Methane Mass Fraction Research Articles

SELECTION OF GAS MIXER PARAMETERS FOR DIESEL CONVERSION GENERATOR MOTOR IN GAS DIESEL

According to literary sources, options for converting diesel engines into dual-fuel engines for operation on any fuel, in particular, natural gas (NG), were analyzed. The conversion method with external mixture formation and an ignition dose of liquid fuel involves the preparation of a gas-air mixture of the required composition in a special device. The methodology for choosing the design parameters of the gas mixer for the organization of the work process of a V-shaped diesel engine type 12Ch 15/17.5, converted into a gas diesel, which works as part of a motor-generator unit of backup power supply, is given. The basic design of the diesel motor-generator was analyzed. A comparative calculation of the working processes of diesel and gas-diesel variants of execution (with an ignition dose of diesel fuel of 10%) was carried out. The requirements for the design and location of the gas mixer have been formed. In the work, using 3D modeling technologies, the geometry of the gas mixer and its flow part were formed. Using the method of finite volumes, the calculation grid was synthesized and its adaptation near solid walls was carried out. Next, a series of numerical experiments was conducted in a three-dimensional setting to evaluate the throughput and quality of mixing network methane with air (when the robot is operating at typical operating modes). The distribution of flow velocities in the vertical and horizontal planes of the flow part of the gas mixer was evaluated, the change in pressure along the height of the gas mixer and the distribution of the mass fraction of methane in the flow part of the engine intake tract were analyzed, and scientific and practical recommendations were developed to ensure the efficient operation of gas diesel as part of a motor-generator installation. It is shown that the proposed design of the gas mixer allows effective mixing of methane with air when operating in the entire power range of the considered engine. The use of 3D modeling technologies, with the use of modern numerical methods, allows you to assess the operating conditions of the mixture by macro indicators and in local sub-regions, which allows, in the future, to develop recommendations for increasing the efficiency of the process of preparing the fuel-air mixture.

A Numerical Investigation on Turbulent CH4-air Combustion Flames of a Multi-Regime Burner

ABSTRACT The interaction between premixed and non-premixed methane-air mixtures affect the flame structure. The flow field is improved by supplying the lean and rich mixture. The objective of this work is to study the effect of the re-circulation zone on premixed and non-premixed methane-air mixture in a multi-regime burner using numerically. The two-dimensional, axis symmetric, steady state, compressible turbulent reactive flow is simulated using standard k − ε model with the eddy dissipation concept (EDC). The chemical kinetics developed by the Gas Research Institute (CHEMKIN-II, GRI-3.0) has been combined with the governing equations using the open source CFD-tool box OpenFOAM. The flames have been tested for different equivalence ratios of jet ( ϕ j = 1.4, 1.8, 2.2, and 2.6) where, slot-1 velocity varied as 7.5 m / s and 15 m / s . The grid independent results of the temperature T and mixture fraction Z are found in a good agreement with the experimental data. The qualitative and quantitative study of the temperature T , mixture fraction Z , mass fraction of carbon monoxide Y CO , mass fraction of methane Y C H 4 and progress variable Y c have been presented. The results show that a lifted reaction zone close to the jet, and a re-circulation zone between the inner and outer premixed reaction zones, which stabilizes the combustion between slot-1 and slot-2. Increasing the jet equivalent ratio ϕ j reduces the temperature and extends the internal premixed reaction zone. This is due to the mixture fraction ratio Z exceeding the flammability limit near the jet exit, which occurs when Z is within the range of 0.027 to 0.09 . The maximum temperature value of approximately 2125 K is consistent with the variation in ϕ j . The re-circulation zone shows a constant temperature of 2000 K, where methane is completely burned and is not affected by the values of jet equivalent ratios.

Research of Indoor Methane Mass Fraction and Explosion Hazard Prediction Model Based on EKF

In order to realize the intelligence of the indoor methane supervision system and to deeply analyze and apply the data collected by sensor devices, this paper predicts the indoor methane mass fraction by extended Kalman filter and realizes the prediction of explosion consequences by TNT equivalent method, so as to establish an indoor methane warning model for data collection and analysis. And taking a room of 3×3×3m3 as an example, the indoor natural gas leakage is simulated by CFD, and the data of methane mass fraction change with time is obtained for model simulation and explosion consequence prediction calculation. It is found that the Kalman filter can predict the dynamic change of methane in the room, and the methane concentration in the room gradually reaches the equilibrium state after 10,000s, and the concentration is stable at 3%. The calculation results can provide direction for the accident investigation and provide reference for the decision of accident disposal.

