Injection of N-Radicals into Diesel Engine Exhaust Treated by Plasma for Improved NO_x Removal: A Feasibility Study

Reported in this paper is a feasibility study on the injection of plasma induced N radicals for the abatement of NO and NOx present in the actual diesel exhaust. The radical laden diesel exhaust was further treated by discharge plasma in a dielectric barrier discharge reactor. N radicals were produced in a separate plasma reactor filled with BaTiO3 pellets and were then injected into the treatment zone, There was a significant improvement in the efficiency when the radicals were injected compared to that when there was no radical injection. The efficiency of NOx removal at 0 load with plasma alone was 14% whereas with the injection of N radicals it went up to 38%, The results of the experiments conducted at different loads are discussed,

Discharge Plasma Assisted Adsorbents for Exhaust Treatment: A Comparative Analysis on Enhancing NO_x Removal

An analysis has been made on the discharge plasma coupled with an adsorbent system for NOx removal. The cascaded plasma-adsorbent system may be perceived as a better alternative for the existing adsorbent-based abatement system in the industry. In this study the exhaust is sourced from a diesel generator set. It was observed that better NO removal in a plasma reactor can be made possible by achieving higher average fields and subsequent NO2 removal can be improved using an adsorbent system connected in cascade with the plasma system. The paper describes various findings pertaining to these comparative analyses.

Study of Pulsed Plasma in a Crossed Flow Dielectric Barrier Discharge Reactor for Improvement of NO_x Removal in Raw Diesel Engine Exhaust

Improved performance of plasma in raw engine exhaust treatment is reported. A new type of reactor referred to as of cross-flow dielectric barrier discharge （DBD） was used, in which the gas flow is perpendicular to the corona electrode. In raw exhaust environment, the cross-flow （radial-flow） reactor exhibits a superior performance with regard to NOx removal when compared to that with axial flow of gas. Experiments were conducted at different flow rates ranging from 2 L/min to 25 L/min. The plasma assisted barrier discharge reactor has shown encouraging results in NOx removal at high flow rates.

NO_x Removal by Oxidation on Alumina Supported Metal Oxide Catalysts Followed by Alkaline Absorption

NO oxidation is the key reaction for the oxidative NO x removal process.In this work,the catalytic NO oxidation performance of the Al2O3 supported metal oxide catalysts(M-Al2O3,M=V,Mn,Fe,Co,Ni and Ce)is evaluated.The oxidation product is absorbed by the alkaline solution for NO x removal.The NO oxidation activity increases in the following order:V<<Ce<Ni<Fe<Co<Mn.As the NO oxidation involves the O uptake into the metal oxide lattice and oxidation of the adsorbed NO by the lattice O,the highest activity of Mn is attributed to the appropriate redox potential of Mn,which favors both the O uptake and the NO oxidation steps.For all the M-Al2O3 catalysts,there is an intermediate temperature to achieve maximum NO conversion,which is lower for more efficient M-Al2O3 catalyst.The temperature dependence suggests that the NO oxidation at low temperature is kinetically controlled while it is thermodynamically limited at higher temperature.The NO x removal ratio by the alkaline solution absorption increases with the NO2/NO ratio,with a maximum removal ratio of 80%when the NO2/NO ratio is higher than 3,indicating that a very high NO conversion is unnecessary.

Achieving Better NO_x Removal in Discharge Plasma Reactor by Field Enhancement

Application of plasma chemistry for gas cleaning is gaining prominence in recent years, mainly from an energy efficiency point of view. In this paper we conducted a comparative study of NO/NOx removal using two different types of dielectric barrier discharge electrodes, wire- cylinder reactor, pipe-cylinder reactor. Investigations were first carried out with synthetic gases to obtain the baseline information on the NO/NOx removal with respect to the two geometries studied. Further, experiments were carried out with raw diesel exhaust under loaded condition. A high NOx removal efficiency of 90% was observed for the pipe-cylinder reactor as compared to that of 53.4% for the wire-cylinder reactor. Furthermore, for the same energy consumed per NO molecule （about 73 eV/NO molecule）, the removal efficiency increased from 67% for the wire- cylinder to about 98% for the pipe-cylinder which was quite appreciable.

