Isothermal pVTmeasurements on gas hydrocarbon mixtures using a vibrating-tube apparatus

Measurements of the ( pρT) properties of three natural gas mixtures were carried out at temperatures from 265 K to 335 K and at pressures up to 15 MPa using a densimeter consisting mainly of a DMA 512P measuring cell and a DMA 60 evaluating unit (Anton Paar, Graz, Austria). Four isotherms {(253.15, 273.15, 293.15 and 323.15) K} and seven pressure levels from 0.1 MPa to 15 MPa were investigated for each natural gas mixture at densities ranging from 6 kg · m  ^− 3to 212 kg · m  ^− 3. The natural gas mixtures were two real gases from transport pipelines systems of natural gas distributors in the Czech Republic. One sample contained natural gas with nitrogen addition. Four equations of state were examined. The relative deviations of calculated density values from the EOS ranged from (  − 5.8 to 1.8) per cent. The best results were obtained from the AGA8-DC92 EOS, with the relative deviations of calculated density value being within the range (  − 0.02 to 0.02) per cent.     

Reforming of CO<Subscript>2</Subscript>-Containing Natural Gas Using an AC Gliding Arc System: Effects of Operational Parameters and Oxygen Addition in Feed

In this research, the reforming of simulated natural gas containing a high CO₂ content under AC non-thermal gliding arc discharge with partial oxidation was conducted at ambient temperature and atmospheric pressure, with specific regards to the concept of the direct utilization of natural gas. This work aimed at investigating the effects of applied voltage and input frequency, as well as the effect of adding oxygen on the reaction performance and discharge stability in the reforming of the simulated natural gas having a CH₄:C₂H₆:C₃H₈:CO₂ molar ratio of 70:5:5:20. The results showed marked increases in both CH₄ conversion and product yield with increasing applied voltage and decreasing input frequency. The selectivities for H₂, C₂H₆, C₂H₄, C₄H₁₀, and CO were observed to be enhanced at a higher applied voltage and at a lower frequency, whereas the selectivity for C₂H₂ showed an opposite trend. The use of oxygen was found to provide a great enhancement of the plasma reforming of the simulated natural gas. For the combined plasma and partial oxidation in the reforming of CO₂-containing natural gas, air was found to be superior to pure oxygen in terms of reactant conversions, product selectivities, and specific energy consumption. The optimum conditions were found to be a hydrocarbons-to-oxygen feed molar ratio of 2/1 using air as an oxygen source, an applied voltage of 17.5 kV, and a frequency of 300 Hz, in providing the highest CH₄ conversion and synthesis gas selectivity, as well as extremely low specific energy consumption. The energy consumption was as low as 2.73 × 10⁻¹⁸ W s (17.02 eV) per molecule of converted reactant and 2.49 × 10⁻¹⁸ W s (16.60 eV) per molecule of produced hydrogen.     

Method for the determination of the solubility of gases in liquids

A rapid and experimentally simple method for the determination of the solubilities of oxygen or hydrogen in liquids is presented The method employs a membrane-enclosed amperometric detector of the well known Clark type to measure the partial pressure of the gas when distributed at equilibrium between the liquid and a gas space for a series of internal volumes of the system. The amounts of all substances and the temperature are maintained constant throughout the series although the internal pressure changes as a result of the volume changes. The glass apparatus is water jacketed for temperature control, has inlet and outlet ports for gas, and the amperometric sensor is mounted in a gas-tight sliding fitting for effecting the volume changes. The liquid content is vigorously stirred by a magnetic bar during measurements. Equations for the interpretation of results at different internal volumes take into account the conservation of the solvent and of the gas, the dependence of the volume of the liquid on the concentration of dissolved gas and Henry's law describing the distribution of the gas between gas and liquid phases at equilibrium. The solution of these equations yields an equation for the dependence of the measured partial pressure on volume, which includes the Henry's law constant H as a parameter. Conditions can usually be arranged to give a straight line dependence of volume on the reciprocal of partial pressure. The method has been applied to several common liquids, and has been shown to produce results which agree with literature solubilities to within about ±5%. Examples which have been studied include oxygen in water (H=4.039 × 10⁶ kPa at 20°C), in acetone (1.25 × 10⁵ kPa at 20°C), in ethanol (1.758 × 10⁵ kPa at 20°C) and in toluene (1.05 × 10⁵ kPa at 20°C) as well as hydrogen in water (6.89 × 10⁶ kPa at 20°C).     

