Steam gasification reactivity of char from rapid pyrolysis of bio-oil/char slurry

A slurry of bio-oil and char originating from wood pyrolysis is a promising gasifier feed-stock because of its high energy density. When such a slurry is injected into a high temperature gasifier it undergoes a rapid pyrolysis yielding a char which then reacts with steam. The char produced by pyrolysis of an 80 wt% bio-oil/20 wt% char mixture at heating rates of 100-10,000 °C/s was subjected to steam gasification in a thermogravimetric analyzer. The original wood char from the bio-oil production was also tested. Gasification was conducted with 10-50 mol% steam at temperatures from 800 to 1200 °C. Reactivity of the slurry chars increased with pyrolysis heating rate, but was lower than that of the original chars. Kinetic parameters were established for a power-law rate model of the steam-char reaction, and compared to values from the literature. At temperatures over 1000 °C, the gasification rates appeared to be affected by diffusional resistance.     

Influence of temperature and alumina catalyst on pyrolysis of corncob

Corncob has been investigated as an alternative feedstock to obtain fuels and chemicals via pyrolysis in fixed-bed reactor. The influence of pyrolysis temperature in the range 300-800 °C as well as the catalyst effects on the products was investigated in detail and the obtained results were compared. The results indicated that a maximum oil yield of 22.2% was obtained at a moderate temperature of 600 °C. The oil yield was reduced when the temperature was increased from 600 to 800 °C, whereas the gas yield increased.Pyrolysis oils were examined by using instrumental analysis, ¹H NMR spectroscopy and GC/MS. This analysis revealed that the pyrolysis oils were chemically very heterogeneous at all temperatures. It was determined that the most abundant compounds composing the bio-oil were phenolics.It was observed that the catalyst decreased the reaction temperature. Most of the components obtained using a catalyst at moderate temperatures was close to those obtained at high temperatures without using a catalyst. Moreover, the use of a catalyst and the high temperatures of the reactions also decreased the amount of oxygenated compounds produced.According to these results, corncob bio-oils can be used as fuel and constitute a valuable source of chemical raw materials.     

Application of the Shvo catalyst in homogeneous hydrogenation of bio-oil obtained from pyrolysis of white poplar: New mild upgrading conditions

Upgrading of bio-oils obtained from the fast pyrolysis of biomasses requires the development of efficient catalysts able to work under mild conditions and to cope with the complex chemical nature of the reactant. The present work focuses on the use of the ruthenium based Shvo homogeneous catalyst for the hydrogenation of model mixtures (vanillin, cinnamaldehyde, methylacetophenone, glycolaldehyde, acetol, acetic acid) and of a real bio-oil. The hydrogenation of model compounds has been investigated both in mono- and biphasic mixtures under a P(H₂) = 10 atm in the temperature range of 90-145 °C varying the substrate to catalyst molar ratio from 2000:1 to 200:1. Employing the most active reaction conditions (substrate/catalyst 200:1, T = 145 °C, P(H₂) = 10 atm) the Shvo catalyst maintains its performances under acidic “bio-oil conditions” leading to the almost quantitative conversion of the polar double bonds within 1 h. The activity of the Shvo catalyst was also investigated for the hydrogenation of a bio-oil from poplar in solvent free conditions. Hydrogenation deeply changed the chemical nature of the pyrolysis oil. Aldehydes, ketones and non-aromatic double bonds were almost totally hydrogenated. The catalytic system also promoted the hydrolysis of sugar oligomers into monomers.     

Hydrogen production via catalytic steam reforming of fast pyrolysis bio-oil in a two-stage fixed bed reactor system