基于物理信息神经网络的燃煤锅炉NO_x排放浓度预测方法

准确的NO_(x)浓度预测对保障燃煤锅炉安全运行和降低污染物排放具有重要意义。基于机器学习的NO_x排放浓度预测方法计算速度快、拟合精度高,但缺少可解释性,且过度依赖训练样本,在样本不充分的情况下模型泛化能力差。为此,该文提出一种基于物理信息神经网络的燃煤锅炉NO_x排放浓度预测方法,将煤量、氧量、分离燃尽风(separated overfireair,SOFA)开度与NO_x排放浓度之间的单调关系嵌入到神经网络中,促使模型服从机理约束,避免机器学习过拟合或欠拟合,提升模型在锅炉宽工况条件下的准确性。以某660 MW燃煤锅炉为研究对象,算例分析表明,提出的预测方法明显优于随机森林、支持向量机和神经网络等常规机器学习方法,即使在未知工况下也能遵循参数间单调性关系,具有较好的可解释性和泛化能力。

Background removal from global auroral images:Data-driven dayglow modeling

Global images of auroras obtained by cameras on spacecraft are a key tool for studying the near-Earth environment.However,the cameras are sensitive not only to auroral emissions produced by precipitating particles,but also to dayglow emissions produced by photoelectrons induced by sunlight.Nightglow emissions and scattered sunlight can contribute to the background signal.To fully utilize such images in space science,background contamination must be removed to isolate the auroral signal.Here we outline a data-driven approach to modeling the background intensity in multiple images by formulating linear inverse problems based on B-splines and spherical harmonics.The approach is robust,flexible,and iteratively deselects outliers,such as auroral emissions.The final model is smooth across the terminator and accounts for slow temporal variations and large-scale asymmetries in the dayglow.We demonstrate the model by using the three far ultraviolet cameras on the Imager for Magnetopause-to-Aurora Global Exploration(IMAGE)mission.The method can be applied to historical missions and is relevant for upcoming missions,such as the Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)mission.

Long-term outcomes after endoscopic removal of malignant colorectal polyps:Results from a 10-year cohort

BACKGROUND Choosing an optimal post-polypectomy management strategy of malignant colorectal polyps is challenging,and evidence regarding a surveillance-only strategy is limited.AIM To evaluate long-term outcomes after endoscopic removal of malignant colorectal polyps.METHODS A single-center retrospective cohort study was conducted to evaluate outcomes after endoscopic removal of malignant colorectal polyps between 2010 and 2020.Residual disease rate and nodal metastases after secondary surgery and local and distant recurrence rate for those with at least 1 year of follow-up were invest-igated.Event rates for categorical variables and means for continuous variables with 95%confidence intervals were calculated,and Fisher’s exact test and Mann-Whitney test were performed.Potential risk factors of adverse outcomes were RESULTS In total,135 lesions(mean size:22.1 mm;location:42%rectal)from 129 patients(mean age:67.7 years;56%male)were enrolled.The proportion of pedunculated and non-pedunculated lesions was similar,with en bloc resection in 82%and 47%of lesions,respectively.Tumor differentiation,distance from resection margins,depth of submucosal invasion,lymphovascular invasion,and budding were reported at 89.6%,45.2%,58.5%,31.9%,and 25.2%,respectively.Residual tumor was found in 10 patients,and nodal metastasis was found in 4 of 41 patients who underwent secondary surgical resection.Univariate analysis identified piecemeal resection as a risk factor for residual malignancy(odds ratio:1.74;P=0.042).At least 1 year of follow-up was available for 117 lesions from 111 patients(mean follow-up period:5.59 years).Overall,54%,30%,30%,11%,and 16%of patients presented at the 1-year,3-year,5-year,7-year,and 9-10-year surveillance examinations.Adverse outcomes occurred in 9.0%(local recurrence and dissemination in 4 patients and 9 patients,respectively),with no difference between patients undergoing secondary surgery and surveillance only.CONCLUSION Reporting of histological features and adherence to surveillance colonoscopy needs improvement.Long-term adverse outcome rates might be higher than previously reported,irrespective of whether secondary surgery was performed.