The influence law of the film percentage and injection on gas film cooling effect of the liquid oxygen/methane attitude control engine

At present, the performance and thermal protection requirements of the attitude control engine as the power source for spacecraft attitude maintenance and adjustment are gradually becoming higher. In the field of gas film cooling, the influence law related to heat and mass transfer for attitude control engines with the liquid oxygen (LOX) /methane remains unclear. In the present study, the discrete phase model, the eddy-dissipation concept model and the 18-step methane simplification mechanism were used to simulate gas film cooling. The influences of the percentage, injection form and incidence angle of a gas film on the structure and cooling effect were analyzed. With the increase in gas film percentage, the maximum cooling efficiency increases and the increment shows a decreasing trend. In adopting the gas film injection scheme of round orifices, attention must be paid to the edge area of the gas film, where the cooling effect is easy to occur under poor conditions. Changing to the circumferential seam cooling scheme can significantly improve the thermal protection of the injection panel. The reflux area near the wall absorbs the methane in the core area close to the wall, which reduces the convective heat transfer coefficient near the wall. As the gas film incidence angle increases, the area with higher mass fraction of methane moves toward the head. The law of different parameters on the cooling effect is obtained by taking into account the interaction between the gas film and the mainstream. The gas film incidence angle cannot be lower than 10°, and a gas film incidence angle between 15° and 20° should preferably be taken. Such findings can facilitate the further development of attitude control engines with liquid oxygen and liquid methane and can guide the design of attitude control engines with gas film cooling.

Numerical Study on Optics and Heat Transfer of Solar Reactor for Methane Thermal Decomposition

This study aims to reduce greenhouse gas emissions to the atmosphere and effectively utilize wasted resources by converting methane, the main component of biogas, into hydrogen. Therefore, a reactor was developed to decompose methane into carbon and hydrogen using solar thermal sources instead of traditional energy sources, such as coal and petroleum. The optical distributions were analyzed using TracePro, a Monte Carlo ray-tracing-based program. In addition, Fluent, a computational fluid dynamics program, was used for the heat and mass transfer, and chemical reaction. The cylindrical indirect heating reactor rotates at a constant speed to prevent damage by the heat source concentrated at the solar furnace. The inside of the reactor was filled with a porous catalyst for methane decomposition, and the outside was surrounded by insulation to reduce heat loss. The performance of the reactor, according to the cavity model, was calculated when solar heat was concentrated on the reactor surface and methane was supplied into the reactor in an environment with a solar irradiance of 700 W/m2, wind speed of 1 m/s, and outdoor temperature of 25 °C. As a result, temperature, methane mass fraction distribution, and heat loss amounts for the two cavities were obtained, and it was found that the effect on the conversion rate was largely dependent on a temperature over 1000 °C in the reactor. Moreover, the heat loss of the full-cavity model decreased by 12.5% and the methane conversion rate increased by 33.5%, compared to the semi-cavity model. In conclusion, the high-temperature environment of the reactor has a significant effect on the increase in conversion rate, with an additional effect of reducing heat loss.

Laser-based measurement and numerical simulation of methane-air jet flame suppression with water mist

Fire incidents caused by leaks from natural gas pipelines should be quickly controlled by using clean and efficient approaches, such as water mist. Previous studies on the methane-air jet fire suppression by water mist have paid not only little attention to the OH radical distribution characterizing the combustion intensity, but also critical extinguishing conditions of jet fires. Therefore, planar laser-induced fluorescence of the OH radical is obtained to visualize OH radical distribution in fire suppression. Fire Dynamics Simulator v 6.7.4 is applied to simulate the flame-spray interaction and detail the instantaneous fire-extinguishing process by the flow field, gas temperature, reaction methane mass fraction and radiation attenuation in non-lift-off jet flame scenarios. The results show that, considering variation of the jet flame tilt angle, the jet fires can be effectively suppressed when the gas-spray momentum ratio is below 0.0068 in non-tilted cases and normalized Reynold number is less than 2.56 in tilted cases. In the terms of water mist system optimization, the installation location of 1.45 times the pipe diameter was considered as the maximum nozzle horizontal position for fire suppression in the flame Froude number range of 0.2∼1.5. Besides, the OH-PLIF measurement revealed that fire suppression resulting from the kinetics effect depends on whether the OH* flame structure is quickly broken by the downward spray thrust. This study may provide suggestions for natural gas fire suppression with water mist system, and give help for the reduction of greenhouse gas emissions under Paris Agreement.