Hydrogen production was prepared via catalytic steam reforming of fast pyrolysis bio-oil in a two-stage fixed bed reactor system. Low-cost catalyst dolomite was chosen for the primary steam reforming of bio-oil in consideration of the unavoidable deactivation caused by direct contact of metal catalyst and bio-oil itself. Nickel-based catalyst Ni/MgO was used in the second stage to increase the purity and the yield of desirable gas product further. Influential parameters such as temperature, steam to carbon ratio (S/C, S/CH₄), and material space velocity (W_BHSV, GHSV) both for the first and the second reaction stages on gas product yield, carbon selectivity of gas product, CH₄ conversion as well as purity of desirable gas product were investigated. High temperature (> 850 °C) and high S/C (> 12) are necessary for efficient conversion of bio-oil to desirable gas product in the first steam reforming stage. Low W_BHSV favors the increase of any gas product yield at any selected temperature and the overall conversion of bio-oil to gas product increases accordingly. Nickel-based catalyst Ni/MgO is effective in purification stage and 100% conversion of CH₄ can be obtained under the conditions of S/CH₄ no less than 2 and temperature no less than 800 °C. Low GHSV favors the CH₄ conversion and the maximum CH₄ conversion 100%, desirable gas product purity 100%, and potential hydrogen yield 81.1% can be obtained at 800 °C provided that GHSV is no more than 3600 h^− 1. Carbon deposition behaviors in one-stage reactor prove that the steam reforming of crude bio-oil in a two-stage fixed bed reaction system is necessary and significant.     

Solid oxide derived from waste shells of Turbonilla striatula as a renewable catalyst for biodiesel production

Biodiesel production via transesterification of mustard oil with methanol using solid oxide catalyst derived from waste shell of Turbonilla striatula was investigated. The shells were calcined at different temperatures for 4 h and catalyst characterizations were carried out by X-ray diffraction (XRD), scanning electron microscope (SEM), energy dispersive spectrometer (EDS), Fourier transform infrared spectrometer (FT-IR), thermogravimetric analysis (TGA)/differential scanning calorimetry (DSC) and Brunauer-Emmett-Teller (BET) surface area measurements . Formation of solid oxide i.e. CaO was confirmed at calcination temperature of 800 °C. The effect of the molar ratio of methanol to oil, the reaction temperature, catalyst calcination temperature and catalyst amount used for transesterification were studied to optimize the reaction conditions. Biodiesel yield of 93.3% was achieved when transesterification was carried out at 65 ± 5 °C by employing 3.0 wt.% catalyst and 9:1 methanol to oil molar ratio. BET surface area indicated that the shells calcined in the temperature range of 700 °C-900 °C exhibited enhanced surface area and higher pore volume than the shells calcined at 600 °C. Reusability of the catalysts prepared in different temperatures was also investigated.     

Biofuels from waste fish oil pyrolysis: Continuous production in a pilot plant

Fast pyrolysis of waste fish oil was performed in a continuous pyrolysis pilot plant. The experiment was carried out under steady-state conditions in which 10 kg of biomass was added at a feed rate of 3.2 kg h⁻¹. A bio-oil yield of 72-73% was obtained with a controlled reaction temperature of 525 °C. The bio-oil was distilled to obtain purified products with boiling ranges corresponding to light bio-oil and heavy bio-oil. These biofuels were characterized according to their physico-chemical properties, and compared with the Brazilian-fuel specifications for conventional gasoline and diesel fuels. The results show that the fast pyrolysis process represents an alternative technique for the production of biofuels from waste fish oil with characteristics similar to petroleum fuels.     

Oxygen reducing activity of methanol-tolerant catalysts by high-temperature pyrolysis

This study demonstrates the feasibility of platinum-free catalysts, which exhibit not only a high activity in the oxygen reduction reaction (ORR) but also a high tolerance of methanol. A cobalt (II) tetramethoxyphenylporphyrin (CoTMPP) precursor was dispersed in N,N-dimethylmethanamide (DMF), which was ultrasonically stirred for 30 min to yield a homogeneous solution, and then filtered to remove the solvent. The CoTMPP precipitate was pyrolyzed at temperatures of 300, 500, 700 and 900 °C in N₂ atmosphere. Raman spectra include strong peaks at 1330 and 1550 cm^− 1, which are associated with the D- and G-peaks of pyrolyzed CoTMPP above 500 °C, revealing that the original porphyrin structure of CoTMPP yields a network structure of poly-aromatic hydrocarbons upon the pyrolysis. Pyrolyzed CoTMPP loaded on carbon blacks (CoTMPP/C) at 700 °C exhibits a higher ORR activity than other various pyrolysis temperatures. In a methanol-containing solution, pyrolyzed CoTMPP/C preferentially undergoes the ORR rather than the methanol oxidation reaction, and so exhibits a high tolerance of methanol. Pyrolyzed CoTMPP has the pyrrolic nitrogen, and part of the cobalt-containing nitrogen chelate is cleaved and bound to other atoms, forming Co―N_x―C_{y (x + y = 4),} which are responsible for the ORR activity and the high tolerance of methanol.     