Marine CO_(2) Removal Joins Race to Scale Up Mitigation Tech

In June 2024,startup company Equatic(Santa Monica,CA,USA)announced that it had begun engineering work on the world’s largest and first commercial scale facility using the ocean to remove CO_(2) from the atmosphere[1].The company claims its plant at a yet-to-be determined site in Quebec,Canada,will be operational by 2027,sequestering 300 t of CO_(2) per day at full capacity.Equatic is already building a similar,but smaller,facility called Equatic-1 in Singapore(Fig.1)[2].That project,expected to be completed in 2025,will have the capacity to remove 10 t of CO_(2) per day.

Filtration performance and modeling of granular bed for dust removal from coal pyrolytic vapors

Dust removal from pyrolytic vapors at high temperatures is an obstacle to the industrialization of the coal pyrolysis process.In this work,a granular bed with expanded perlites as filtration media was designed and integrated into a 10 t·d^(–1)coal pyrolysis facility.The testing results showed that around 97.56%dust collection efficiency was achieved.As a result,dust content in tar was significantly lowered.The pressure drop of the granular bed maintained in the range of 356 Pa to 489 Pa.The dust size in the effluent after filtration exhibited a bimodal distribution,which was attributed to the heterogeneity of the dust components.The effects of filtration bed on pyrolytic product yields were also discussed.A modified filtration model based on the macroscopic phenomenological theory was proposed to describe the performance of the granular bed.The computation results were well agreed with the experimental data.

Damage evolution and removal behaviors of GaN crystals involved in double-grits grinding

Elucidating the complex interactions between the work material and abrasives during grinding of gallium nitride(GaN)single crystals is an active and challenging research area.In this study,molecular dynamics simulations were performed on double-grits interacted grinding of GaN crystals;and the grinding force,coefficient of friction,stress distribution,plastic damage behaviors,and abrasive damage were systematically investigated.The results demonstrated that the interacted distance in both radial and transverse directions achieved better grinding quality than that in only one direction.The grinding force,grinding induced stress,subsurface damage depth,and abrasive wear increase as the transverse interacted distance increases.However,there was no clear correlation between the interaction distance and the number of atoms in the phase transition and dislocation length.Appropriate interacted distances between abrasives can decrease grinding force,coefficient of friction,grinding induced stress,subsurface damage depth,and abrasive wear during the grinding process.The results of grinding tests combined with cross-sectional transmission electron micrographs validated the simulated damage results,i.e.amorphous atoms,high-pressure phase transition,dislocations,stacking faults,and lattice distortions.The results of this study will deepen our understanding of damage accumulation and material removal resulting from coupling between abrasives during grinding and can be used to develop a feasible approach to the wheel design of ordered abrasives.

Efficient removal of U(VI) from wastewater by a sponge-like 3D porous architecture with hybrid electrospun nanofibers

Removal of uranium(VI)from nuclear wastewater is urgent due to the global nuclear energy exploitation.This study synthesized novel sponge-like 3D porous materials for enhanced uranium adsorption by combining electrospinning and fibrous freeze-shaping techniques.The materials possessed an organic-inorganic hybrid architecture based on the electrospun fibers of polyacrylonitrile(PAN)and SiO_(2).As a sup-porting material,the surface of fibrous SiO_(2) could be further functionalized by cyano groups via(3-cyanopropyl)triethoxysilane.All the cyano groups were turned into amidoxime(AO)groups to obtain a amidoxime-functionalized sponge(PAO/SiO_(2)-AO)through the subsequent ami-doximation process.The proposed sponge exhibited enhanced uranium adsorption performance with a high removal capacity of 367.12 mg/g,a large adsorption coefficient of 4.0×10^(4)mL/g,and a high removal efficiency of 97.59%.The UO_(2)^(2+)adsorption kinetics perfectly conformed to the pseudo-second-order reaction.The sorbent also exhibited an excellent selectivity for UO_(2)^(2+) with other interfering metal ions.2023 Hohai University.Production and hosting by Elsevier B.V.

Influence of filler characteristics on particle removal in fluid catalytic cracking slurry under an alternating electric field

The characteristics of the packing material under an alternating electric field are an important factor in the removal of FCCS particles.In this study,the electric field distribution of a separation unit consisting of packed spheres under an alternating electric field is simulated,and the movement mechanism of catalyst particles is analysed.An"effective contact point"model is derived to predict the adsorption of filler contact points on catalyst particles under the alternating electric field,and the model is validated by simulations and experiments.The numerical calculation and experimental results indicate that the electrical properties of the filler spheres,the filler angleθ,and the frequency f of the alternating electric field affect the adsorption of catalyst particles.As the frequency of the electric field increases,the particle removal efficiency of the high-conductivity filler(silicon carbide)increases and then settles,and the separation efficiency of the low-conductivity filler(glass,zirconia)is not sensitive to the change in electric field frequency.