Application of hydroxy sodalite films as novel water selective membranes

Supported hydroxy sodalite (H-SOD) membranes were prepared on α-alumina disks using direct hydrothermal synthesis at 413 K for 3.5 h. The continuity of the membranes was verified using single gas permeation of He and N₂ at ambient conditions. The membranes were impermeable to N₂ and He, which validated absence of defects in the membrane structure. The membranes were used in dewatering several organic alcohol/water mixtures (organic alcohol being: methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, 1-pentanol, and 2-pentanol). The influence of feed temperature (303–473 K), feed concentration (0–100 mol% alcohol in the feed), and absolute feed pressure (1.6–2.4 MPa) on the water flux were analyzed. The absolute feed pressure had no effect on the water permeance. The membrane exhibited a water/alcohol separation factor larger than 10⁶ and showed excellent thermal, mechanical, and operation stability in continuously dehydrating a water/ethanol mixture (72 mol% water) by pervaporation at 473 K and 2.2 MPa for 125 h. The normalized water flux correlated well with the water feed concentration for the primary alcohols. Below 40 mol% water in mixtures with secondary alcohols the water flux was three orders of magnitude lower. The water mobility through the membrane had an activation energy of ∼15 kJ/mol.     

Development of a new gas sensor for binary mixtures based on the permselectivity of polymeric membranes: Application to carbon dioxide/methane and carbon dioxide/helium mixtures

Membrane-based gas sensors were developed and used for determining the composition on bi-component mixtures in the 0-100% range, such as oxygen/nitrogen and carbon dioxide/methane (biogas). These sensors are low cost and are aimed at a low/medium precision market.The paper describes the use of this sensor for two gas mixtures: carbon dioxide/methane and carbon dioxide/helium. The membranes used are poly(dimethylsiloxane) (PDMS) and Teflon-AF hollow fibers. The response curves for both sensors were obtained at three different temperatures. The results clearly indicate that the permeate pressure of the sensors relates to the gas mixture composition at a given temperature. The data is represented by a third order polynomial. The sensors enable quantitative carbon dioxide analysis in binary mixtures with methane or helium. The response of the sensors is fast (less than 50 s), continuous, reproducible and long-term stable over a period of 2.3×10⁷ s (9 months). The absolute sensitivity of the sensors depends on the carbon dioxide feed concentration ranging from 0.03 to 0.13 MPa.     

Conductivity of Dilute Aqueous Electrolyte Solutions at High Temperatures and Pressures Using a Flow Cell

A flow-through electrical conductance cell was assembled in order to measuremolar conductances of dilute aqueous electrolytes with a high degree of accuracyat high temperatures and pressures. The design of the cell is based on the conceptdeveloped at the University of Delaware and built in 1995, with modificationsthat will allow the cell to operate at much higher temperatures (to 600°C) andpressures (to 300 MPa). At present, the cell has been tested successfully bymeasuring aqueous (10^–4-10^–3 mol-kg^–1) solutions of LiCl, NaCl, and KCl attemperatures 25–410°C and pressures 9.8–33 MPa. The results are in goodagreement with reported values, including those measured with the Delawareflow-through cell. These new results are also complementary to our previousresults, which were measured with a static high-pressure cell. Measurements attemperatures near the critical point of water (374°C, 22.1 MPa) require the useof lower solution concentrations that were unachievable in the past with thestatic cell.     

CO在超临界水中的转化以及碱性钾盐的影响

构建了CO高压溶解的进气系统,在连续式反应系统中对超临界水条件下CO的转化规律进行了研究;针对生物质超临界水气化中钾盐的多样性,选择KHCO₃、K₂CO₃和KOH等三种钾盐成分,研究了它们在不同工艺条件（450-600℃、23-29 MPa、停留时间3-6 s）下对超临界水中水煤气转化过程的影响。结果表明,在无催化条件下,提高反应温度、延长停留时间均提高了CO的转化率,而压力对其影响在低压下（23-25 MPa）比较大,高压下（25-29 MPa）比较小,水煤气转化的反应动力学方程为k=10^3.75×exp（-0.66×10⁵/RT）（s^-1）。碱性钾盐均能显著提高CO转化率,其催化促进程度从大到小依次为：KHCO₃>K₂CO₃>KOH。添加碱性钾盐时,提高反应温度、延长停留时间均提高CO转化率,而压力的影响比较复杂。碱性盐对水煤气转化反应的催化是通过草酸盐（HC₂O₄^-）和甲酸盐（HCOO^-）作为中间产物进行的。     