Production of biodiesel through transesterification of Jatropha oil using KNO3/Al2O3 solid catalyst

The purpose of the work to study biodiesel production by transesterification of Jatropha oil with methanol in a heterogeneous system, using alumina loaded with potassium nitrate as a solid base catalyst. Followed by calcination, the dependence of the conversion of Jatropha oil on the reaction variables such as the catalyst loading, the molar ratio of methanol to oil, reaction temperature, agitation speed and the reaction time was studied. The conversion was over 84% under the conditions of 70 °C, methanol/oil mole ratio of 12:1, reaction time 6 h, agitation speed 600 rpm and catalyst amount (catalyst/oil) of 6% (w). Kinetic study of reaction was also done.     

Effects of particle size on the fast pyrolysis of oil mallee woody biomass

This study aims to investigate the effects of biomass particle size (0.18-5.6 mm) on the yield and composition of bio-oil from the pyrolysis of Australian oil mallee woody biomass in a fluidised-bed reactor at 500 °C. The yield of bio-oil decreased as the average biomass particle size was increased from 0.3 to about 1.5 mm. Further increases in biomass particle size did not result in any further decreases in the bio-oil yield. These results are mainly due to the impact of particle size in the production of lignin-derived compounds. Possible inter-particle interactions between bio-oil vapour and char particles or homogeneous reactions in vapour phases were not responsible for the decreases in the bio-oil yield. The bio-oil samples were characterised with thermogravimetric analysis, UV-fluorescence spectroscopy, Karl-Fischer titration as well as precipitation in cold water. It was found that the yields of light bio-oil fractions increased and those of heavy bio-oil fractions decreased with increasing biomass particle size. The formation of pyrolytic water at low temperatures (<500 °C) is not greatly affected by temperature or particle size. It is believed that decreased heating rates experienced by large particles are a major factor responsible for the lower bio-oil yields from large particles and for the changes in the overall composition of resulting oils. Changes in biomass cell structure during grinding may also influence the yield and composition of bio-oil.     

Effect of crystallization temperature on the in situ valorization of physic nut (Jatropha curcus L.) wastes using synthetic HZSM-5 catalyst

Physic nut waste is selected as the biomass feedstock for fast pyrolysis as it is available in large amounts from biodiesel production in Thailand. The volatile matter and fixed carbon contents are 73.8% and 13.6% while ash contents are 5.8%. Carbon is the main element with 49.03 wt%. The oxygen content of 39.0 wt% is considerably high which could directly convert to the oxygenated pyrolysis liquid products. To decrease oxygenated compounds, HZSM-5 was used as a catalyst to upgrade pyrolytic products from fast pyrolysis using analytical pyrolysis–GC/MS method. The HZSM-5 catalyst was successfully synthesized by hydrothermal method at 160–180 °C for 24 h. The particle size, surface area, and pore diameter were 11.25–15.52 μm, 567–582 m²/g, and 21.78–26.11 Å, respectively. The pyrolysis was performed at 500 °C with the Jatropha wastes to catalyst ratio of 1:1–1:10. The presence of HZSM-5 contributed to eliminate the undesirable oxygenated compounds such as acids and ketones which could alleviate problem regarding acidity and instability in bio-oil. In addition, it enhanced significantly the yields of desirable hydrocarbon compounds. The increase in catalyst contents had an effect on the enhancement of hydrocarbons yields, and tended to promote deoxygenation and denitrogenation. At moderate biomass to catalyst ratio (1:5), HZSM-5 synthesized at 170 °C contributed to improve the hydrocarbon yields of 95%, including mainly toluene and xylene, which are valuable products because of their high heating value properties.     

