Leakage Conditions Research Articles

Characteristics of lean oxygen combustion and dynamic microreaction process of water-soaked coal

Oxidative spontaneous combustion is likely to occur after long-term water immersion in the gob area of coal mines. Mostly, the oxidation process is slowly carried out under different air leakage conditions. This paper summarizes the four stages of the low-temperature oxidation of water-soaked coal samples through temperature-programmed experiments. Using infrared spectroscopy and thermal analysis experiments, the migration laws of the functional groups and the thermal reaction characteristics of the four stages were investigated. The results show that as the oxygen concentration increases, the gas product concentration increases, and the activation energy of the deep oxidation stage decreases. With the progress of the heating stage, when the oxygen concentration is higher than 10%, the change in each functional group is larger, and the conversion of the functional group and the intermediate complex is relatively closer at an oxygen concentration of 21%. The low-temperature oxidation reaction is a parallel process of the pyrolysis and micro-oxygen absorption, and the DTG size is not affected by the oxygen concentration at the critical temperature. The higher the oxygen concentration is, the lower the initial exothermic temperature is, which promotes the exothermic process in the deep oxidation and oxidation-limited stages. The microreaction mechanism among coal, oxygen and water molecular chemisorption is constructed. By controlling the coal oxidation reaction stages under different air leakage conditions, the spontaneous combustion of water-soaked coal in the goaf is avoided.

Application of an improved naive Bayesian analysis for the identification of air leaks in boreholes in coal mines

Borehole extraction is the basic method used for control of gases in coal mines. The quality of borehole sealing determines the effectiveness of gas extraction, and many influential factors result in different types of borehole leaks. To accurately identify the types of leaks from boreholes, characteristic parameters, such as gas concentration, flow rate and negative pressure, were selected, and new indexes were established to identify leaks. A model based on an improved naive Bayes framework was constructed for the first time in this study, and it was applied to analyse and identify boreholes in the 229 working face of the Xiashijie Coal Mine. Eight features related to single hole sealing sections were taken as parameters, and 144 training samples from 18 groups of real-time monitoring time series data and 96 test samples from 12 groups were selected to verify the accuracy and speed of the model. The results showed that the model eliminated strong correlations between the original characteristic parameters, and it successfully identified the leakage conditions and categories of 12 boreholes. The identification rate of the new model was 98.9%, and its response time was 0.0020 s. Compared with the single naive Bayes algorithm model, the identification rate was 31.8% better, and performance was 55% faster. The model developed in this study fills a gap in the use of algorithms to identify types of leaks in boreholes, provides a theoretical basis and accurate guidance for the evaluation of the quality of the sealing of boreholes and borehole repairs, and supports the improved use of boreholes to extract gases from coal mines.

Frequency response function method for dynamic gas flow modeling and its application in pipeline system leakage diagnosis

Timely diagnosing leakages is significant for the safety and reliability of gas pipeline systems, where an efficient and accurate modeling and solution method is critical to identify the leakage rate and location. Here, a frequency response function-based modeling method for dynamic gas flow in pipelines is proposed. Based on the frequency-domain flow resistance of pipelines and Fourier Transform, original dynamic flow model is transformed into the frequency response function model consisting of linear lumped transmission constraints, nonlinear frequency response function, and nonlinear pipeline resistance characteristics, which are efficiently solved according to their different mathematical properties. Dynamic simulation cases show the proposed modeling and solution method greatly improves the computational efficiency keeping the accuracy. Besides, taking the difference between measurements and simulation results under leakage condition as objective, an iterative bilayer optimization algorithm is proposed based on the mathematical categorization of system constraints to efficiently diagnose leakages. Four leakage diagnosis cases in single pipeline and pipeline network with measurement noise and transient boundary conditions are studied to validate the leakage diagnosis method. Absolute location errors in the results are all within 1%, demonstrating the accuracy and robustness of the proposed method for single leakages and multiple leakages occurring successively or simultaneously.