Effect of pressure on the solubilities ofo-,m- andp-xylene in water

The solubilities of o-, m- and p-xylene in water were measured at 25.0°C up to 250, 385, and 50 MPa, respectively. The solubility increased with increasing pressure up to 120 MPa (50 MPa for p-xylene) and then decreased. The reaction volumes, V^o accompanying the dissolution at 0.1 MPa were estimated as –3.6±0.5, –3.4±0.5, and –4.1±0.5 cm³-mol^–1 for o-, m-, and p-xylene, respectively, from the pressure dependences of the solubilities. The limiting partial molar volumes, of p- and o-xylene in water under high pressure were estimated from V^o and the molar volume of the xylene. The partial molar volumes decreased with increasing pressure. The reaction volume for the formation of intra-molecular pairwise hydrophobic interaction between the methyl groups, as proposed by Ben-Naim, is discussed for the V^o of p- and o-xylene at 0.1 MPa.     

Near-infrared spectra of water and aqueous electrolyte solutions at high pressures

The near-infrared spectra (9500 to 11000 cm^–1) of pure water and aqueous solutions of alkali halides, MgCl₂, NaClO₄, and R₄NBr were measured at temperatures between 10 and 55°C and pressures up to 500 MPa. From the analysis of the absorption spectra the following conclusions are drawn. (1) The ice I-like open structure is destroyed and the packed structure is formed as the pressure is increased. (2) The open structure of water is destroyed by the addition of alkali halides and MgCl₂ and water molecules are restricted around the ions by ion-dipole interactions. This results in a loosening of the O–H bond. (3) The perchlorate ion destroys the open structure of water and the ion-dipole interaction with water is insignificant. (4) The Bu₄N⁺ ion forms water structure around the ion similar to that of the clathrate open structure.     

Measurement and calculation of gas compressibility factor for condensate gas and natural gas under pressure up to 116 MPa

The volumetric properties of two reservoir fluid samples collected from one condensate gas well and one natural gas well were measured under four groups of temperatures, respectively, with pressure up to 116 MPa. For the two samples examined, the experimental results show that the gas compressibility factor increases with the increase of pressure. But the influence of the temperature is related to the range of the experimental pressure. It approximately decreases with the increase of temperature when the pressure is larger than (45 to 50) MPa, while there is the opposite trend when the pressure is lower than (45 to 50) MPa. The dew point pressure was also determined for the condensate gas sample, which decreases with the increase of temperature. The capabilities of four empirical correlations and a thermodynamic model based on equation of state for describing gas compressibility factor of reservoir fluids under high pressure were investigated. The comparison results show that the thermodynamic model recommended is the most suitable for fluids whatever produced from high-pressure reservoirs or conventional mild-pressure reservoirs.     

Influence of biomass on hydrodynamics of an internal loop airlift reactor

The effect of the biomass presence on the overall circulation velocity, the linear velocities both in the riser and the downcomer and the overall gas hold-up was studied in a three-phase internal loop airlift reactor (ILALR). The measured data were compared with those obtained using a two-phase system (air—water). All experiments were carried out in a 40 dm³ ILALR at six different biomass concentrations (ranging from 0 g dm⁻³ to 7.5 g dm⁻³), at a temperature of 30°C, under atmospheric pressure. Air and water were used as the gas and liquid model media, respectively. Pellets of Aspergillus niger produced during the fermentation of glucose to gluconic acid in the ILALR were considered solid phase. In addition, liquid velocities were measured during the fermentation of glucose to gluconic acid using Aspergillus niger. All measurements were performed in a bubble circulation regime. At given experimental conditions the effect of the biomass on the circulation velocities in the ILALR was negligible. However, increasing of the biomass concentration led to lower values of the total gas hold-up. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Tuning methane content in gas hydrates via thermodynamic modeling and molecular dynamics simulation

