Langmuir Formula Research Articles

Molecular modeling of CO2 affecting competitive adsorption within anthracite coal

This study aimed to investigate the adsorption properties of CO2, CH4, and N2 on anthracite. A molecular structural model of anthracite (C208H162O12N4) was established. Simulations were performed for the adsorption properties of single-component and multi-component gases at various temperatures, pressures, and gas ratios. The grand canonical ensemble Monte Carlo approach based on molecular mechanics and dynamics theories was used to perform the simulations. The results showed that the isotherms for the adsorption of single-component CO2, CH4, and N2 followed the Langmuir formula, and the CO2 adsorption isotherm growth gradient was negatively correlated with pressure but positively correlated with temperature. When the CO2 injection in the gas mixture was increased from 1 to 3% for the multi-component gas adsorption, the proportion of CO2 adsorption rose from 1/3 to 2/3, indicating that CO2 has a competing-adsorption advantage. The CO2 adsorption decreased faster with increasing temperature, indicating that the sensitivity of CO2 to temperature is stronger than that of CH4 and N2. The adsorbent potential energies of CO2, CH4, and N2 diminished with rising temperature in the following order: CO2 < CH4 < N2.

Controlling metal ion migration in contaminated groundwater with Iraqi clay barriers for water resource protection.

This study investigates the effectiveness of using Iraqi clay as a low-permeability layer to prevent the migration of lead and nickel ions in groundwater-aquifers. Tests of batch operation have been conducted to determine the optimal conditions for removing Pb2+ ions, which were found to be 120 minutes of contact time, a pH of 5, 0.12 g of clay per 100 mL of solution, and an agitation of 250 rpm. These conditions resulted in a 90% removal efficiency for a 50 mg L-1 initial concentration of lead ions. To remove nickel ions with an efficiency of 80%, the optimal conditions were 60 minutes of contact time, a pH of 6, 12 g of clay per 100 mL of solution, and an agitation of 250 rpm. Several sorption models were evaluated, and the Langmuir formula was found to be the most effective. The highest sorption capacities were 1.75 and 137 mg g-1 for nickel and lead ions, respectively. The spread of metal ions was simulated using finite element analysis in the COMSOL multiphysics simulation software, taking into account the presence of a clay barrier. The results showed that the barrier creates low-discharge zones along the down-gradient of the barrier, reducing the rate of pollutant migration to protect the water sources.

The Phase Behaviors of Confined Shale Fluids Considering Adsorption Effect

AbstractThe molecular adsorption in nano-scale shale pores results in the reduction of effective pore volume and further strengthens the confinement effect. This study aims at examining the adsorption effect coupled with confinement effects on phase behaviors of shale fluids. First, a modified extended Langmuir formula was developed to calculate the adsorption amount for a multi-component shale mixture. A modified cubic Peng–Robinson equation of state was proposed, and the occupied volume by the adsorbed phase was taken into account. The saturation pressures and fluid properties under the confinement effects and adsorption isotherms were examined. In order to examine the change of phase properties during a gas injection process in a shale condensate reservoir, we gradually increase the mole fractions of N2 or CO2 in shale condensate mixtures by coupling with confinement effects. We found that the thickness of the adsorption film reduces the effective pore throat, leading to intensified confinement effects and smaller bubble point pressures. When the gas adsorption layer is considered, a more significant decrease in density and viscosity is observed. The critical pressure of the condensate fluids increases and the critical temperature decreases with the continuous N2 injection. Contrary to N2 injection, the critical pressure decreases and the critical temperature moves upwards with CO2 injection. For condensate that accumulates in nano-pores (e.g., r ≤ 6 nm), the condensate fluid always exists in gas status during the gas injection and the subsequent production processes.