Research and development on mechanism of removal of indoor volatile organic compounds by plants

Background,aim,and scope Owing to the rapid development of modernisation and urbanisation,living standards have gradually improved.However,the widespread use of high-energy-consuming indoor appliances and furniture has made indoor environments a primary environmental problem affecting human health.Sick building syndrome(SBS)and building-related illness(BRI)have occurred,and indoor air conditions have been extensively studied.Common indoor pollutants include CO,CO_(2),volatile organic compounds(VOCs)(such as the formaldehyde and benzene series),NOx(NO and NO_(2)),and polycyclic aromatic hydrocarbons(PAHs).VOCs have replaced SO_(2)as the“The Fourteenth Five-Year Plan”urban air quality assessment new indicators.Indoor VOCs can cause diseases such as cataract,asthma,and lung cancer.To protect human health,researchers have proposed several indoor air purification technologies,including adsorption,filtration,electrostatic dust removal,ozonation,and plant purification.However,each technology has drawbacks,such as high operating costs,high energy consumption,and the generation of secondary waste or toxic substances.Plant degradation of VOCs as a bioremediation technology has the characteristics of low cost,high efficiency,and sustainability,thereby becoming a potential green solution for improving indoor air quality.This study introduces the research status and mechanism of plant removal of indoor VOCs and provides an experimental basis and scientific guidance for analysing the mechanism of plant degradation of pollutants.Materials and methods This study reviews studies on the harm caused by indoor pollutants to human health and related sources,mainly investigating the degradation of indoor formaldehyde,BTEX(benzene,toluene,ethylbenzene,and xylene)plant mechanisms,and research results.Results Plants can remove VOCs via stomatal and non-stomatal adsorption,interfoliar microbial,rhizosphere microbial,and growth media.Benzene,toluene,and xylene(BTX)are adsorbed by pores,hydroxylated into fumaric acid,and then removed into CO_(2) and H_(2)O by TCA.Formaldehyde enters plant leaves through the stomata and epidermal waxy substances and is adsorbed.After the two steps of enzymatic oxidation,formic acid and CO_(2) are generated.Finally,it enters the Calvin cycle and removes glucose and other nontoxic compounds.Discussion The non-stomatal degradation of VOCs can be divided into adsorption by cuticular wax and active adsorption by plant surface microorganisms.The leaf epidermal waxy matter content and the lipid composition of the epidermal membrane covering the plant surface play important roles in the non-stomatal adsorption of indoor air pollutants.The leaf margin of a plant is an ecological environment containing various microbial communities.The endophytic and inoculated microbiota in plant buds and leaves can remove VOCs(formaldehyde and BTEX).Formaldehyde can be directly absorbed by plant leaves and converted into organic acids,sugars,CO_(2) and H_(2)O by microbes.Bioremediation of indoor VOCs is usually inefficient,leading to plant toxicity or residual chemical substance volatilisation through leaves,followed by secondary pollution.Therefore,plants must be inoculated with microorganisms to improve the efficiency of plant degradation of VOCs.However,the effectiveness of interfoliar microbial removal remains largely unknown and several microorganisms are not culturable.Therefore,methods for collecting,identifying,and culturing microorganisms must be developed.As the leaf space is a relatively unstable environment,the degradation of VOCs by rhizosphere microorganisms is equally important,and formaldehyde is absorbed more by rhizosphere microorganisms at night.The inoculation of bacteria into the rhizosphere improves the efficiency of plants in degrading VOCs.However,most of these studies were conducted in simulation chambers.To ensure the authenticity of these conclusions,the ability of plants to remove indoor air pollutants must be further verified in real situations.Conclusions Plant purification is an economical,environment-friendly,and sustainable remediation technology.This review summarises the mechanisms of VOC plant degradation and presents its limitations.Simultaneously,it briefly puts forward a plant selection scheme according to different temperatures,light,and specific VOCs that can be absorbed to choose the appropriate plant species.However,some studies have denied the purification effect of plants and proposed that numerous plants are required to achieve indoor ventilation effects.Therefore,determining the ability of plants to remove indoor VOCs requires a combination of realistic and simulated scenarios.Recommendations and perspectives Plants and related microorganisms play an important role in improving indoor air quality,therefore,the effect of plants and the related microorganisms on improving indoor air quality must be studied further and the effect of plants on indoor VOCs will be the focus of future research.