Storage and transportation of natural gas as gas hydrate (“gas-to-solids technology”) is a promising alternative to the established liquefied natural gas (LNG) or compressed natural gas (CNG) technologies. Gas hydrates offer a relatively high gas storage capacity and mild temperature and pressure conditions for formation. Simulations based on the van der Waals–Platteeuw model and molecular dynamics (MD) are employed in this study to relate the methane gas content/occupancy in different hydrate systems with the hydrate stability conditions including temperature, pressure, and secondary clathrate stabilizing guests. Methane is chosen as a model system for natural gas. It was found that the addition of about 1% propane suffices to increase the structure II (sII) methane hydrate stability without excessively compromising methane storage capacity in hydrate. When tetrahydrofuran (THF) is used as the stabilizing agent in sII hydrate at concentration between 1% and 3%, a reasonably high methane content in hydrate can be maintained (∼85–100, v/v) without dealing with pressures more than 5 MPa and close to room temperature.     

Metal carbonyl catalysis of carbon monoxide and formate reactions

The water gas shift reaction (CO + H₂O = CO₂+ H₂) is catalyzed by aqueous metal carbonyl systems derived from simple mononuclear carbonyls such as Fe(CO)₅ and M(CO)₆ (M = Cr, Mo, and W) and bases in the 140–200 °C temperature range. The water gas shift reaction in a basic methanol-water solution containing Fe(CO)₅ is first order in [Fe(CO)₅], zero order in [CO], and essentially independent of base concentration and appears to involve an associative mechanism with a metallocarboxylate intermediate [(CO)₄Fe-CO₂H]^–. The water gas shift reactions using M(CO)₆ as catalyst precursors are first order in [M(CO)₆], inverse first order in [CO], and first order in [HCO₂ ^–] and appear to involve a dissociative mechanism with formatometallate intermediates [(CO)₅M-OCHO]^–.The Reppe hydroformylation of ethylene to produce propionaldehyde and 1-propanol in basic solutions containing Fe(CO)₅ occurs at 110–140 °C. This reaction is second order in [Fe(CO)₅], first order in [C₂H₄] up to a saturation pressure >1.5 MPa, and inhibited by [CO]. These experimental results suggest a mechanism where the rate-determining step involves a binuclear iron carbonyl intermediate. The substitution of Et₃N for NaOH as the base facilitates the reduction of propionaldehyde to 1-propanol but results in a slower rate for the overall reaction.The homogeneous photocatalytic decomposition of the formate ion to H₂ and CO₂ in the presence of Cr(CO)₆ appears to be closely related to the water gas shift reaction. The rate of H₂ production from the formate ion exhibits saturation kinetics in the formate ion and is inhibited by added pyridine. The infrared spectra of the catalyst solutions indicate an LCr(CO)₅ intermediate. Photolysis of the Cr(CO)₆/formate system in aqueous methanol in the presence of an aldehyde RCHO (R =n-heptyl,p-tolyl, andp-anisyl) results in catalytic hydrogenation of the aldehyde to the corresponding alcohol RCH₂OH by the formate ion. Detailed kinetic studies onp-tolualdehyde hydrogenation by this method indicates saturation kinetics in formate ion, autoinhibition by thep-tolualdehyde, and a threshold effect for Cr(CO)₆ at concentrations >0.004 mol L^–1. The presence of an aldehyde can interrupt the water gas shift catalytic cycle by interception of an HCr(CO)₅ ^– intermediate by the aldehyde.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1533–1539, September, 1994.     