Cavitation bubble collapse and rebound in water: Influence of phase transitions

The influence of the mass transfer across the bubble surface due to evaporation and condensation on the cavitation (vapor) bubble collapse and rebound in water under room conditions has been studied. The bubble is spherical with an initial radius of 1.92mm. The dynamics of the vapor in the bubble and the surrounding liquid is governed by the gas dynamics equations. The effects of the liquid viscosity and heat conductivity of both fluids are taken into account. The liquid and vapor states are mainly described by the known wide-range equations by Nigmatulin and Bolotnova. The mass transfer is governed by the accommodation coefficient αac in the Hertz–Knudsen–Langmuir formula. It has been found that at αac in the range 0.001−0.075 the vapor in the bubble is homobaric at collapse. As αac increases in the range αac>0.075, an isentropic compression wave convergent to the bubble center is formed in the bubble. At focusing of this wave at the bubble center, a divergent (reflected from the center) isentropic compression wave occurs. With rising αac the intensities of these convergent and divergent waves increase. The divergent wave partially penetrates to the liquid in the form of an isentropic divergent wave. With growing αac the penetrated wave becomes steeper. At αac≈0.25 the divergent isentropic wave in the bubble transforms into a shock wave during its propagation to the bubble surface. This shock wave partially penetrates to the liquid in the form of a divergent shock wave. At small αac the outgoing pulse in liquid is shockless. Starting with αac≈0.03, it becomes discontinuous. In the range 0.03≤αac≤0.12 the shock pulse results from only large pressure gradients in the liquid in the vicinity of the bubble at the beginning of rebound. In the range 0.12<αac<0.25 the discontinuous outgoing pulse is formed from the divergent isentropic compression wave arisen in liquid as a result of partial escape of the isentropic wave out of the bubble. At αac>0.25 the shock pulse is formed directly on the bubbles surface as a result of the partial penetration of the divergent shock wave from the bubble to liquid. The obtained numerical results are in good agreement with available numerical and experimental data.

Surface-functionalized pomelo peel-derived biochar with mercapto-1,2,4-triazloe for selective elimination of toxic Pb (II) in aqueous solutions

A novel biochar adsorbent (GP-AMT) is prepared by functionalizing biochar derived from pomelo peel to eliminate Pb (II) from water. GP-AMT was characterized by FTIR, SEM, BET, TGA and XPS. GP-AMT has a large specific area and is multiaperture. The adsorption performance was studied. At the pH = 5, the maximum uptake amount of Pb(II) on GP-AMT reached 420 mg/g. The sorption behavior of GP-AMT obeys with Langmuir and pseudo second-order formula, which shows that the adsorbing property of GP-AMT is uniform chemical sorption. Thermodynamic studies attested that the sorptionwasan irreversibleendothermic course. GP-AMT demonstrated excellent selectivity and reproducibility. After 5 cycles, it still has an excellentsorptionproperty. XPS and zeta potential analysis revealed that the adsorbing nature of GP-AMT for heavy metal ions was coordination and ion exchange. In conclusion, surface modification of biochar can significantly improve its sorption capacity, selectivity and regenerative ability for Pb(II), and reduce the pomelo peel waste pollution.

The response mechanism of surface acoustic wave gas sensors in real time

A simulation model to describe the real-time response mechanism of the surface acoustic wave (SAW) gas sensors was established. This model was based on the perturbation theory, the Langmuir formula and the fundamental transport equations. Perturbation theory was utilized to describe the relationship between the sensor’s output and the mass loading on the detector’s surface. The Langmuir formula and fundamental transport equations were quoted to depict the adsorption–desorption behavior of gas on the sensitive film. According to these theories, the mass loading curve was obtained by using the finite element method with COMSOL. By configuring a SAW gas sensor coated with zinc oxide quantum dots, an experiment was performed to measure the frequency shifts caused by adsorbing and desorbing dimethyl methyl phosphonate. Excellent repeatability was observed in gas sensing experiments. The simulation curve is consistent with the experimental results.

Logging evaluation of free-gas saturation and volume content in Wufeng-Longmaxi organic-rich shales in the Upper Yangtze Platform, China

Abstract The Wufeng-Longmaxi shale is the most important target for the exploration and production of shale gas in China. There are two important parameters of great importance to shale gas evaluation: free gas saturation and content. However, current models that have been proposed based on the use of sandstone are not applicable to this shale gas reservoir due to differences in conductivity mechanisms between these two types of reservoirs. In this study, after the pore volume of gas shale had been classified into three phases, those being the adsorbed phase pore, free phase pore, and bound water pore, we proposed a method to calculate the free gas saturation and content from well logging data based on the pore volume model. Our method utilizes the following procedures: 1) determining the total porosity on the basis of the matrix value of dry clay; 2) establishing a quantitative correlation of the bound water content to the clay content and then determining the bound water porosity; 3) calculating the absorbed gas content by Langmuir formula; 4) calculating the adsorbed phase porosity according to the principle of mass conservation after determining the underground density of the adsorbed phase (in the range of 0.4–1.2 g/cm3); and 5) determining the free gas saturation and free gas content. Field examples show that the predicted shale porosity, free gas, and adsorbed gas contents calculated by using our proposed model accurately coordinate with the core derived results, which verified that the proposed method was valuable to evaluating the Wufeng-Longmaxi shale gas reservoir.