Experimental research on the two-phase explosive boiling mechanism of superheated liquid under different leakage conditions

In this study, a 17 L cube vessel was designed to simulate the explosive boiling of high-pressure liquefied gas after the leakage of the storage tank. The influence of leakage conditions such as crack position, crack diameter, and initial liquid fill level were investigated. Results indicate that when the crack is at the gas phase and gas-liquid interface, the rapid boiling of the liquid is caused by the leakage and significant pressure rebound is occurred. What’s more, cracks located under the gas-liquid phase may also cause a significant rebound in pressure. As the crack diameter increases, the two-phase flow boiling intensity first increases and then decreases, and it reaches the maximum when the diameter is 30 mm. Furthermore, a concept of the critical liquid level difference was proposed, and its influencing factors were studied. Under the experimental conditions in this article, BLEVE will not occur if the height between the liquid level and the crack is above the critical liquid level difference.

Based on abnormal fluctuations in user-side flow simulation analysis of low- and medium-pressure gas pipeline leakage monitoring.

Due to the weak monitoring equipment for low- and medium-pressure gas pipelines, it is not easy to identify small flow leaks. The detection methods are mostly traditional manual inspections or night pressure-maintaining leak detection methods, which cannot be automatically monitored and sensed immediately. The abnormal fluctuations in client traffic caused by pipeline leaks studied in this paper can locate and detect leak locations more effectively. This paper analyzes the theoretical formula of leakage location based on flow data and finds out how to use the abnormal fluctuation of user-side flow to detect and locate gas pipeline leakage. First of all, this article uses the simulation software Pipeline Studio to construct the medium and low-pressure pipeline model. On this basis, 6 sets of leakage conditions were designed and simulated dynamically. Finally, the simulation results are analyzed, and the results show that: 1) The advisable monitoring period for monitoring abnormal fluctuations of user-side traffic is 10s. 2) There are two relationships between abnormal flow fluctuations and leakage position. They are: when the leakage point is at the first 40% of the relative distance from the gas source, the disturbance amplitude first increases and then decreases, and at the last 60%, it continues to decrease.; The closer the leak is to the user end, the more significant the abnormal flow fluctuations will be. On the contrary, the smaller the abnormal flow fluctuations will be; 3) No matter where the leakage occurs, the abnormal flow fluctuations in the 2nd and 3rd seconds after the leak occurs tend to be consistent. The proposal of the advisable monitoring period and the relationship between abnormal fluctuations of flow and the location of leakage provides a theoretical basis for the use of abnormal fluctuations of user-side flow for gas pipeline leakage detection and location.

Experimental and Numerical Study of Natural Gas Leakage and Explosion Characteristics.

Frequent occurrence of indoor natural gas explosion accidents seriously threatens the safety of people and property. To determine the law of indoor natural gas leakage and explosion hazards, based on experiment and simulation, the nature of natural gas explosion, the distribution law of natural gas volume fraction, flame propagation, temperature, and shock wave overpressure were studied. The results show that the flame structure can be divided into three zones, i.e., preheat zone, reaction zone, and product zone. OH + CO ⇔ H + CO2 is the main exothermic reaction in the combustion process. The overall distribution law of natural gas volume fraction shows that the higher the position, the greater the volume fraction, and the closer the distance to the leak source at the same height, the greater the volume fraction, and the natural gas volume fraction of the hose falling off is the largest under different leakage conditions. The difference in the wrapping structure of the kitchen package has a significant impact on the diffusion distribution of natural gas. The flame development goes through five stages of ignition, slow burning, detonation, slow burning, and extinguishing. The indoor temperature reaches about 1400 °C. Although the simulated value of shock wave overpressure is larger than the experimental value, the relationship between overpressure and distance is expressed by Y = A + B * ln(X + C). This study can provide certain technical support for natural gas accident rescue. The research can provide certain technical support for natural gas accident rescue and can also be used for accident investigation to form the determination procedure and method of leakage location and leakage amount.

Design and analysis of emergency protection scheme for manned spacecraft under leakage condition

Spacecraft may encounter emergency pressure relief situations during manned space exploration missions, such as when micrometeoroids break through the bulkheads. The pressure emergency is one of the main threats to the missions in low earth orbit or deep space explorations to the Moon and Mars. It is critical to develop a pressure protection scheme for emergency contingencies. In this study, in order to improve the safety and reliability of spacecraft protection, a periodic recompression recovery scheme (PRRS) is proposed for cabin pressure protection. The PRRS adopts a combined mode of cabin emergency recompression, cabin pressure maintenance, gas recovery, and spacesuit protection, which can provide astronauts with a variety of safety protection methods. A mathematical model of cabin pressure control is established by using the lumped parameter method, and the gas consumption of three types of pressure protection systems are compared. The PRRS adopts the mature technologies and could provide the reliable pressure emergency protection. Compared with the traditional continuous gas supply scheme, the PRRS can reduce gas consumption by more than 85%. In the case of limited spacecraft gas resources, the PRRS promises a longer survival time for returning astronauts. This study can provide a design idea for the overall design of manned spacecraft in the future.