Formation of fullerenes by pyrolysis of perchlorofulvalene and its derivatives

In a retro-synthetic approach, [60]fullerene might be accessible by condensing six fulvalene fragments. In order to explore the potential of such a route for direct synthesis of [60]fullerene we have investigated the pyrolysis of perchlorofulvalene (PCF). Low temperature pyrolysis of PCF at 250 °C resulted mainly in the formation of dimers, trimers, tetramers and products of subsequent intramolecular condensation of these oligomers. Increasing the temperature to 300-350 °C leads to the formation of perchlorinated polynuclear aromatic hydrocarbons. Pyrolysis at 400-450 °C gives a cross-linked polymer structure which is the result of intermolecular condensation of the polynuclear aromatic intermediates. Pyrolysis at higher temperatures (>500 °C) mainly leads to graphite. It was found that the two-step pyrolysis of PCF (heating first at 450 °C, after that at 750 °C) yielded a fullerene containing soot via an intermediate polynuclear aromatic net. High temperature rearrangement of the latter gave fullerenes C₆₀ and C₇₀. The best results were obtained when a PCF oligomer obtained by Ullmann condensation was used as a precursor. By two-step pyrolysis and further high vacuum sublimation of the soot the fullerenes C₆₀ and C₇₀ were obtained in extractable amounts.     

Pyrolysis characteristics of Oriental white oak: Kinetic study and fast pyrolysis in a fluidized bed with an improved reaction system

The kinetic parameters for the pyrolysis of Oriental white oak were evaluated by thermogravimetric analysis (TGA). The white oak was pyrolyzed in a fluidized bed reactor with a two-staged char separation system under a variety of operating conditions. The influence of the pyrolysis conditions on the chemical and physical characteristics of the bio-oil was also examined. TGA showed that the Oriental white oak decomposed at temperatures ranging from 250 to 400 °C. The apparent activation energy ranged from 160 to 777 kJ mol^− 1. The optimal pyrolysis temperature for the production of bio-oil in the fluidized bed unit was between 400 and 450 °C. A much smaller and larger feed size adversely affected the production of bio-oil. A higher fluidizing gas flow and higher biomass feeding rate were more effective in the production of bio-oil but the above flow rates did not affect the bio-oil yields significantly. Recycling a part of the product gas as a fluidizing medium resulted the highest bio-oil yield of 60 wt.%. In addition, high-quality bio-oil with a low solid content was produced using a hot filter as well as a cyclone. With exception of the pyrolysis temperature, the other pyrolysis conditions did not significantly affect the chemical and physical characteristics of the resulting bio-oil.     

Hydrothermal alteration of sedimentary organic matter in the presence and absence of hydrogen to tar then oil

Hydrothermal alteration (hydrous pyrolysis) experiments, in the absence and presence of H₂ (reductive), were conducted on organic matter from marine and lacustrine sediments. The experiments were carried out at discrete temperatures from 150 °C to 350 °C to assess the yields and compositions of the bitumen (tar) formed and subsequently at higher temperatures the oil generated. The yield of bitumen was observed to increase with increasing temperatures. Under hydrous pyrolysis conditions with hydrogen, the yield increases by an order of magnitude and immature lacustrine organic matter shows the highest yield. Bitumen, the extractable organic matter at temperatures below 250-300 °C, contains mainly polar compounds, an unresolved complex mixture (UCM) of branched and cyclic compounds, with low amounts of saturated hydrocarbons. The polar compounds include n-alkanoic acids, n-alkanedioic acids, n-alkanols, isoprenoid ketones and methyl alkanoates. At temperatures above 300 °C, the bitumens transform into petroleum products with saturated hydrocarbons (n-alkanes and biomarkers) and UCM as the major components (>95% of total yield). The degree of maturation of the generated oil increases with increasing temperature under both pyrolysis conditions to full maturity at >350 °C. Although, the bitumen yield is much higher under conditions with added hydrogen, the maturity of the generated oil is lower than with just hydrous pyrolysis.     

Poly-dimethylsiloxane (PDMS) based micro-reactors for steam reforming of methanol

A miniaturized methanol steam reformer with a serpentine type of micro-channels was developed based on poly-dimethylsiloxane (PDMS) material. This way of fabricating micro-hydrogen generator is very simple and inexpensive. The volume of a PDMS micro-reformer is less than 10 cm³. The catalyst used was a commercial Cu/ZnO/Al₂O₃ reforming catalyst from Johnson Matthey. The Cu/ZnO/Al₂O₃ reforming catalyst particles of mean diameter 50-70 μm was packed into the micro-channels by injecting water based suspension of catalyst particles at the inlet point. The miniaturized PDMS micro-reformer was operated successfully in the operating temperatures of 180-240 °C and 15%-75% molar methanol conversion was achieved in this temperature range for WHSV of 2.1-4.2 h⁻¹. It was not possible to operate the micro-reformer made by pure PDMS at temperature beyond 240 °C. Hybrid type of micro-reformer was fabricated by mixing PDMS and silica powder which allowed the operating temperature around 300 °C. The complete conversion (99.5%) of methanol was achieved at 280 °C in this case. The maximum reformate gas flow rate was 30 ml/min which can produce 1 W power at 0.6 V assuming hydrogen utilization of 60%.     

