Risk assessment model of tunnel water inrush based on improved attribute mathematical theory

Tunnel water inrush is one of the common geological disasters in the underground engineering construction.In order to effectively evaluate and control the occurrence of water inrush,the risk assessment model of tunnel water inrush was proposed based on improved attribute mathematical theory.The trigonometric functions were adopted to optimize the attribute mathematical theory,avoiding the influence of mutation points and linear variation zones in traditional linear measurement functions on the accuracy of the model.Based on comprehensive analysis of various factors,five parameters were selected as the evaluation indicators for the model,including tunnel head pressure,permeability coefficient of surrounding rock,crushing degree of surrounding rock,relative angle of joint plane and tunnel section size,under the principle of dimension rationality,independence,directness and quantification.The indicator classifications were determined.The links among measured data were analyzed in detail,and the objective weight of each indicator was determined by using similar weight method.Thereby the tunnel water inrush risk assessment model is established and applied in four target segments of two different tunnels in engineering.The evaluation results and the actual excavation data agree well,which indicates that the model is of high credibility and feasibility.

THE STUDY ON THREE-DIMENSIONAL MATHEMATICAL MODEL OF RIVER BED EROSION FOR WATER-SEDIMENT TWO-PHASE FLOW

Based on the tensor analysis of water-sediment two-phase how, the basic model equations for clear water flow and sediment-laden flow are deduced in the general curve coordinates for natural water variable-density turbulent how. Furthermore, corresponding boundary conditions are also presented in connection with the composition and movement of non-uniform bed material. The theoretical results are applied to the calculation of the float open caisson in the construction period and good results are obtained.

Mathematical Model of the Geothermal Water Resources in the South Hot Spring System in Chongqing

The geothermal waters of south hot spring, small hot spring and Qiaokouba in Chongqing, are all part of the south hot spring geothermal water system. Exploitation has caused a decline in the water levels of the south and small hot springs, which have not flowed naturally for 15 years. Now, bores pump geothermal water to the springs. If the water level drops below the elevation of the rivers, river-water will replenish the geothermal water, destroying this resource. It is therefore an urgent task to model the geothermal water system, to enable sustainable development and continued use of the geothermal water in Qiaokouba. A numerical simulation of the geothermal water system was adopted and a quantitative study on the planning scheme was carried out. A mathematical model was set up to simulate the whole geothermal water system, based on data from the research sites. The model determined the maximum sustainable water yield in Qiaokouba and the two hot springs, and the south hot spring and small hot spring sustainable yields are 1 100 m^3/d and 700 m^3/d from 2006 to 2010, 1 300 m^3/d and 1 000 m^3/d from 2011 to 2015, and 1 500 m^3/d and 1 200 m^3/d from 2016 to 2036. The maximum exploitable yield is 3 300 m^3/d from 2006 to 2036 in Qiaokouba. The model supplies a basis to adequately exploit and effectively protect the geothermal water resources, and to continue to develop the geothermal water as a tourist attraction in Chongqing.

Numerical solution of a mathematical model for water wavesin large coastal areas

Based on the evolution equation for water waves, a mathematical model for wave propaga tion in large mild - slope areas is derived. The model is solved by the finite difference method with the staggered grid system. The computational results are in good agreement with experimental data and show that the model can obtain better results with relatively coarser grids. The model can be used to simulate water wave propagation in large coastal areas and can be efficiently solved without much programming effort.

Designing for Long Campaign Life Blast Furnace (1)──The Mathematical Model of Temperature Field for Blast Furnace Lining and Cooling Apparatus and New Concept of Long Campaignship Blast Furnace Cooler Design

The physical and mathematical model of temperature field for blast furnace stave coolers was established. The computation results show that the heat resistance of 2-6 mm water scale within the cooling pipe is about 7%-20% of the total heat resistance of cooling stave body, as for drilling duct type, the heat resistance of 2-6 mm water scale is about 88%-98% of the total heat resistance. Using drilling duct or full cast pipe can eliminate gas clearance and coating layer between pipes and cast iron body and reduce the heat resistance of the cooler sharply and improve the coefficient of heat transfer to a great extent. The water velocity within coolers can be kept at the 1evel of 0.5- 1 .5 m/s, the higher water velocity can not decrease the hot surface temperature, but can increase energy consumption for cooling water.