Study on Severe Accidents of the New Generation WWER-1200 Reactor

As the safety of new generation reactors regarding conditions of radioactive material leakage into the environment greatly attracted the attention of engineers and scientists in the nuclear industry, because if these nuclear radioactive materials enter the environment, they will leave irreversible influences on humans and the environment for years, hence, it is environmentally very essential to investigate the safety of nuclear reactors. The wwer-1200 reactor is a reactor under preparation, and many investigation has been performed on its safety, and all research has revealed that this reactor is safe during all accidents. In this research, numerous severe accidents were examined in this reactor. The results indicated that in only one case this reactor go beyond its design safety situations, which is the concurrent incidence of cooling-water loss and a fracture in the lower part of the reactor chamber without emergency cooling systems. And the results revealed the temperature of the fuel pellet and fuel sheath as the central safety layer

Impact of treatment with sling placement for stress urinary incontinence on quality of life: case report and literature review

Introduction: urinary incontinence is defined as a condition of involuntary leakage of urine. Although minimal, incontinence is associated with a significant decline in quality of life, social, professional, and mental health, as well as sexual dysfunction in these women. Objective: To report the impact of sling used on the long-term quality of life of a patient with stress urinary incontinence. Case Report: 37-year-old patient without comorbidities, five pregnancies, three natural deliveries, one cesarean section, and one abortion, with an interval between deliveries of approximately one year. She began to experience mild urinary incontinence at medium and heavy exertion (cycling, climbing stairs quickly, carrying weight) or in near-maximum bladder capacity, in drips, with progressive worsening of symptoms over time that negatively impacted her quality of life. After several outpatient evaluations and with the persistence of symptoms, the patient underwent insertion of a mid-urethral sling. Conclusion: the use of a urethral sling had a positive impact on the control of incontinence and improvement in the long-term quality of life of a young patient with stress urinary incontinence.

Forecasting Piston Rod Seal Failure Based on Acoustic Emission Features in ARIMA Model

Fluid leakage due to piston rod seal failure in hydraulic cylinders results in unscheduled maintenance, machine downtime and loss of productivity. Therefore, it is vital to understand the piston rod seal failure at initial stages. In literature, very few attempts have been made to implement forecasting techniques for piston rod seal failure in hydraulic cylinders using acoustic emission (AE) features. Therefore, in this study, we aim to forecast piston rod seal failure using AE features in the auto regressive integrated moving average (ARIMA) model. AE features like root mean square (RMS) and mean absolute percentage error (MAPE) were collected from run-to-failure (RTF) tests that were conducted on a hydraulic test rig. The hydraulic test rig replicates the piston rod movement and fluid leakage conditions similar to what is normally observed in hydraulic cylinders. To assess reliability of our study, two RTF tests were conducted at 15 mm/s and 25 mm/s rod speed each. The process of seal wear from unworn to worn state in the hydraulic test rig was accelerated by creating longitudinal scratches on the piston rod. An ARIMA model was developed based on the RMS features that were calculated from four RTF tests. The ARIMA model can forecast the RMS values ahead in time as long as the original series does not experience any large shifts in variance or deviates heavily from the normal increasing trend. The ARIMA model provided good accuracy in forecasting the seal failure in at least two of four RTF tests that were conducted. The ARIMA model that was fitted with 15 pre-samples was used to forecast 10 out of sequence samples, and it showed a maximum moving absolute percentage error (MAPE value) of 28.99 % and a minimum of 4.950 %. The forecasting technique based on ARIMA model and AE features proposed in this study lays a strong basis to be used in industries to schedule the seal change in hydraulic cylinders.