The influence of a new fabrication procedure on the catalytic activity of ruthenium-selenium catalysts

A new procedure has been introduced to enhance catalytic activity of ruthenium-selenium electro-catalysts for oxygen reduction, in which materials are treated under hydrogen atmosphere at elevated temperatures. The characterisation using scanning electron microscopy, energy dispersive spectroscopy or energy dispersive X-ray spectroscopy exhibited that the treatment at 400 °C made catalysts denser while their porous nature remained, led to a good degree of crystallinity and an optimum Se:Ru ratio. The half cell test confirms feasibility of the new procedure; the catalyst treated at 400 °C gave the highest reduction current (55.9 mA cm⁻² at −0.4 V) and a low methanol oxidation effect coefficient (3.8%). The direct methanol fuel cell with the RuSe 400 °C cathode catalyst (2 mg RuSe cm⁻²) generated a power density of 33.8 mW cm⁻² using 2 M methanol and 2 bar oxygen at 90 °C. The new procedure produced the catalysts with low decay rates. The best sample was compared to the Pt and to the reported ruthenium-selenium catalyst. Possible reasons for the observations are discussed.     

Titanium-doped alumina for catalytic dehydration of methanol to dimethyl ether at relatively low temperatures

Mesoporous Al-Ti oxide composites with molar %Ti of 3, 5, 10, and 20 as well as pure γ-alumina were prepared using a template-free sol-gel method in the absence of a catalyst. The prepared composites were characterized by powder XRD, FTIR spectroscopy and N₂ adsorption for BET surface area and porosity measurements. The composites and the pure alumina possessed relatively high surface areas, 350-410 m²/g, and high porosities after calcination at 500 °C. FTIR spectroscopy was employed to study the products of the catalytic dehydration of methanol to dimethyl ether, DME, over the prepared catalysts at reaction temperatures between 180 and 300 °C. Compared with pure γ-alumina, the Ti-modified alumina with %Ti < 10 showed higher catalytic activity in the methanol dehydration and better selectivity to DME. Composites with %Ti of 3 and 5 showed the highest activity at relatively lower temperatures than the other catalysts where they showed their highest activity at 190 and 200 °C, respectively. The activity of all studied catalysts slightly decreased as the temperature was raised to 300 °C and dropped considerably when the temperature was decreased to 180 °C. However, the activity of Al-Ti-3 dropped only slightly at both temperatures. The selectivity to DME was dependent on the reaction temperature where 100% DME selectivity was obtained at temperatures ?220 °C and as the temperature was raised to 300 °C, some CH₄ and CO₂ formed on the account of DME.     

Comparison of the univariate and multivariate methods in the optimization of experimental conditions for determining Cu, Pb, Ni and Cd in biodiesel by GFAAS

Experimental design was used as a tool to define the optimum pyrolysis and atomization temperatures for four analytes (Cu, Pb, Ni and Cd) in biodiesel samples. Two chemical modifiers (Pd + Mg and W) and two distinct sample preparation procedures (microemulsion and wet digestion in a focused microwave system) were also investigated. The pyrolysis and atomization temperatures were optimized using 2⁴ factorial design for Cu, Pb, Ni and Cd, with 16 assays carried out for each analyte. The results for Cu and Pb indicated that variables of sample preparation for digestion by focused microwave was the most important one for both analytes. The pyrolysis and atomization temperatures applied were 1000 °C and 2200 °C for Cu and 500 °C and 2000 °C for Pb. None of the variables analyzed here were important for Ni, and the pyrolysis and atomization temperatures chosen for this element were 800 °C and 2300 °C. A different factorial design was used for Cd. The variables of medium and modifier were not important for this element, and the lowest temperatures, Tp-500 °C and Ta-1400 °C, were chosen based on this second design. The importance of factorial design in the simultaneous optimization of several variables studied by GFAAS was confirmed, for it involves fewer experiments and hence, lower costs, greater speed and higher efficiency.     