Design improvement of compressed natural gas (CNG)-Air mixer for diesel dual-fuel engines using computational fluid dynamics

This project carried out a computational fluid dynamics (CFD) analysis using ANSYS Fluent 14.5 software to design a compressed natural gas (CNG)-air mixer for CNG-diesel dual fuel engine. This study aimed to examine the performance of existing secondary fuel premixing controller (SFPMC) commercial mixer and modify its design in terms of air fuel ratio (AFR) and CNG-air mixture homogeneity (CAMH). The design modification of the mixer involved changing the surface of control valve shaft, gas manifold, position and directions of the CNG outlet holes. Results from simulation indicated that the original mixer was unable to control AFR since it changed from 8 at the engine speed of 1000 rpm to 176.39 at the engine speed of 3600 rpm when gas inlet pressure is fixed. However, AFR for the optimized mixer is between 17.21 and 17.4, a range close to stoichiometric AFR with various engine speeds and specific locations of the control valve. In terms of CNG-air mixture homogeneity, the uniformity index (UI) of methane mass fraction (MCh4) at the outlet of the original mixer is between 0.555 when engine speed is 1000 rpm and 0.578 when engine speed is 3600 rpm. However UI of MCh4 at the outlet of optimized mixer is between 0.995 when engine speed is 1000 rpm and 0.961 when engine speed is 3600 rpm. That means the CNG and air are homogeneously mixed at the outlet of optimized mixer in comparison with the original mixer. In summary, changing the surface of control valve shaft from cylindrical to conical shape lead to gradually opening the gas way and allow to rising the gas flow rate with increasing of air mass flow rate due to growing of engine speed, so the AFR is controlled in comparison with the origin mixer. Besides, changing the asymmetrically distributed seven gas injection holes near the mixer outlet to equal distribution 10 gas injection holes far from the mixer outlet perpendicularly to the air flow stream resulted in excellent homogeneity of the air and gas mixture in the optimized mixer.

Effects of Plasma Discharges on the Ignition of a Laminar Nonpremixed Jet Flame

This paper experimentally investigates the effect of plasma discharges on the ignition of a laminar nonpremixed methane jet flame in a stream of co-flow air. The Reynolds number of the jet flame, based on the nominal jet velocity and the nozzle diameter, is approximately Re $_{j} = 2000$ . The plasma discharge, a corona type, is produced between two tungsten wires with a diameter of 0.5 mm and a gap of 15 mm. Results show that the application of plasma discharge in a near-nozzle region is capable of ignition of the flame studied here, even though most of the ignition locations are in the lean side of the stoichiometric methane mass fraction. In general, the ignition probability (i.e., flame ignition is successfully achieved) is relatively larger as the discharge is closer to the stoichiometric methane mass fraction. In addition, the ignition probability is seen to increase with the discharge energy density. Results of the most probable ignition time, defined as the mode of the probability density function of the required flame ignition time, are consistent with those of the ignition probability. The most probable ignition time is seen to decrease with the increased ignition probability. Overall, the shorter ignition time occurs when the discharge is closer to the stoichiometric methane mass fraction or when the discharge energy density becomes larger. The estimated reduced electric field suggests the importance of the electron-impact dissociation induced by plasma discharges to the flame ignition.

Simulation of combustion in a porous-medium diesel engine

The future internal-combustion (IC) engines should have minimum emissions level under lowest feasible fuel consumption. This aim can be achievable with a homogeneous combustion process in diesel engines. We used a porous medium (PM) to homogenize the combustion process. This research studies simulation of a direct-injection diesel engine, equipped with a chemically inert hemispherical PM. Methane is injected into a hot PM, assuming mounted up the cylinder in head. Combustion with lean mixture occurs inside PM. A numerical model of PM engine was carried out using a modified version of the KIVA-3V code. PM results were evaluated with experimental data of unsteady combustion-wave of methane in a porous tube. The results show the mass fraction of methane, CO, NO and temperature in solid and gas phases of the PM and in-cylinder fluid. Also presented are the effects of injection timing and compression ratio on combustion.