Data Driven Seal Wear Classifications using Acoustic Emissions and Artificial Neural Networks

The work presented in this paper is built on a series of experiments aiming to develop a data-driven and automated method for seal diagnostics using Acoustic Emission (AE) features. Seals in machineries operate in harsh conditions, and seal wear in hydraulic cylinders results in fluid leakage, and instability of the piston rod movement. Therefore, regular inspection of seals is required using automated approaches to improve productivity and to reduce unscheduled maintenance. In this study, we implemented a data-driven diagnostics approach which utilizes AE measurements along with light weight Artificial Neural Networks (ANN) as a classifier to investigate the performance and resources (hardware & software) required for implementing a real-time soft sensor unit for monitoring seal wear condition. We used a feedforward multilayer perceptron ANN (Scaled Conjugate Gradient- SCG algorithm) that is trained with the back propagation algorithm, which is a popular network architecture for a multitude of applications (automotive, oil and gas, electronics). We benchmark the developed method against previous work conducted based on Support Vector Machine (SVM), and we compare ANN performance in classifying the running condition of seals in hydraulic cylinders by applying it to both raw (full frequency spectrum) and down sampled frequency measurements. The experiments were performed at varying pressure conditions on a hydraulic test rig that can simulate fluid leakage conditions like that of hydraulic cylinders. The test cases were generated with seals of three different conditions (unworn, semi-worn, worn). From the AE spectrum, the frequency bands were identified with peak power and by heterodyning the signal. This technique results in 10X down sampling without losing the information of interest. Further, the signal was divided into smaller “snapshots” to facilitate rapid diagnosis. In these tests, the diagnosis was made on short-time windows, as low as 0.3 seconds in length. A general set of 16 time and frequency domain features were designed. Then a training set was developed using relevant set of features (4, 5, and 16 features). The data was used to train the ANN (70% training – 30% test & validation) and SVM (60 % training - 40% test and validation). Classification of down sampled measurements, both ANN and SVM were able to accurately classify the status irrespective of the pressure conditions, with an accuracy of ~99% with execution time less than seconds. Therefore, the proposed approach can be applied as part of an automated seal wear classification technique based on AE and ANN/SVM and can be used for real-time monitoring of seal wear in hydraulic cylinders.

Flame Spread Pulsation Characteristics of Transformer Oil Vertical Spill Fire

Abstract To investigate the effects of fuel discharge rate and initial fuel temperature on flame pulsation characteristics of vertical spill fire, a series of experiments under continuous leakage conditions are conducted on a specially designed experimental setup, for which transformer oil is selected as the fuel. Results show that the vertical spill fire burning area can be divided into three parts. Both the main flame and the flash flame are involved in the flame pulsation behavior, and the essence of the flame pulsation of the vertical spill fire is the periodic alternation of the diffusion flame and the premixed flame. Flame pulsation frequency shows a linear negative correlation with the fuel leakage rate, it decreases from 3.56 Hz (4.98 ml m−1s−1) to 2.439 Hz (15.93 ml m−1s−1), and it has a positive correlation with the initial fuel temperature. As the fuel discharge rate increases, the pulsation amplitude increases while the flame transient spread rate decreases, both of them have no significant correlation with the initial fuel temperature. The ratio of the average flame pulsation amplitude to the maximum pulsation amplitude is between 0.57 and 0.76. The flame transient spread rate shows a negative correlation with the fuel discharge rate, the maximum flame spread velocity reaches 3.17 m/s and 2.85 m/s in the growing phase and shrinking phase respectively. Due to the entrainment effect of the flame plume, the flame transient spread rate in the shrinking phase is higher than that in the growing phase. Analyzed the diffusion process of fuel vapor and the heat transfer mechanism of vertical spill fire, the control of fuel leakage rate and initial temperature on the flame pulsation characteristics is mainly manifested in its influence on the fuel evaporation and diffusion process and the length of preheating area. This work provides data supplement on the flame spread of liquid fuel spill fire.