Physical and Mathematical Modeling of the Argon-Oxygen Decarburization Refining Process of Stainless Steel

The available studies in the literature on physical and mathematical modeling of the argon oxygen decarburization (AOD) process of stainless steel have briefly been reviewed. The latest advances made by the author with his research group have been summarized. Water modeling was used to investigate the fluid flow and mixing characteristics in the bath of an 18 t AOD vessel, as well as the 'back attack' action of gas jets and its effects on the erosion and wear of the refractory lining, with sufficiently full kinematic similarity. The non rotating and rotating gas jets blown through two annular tuyeres, respectively of straight tube and spiral flat tube type, were employed in the experiments. The geometric similarity ratio between the model and its prototype (including the straight tube type tuyeres) was 1:3. The influences of the gas flow rate, the angle included between the two tuyeres and other operating parameters, and the suitability of the spiral tuyere as a practical application, were examined. These latest studies have clearly and successfully brought to light the fluid flow and mixing characteristics in the bath and the overall features of the back attack phenomena of gas jets during the blowing, and have offered a better understanding of the refining process. Besides, mathematical modeling for the refining process of stainless steel was carried out and a new mathematical model of the process was proposed and developed. The model performs the rate calculations of the refining and the mass and heat balances of the system. Also, the effects of the operating factors, including adding the slag materials, crop ends, and scrap, and alloy agents; the non isothermal conditions; the changes in the amounts of metal and slag during the refining; and other factors were all considered. The model was used to deal with and analyze the austenitic stainless steel making (including ultra low carbon steel) and was tested on data of 32 heats obtained in producing 304 grade steel in an 18 t AOD vessel. The changes in the bath composition and temperature during the refining process with time can be accurately predicted using this model. The model can provide some very useful information and a reliable basis for optimizing the process practice of the refining of stainless steel and control of the process in real time and online.

Three-Dimension Mathematical Model of Total Phosphor in the Reservoir and Application

Taking the transport of total phosphor pollutants in the Beijing Miyun reservoir for example,we have obtained three dimensional distributing regularity of total phosphor pollutants by the calculation of the linear interpolation value of each point between horizontal layers. The credibility analysis in allusion to this method was carried out and the programming scheme for realizing this method was set forth.

Impact of pertinent parameters on foam behavior in the entrance region of porous media:mathematical modeling

Foam injection is a promising solution for control of mobility in oil and gas field exploration and development,including enhanced oil recovery,matrix-acidization treatments,contaminated-aquifer remediation and gas leakage prevention.This study presents a numerical investigation of foam behavior in a porous medium.Fractional flow method is applied to describe steady-state foam displacement in the entrance region.In this model,foam flow for the cases of excluding and including capillary pressure and for two types of gas,nitrogen(N2)and carbon dioxide(CO2)are investigated.Effects of pertinent parameters are also verified.Results indicate that the foam texture strongly governs foam flow in porous media.Required entrance region may be quite different for foam texture to accede local equilibrium,depending on the case and physical properties that are used.According to the fact that the aim of foaming of injected gas is to reduce gas mobility,results show that CO2 is a more proper injecting gas than N2.There are also some ideas presented here on improvement in foam displacement process.This study will provide an insight into future laboratory research and development of full-field foam flow in a porous medium.

Mathematical model of flow characteristic in multi-strand continuous casting tundishes