Hierarchical Reduced Graphene Oxide-MnO_(2)@Polypyrrole Coaxial Nanotube Composite Hydrogel as a Potential Adsorbent for Cr(Ⅵ)Removal

A hierarchical reduced graphene oxide-MnO_(2)@polypyrrole coaxial nanotube composite hydrogel was prepared via oxidative polymerization of pyrrole in the presence of MnO_(2)nanotubes,followed by the hydrothermal treatment of graphene oxide and MnO_(2)@polypyrrole coaxial nanotubes.The stable composite hydrogel with a hierarchical network was composed of one-dimensional MnO_(2)@polypyrrole coaxial nanotube and two-dimensional graphene nanosheet and characterized by scanning electron microscope,Fourier transform infrared spectroscopy,X-ray diffraction,Brunauer-Emmett-Teller surface,and X-ray photoelectron spectroscopy measurements.The composite hydrogel can be used as an efficient adsorbent for Cr(Ⅵ)removal due to the synergistic interaction between graphene and MnO_(2)@polypyrrole and the hierarchical structure of the hydrogel.Moreover,the composite hydrogel is easily separated because of its stable monolith,and it is reusable(76.8%of removal ability remaining after five adsorption-desorption cycles).The simple fabrication and cost-effective separation process together with the excellent absorption performance endow the composite hydrogel with great potential for practical wastewater treatment.

CAS-ESM2.0 Dataset for the Carbon Dioxide Removal Model Intercomparison Project(CDRMIP)

Understanding the response of the Earth system to varying concentrations of carbon dioxide(CO_(2))is critical for projecting possible future climate change and for providing insight into mitigation and adaptation strategies in the near future.In this study,we generate a dataset by conducting an experiment involving carbon dioxide removal(CDR)—a potential way to suppress global warming—using the Chinese Academy of Sciences Earth System Model version 2.0(CASESM2.0).A preliminary evaluation is provided.The model is integrated from 200–340 years as a 1%yr^(−1) CO_(2) concentration increase experiment,and then to~478 years as a carbon dioxide removal experiment until CO_(2) returns to its original value.Finally,another 80 years is integrated in which CO_(2) is kept constant.Changes in the 2-m temperature,precipitation,sea surface temperature,ocean temperature,Atlantic meridional overturning circulation(AMOC),and sea surface height are all analyzed.In the ramp-up period,the global mean 2-m temperature and precipitation both increase while the AMOC weakens.Values of all the above variables change in the opposite direction in the ramp-down period,with a delayed peak relative to the CO_(2) peak.After CO_(2) returns to its original value,the global mean 2-m temperature is still~1 K higher than in the original state,and precipitation is~0.07 mm d^(–1) higher.At the end of the simulation,there is a~0.5°C increase in ocean temperature and a 1 Sv weakening of the AMOC.Our model simulation produces similar results to those of comparable experiments previously reported in the literature.

Nitrogen and Phosphorus Removal from Lake Kinneret Inputs

The Hula Valley was drained in 1957. The land use was modified from natural wetland and old shallow lake ecosystems to agricultural development. About half of the drained land area was utilized for aquaculture. Population size was enhanced and the diary was developed intensively resulting in the enhancement of domestic and husbandry sewage production that increased as well. The natural intact Hula Valley-Lake Kinneret ecosystem was heavily anthropogenically interrupted: The Hula was drained and Kinneret became a national source for domestic water supply. Some aspects of the environmental and water quality protection policy of the system are presented. The causation and operational management implications for the reduction of Nitrogen and Phosphorus migration from the Hula Valley are discussed. Drastic (81%) restriction of aquaculture accompanied by sewage totally removed achieved a reasonable improvement in pollution control which was also supported by the Hula Project. The implications of anthropogenic intervention in the process of environmental management design are presented.