Determination of arsenic and arsenic compounds in natural gas samples

Organic arsenic compounds (trialkylarsines) present in natural gas were extracted by 10 cm³ of concentrated nitric acid from 1 dm³ of gas kept at ambient pressure and temperature. The flask containing the gas and the acid was shaken for 1 h on a platform shaker set at the highest speed. The resulting solution was mixed with concentrated sulfuric acid and heated to convert all arsenic compounds to arsenate. Total arsenic was determined in the mineralized solutions by hydride generation. The arsenic concentrations in natural gas samples from a number of wells in several gas fields were in the range 0.01–63 μ As dm^?3. Replicate determinations of arsenic in a gas sample with an arsenic concentration of 5.9 μ dm^?3 had a relative standard deviation of 1.7%. Because of the high blank values, the lowest arsenic concentration that could be reliably determined was 5 ng As dm^?3 gas. Analysis of nonmineralized extracts by hydride generation identified trimethylarsine as the major arsenic compound in natural gas. Low-temperature gas chromatography-mass spectrometry showed more directly than the hydride generation technique, that trimethylarsine accounts for 55–80% of the total arsenic in several gas samples. Dimethylethylarsine, methyldiethylarsine, and triethylarsine were also identified, in concentrations decreasing with increasing molecular mass of the arsines.     

A Uniformly Oriented MFI Membrane for Improved CO2 Separation

Membrane separation of CO₂ from natural gas, biogas, synthesis gas, and flu gas is a simple and energy‐efficient alternative to other separation techniques. But results for CO₂‐selective permeance have always been achieved by randomly oriented and thick zeolite membranes. Thin, oriented membranes have great potential to realize high‐flux and high‐selectivity separation of mixtures at low energy cost. We now report a facile method for preparing silica MFI membranes in fluoride media on a graded alumina support. In the resulting membrane straight channels are uniformly vertically aligned and the membrane has a thickness of 0.5 μm. The membrane showed a separation selectivity of 109 for CO₂/H₂ mixtures and a CO₂ permeance of 51×10^?7 mol m^?2 s^?1 Pa^?1 at ?35 °C, making it promising for practical CO₂ separation from mixtures.     

Water splitting in low-temperature ac plasmas at atmospheric pressure

Plasma-induced water splitting at atmospheric pressure has been studied with a novel fan-type Pt reactor and several tubular-type reactors: an all-quartz reactor, a glass reactor, and three metal reactors with Pt. Ni, and Fe as electrodes. Reaction products have been analyzed by using GC (gas chromatography) and Q-MS (quadrupole mass spectrometry). Optical emission spectroscopic studies of the process have been carried out by employing a CCD (charge-coupled device) detector. Water splitting with tubular quartz and glass reactors is probably non-catalytic. However, a heterogeneous catalytic function of surface of metal electrodes has been observed. The variation of hydrogen yield (Y_H) and energy efficiency (E_e) with operational parameters such as input voltages (U_in), flow rates of carrier gas (F_He), and concentrations of water (C_W) has been examined. Plasma-induced water splitting can be described with a kinetic equation of-dC_w/dt = kC_W ^0.2. The rate constants at 3.25 kV are 2.8 × 10⁻⁴, 3.5 × 10⁻³, and 3.4 × 10⁻² mol^0.8L^−0.8 min⁻¹ for tubular glass reactor, a tubular Pt reactor, and a fan-type Pt reactor, respectively. A CSTR (continuous-stirred tank reactor) and PFR (piston-flow reactor) model have been applied to a fan-type reactor and tubular reactor, respectively. A mechanism on the basis of optical emission spectroscopic data has been obtained comprising the energy transfer from excited carrier gas species to water molecules, which split via radicals of HO^·, O^·, and H^· to form H₂ and O₂. The fan-type Pt reactors exhibit highest activity and energy efficiency among the reactors tested. Higher yields of hydrogen are achieved at higher input voltages, low flow rates, and low concentrations of water (Y_H = 78 % at U_in of 3.75 kV, F_He of 20 mL/min, and C_W of 0.86 %). The energy efficiency exhibits an opposite trend (E_e = 6.1 % at U_in of 1.25 kV, F_He of 60 mL/min and C_W of 3.1 %).     

Prediction of water content of sour and acid gases

Estimating the feasibility of acid gas geological disposal requires the knowledge of the water content of the gas phase at moderate pressures and temperatures (typically below 50 MPa, below 380 K) and up to 6 mol NaCl. In this paper, a non-iterative model is developed to predict the water content of sour and acid gases at equilibrium with pure water and brine. This model is based on equating the chemical potential of water and using the modified Redlich–Kwong equation of state to calculate the fugacity of the gas phase. The water content of pure CH₄, CO₂ and H₂S are represented with average absolute deviations of less than 3.36, 7.04 and 8.4%, respectively. Experimental data of the water content of mixtures of the acid gases were reproduced with average absolute deviations of less than 6.32%.     