In this paper, the subject of mathematical model is a series of math expressions, which is used to calculate different regions＇ volume fraction and analyze flow characterization in multi-strand tundish. But research about mathematical model for multi-strand tundish is few, and so far, there has been no acknowledged math model for multi- strand tundish to describe its flow characteristic. If Sahai＇s model, which is originally proposed for the case of single-strand tundish （proposed in reference, and this model is widely used in the world）, is applied to describe flow feature in multi-strand tundish, the calculation results would be unreasonable. Based on the data of watermodel experiment results, the sum of each strand＇s dead region＇s volume fraction is bigger than 100%, and this obviously doesn＇T agree with reality; and the value of dead region＇s volume fraction is calculated to be minus according to mathematical simulation results data in another case. What＇s more, Sahai＇s model does not propose the standard of plotting the RTD-curve, and this makes scholars around the world can＇t achieve consensus of views about plotting RTD-curve. And the model doesn＇t consider the bypass flow and can＇t calculate its volume fraction, but bypass flow is critical to tundish metallurgy. And through Sahai＇s model, the calculation result of plug flow region＇s volume fraction is also not reasonable, because the model doesn＇t well describe the essence of plug flow. So these suggest that it is not reliable to apply Sahai＇s single-strand tundish model to multi-strand tundish case. Then a new model is attempted to propose in this paper for your discussion. In the new model, the standard of plotting RTD curve is definitely proposed, and relative calculation method is also proposed; and the feature of dead region is carefully studied and the model proposes a new method to calculate its volume fraction, and the calculation formula about its volume fraction can be adjustable according the actual demand; what＇s more, the new model considers the bypass flow and proposes a method to calculate its volume fraction for the first time, and then volume fraction of plug flow region, backmix flow region, dead region and bypass flow can be calculated and obtained at the same time; and this new model can better capture the deviation of reality flow pattern from ideal plug flow pattern, and reflects the feature of plug flow.

A MATHEMATICAL MODEL FOR POWER PLANT HEATERS

This paper studies the modelling and simulation for all forms of hcaters.The assumption of former days that the temperature of condensation is the saturationtemperature corresponding to heater pressure in steam side is no longer used.On the basisof the laws of conservation of mass,energy and momentum,the mathematical model ofheaters is established and the simulation calculation of a 125MW unit is made.The rcsultshows that the model is applicable for various kinds of steam-water heater in power plant.

PHYSICAL AND MATHEMATICAL MODELS OF POLLUTION DISPERSION IN THE YANGTZE ESTUARY

The method of combining a physical model with a mathematical model is described to study the concentration profile of pollutant dispersion in the Yangtze Estuary. the Experiments are described regarding a jet in a tidal physical model and two-dimensional calculations of diffusion using momentum and mass conservation equations of unsteady flow. The feature of dispersion in the tidal flow, which is different from that in the steady flow such as rivers, is explained. Dilution and dispersion mainly depend on the volume of runoff and tidal range. The results of the measurement and calculation are presented, and it can be seen that they are in good agreement.

Mathematical Modeling for Isotherms of Mango Pulp Powder,Obtained by Atomization

Mango, as the other fruits, is a perishable food that can be easily deteriorated and presents high levels of post-harvest loss. Therefore, dehydration is an important alternative to use the production excess. In this context, this work aimed at evaluating the hygroscopic behavior of the integral mango pulp powder, obtained by atomization, by means of adsorption isotherm. After applying BET’s, GAB’s, Henderson’s and Oswin’s mathematical models, it was possible to identify that the equations for two models were perfectly adjusted to the experimental results of mango pulp powder. Henderson’s model was the best adjusted experimental curve and showed the lowest average error (E) and the highest determination coefficient (R2) at all temperatures studied.

The Application of a Mathematical Modelling of Drying Kinetics in the Natural Solar Drying of Banana

In this work, a new mathematical modelling of drying kinetics is described. At first, the modelling of the transfer speed （St） of water was performed. Then St was used as basis to state the drying rate model. The drying rate depends not only on drying time, but also on some modelling parameters which are themselves time-dependent. All the modelling parameters are calculated directly from the experimental drying data. Then the theoretical model of the moisture content was stated. Subsequently, the drying kinetics of natural solar drying of plantain banana was studied as illustration. The drying rate was investigated. The comparison with other models encountered in literatures proved that the current theoretical model was decidedly more accurate. Then the modelling of moisture content of banana was performed and the results were compared with the Henderson and Pabis model. The current theoretical modelling provided by far the best fit.

Modeling the formation of soluble microbial products(SMP) in drinking water biofiltration

Both a theoretical and an empirical model were developed for predicting the formation of soluble microbial products （SMP） during drinking water biofiltration. Four pilot-scale biofilters with ceramsite as the medium were fed with different acetate loadings for the determination of SMP formation. Using numerically simulated and measured parameters, the theoretical model was developed according to the substrate and biomass balance. The results of this model matched the measured data better for higher SMP formation but did not fit well when SMP formation was lower. In order to better simulate the reality and overcome the difficulties of measuring the kinetic parameters, a simpler empirical model was also developed. In this model, SMP formation was expressed as a function of fed organic loadings and the depth of the medium, and a much better fit was obtained.