Effects of thinning and understory removal on water use efficiency of Pinus massoniana:evidence from photosynthetic capacity and stable carbon isotope analyses

Understanding the relationship between forest management and water use efficiency(WUE)is important for evaluating forest adaptability to climate change.However,the effects of thinning and understory removal on WUE and its key controlling processes are not well understood,which limits our comprehension of the physiological mechanisms of various management practices.In this study,four forest management measures(no thinning:NT;understory removal:UR;light thinning:LT;and heavy thinning:HT)were carried out in Pinus massoniana plantations in a subtropical region of China.Photosynthetic capacity and needle stable carbon isotope composition(δ^(13)C)were measured to assess instantaneous water use efficiency(WUE_(inst))and long-term water use efficiency(WUE_(i)).Multiple regression models and structural equation modelling(SEM)identified the effects of soil properties and physiological performances on WUE_(inst)and WUE_(i).The results show that WUE_(inst)values among the four treatments were insignificant.However,compared with the NT stand(35.8μmol·mol^(-1)),WUE_(i)values significantly increased to 41.7μmol·mol^(-1)in the UR,50.1μmol·mol^(-1)in the LT and 46.6μmol·mol^(-1)in HT treatments,largely explained by photosynthetic capacity and soil water content.Understory removal did not change physiological performance(needle water potential and photosynthetic capacity).Thinning increased the net photosynthetic rate(A_n)but not stomatal conductance(g_s)or predawn needle water potential(ψ_(pd)),implying that the improvement in water use efficiency for thinned stands was largely driven by radiation interception than by soil water availability.In general,thinning may be an appropriate management measure to promote P.massoniana WUE to cope with seasonal droughts under future extreme climates.

Burden of routine orthopedic implant removal a single center retrospective study

BACKGROUND Open reduction and internal fixation represent prevalent orthopedic procedures,sparking ongoing discourse over whether to retain or remove asymptomatic implants.Achieving consensus on this matter is paramount for orthopedic surgeons.This study aims to quantify the impact of routine implant removal on patients and healthcare facilities.A retrospective analysis of implant removal cases from 2016 to 2022 at King Fahad Hospital of the University(KFHU)was conducted and subjected to statistical scrutiny.Among these cases,44%necessitated hospitalization exceeding one day,while 56%required only a single day.Adults exhibited a 55%need for extended hospital stays,contrasting with 22.8%among the pediatric cohort.The complication rate was 6%,with all patients experiencing at least one complication.Notably,34.1%required sick leave and 4.8%exceeded 14 d.General anesthesia was predominant(88%).Routine implant removal introduces unwarranted complications,particularly in adults,potentially prolonging hospitalization.This procedure strains hospital resources,tying up the operating room that could otherwise accommodate critical surgeries.Clearly defined institutional guidelines are imperative to regulate this practice.AIM To measure the burden of routine implant removal on the patients and hospital.METHODS This is a retrospective analysis study of 167 routine implant removal cases treated at KFHU,a tertiary hospital in Saudi Arabia.Data were collected in the orthopedic department at KFHU from February 2016 to August 2022,which includes routine asymptomatic implant removal cases across all age categories.Nonroutine indications such as infection,pain,implant failure,malunion,nonunion,restricted range of motion,and prominent hardware were excluded.Patients who had external fixators removed or joints replaced were also excluded.RESULTS Between February 2016 and August 2022,360 implants were retrieved;however,only 167 of those who met the inclusion criteria were included in this study.The remaining implants were rejected due to exclusion criteria.Among the cases,44%required more than one day in the hospital,whereas 56%required only one day.55%of adults required more than one day of hospitalization,while 22.8%of pediatric patients required more than one day of inpatient care.The complication rate was 6%,with each patient experiencing at least one complication.Sick leave was required in 34.1%of cases,with 4.8%requiring more than 14 d.The most common type of anesthesia used in the surgeries was general anesthesia(88%),and the mean(SD)surgery duration was 77.1(54.7)min.CONCLUSION Routine implant removal causes unnecessary complications,prolongs hospital stays,depletes resources and monopolizing operating rooms that could serve more critical procedures.

A new two-step variational model for multiplicative noise removal with applications to texture images

Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.