Improvement of nitrate-leaching control technology using an anion exchange compound on agriculture 1: synthesis of a Mg-Fe system layered double hydroxide and its anion exchange characteristics

ABSTRACTA hydrotalcite-like compound for reducing the leaching of nitrogen from farmland was prepared via a new synthesis procedure, and its chemical structure and anion exchange characteristics were described. The advantage of this new synthesis method is that it is a simple, inexpensive process that involves the mixing of only two types of materials, followed by a hydrothermal reaction that does not require pH or gas control. The materials for synthesis are MgO and FeCl3. Chemical analysis, X-ray diffraction, and scanning electron microscopy were used to confirm an Mg-Fe system hydrotalcite-like compound. The anion exchange capacity was 166 cmolc kg−1, which was determined using NO3− ion as an exchangeable anion. That capacity is equivalent to 23 g N kg−1. The nitrate adsorption isotherm of this compound approximately matched to the isotherm that was predicted by the Langmuir formula. The anion exchange selectivity coefficients of the compound were in the following order: NO3− > Cl− > SO42− > HPO42−. The developed compound is a prospective material for reducing leaching of NO3−N from farmland.

The influence of a change in the electron trajectory in the vacuum-diode anode–cathode gap on the impedance

The analysis of the influence of the electron-trajectory curvature in the anode–cathode gap of a vacuum diode on its impedance during generation of high-current electron beams is performed, and the applicability of the one-dimensional Child–Langmuir formula for the electron-current calculation is evaluated. The results of an experimental study of a flat diode with explosive-emission graphite, copper, and carbon- fabric cathodes and also with a multipointed cathode are presented. These investigations were performed on the TEU-500 accelerator (350–500 kV, 60 ns). A strip diode with a graphite cathode was also studied in the mode of magnetic self-insulation of electrons. The experiments were performed on the TEMP-4М accelerators (150–200 kV, 400–600 ns). The investigation results showed that the satisfactory coincidence of the experimental values of the total current with those calculated from the one-dimensional Child–Langmuir formula (for the working area of the cathode) is observed in diodes not only in the absence of a change in the electron trajectory in the anode–cathode gap but also upon a deflection of the trajectory from the normal to the cathode surface by an angle of <90°. An increase in the electron current owing to a decrease in the anode–cathode gap and an increase in the emission area of the cathode during the cathode-plasma production and also at the expense of the presence of microirregularities on the cathode is properly described by the onedimensional Child-Langmuir formula, if the above factors are taken into account.

煤层气直井排采初期水力模型的建立

为研究在地质资料不足的情况下煤层气井产气量的预测模型，利用Theis公式、Jacob公式对煤层气储层的导水系数、降落漏斗影响半径进行计算，利用Langmuir公式对煤层气临界解吸压力计算，并通过积分计算煤层气井的解吸半径。通过建立大佛寺煤层气直井排采过程的水力模型，进行单井产气量模拟，结果与实际排采曲线吻合程度较好。我们发现：不同排采阶段井底压力与产水量呈线性关系；降落漏斗影响半径与液面降深呈对数关系，与排采时间呈幂指数关系；在客观因素上，导水系数、影响半径对产气量的影响最大。 In order to study the prediction model of gas production of CBM wells in the drainage process with the shortage of geological data, we calculated the transmissibility of reservoir and the conical de-pression influence radius of water cone by using Theis formula and Jacob formula, calculated the critical desorption pressure by using Langmuir formula and calculated the desorption radius of CBM wells by integral. We founded the simulation results and the actual production curve with a better fit degree by model building and gas production fitting of single well. The result showed that there is a linear relationship between the bottom hole pressure in different production stages and water production. The conical depression influence radius of water cone and level drawdown shows a logarithm relationship, and it shows a exponential relationship with the production time. The transmissibility and the influence radius have the greatest effect on the gas production in the objective factors.

