activation energy value indicated it was diffusion controlled reaction. From the products of electrolytic reactions, the mechanisms of electrochemical hydrogenation of thiophene were proposed, consisting of two pathways: openingring followed by hydrogenation, and hydrogenation followed by ring opening.

Nondestructive, real-time determination and visualization of cellulose, hemicellulose and lignin by luminescent oligothiophenes

Enabling technologies for efficient use of the bio-based feedstock are crucial to the replacement of oil-based products. We investigated the feasibility of luminescent conjugated oligothiophenes (LCOs) for non-destructive, rapid detection and quality assessment of lignocellulosic components in complex biomass matrices. A cationic pentameric oligothiophene denoted p-HTEA (pentamer hydrogen thiophene ethyl amine) showed unique binding affinities to cellulose, lignin, hemicelluloses, and cellulose nanofibrils in crystal, liquid and paper form. We exploited this finding using spectrofluorometric methods and fluorescence confocal laser scanning microscopy, for sensitive, simultaneous determination of the structural and compositional complexities of native lignocellulosic biomass. With exceptional photostability, p-HTEA is also demonstrated as a dynamic sensor for real-time monitoring of enzymatic cellulose degradation in cellulolysis. These results demonstrate the use of p-HTEA as a non-destructive tool for the determination of cellulose, hemicellulose and lignin in complex biomass matrices, thereby aiding in the optimization of biomass-converting technologies.

On the mechanism of catalytic hydrogenation of thiophene on hydrogen tungsten bronze.

Hydrogenation of unsaturated organosulfur compounds is an essential process through which these species are converted into cleaner and more useful compounds. Hydrogen bronze materials have been demonstrated to be efficient catalysts in hydrogenation of simple unsaturated compounds. Herein, we performed density functional theory calculations to investigate hydrogenation of thiophene on hydrogen tungsten bronze. Various reaction pathways were investigated and the most favourable routes were identified. Our results suggest that the reaction proceeds with moderate barriers, and formation of tetrahydrothiophene is facile both thermochemically and kinetically. The present study provides a useful insight into the design of hydrogenation thiophene and its derivatives and effective hydrodesulfurization catalysts.

ChemInform Abstract: Asymmetric Hydrogenation of Aromatic Carbocyclic Rings and Thiophenes.

AbstractReview: [30 refs.+ subrefs.]

Simultaneous naphthalene and thiophene hydrogenation over Ni(X)–Pt/HMOR catalysts

A series of Ni(X)–Pt/HMOR catalysts (X=0, 0.5, 1.0, 1.5 and 2.0wt% of Ni and a fixed quantity of Pt=1wt%) were prepared and tested in the hydrogenation (HYD) of naphthalene with and without thiophene and also in the hydroconversion of thiophene. The catalysts were characterized using N2 physisorption, X-ray diffraction (XRD), temperature-programmed reduction (TPR), transmission electron microscopy (TEM) and TEM-EDS elemental analysis. The TPR and TEM results indicate that Pt is mainly located inside the pore system of the mordenite, whereas Ni is located on both the external surface and inside the pore system of the mordenite zeolite. Naphthalene hydrogenation exhibited a high conversion for all the catalysts. In the presence of a sulfur compound and for naphthalene hydrogenation, all the tested catalysts present a fast deactivation. Ni/HMOR catalyst was less active and presents complete deactivation. However, the Ni(0.5)–Pt/HMOR and Pt/HMOR catalysts are able to convert thiophene and produce mainly tetrahydrothiophene. This hydrogenation activity was stable, at least for 12h, showing that the catalytic system can preserve some of the hydrogenating capability. The values of thiophene hydroconversion and the selectivity to tetrahydrothiophene are much higher than the reported for similar systems. The hydrogenation activity is most likely due to the hydrogen spillover.

Asymmetric Hydrogenation of Aromatic Carbocyclic Rings and Thiophenes

Recent advance on asymmetric hydrogenation of aromatic carbocyclic rings and thiophenes has been described with the chiral ruthenium catalyst. It represents a great breakthrough in the area of asymmetric hydrogenation as well as opens up a new pathway for the facile synthesis of valuable optically active carbocyclic rings and dihydro- and tetrahydrothiophenes.