Modeling the diffusion of flammable hydrogen cloud under different liquid hydrogen leakage conditions in a hydrogen refueling station

Constructing hydrogen refueling stations will be popular for hydrogen energy use in the future, and investigating the diffusion characteristics of hydrogen in a leakage incident is quite significant. The instantaneous evolution of flammable hydrogen clouds arising from liquid hydrogen leakage in a hydrogen refueling station is predicted using Ansys Fluent, and parametric analyses are conducted to reveal the effects of storage pressure, source height, and leakage direction on the distributions of the flammable regions. In addition, the feasibilities of heating the ceiling or the ground of the station after the leakage of liquid hydrogen to accelerate the hydrogen dilution are examined. The results show that the flammable region is stabilized at 90 s, the corresponding flammable hydrogen cloud volume is about 333 m3, and the extensions of downwind and vertical directions reach 10 m and 9.3 m. Storage pressure has a finite effect on the downwind diffusion distance of the flammable cloud. A lower source height tends to format the high-concentration hydrogen cloud near the ground while a higher source height helps separate the flammable clouds from the ground. The upward leakage direction leads to the maximum downwind diffusion distance of about 10.2 m while the downward leakage direction makes the high hydrogen concentration region confined below the ceiling. Just maintaining the ceiling at the initial temperature of 300 K is effective for accelerating the hydrogen dilution in the upward leakage. The maximum hydrogen concentration and the flammable volume can be reduced at rates of 0.35 vol % and 8% for every 50 K increase in heating temperature. For the downward leakage, keeping the ground at the initial temperature just works for the first 40 s in reducing the maximum hydrogen concentration, while increasing the heating temperature receives a gradually declined effect on reducing the flammable volume.

A Multivariate Statistical Model of Water Leakage in Urban Water Supply Networks Based on Random Matrix Theory

In this paper, model construction of random matrix theory is carried out to analyze water leakage of urban water supply pipeline network, and a multivariate statistical model of water leakage of urban water supply pipeline network based on random matrix theory is proposed. This paper presents a three-level DMA, short-term water demand prediction method based on water use patterns, aiming to solve the problem of inaccurate water demand prediction caused by climate and social factors. Correlation analysis and factor analysis analyze the main factors affecting daily water demand changes. The extracted information of the main influencing factors and historical monitoring data are used to establish the Elman water demand prediction model. At the same time, the daily water consumption pattern was extracted by correlation analysis, matched with the water consumption pattern of the predicted day, and combined with the expected value of water demand for momentary water demand allocation, which improved the prediction accuracy of short-term water demand. This paper is based on the precise leakage location based on the real-time hydraulic model. The real-time hydraulic model under leakage conditions is established, GA and NSGA2 are designed, and the nondominated ranking algorithm with elite strategy is used to achieve accurate leakage location using hydraulic model calibration search. This paper uses a random matrix algorithm to establish the leakage estimation model. A laboratory case pipe network is built to simulate the water supply conditions in residential areas, and the operating data of the laboratory case pipe network are used to confirm that the random matrix leakage estimation model can estimate the leakage. The applicability of the random matrix leakage estimation model and the wavelet transform algorithm for leakage calculation are compared in an engineering example. The example confirms that the leakage amount calculated by the random matrix model has a less relative error and more similar trend than the wavelet transform algorithm.

Dead space washout by intentional leakage flow during conventional ventilation of premature infants-an experimental study.

ObjectiveInvasive mechanical ventilation poses a strong risk factor for the development of chronic lung disease in preterm infants. A reduction of the dead space as part of the total breathing volume would reduce the ventilation effort and thereby lower the risk of ventilator‐induced lung injuries. In this experimental study, we compared the efficacy of mechanical dead space washout via uncontrolled and controlled leakage flow in their ability to eliminate CO2 during conventional ventilation in preterm infants.MethodsThree frequently used neonatal ventilators, operating under standard conventional ventilating parameters, were individually connected to a test lung. To maintain a constant physiological end‐expiratory pCO2 level during ventilation, the test lung was continuously flooded with CO2. A side port in the area of the connector between the endotracheal tube and the flow sensor allowed breathing gas to escape passively or in a second experimental setup, regulated by a pump. Measurements of end‐expiratory pCO2 were taken in both experiments and compared to end‐expiratory pCO2 levels of ventilation without active dead space leakage.ResultsFollowing dead space washout, a significant reduction of end‐expiratory pCO2 was attained. Under conditions of uncontrolled leakage, the mean decrease was 14.1% while controlled leakage saw a mean reduction of 16.1%.ConclusionWashout of dead space by way of leakage flow is an effective method to reduce end‐expiratory pCO2. Both controlled and uncontrolled leakage provide comparable results, but precise regulation of leakage allows for a more stable ventilation by preventing uncontrolled loss of tidal volume during inspiration.

