A MATHEMATICAL MODEL OF A GAS-WATER RESERVOIR

Pollution of sub-surface water reservoirs mainly rivers and streams through contaminated water point sources (CWPS) was studied. The objective was to formulate a discrete time delay mathematical model which describes the dynamics of reservoir pollution using mixing-problem processes that involve single species contaminants such as nitrates, phosphorous and detergents. The concentration  of pollutants was expressed as a function of the inflow and outflow rates using the principle for the conservation of mass. Systems of ODEs generated from principles of mixing problems were refined into a system of DDEs so that the concentration of pollutant leaving the reservoir at time would be determined at some earlier instant, for the delay. The formulated model is a mathematical discrete time delay model which would be used to describe the dynamics of sub-surface water reservoir pollution. The results from the validation of the model were analyzed   to determine how time delays in the mixing processes affect the rate of particle movement in water reservoirs.

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Hydrogeological and Hydro Chemical Evaluation of Groundwater in Karbala Region Using Geographic Information System (GIS)

Engineering and Technology Journal ◽

10.30684/etj.v38i4a.492 ◽

2020 ◽

Vol 38 (4A) ◽

pp. 515-522

Author(s):

Marwa S. Hussein ◽

Imzahim A. Alwan ◽

Tariq A. Hussain

Keyword(s):

Mathematical Model ◽

System Modeling ◽

Water Reservoir ◽

Unconfined Aquifer ◽

Groundwater Table ◽

Flow State ◽

Groundwater Levels ◽

Chemical Evaluation ◽

Unsteady Flow Condition ◽

High Production

The study area is located in the holy governorate of Karbala, Iraq; the research studied a predictive mathematical model of groundwater within Dibdiba Formation and by fifty (50) wells distributed randomly within the boundaries of the study area, all of them fall within the unconfined aquifer. Likewise, there is no component to direct the activity of these wells, where a mathematical model for the study area has been developed using the groundwater system modeling program (GMS v.10). The area was divided into a grid where the dimensions of a single cell ranged from 250m×250m. The model of the steady flow state was adjusted utilizing pressure driven conductivity extending from 9 to 15 m/day with a 0.15 storage coefficient to match the groundwater levels measured with the calculated groundwater table. The model was run for unsteady flow condition in the first scenario with fifty (50) wells and five (5) years. The drawdown in the groundwater tables ranged between (0.05-1.05) m. In the second scenario, the model was run after adding thirty-six (36) wells for five (5) years, groundwater limits 0.15-1.15 meters. The drawdown values are concentrated near wells sites, and the drawdown decline as we move away from the sites of these wells and this reflects the nature of the water reservoir located in the study area, which is characterized by high production where compensation resulting from the operation of the wells decline rapidly by the reservoir. Therefore, the values of the drawdown in elevations appeared very low. The study also showed the possibility of drilling additional wells in this area, depending on this model to benefit from them in the future for different uses.

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COMPUTER SIMULATION OF DETERMINING SILTATION VOLUMES OF WATER RESERVOIR STORAGE ON THE AKSAY RIVER

Herald of Dagestan State Technical University Technical Sciences ◽

10.21822/2073-6185-2019-46-4-102-112 ◽

2020 ◽

Vol 46 (4) ◽

pp. 102-112

Author(s):

M. R. Magomedova ◽

Z. A. Kurbanova ◽

B. A. Shangereeva

Keyword(s):

Mathematical Model ◽

Computer Simulation ◽

Random Process ◽

Process Model ◽

Probabilistic Approach ◽

Water Reservoir ◽

Temporal Correlation ◽

Programming System ◽

Reservoir Storage ◽

Hydrological System

Objectives. The development of a mathematical model for the increased turbidity zones of the Aksay river in order to determine the siltation volumes of the Aksay water reservoir storage.Method. The mathematical model is developed using the theory of probability and the theory of random process outliers. The model takes the normal distribution of the horizontal and vertical components of the instantaneous flow velocities into account, as well as the Rayleigh law of the distribution of their maxima. The proposed model is used to calculate the “turbidity tail” of the Aksay river.Result. Due to the multifactorial nature of the continuously associated processes of siltation and deposition of suspended and bottom sediments in the upper pounds of the Aksay reservoir storage hydrological system, a mathematical model of the reservoir accretion process is developed. This model provides the reliability of accretion forecasting with spatial and temporal correlation with the siltation process model, which is actually feasible on the basis of computer simulation.Conclusion. The developed model, which is based on a probabilistic approach and the theory of random process outliers, reflects the overall process of sediment transport in open channels. The development and execution of simulation programmes is carried out using the Microsoft Developer Studio (MDS) and the Fortran Power Station algorithmic language, which comprises not only a programming system, but also a set of tools for supporting large software projects integrated into MDS.