Densities and Apparent Molar Volumes of Aqueous H<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript>BO<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript> Solutions at Temperatures from 296 to 573 K and at Pressures up to 48 MPa

Densities of four aqueous H₃BO₃ solutions (0.062, 0.155, 0.315, and 0.529 mol-kg^–1) have been measured in the liquid phase with a constant volume piezometer immersed in a precisely controlled liquid thermostat. Measurements were made at temperatures between 296 and 573 K and pressures from 0.82 to 48 MPa. The total uncertainties of the density, pressure, temperature, and molality measurements were estimated to be less than 0.06%, 0.05%, 10 mK, and 0.0005 mol-kg^–1, respectively. The accuracy of the method was confirmed by PVT measurements on pure water for two isobars (30 and 39 MPa) at temperatures from 313 to 573 K. The experimental and calculated (IAPWS formulation) densities for pure water show excellent agreement which is within their experimental uncertainties (average absolute deviation, AAD=0.012%;). Apparent and partial molar volumes were derived using the measured densities for solutions and pure water, and these results were extrapolated to zero concentration to yield the partial molar volumes of the electrolyte (H₃BO₃) at infinite dilution. The temperature, pressure, and concentration dependencies of the apparent and partial molar volumes were studied. Small pressure and concentration effects on the apparent molar volumes were found at temperatures up to 500 K. The parameters of a polynomial type of equation of state for the specific volume V_sol(P, T, m) as a function of pressure, temperature, and molality were obtained with a least-squares method using the experimental data. The root-mean-square deviation between measured and calculated values from this polynomial equation of state is ±0.2 kg-m^–3 for density. Measured values of the solution densities and the apparent and partial molar volumes are compared with data reported in the literature.     

Application of gas chromatography–tandem mass spectrometry (GC/MS/MS) for the analysis of deuterium enrichment of water

Incorporation of deuterium from deuterium oxide (²H₂O) into biological components is a commonly used approach in metabolic studies. Determining the dilution of deuterium in the body water (BW) pool can be used to estimate body composition. We describe three sensitive GC/MS/MS methods to measure water enrichment in BW. Samples were reacted with NaOH and U‐¹³C₃‐acetone in an autosampler vial to promote deuterium exchange with U‐¹³C₃‐acetone hydrogens. Headspace injections were made of U‐¹³C₃‐acetone‐saturated air onto a 30‐m DB‐1MS column in electron impact‐mode. Subjects ingested 30 ml ²H₂O, and plasma samples were collected. BW was determined by standard equation. Dual‐energy X‐ray absorptiometry scans were performed to calculate body mass, body volume and bone mineral content. A four‐compartmental model was used to estimate body composition (fat and fat free mass). Full‐scan experiments generated an m/z 45 peak and to a lesser extent an m/z 61 peak. Product fragment ions further monitored included 45 and 46 using selected ion monitoring (Method1), the 61 > 45 and 62 > 46 transition using multiple reaction monitoring (MRM; Method2) and the neutral loss, 62 > 45, transition (Method3). MRM methods were optimized for collision energy (CE) and collision‐induced dissociation (CID) argon gas pressure with 6 eV CE and 1.5 mTorr CID gas being optimal. Method2 was used for final determination of ²H₂O enrichment of subjects because of lower natural background. We have developed a sensitive method to determine ²H₂O enrichment in BW to enable measurement of FM and FFM. Copyright © 2015 John Wiley & Sons, Ltd.     

Adsorption of Pure Gases and Mixtures on Porous Solids up to High Pressures

Physisorption equilibria of multicomponent gases on microporous solids like zeolites or activated carbons are considered. An overview about adsorption measurements of pure gases H₂, He, O₂, N₂, Ar, CO₂, CO, CH₄, C₂H₄ and C₂H₆ and some of their mixtures in the pressure range vacuum < p < 50 MPa at different temperatures 10^∘C–70^∘C were investigated. Also a thermodynamic formalism based on a modified van Ness method and on a new 3 parameter Isotherm equation (3-PIG) to describe the excess amount adsorbed was developed. Results are shown and discussed. Dedication to the memory of W. Schirmer.