Study on analytical model of gas diffusion in underground pipe network

Through the analysis of gas pipeline leakage causes and gas leakage diffusion model, the preventive measures for gas leakage accidents are put forward, which is of great significance for the harm of gas leakage and explosion accidents. In this paper, the mathematical model of gas leakage is established through hydrodynamics and pipeline gas motion equation, and the leakage process is analyzed by means of numerical simulation, the change law of gas dynamic leakage is obtained from the aspects of gas leakage conditions, gas movement and diffusion law.

Numerical experimental design application in consequence analysis of ammonia leakage

Ammonia is a colorless gas, corrosive, and highly toxic. This compound can cause irreversible consequences for humans and the environment depending on the concentration. Currently, accidents involving ammonia leakage in industrial facilities are recurring. Thus, outlining contingency and mitigation strategies is crucial for the industry. In this work, we performed several simulations of ammonia leakage scenarios using the ALOHA® 5.4.7 software. Moreover, we propose a well-validated model with significant parameters to estimate the gas cloud volume for a range of environmental and leak conditions. The simplicity of this model facilitates its utilization and may enrich risk analysis and help in proposing adequate safety measures for specific atmospheric and leakage conditions.

Mapping water pipeline leakage by ground-penetrating radar diffraction imaging

Investigation of water pipeline leakage is a matter of great significance for water resources management. Among various approaches, ground-penetrating radar (GPR) attracts increasing attention as a fast and noninvasive technique. However, this method suffers from uncertainties in the stage of interpretation because diffractions from the leak region often are too weak to be identified. To address this problem, we have developed the use of diffraction imaging to enhance imaging and characterization of water leakage. Numerical seepage simulation allows us to establish an equivalent computational analog for a known leak condition. After the collection of parallel GPR survey lines, we apply diffraction separation and imaging techniques on 2D and 3D data. Although the actual situation is generally well reproduced by 2D and 3D results, 3D diffraction imaging provides improved mapping of leakage compared with its 2D counterpart. We then apply the method to field data collected at a training base for water pipeline leakage control in Shaoxing, China. The prediction from imaging results corresponds well with the true position and type of leakage. The laboratory and field experiments substantiate the viability of GPR diffraction imaging and illustrate the potential of using GPR to detect small water leaks.

Leakage Diagnosis of Air Conditioning Water System Networks Based on an Improved BP Neural Network Algorithm

Compared with traditional pipe networks, the complexity of air conditioning water systems (ACWSs) and the alternation of cooling and heating are more likely to cause pipe network leakage. Pipe leakage failure seriously affects the reliability of the air conditioning system, and can cause energy waste or reduce human comfort. In this study, a two-stage leakage fault diagnosis (LFD) method based on an Adam optimization BP neural network algorithm, which locates leakage faults based on the change values of monitoring data from flow meters and pressure sensors in air conditioning water systems, is proposed. In the proposed LFD method, firstly, the ACWS network’s hydraulic model is built on the Dymola platform. At the same time, a cuckoo algorithm is used to identify the pipe network’s characteristics to modify the model, and the experimental results show that the relative error between the model-simulated value and the actual values is no more than 1.5%. Secondly, all possible leakage conditions in the network are simulated by the model, and the dataset is formed according to the change rate of the observed data, and is then used to train the LFD model. The proposed LFD method is verified in a practical project, where the average accuracy of the first-stage LFD model in locating the leaking pipe is 86.96%; The average R2 of the second-stage LFD model is 0.9028, and the average error between the predicted location and its exact location with the second-stage LFD model is 6.3% of the total length of the leaking pipe. The results show that the proposed method provides a feasible and convenient solution for timely and accurate detection of pipe network leakage faults in air conditioning water systems.

A Class of Variational\u2013Hemivariational Inequalities for Bingham Type Fluids

In this paper we investigate a new class of elliptic variational–hemivariational inequalities without the relaxed monotonicity condition of the generalized subgradient. The inequality describes the mathematical model of the steady state flow of incompressible fluid of Bingham type in a bounded domain. The boundary condition represents a generalization of the no leak condition, and a multivalued and nonmonotone version of a nonlinear Navier–Fujita frictional slip condition. The analysis provides results on existence of solution to a variational–hemivariational inequality, continuous dependence of the solution on the data, existence of solutions to optimal control problems, and the dependence of the solution on the yield limit. The proofs profit from results of nonsmooth analysis and the theory of multivalued pseudomontone operators.