A Computational Model of Water Migration Flux in Freezing Soil in a Closed System

A computational model of water migration flux of fine porous soil in frost heave was investigated in a closed system. The model was established with the heat-m ass conservation law and from some previous experimental results. Through defini ng an auxiliary function an empirical function in the water migration flux, whic h is difficult to get, was replaced. The data needed are about the water conte nt along the soil column after test with enough long time. We adopt the test dat a of sample soil columns in [1] to verify the model. The result shows it can reflect the real situation on the whole.

A Review of Water Quality Optimisation Models and Techniques

This paper presents a state of the art review of water quality optimisation models and techniques from early 1970s to date in terms of the model/technique category, model/technique type, purpose and application. The models are categorised into Mathematical Programming Models and Meta-heuristic Programming Models. Similarly, the techniques are categorised into Mathematical Programming Techniques and Meta-heuristic Programming Techniques. The review is concluded by drawing attention to the rare nature of application of interior-point methods to water quality optimisation.

Development of Performance Models for Boiler Feed Water Treatment Ion Exchange Facility

The treatments of raw water using resins embedded with cation and anion were investigated in this study via a developed mathematical model. The developed mathematical model was used to predict the amount of sodium (Na+), calcium (Ca2+), magnesium (Mg2+) and ammonium (NH4+ ) ions removed by the resin embedded with hydrogen ion (H+) in the cation bed. The model was also used to investigate the amount of chloride (Cl-) and sulphate (SO42- ) ions treated by the resin embedded with hydroxyl ion (OH-) in the anion bed. The effect of flow rate and superficial velocity were also investigated. The simulation results showed that there was significant reduction of Na+, Ca2+, Mg2+, , Cl- and SO4 2-from their initial concentrations in raw water. This showed that the mathematical model was able to predict the concentrations of cations and anions investigated in this study. The result revealed that the flow rate of water has effect on the treatment of cations and anions in raw water using ion-exchange resins. Thus, operating the resin beds at very high flow rate reduced its performance while at very low flow rate the residence time of wastewater on the bed increased with resultant increase in performance. Similarly, high superficial velocity reduced the amount of ion concentration removed by the resin in both beds. The total final concentrations of cations in the cation bed by the model were 0.0003156, 0.0003452 and 0.0036 mol/m3 at 4.0, 4.5 and 6.5 m/min respectively while that from the anion bed were 0.0002597, 0.0002769 and 0.00205 mol/m3 at 4.0, 4.5 and 6.5 m/min respectively. The predicted model results, when compared with the maximum allowable limit of total concentration of both cations and anions of a functional industrial company (Notore chemical), showed a maximum percentage deviation ranging from 2.00% to 3.53%. This showed that the developed model has achieved its set objectives.

Research on Plane 2-D Sediment Model of a Watercourse on Yangtze River

To provide basis for sand excavation of hydraulic fill and land forming in Daohukou region in a watercourse (Wuhan reach) on Yangtze River, a 2-D water-sand mathematic model of this river reach is established. The variation of water levels of this reach and the back silting of watercourse after sand excavation are calculated. The rationality of the results calculated by this model and the measured data are validated and analyzed. The results show that, this model is reasonable and reliable.

BASIC THEORY AND MATHEMATICAL MODELING OF URBAN RAINSTORM WATER LOGGING

In this paper, a mathematical model for the urban rainstorm water logging wasestablished on the basis of one- and two-dimensional unsteady flow theory and the technique ofnon-structural irregular grid division. The continuity equation was discretized with the finitevolume method. And the momentum equations were differently simplified and discretized for differentcases. A method of ''special passage'' was proposed to deal with small-scale rivers and open channels.The urban drainage system was simplified and simulated in the model. The method of ''open slot'' wasapplied to coordinate the alternate calculation of open channel flow and pressure flow in drainagepipes. The model has been applied in Tianjin City and the verification is quite satisfactory.

A mathematical model for the description of the transport behavior of exchange cations in aquifer during sea water intrusion

In order to describe quantitatively the cation exchange action between water and rockand the transport behavior of exchange cations in the process of sea water intrusion, a newthree-dimensional mathematical model, which can simulte simultaneously the transport be-havior of exchange cations Na+, Mg2+ and Ca2+ is set up. This model is applied in prac-tice and the simulated values agree very well with the field data.