Test of a hydrodesulfurization catalyst in a biomass tar removal process with catalytic steam reforming

In order to remove tars from a synthesis-gas produced with an allothermal, pressurized fluidized-bed biomass gasifier, a catalytic gas-cleaning-process is used. The tars are removed by means of catalytic steam reforming on a commercial nickel catalyst at temperatures of around 500°C in a packed bed reactor. The synthesis-gas enters the reforming reactor at 300°C. Due to the strongly exothermic methanation-reaction the catalyst bed heats up to temperatures high enough to achieve sufficient catalyst activity for tar reforming. Ni-catalysts are sensitive for sulfur poisoning, therefore the main sulfur component in the hydrogen-rich synthesis-gas, hydrogen sulfide (H2S), is adsorbed in a packed bed reactor, filled with ZnO, upstream the tar reformer. Beside H2S there are further sulfur compounds in the gas stream which cannot be removed efficiently by means of ZnO. The aim of this work is to investigate whether it is possible to use a commercially available Co–Mo catalyst for hydrodesulfurization (HDS) upstream the ZnO-bed in order to convert organic sulfur compounds into H2S. Hydrodesulfurization processes are state-of-the-art in large-scale petrochemistry. The process-conditions in this common use-case differ from these in the application discussed within this work. To examine the ability of HDS in the process discussed here, specific HDS-tests and overall system tests were carried out with a synthesis-gas from a laboratory gasifier. The used synthesis-gas was produced with an allothermal fluidized bed gasifier with wood pellets as fuel. The HDS-catalyst started to show activity for hydrogenation of thiophene at a temperature of 350°C under atmospheric pressure. The use of hydrodesulfurization showed a positive influence on the catalyst deactivation of the subsequent Ni-catalyst.

Density Functional Theory Study of Thiophene Hydrodesulfurization on &lt;em&gt;&amp;gamma;&lt;/em&gt;-Mo&lt;sub&gt;2&lt;/sub&gt;N(100) Surface

利用密度泛函理论研究了γ-Mo2N（100）表面上的噻吩加氢脱硫（HDS）过程.噻吩在γ-Mo2N（100）表面上不同作用形式的结构优化结果显示,η5-Mo2N吸附构型最稳定,具有最大的吸附能（-0.56 eV）,此时噻吩通过S原子与Mo2原子相连平行表面吸附在四重空位（hcp位）.H原子和噻吩在hcp位发生稳定共吸附,hcp位是噻吩HDS的活性位点.噻吩在γ-Mo2N（100）表面进行直接脱硫反应,HDS过程分为S原子脱除和C4产物加氢饱和两部分.过渡态搜索确定了HDS最可能的反应机理及中间产物,首个H原子的反应需要最大的活化能（1.69 eV）,是噻吩加氢脱硫的控速步骤.伴随H原子的不断加入,噻吩在γ-Mo2N（100）表面上优先生成―SH和丁二烯,随后―SH加氢生成H2S,丁二烯加氢饱和生成2-丁烯和丁烷.由于较弱的吸附,H2S、2-丁烯和丁烷很容易在γ-Mo2N（100）表面脱附成为产物.

Asymmetric Hydrogenation of Thiophenes and Benzothiophenes

An efficient and highly asymmetric ruthenium-N-heterocyclic carbene-catalyzed hydrogenation of substituted thiophenes and benzothiophenes is described, providing a new strategy for the formation of valuable enantiomerically pure tetrahydrothiophenes and 2,3-dihydrobenzothiophenes.

Screening of Heterogeneous Multimetallic Nanoparticle Catalysts Supported on Metal Oxides for Mono-, Poly-, and Heteroaromatic Hydrogenation Activity

A series of oxide supported mono-, bi-, and trimetallic nanoparticle catalysts were synthesized and screened for catalytic activity for the hydrogenation of mono-, poly-, and heteroaromatic substrates. Seventy-two different catalysts were screened for catalytic activity for the hydrogenation of toluene, naphthalene, pyridine, indole, quinoline, thiophene, and benzothiophene under mild conditions; five of these seven substrates were successfully hydrogenated under the reaction conditions. Bulk kinetic studies, including temperature and pressure studies, were performed using select catalysts for the hydrogenation of one hydrocarbon (naphthalene) and one-heteroatom substituted-substrate (quinoline). A quinoline loading study was also conducted in which the ratio of substrate/catalyst was varied. Standard materials characterization techniques including transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), and X-ray diffraction (XRD) were also used to acquire information about the size, oxidation state, and crystallinity of the nanoparticle catalysts.