Explosive Emission Properties of Cathode Materials in Relativistic Electron Beam Generation

Relativistic electron beam generation studies have been carried out in LIA-400 system through explosive electron emission for various cathode materials. This paper presents the emission properties of different cathode materials at peak diode voltages varying from 10 to 220 kV and at peak current levels from 0.5 to 2.2 kA in a single pulse duration of 160-180 ns. The cathode materials used are graphite, stainless steel, and red polymer velvet. The perveance data calculated from experimental waveforms are compared with 1-D Child Langmuir formula to obtain the cathode plasma expansion velocity for various cathode materials. Various diode parameters are subject to shot to shot variation analysis. Velvet cathode proves to be the best electron emitter because of its lower plasma expansion velocity and least shot to shot variability.

Deformations of fossil coals on swelling in an atmosphere of carbon dioxide

The results of the simultaneous control of the sorption of gaseous CO2 and the swelling of fossil coals from the Donets Basin under quasi-equilibrium conditions were analyzed. It was established that the isotherms of sorption and deformation obey the Langmuir formula in the region of sorbate pressures to 4.5MPa. A linear correlation between the Langmuir sorption and deformation coefficients was found for a group of coals with the high yield of volatile substances, and a swelling criterion was established. A nonlinear relationship between the swelling of coal and the amount of the sorbed substance was obtained.

Numerical evaluation of Cs adsorption in PB column by extended Langmuir formula and one-dimensional adsorption model

Adsorption property of granulated Prussian blue adsorbent on radioactive cesium was evaluated for efficient decontamination in Fukushima area. The adsorbent was found to show an inflective adsorption isotherm, which was expressed by extended Langmuir formula with three adsorption sites. Adsorption speeds of each site were evaluated by time-dependent batch experiment. The simulation using derived parameters and one-dimensional adsorption model successfully reproduced the experimental data of cesium decontamination by small and large columns.

Adsorption Removal of Phosphorus from Wastewater by Steel Slag Filter Material

Spherical steel slag filter material with high porosity, large specific surface area was made by using steel slag as the main raw material, adding binder and pore forming agent. The influences of PH, phosphorus concentration and adsorption time on the adsorption effect of steel slag filter material were investigated. The adsorption characteristics of steel slag filter on phosphorus were studied based on adsorption isotherm model and adsorption kinetics model. Adsorption results were used to fit Langmuir and Freundlish formula. The correlation of Freundlish model was significant and the correlation coefficient was 0.92907.

Statistical Foundation of Empirical Isotherms

We show that most of the empirical or semi-empirical isotherms proposed to extend the Langmuir formula to sorption (adsorption, chimisorption and biosorption) on heterogeneous surfaces in the gaseous and liquid phase belong to the family and subfamily of the BurrXII cumulative distribution functions. As a consequence they obey relatively simple differential equations which describe birth and death phenomena resulting from mesoscopic and microscopic physicochemical processes. Using the probability theory, it is thus possible to give a physical meaning to their empirical coefficients, to calculate well defined quantities and to compare the results obtained from different isotherms. Another interesting consequence of this finding is that it is possible to relate the shape of the isotherm to the distribution of sorption energies which we have calculated for each isotherm. In particular, we show that the energy distribution corresponding to the Brouers-Sotolongo (BS) isotherm [1] is the Gumbel extreme value distribution. We propose a generalized GBS isotherm, calculate its relevant statistical properties and recover all the previous results by giving well defined values to its coefficients. Finally we show that the Langmuir, the Hill-Sips, the BS and GBS isotherms satisfy the maximum Bolzmann-Shannon entropy principle and therefore should be favoured.

Preparation of Compound Clinoptilolite Filter Material and Performance of Ammonia Nitrogen Removal

This experiment use natural clinoptilolite powder as main materials to prepare the large specific surface and high porosity spherical compound filter material by adding adhesive and pore-forming agent etc.This compound filter material has favourable effect when treating sanitary wastewater. The static adsorption test showed that the absorption ratio of ammonia-nitrogen is 58.5% when the compound filter material dosage was 100g/L, NH4+-N concentration was 100mg/L and the contact time was 40min.The cure fitting of the adsorption isotherm of NH4+-N on the compound filter material could be well described by the Langmuir formula and R2 (the coefficient of determination) is 0.99216. At the stably running phase, when the average concentrations of influent NH3-N was 35mg/L, the average removal ratio and concentration of effluent NH4+-N reached 83.51% and 5.81mg/L which could meet the first degree of national wastewater discharge standard (GB 8978-1996).