Deactivating species in the transformation of crude bio-oil with methanol into hydrocarbons on a HZSM-5 catalyst

A study has been carried out by using different techniques (TPO, FTIR, Raman, ¹³C NMR, GC/MS of the coke dissolved in CH₂Cl₂) on the nature of the coke deposited on a HZSM-5 catalyst modified with Ni in the transformation of the crude bio-oil obtained by flash pyrolysis of lignocellulosic biomass (pine sawdust) into hydrocarbons. The reaction system has two steps in-line. In the first one, the components of crude bio-oil derived from the pyrolysis of biomass lignin are polymerized at 400 °C. In the second one, the remaining volatile oxygenates are transformed into hydrocarbons in a fluidized bed catalytic reactor at 450 °C. The reaction has been carried out with different bio-oil/methanol mass ratios in the feed (from 100/0 to 0/100). Co-feeding methanol significantly attenuates coke deposition, and the nature of the coke components varies according to the bio-oil/methanol ratio in the feed. When bio-oil is co-fed, the coke deposited on the catalyst has a significant content of oxygenates and oxo-aromatics and consists of two fractions, identified by temperature programmed oxidation, corresponding to external and internal coke in the zeolite crystals. The fraction of external coke is soluble in CH₂Cl₂, with a high content of oxygenates and oxo-aromatics, and is generated by polymerization of products derived from biomass lignin pyrolysis activated by the zeolite acid sites. The fraction of coke retained within the zeolite crystals is partially insoluble and is formed by several routes: from the intermediates in the transformation of both methanol and bio-oil oxygenates into hydrocarbons; by evolution of the other coke fraction; from the hydrocarbons (with high aromatics content) in the reaction medium.     

Continuous synthesis of metal nanoparticles in supercritical methanol

Metal nanoparticles were synthesized continuously in supercritical methanol (scMeOH) without using reducing agents at a pressure of 30 MPa and at various reaction temperatures ranging 150-400 °C. Wide angle X-ray diffraction (WAXD) analysis revealed that metallic nickel (Ni) nanoparticles were synthesized at a reaction temperature of 400 °C while mixtures of nickel hydroxide (α-Ni(OH)₂) and metallic Ni were produced at lower reaction temperatures of 250-350 °C. In contrast, metallic silver (Ag) nanoparticles were produced at reaction temperatures above 150 °C while metallic cupper (Cu) nanoparticles were produced at reaction temperatures above 300 °C. Mixtures of copper oxide (CuO and Cu₂O) and metallic Cu were produced at lower reaction temperatures of 250 °C. Scanning electron microscopy (SEM) showed that the particles size and morphology changed drastically as the reaction temperature increased. The average diameters of Ni, Cu and Ag particles synthesized at 400 °C were 119 ± 19 nm, 240 ± 44 nm, and 148 ± 32 nm, respectively. The scMeOH acted both as a reaction medium and a reducing agent. A possible reduction mechanism in scMeOH is also presented.     

Transesterification of palm oil and esterification of palm fatty acid in near- and super-critical methanol with SO4-ZrO2 catalysts

Sulfated zirconia (SO₄-ZrO₂) catalysts, prepared with three different sulfur loading contents (0.75%, 1.8% and 2.5%) at two calcination temperatures (500 °C and 700 °C), were tested for use in the transesterification of purified palm oil (PPO) and the esterification of palm fatty acid (PFA) in near-critical and super-critical methanol. Techniques including BET, XRD, NH₃- and CO₂-TPD revealed that the sulfur content and calcination temperature strongly affects the catalyst base-acid site, specific surface area, average pore size, phase structure, and thus the catalytic reactivity. The most suitable sulfur loading content was found to be 1.8% and the optimum calcination temperature 500 °C. The results show that the use of SO₄-ZrO₂ reduces esterification reaction times, the amount of methanol necessary and the required reaction temperature. The reactions at 250 °C in the presence of the SO₄-ZrO₂ catalyst at 0.5 w/w% catalyst to PPO or PFA were found to give the highest FAMEs conversions. Under these conditions, 90% and 75% conversions were achieved within 10 and 1 min from PPO (at 25:1 MeOH:PPO molar ratio) and PFA (at 6:1 MeOH:PFA molar ratio), respectively.