Numerical Study of Ignition Process in Turbulent Shear-less Methane-air Mixing Layer

In this work, ignition process in a turbulent shear-less methane-air mixing layer is numerically investigated. A compressible large eddy simulation method with Smagorinsky sub-grid scale model is used to solve the flow field. Also, a thickened flame combustion model and DRM-19 reduced mechanism are used to compute species distribution and the heat release. Non-reacting mean and RMS axial velocity profiles and mean mixture fraction are validated against experimental data. Instantaneous mixture fraction contours show that the large bursts penetrate from the fuel stream into that of the oxidizer and vice versa and a random behaviour in the cross-stream direction. Flame kernel initiation, growth and propagation are analysed and compared with the experimental data. The ignition results show that the flame is not stable and blow-off occurs, but a more detailed investigation shows that local and short time flame stabilization exist during blow-off. During these local stabilization, heat release increased at the upstream edge of the flame. Most_upstream flame edge scalar analysis shows that the methane mass fraction has a dominant role in the local flame stabilization. OH, HO2, CH2O and heat release contours demonstration reveal that HO2 and CH2O mass fraction as well as the heat release reach a maximum on the border of the flame, but the maximum OH concentration is located in the middle of flame kernel.

Transient Thermochemical Storage Performance of Methane Reforming in Semi-cavity Reactor Heated by Solar Dish System

Abstract The transient thermochemical storage performance of methane reforming with carbon dioxide in a semi-cavity reactor heat by a dish solar system was numerically investigated. A 3D transient numerical model with Gaussian solar irradiation from dish solar system was proposed to simulate the temperature and species concentration distribution inside the reactor. Along the flow direction, the bed temperature first increases and then decreases, and its maximum appear behind the centre of the reactor. During the starting stage, the bed temperature sharply increases, and the methane mass fraction quickly decreases for the reaction, while the chemical energy storage efficiency and the total energy storage efficiency increase more quickly than the sensible heat energy storage efficiency. When DNI is decreased for a short time, the incident energy flux quickly decreases, while the methane conversion and energy storage change very little, so the energy storage efficiency remarkably increases.

Computational Study of Indoor Pollutant Dispersion of an Apartment

Objectives: Indoor Air Quality (IAQ) is very important for the health of human beings. Proper ventilation of apartment can improve IAQ. The objective of the study is to analyse the pollutant dispersion behaviour inside the fluid domain at fixed boundary conditions. Methods/Statistical Analysis: A 2BHK apartment has been taken for study. The fluid domain of apartment has been simulated in the Computational Fluid Dynamics (CFD) software “ANSYS Fluent 16.2”. Four inlet doors, four inlet windows, one outlet door, one outlet window and two ventilations from toilets were taken in the apartment. Seven inlet pollutant sources at the middle of the bottom of each enclosed area i.e. drawing/dining room, master bedroom, bedroom 1, kitchen, toilet 1 and toilet 2 have been considered. The methane gas is selected as the pollutant in the study. The k-epsilon (2 equations) model has been used and methane-air mixture has been taken for species transport. Findings: The methane mass fraction has been studied at different planes and at different locations of the domain. It was observed that the pollutant dispersion phenomena were varying at different locations and with this the highest methane mass fraction zone have been discussed. Application/Improvements: Simulated model can be useful in urban management and planning to find the best geometrical configurations of infrastructure, especially residential, to achieve proper and effective ventilations. Present model can also be more effective with environmental wind tunnel validations.

Computational studies of oxy-fuel combustion in fired tube boilers integrated with an ion transport membrane.