Thiophene hydrodesulfurization catalysis on supported Ru clusters: Mechanism and site requirements for hydrogenation and desulfurization pathways

Kinetic and isotopic methods were used to probe elementary steps and site requirements for thiophene hydrogenation and desulfurization on Ru metal clusters. Turnover rates for these reactions were unaffected by whether samples were treated in H 2 or H 2S to form metal and sulfide clusters, respectively, before reaction. These data, taken together with the rate and extent of sulfur removal from used samples during contact with H 2, indicate that active structures consist of Ru metal clusters saturated with chemisorbed sulfur at temperatures, pressures, and H 2S levels relevant to hydrodesulfurization catalysis. Turnover rates and isotopic data over a wide range of H 2, H 2S, and thiophene pressures are consistent with elementary steps that include quasi-equilibrated H 2 and H 2S heterolytic dissociation and thiophene binding with η 1(S) or η 4 coordination onto sulfur vacancies. We conclude that hydrogenation proceeds via addition of protons (H δ+, as –S–H δ+ from H 2 or H 2S dissociation) to η 4 thiophene species, while desulfurization involves C–S activation in η 1(S) species aided by H δ− species formed via H 2 dissociation. Reactant concentrations influence hydrogenation and desulfurization turnover rates to the same extent, suggesting that the involvement of similar active structures, consisting of vacancies on sulfur-covered Ru clusters. Smaller turnover rates and stronger H 2S inhibition on smaller Ru clusters for hydrogenation and desulfurization routes reflect the stronger sulfur binding and the smaller vacancy concentrations on small clusters, which contain exposed atoms with lower average coordination. A preference for η 1(S) over η 4 thiophene species at the higher sulfur coverages that prevail on smaller Ru clusters causes desulfurization and hydrogenation rate ratios to increase with decreasing cluster size. We conclude that hydrogenation and desulfurization routes require similar active sites and that weaker M–S bonds lead to higher concentrations of kinetically-relevant sulfur vacancies. These elementary steps and site requirements are likely to also prevail on metals and sulfides with M–S bond strengths similar or higher than Ru–S, for which vacancy sites are also present as minority species.

The influence of reducing and sulfiding conditions on the properties of unsupported MoS 2-based catalysts

Unsupported MoS 2 catalysts were obtained from the decomposition of ammonium tetrathiomolybdate (ATM) at variable temperatures (400–700 °C) and under different gas compositions, from pure H 2S to pure H 2. The catalysts were further studied in the non-promoted state or promoted by Ni and Co. Catalytic activity and selectivity were studied in the model reaction of thiophene hydrodesulfurization (HDS). Surface areas, crystalline phase and particle size distributions were determined by Brunauer–Emmet–Teller (BET), X-ray diffraction (XRD) and transmission electron microscopy (TEM), respectively. A comparison of average values calculated from these techniques has enabled the understanding of the morphology of the solids. The catalysts were characterized before and after catalytic tests by X-ray photoelectron spectroscopy (XPS), laser Raman spectroscopy (LRS) and temperature-programmed reduction (TPR). Comparison of catalytic activity trends with the results of the characterizations show that over-stoichiometric sulfur, present in the fresh catalysts in the form of edge-located S 2 2 - species, plays a key role for the activity of unsupported MoS 2 and for its ability to be promoted. Direct hydrogenation (HYD) of thiophene to butane occurs presumably with the participation of –SH groups, produced from the opening of S–S bridges by hydrogen. Whatever the gas atmosphere, any treatment leading to the removal of over-stoichiometric sulfur leads to a decrease in HYD selectivity. Thus, very similar catalytic properties were observed for MoS 2 annealed at 700 °C in pure H 2, H 2S or N 2 gases. Ni and Co introduced by means of reflux with acetylacetonates, gave identical promotion trends for all the MoS 2 samples. The solids treated in pure H 2S could not take up promoter atoms at the edges, whereas for the H 2-reduced samples high promotion levels were achieved. The degree of stacking does not seem to have a significant impact on the thiophene HDS activity and selectivity of the unsupported MoS 2 catalysts.

Pyrolysis Gasoline Hydrogenation in the Second-Stage Reactor: Reaction Kinetics and Reactor Simulation

The second-stage rector is the last unit in the purification of pyrolysis gasoline for production of aromatics. The feedstock contains a small amount of olefin and organic sulfur but a large amount of benzene as high as 51 wt %. It is therefore a difficulty to remove sulfur and olefin thoroughly while keeping the aromatics unconverted, since the reaction is normally conducted at 280−330 °C and 2.5−3.0 MPa in the presence of excessive hydrogen. To evaluate the property of a commercial catalyst LY-9802 with Co−Mo−Ni supported over γ-Al2O3, hydrogenation kinetics of thiophene, olefin, and benzene were measured, and the results show the catalyst is very active for the hydrogenation of thiophene and olefin but is inactive for the saturation of benzene. To simulate the operating behavior of the reactor, one-dimensional heterogeneous model was applied, and it was found that the gas−solid interfacial difference in temperature and concentration is negligible. From the variation of the operating variables, such as ...