Generalized Bohm’s criterion and negative anode voltage fall in electric discharges

The value of the voltage fall across the anode sheath is found as a function of the current density. Analytic solutions are obtained in a wide range of the ratio of the directed velocity of plasma electrons v 0 to their thermal velocity v T . It is shown that the voltage fall in a one-dimensional collisionless anode sheath is always negative. At the small values of v 0/v T , the obtained expression asymptotically transforms into the Langmuir formula. Generalized Bohm’s criterion for an electric discharge with allowance for the space charge density ρ(0), electric field E(0), ion velocity v i (0), and ratio v 0/v T at the plasma-sheath interface is formulated. It is shown that the minimum value of the ion velocity v * (0) corresponds to the vanishing of the electric field at one point inside the sheath. The dependence of v * (0) on ρ(0), E(0), and v 0/v T determines the boundary of the existence domain of stationary solutions in the sheath. Using this criterion, the maximum possible degree of contraction of the electron current at the anode is determined for a short high-current vacuum arc discharge.

Theory of Anode Region of Short High-Current Vacuum Arc

A model of the anode region of a high-current vacuum arc is developed, which explicitly takes into consideration the ratio of the drift velocity of the electrons in plasma <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$v_{0}$ </tex></formula> to their thermal velocity <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$v_{T}$</tex></formula> as a parameter of the electron velocity distribution function in the anode sheath. A transcendental equation for determining the value of the negative anode drop (AD) as a function of ratio <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$v_{0}/v_{T}$</tex> </formula> is obtained. It is shown that, in contrast to the well-known Langmuir formula in a 1-D model of a collisionless sheath, the AD remains negative for any value of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$v_{0}/v_{T}$</tex> </formula> relation. For small values of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$v_{0}/v_{T} \ll 1$</tex></formula> , the expression obtained asymptotically passes into the Langmuir formula. The dependence of the AD value on the current density is used as a boundary condition at the anode in solving the 2-D problems in the theory of short vacuum arc. In accordance with the Langmuir formula, a region with a positive AD is formed at the anode when the current density increases. The results of this paper show that the region with a positive AD is absent.

Adsorption Performance of Ammonia onto Compound Clinoptilolite Filter Material

In order to combine the microbial metabolism characteristics in biological aerated filter (BAF) with the adsorption and ion-exchange ability of natural clinoptilolite to treat sanitary wastewater, the experiment use clinoptilolite powder as main materials to prepare the large specific surface and high porosity spherical compound filter material by adding adhesive and pore-forming agent etc and get better effect on sanitary wastewater treatment.The static adsorption test showed that the adsorb ratios of ammonia-nitrogen is 58.5% when the compound filter material dosage was 100g/L, NH3-N concentration was 100mg/L and the contact time was 40min.The cure fitting of the adsorption isotherm of NH3-N on the compound filter material could be well described by the Langmuir formula and the coefficient of determination is 0.99216.

Theory of the negative anode drop in low-pressure discharges

A kinetic model of the anode region with a negative anode potential drop is proposed, which explicitly takes into account the ratio of the directed velocity of electrons in plasma v0 to their thermal speed vT as a parameter of the electron velocity distribution function. A transcendent equation is derived for determination of the negative anode drop as a function of the ratio v0/vT. It is shown that, unlike the known Langmuir formula, the anode drop remains negative for any value of v0/vT. In the case of small values (v0/vT ≪ 1), the derived expression asymptotically reduces to the Langmuir formula. It is shown that the dependence of electron concentration on the potential differs from the Boltzmann law. The anode regions of the short high-current vacuum-arc discharge and the classical low-pressure discharge are considered as examples. For the vacuum-arc discharge, the current density distribution and the anode drop distribution over the anode surface under strong current contraction are calculated. For the low-pressure discharge, potential drops are calculated across the region of the inhomogeneous near-anode plasma and the space charge layer.