Most industrial processes utilize fossil fuels as energy source which produces greenhouse gases and other hazardous emissions. In the U.S., industry generates circa 21% of greenhouse gases, being thereby the major origin for the emissions. . In order to reduce the pollution effects from industrial processes, standard air-fuel combustion is aimed to be replaced by oxy-fuel combustion, which has been identified to have a zero-emission potential. In this respect, an Ion Transport Membrane (ITM) can be used to produce pure oxygen for oxy-fuel combustion. However, adopting an ITM into the reactor of a fired tube boiler has been a major challenge due to the simultaneous oxygen permeation, combustion and heat transfer that occur through the walls of the reactor. For this reason, successful employment of an ITM is of critical importance, and thereby motivates the present work. Specifically, a Computation Fluid Dynamics (CFD) analysis has been carried out on a small-scale fired tube boiler model incorporated with an ITM. The thermal and chemical characteristics of oxy-methane gaseous combustion under constant reactor wall temperature have been investigated. In particular, the reactors performance at elevated temperature has been analyzed. It is observed that oxygen permeation, heat transfer and combustion characteristics can be optimized at elevated temperature of 1373K. Also, increasing the mass fraction of methane in this reactor to 6% facilitates both the heat transfer and combustion in the reactor. At the same time, increasing the mass flow rates of both the air and fuel streams does not impact the reactor performance significantly. This work is supported by West Virginia University’s Department of Mechanical and Aerospace Engineering through the Center for Alternative Fuels, Engines and Emissions.

Investigation of performance of fire-tube boilers integrated with ion transport membrane for oxy-fuel combustion

Summary The performance of a carbon free fire-tube boiler utilizing two-pass oxygen transport reactors was numerically investigated. The influences of the oxygen transport reactors wall temperature on the reaction rate, oxygen permeation and heat flux were quantified. The performance of the reactors has been investigated at elevated temperature. It is observed that both heat transfer and combustion characteristics can be optimized at an elevated temperature of 1373 K. Increasing the mass fraction of methane in this reactor to 6% results in improvement of the heat transfer and combustion characteristics in the reactor. Further increase in CH4% did not lead to any significant improvement. The fuel flow rate variation did not have any significant impact on the reactor performance. It is indicated that the membrane temperature has significant effect on the reaction rates and oxygen flux in the upstream region in particular. Copyright © 2016 John Wiley & Sons, Ltd.

Initiation of underground fire sources

Porous structure parameters of different rank Kuzbass coal and gas- and mass-exchange processes under coal heating are analyzed. The main part of volatile matter is dissolved in the volume of coal beds. For all coal specimens, it is typical that mass fraction of methane and ethane decreases with temperature while mass fraction of hydrogen, carbonic oxide and ethane increases. The latter gases can be the sources of violent burning of coal beds. UHF pyrolysis of bituminous coal reveals physical balance and composition of gaseous products. The results permit coal rating based on carbonization, enable recommending the use of inert gases in underground fire fighting and allow estimating temperature level in fire source zones in coal beds based on chemical composition of emitted gases.

Effects of pressure and temperature on laminar burning velocity and flame instability of iso-octane/methane fuel blend

In this work, spherically expanding flames are used to measure the unstretched flame propagation speed and Markstein length of an alternative fuel (iso-octane/methane fuel blend) at initial temperatures between 368 and 448K, and pressures between 1 and 5.5bar by using the Schlieren photography method.Methane is added in two volumetric fractions of 70% and 95% to iso-octane in a constant volume chamber. Markstein lengths are obtained via nonlinear methodology over an extensive range of equivalence ratios between 0.85 and 1.2. From these new experimental data, a laminar burning velocity correlation based on unburned gas temperature, pressure, equivalence ratio and methane mass fraction was proposed.It is seen that the unstretched flame propagation speed of blended fuel are located between the pure fuels but did not follow simple mole-fraction based weighted average of parent fuels and flame stability is enhanced by adding more methane to the fuel blend. Initial pressure rise has a suppression effect on flame propagation and pure methane receives the most influence from this effect. Initial temperature rise increase the propagating speed in all mixtures.

Comments on “Experimental investigations on scaled-up methane hydrate production with surfactant promotion: Energy considerations”

Abstract Different opinions are proposed regarding the two major conclusions that Brinchi et al. (2014) described in their recent paper published in this journal [Brinchi et al., J. Petrol. Sci. Eng. 120, 187−193 (2014)]. Although the authors concluded that the gas-compression work is the dominant factor in the total energy consumption required for hydrate production, the gas-compression work should significantly vary depending on the initial pressure of the hydrate-forming gas. The gas-compression work may be insignificant or even eliminated, if a high-pressure natural gas directly supplied from an adjacent gas well is used for the hydrate production. The authors also concluded that the relatively low values of the gas content (the mass fraction of methane contained in each methane-hydrate slurry formed in their study) should be ascribable to the large size (25 L capacity) of their hydrate reactor, suggesting a negative effect of the increasing reactor size on the quality of the available hydrate slurries. It is pointed out that this second conclusion is inconsistent with the related gas content data previously reported by other research groups.

Effect of catalytic cylinders on autothermal reforming of methane for hydrogen production in a microchamber reactor.

A new multicylinder microchamber reactor is designed on autothermal reforming of methane for hydrogen production, and its performance and thermal behavior, that is, based on the reaction mechanism, is numerically investigated by varying the cylinder radius, cylinder spacing, and cylinder layout. The results show that larger cylinder radius can promote reforming reaction; the mass fraction of methane decreased from 26% to 21% with cylinder radius from 0.25 mm to 0.75 mm; compact cylinder spacing corresponds to more catalytic surface and the time to steady state is decreased from 40 s to 20 s; alteration of staggered and aligned cylinder layout at constant inlet flow rates does not result in significant difference in reactor performance and it can be neglected. The results provide an indication and optimize performance of reactor; it achieves higher conversion compared with other reforming reactors.

Component of Clathrate Hydrates Formed in CH<sub>4</sub>-TBAB-H<sub>2</sub>O System

Methane storage data of clathrate hydrates formed in ternary system, methane-tetra-n-butyl ammonium bromide-water (CH4-TBAB-H2O), was measured by a magnetic suspension weight adsorption instrument at the temperature of 273.64 ~ 278.23 K and the pressure of 2.01 ~ 7.07 MPa, for two concentration (20.8 wt % and 43.3 wt %) of TBAB solutions. The hydrates component was qualitatively analyzed. The results showed that the structure of CH4-TBAB semi-clathrate hydrates was deformed at high pressure possibly due to methane molecules replacing TBAB molecules and forming structure I true methane hydrates for the 20.8 wt % TBAB solutions at 273.64 K. For 43.3 wt % TBAB solutions, at the same experimental temperature and pressure, the maximum mass fraction of methane in CH4-TBAB-H2O clathrate hydrates was only 1.64 wt % which was less than the ideal maximum value (3.08 wt %). It showed that for the 20.8 wt % TBAB solutions, TBAB molecules were not replaced by methane molecules but both CH4-TBAB semi-clathrate hydrates and structure I true methane hydrates were formed simultaneously. For 43.3 wt % TBAB solutions, the reason of low methane storage capacity may be that the pressure was not high enough.

Atmospheric pressure methane–hydrogen dc micro-glow discharge for thin film deposition

Atmospheric pressure methane–hydrogen dc micro-plasmas were studied for thin film deposition. Numerical simulations were performed using a hybrid model. The model contained detailed reaction mechanisms for the gas-phase discharge and the surface reactions to predict the species densities in the discharge and the deposition characteristics and its growth rate. Twenty-three species and an eighty-one step reaction mechanism were considered for the gas-phase methane–hydrogen discharge. The surface chemistry consisted of eighteen species and eighty-four reaction steps. The simulations were carried out for a dc parallel plate electrode configuration with an inter-electrode gap of 200 µm. An external circuit was also considered along with the discharge model and surface reactions. Basic plasma properties such as electron and species density, electric field, electron temperature and gas temperature were studied. Special attention was devoted to study the influence of discharge current and methane mass fraction on the plasma characteristics and the deposition characteristics and its rate. The , and concentrations were found to be the dominant hydrogen and hydrocarbon ions, respectively. It was found that in atmospheric pressure methane–hydrogen micro-plasmas, C2H6, C3H8, C2H4 and C2H2 are also present at high densities. CH2 and CH3 were found to be the main radicals, which are prominent growth species for diamond-like-carbon deposition. The simulations indicated significant gas heating in the entire regime of operation. Ion Joule heating was found to be dominant in the sheath whereas Franck–Condon heating and heavy particle reaction induced heating was dominant in the volume. A strong dependence of soot formation on gas temperature was observed. At higher discharge current and methane mass fraction the deposited film was predicted to have higher soot content. Mass spectrometry experiments were conducted to measure the methane conversion factor (cf) and the C2H2 density for different discharge currents. Both the methane cf and C2H2 density showed an increase with increasing discharge current. Predictions from simulations agreed favourably with the mass spectrometry measurements.