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An application of the MIBSA model to the Little Chief Landslide

10.5194/egusphere-egu2020-21441 ◽

2020 ◽

Author(s):

Giuseppe Dattola ◽

Giovanni Battista Crosta ◽

Thomas Stewart

Keyword(s):

Mathematical Model ◽

Water Reservoir ◽

Material Behavior ◽

Material Strength ◽

Failure Behavior ◽

Model Parameters ◽

Time To Failure ◽

Empirical Formulas ◽

Volume Determination ◽

Landslide Volume

The prediction of a landslide behavior is fundamental for the design of early warning system (EWS) as well for the hazard and risk assessment. The evaluation of expected landslide volume (or extent), displacement, velocity and acceleration is mandatory. Very often empirical formulas are used for landslide volume determination whereas semi-empirical methods like the inverse velocity approach are used for time to failure definition.Various approaches have been proposed in the literature to reproduce the landslide behavior in terms of displacement for landslides which are already in an active state or for which displacement data are available for calibration. Some approaches introduce the material viscosity to reproduce the slow motion of the landslide when the driving factor is the fluctuation of the ground water table. Another strategy consists in using numerical methods in which the material strength reduction is introduced. In other cases more sophisticated constitutive models are employed to reproduce the material behavior.In this work, we propose an extension of a simple one dimensional mathematical model which reproduces the post failure behavior considering the landslide as an assembly of blocks interacting between each other and moving along the bedrock. In particular, the model takes into account the shear band mechanical behavior by means of a viscous-plastic model based on the Perzyna&#8217;s approach with strain-hardening. The interactions between blocks are modelled by formulating an interaction law which takes into consideration also the tangential effects due to friction along the lateral block boundaries. The forcing factors can be the piezometric level oscillation, the seismic shaking and the oscillation of external water reservoir level.To validate the mathematical model the numerical results are compared with the Little Chief Landslide located in the North Western Canada along the upper Columbia River valley. The landslide involves a mass of about 800 million of m3 with the stable bedrock depth ranging between 100 and 300 meters. This is an extremely slow landslide which has been investigated since 1960&#8217;s and for which displacements, piezometric levels and their evaluation in time are available for long time out-wards allowing to test the model. The landslide shows a periodic trend for displacements with cyclic accelerations and stable creeping. This allows for the calibration of the model parameters.

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Ecological assessment of surface water quality in a rainless period under the conditions of urban water collection

Geology Geography Ecology ◽

10.26565/2410-7360-2021-54-22 ◽

2021 ◽

Keyword(s):

Mathematical Model ◽

Water Quality ◽

Risk Index ◽

Measurement Data ◽

Water Reservoir ◽

Ecological Assessment ◽

Dust Storms ◽

Drought Risk ◽

Water Reservoirs ◽

Hydrological Regimes

Problem formulation. The global climate warming influences the balance of water reservoirs by lower precipitation, higher evaporation, erosion of soils and other changes. On the territory of Ukraine, the periods without rains, low snow level, warm winters and dry summers, strong winds and dust storms became frequent during the last decades. This led to a change in many hydrological parameters in comparison with the hydrological regimes usual in temperate climates. Therefore, the determination of the ecological assessment of the state of water reservoirs in the conditions of the urban drainage basin in the rainless period is an insufficiently studied and urgent issue. The aim of the article is estimation of quality of the river water in the system of rivers Lopan-Kharkov-Udy on the urban landscale of Kgarkov region. Materials and methods. Field sampling of water and bottom sediments to provide an environmental assessment of the water reservoir; comparison of the results obtained with similar ones obtained for rainy periods and periods of snow melting in different hydrological regimes, and statistical analysis of the measured data. Results. Analysis of the open source data revealed that Kharkov region is among the top three in terms of drinking and technical water needs for various purposes. The region has a maximum possible drought risk index (0.8-1) and high values of water stress indices (2-3) and coastal flood risk (2-3). Water samples taken from different sections of the Lopan and Udy rivers in different seasons showed that some of the parameters exceed the corresponding control values, especially in rainless periods, but in general water quality indices correspond to 1-2 quality classes (depending on the season) for the river Lopan and the 1st class of quality - for the river Udy. Numerical calculations on a mathematical model using the measurement data showed that global warming at 0.5-1° C by 2030 will lead to a significant deterioration in water quality and its availability as the required amount of drinking and industrial water for the region. Scientific novelty. Novel mathematical model is proposed for simple estimations of the water pollution over time at different groth rate of the average temperature accounting for known number of pollutants. Practical significance. The obtained results are useful for further development of the system of water management on urgan territories, testing different hypothesis and scenarios.

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Modeling of Water Generation from Air Using Anhydrous Salts

Energies ◽

10.3390/en14133822 ◽

2021 ◽

Vol 14 (13) ◽

pp. 3822

Author(s):

Shereen K. Sibie ◽

Mohamed F. El-Amin ◽

Shuyu Sun

Keyword(s):

Mathematical Model ◽

Relative Humidity ◽

Water Absorption ◽

Copper Chloride ◽

Water Reservoir ◽

Ambient Air ◽

Water Harvesting ◽

Atmospheric Water ◽

Water Scarce ◽

The Mathematical Model

The atmosphere contains 3400 trillion gallons of water vapor, which would be enough to cover the entire Earth with a one-inch layer of water. As air humidity is available everywhere, it acts as an abundant renewable water reservoir, known as atmospheric water. The efficiency of an atmospheric water harvesting system depends on the sorption capacities of water-based absorption materials. Using anhydrous salts is an efficient process in capturing and delivering water from ambient air, especially under a condition of low relative humidity, as low as 15%. Many water-scarce countries, like Saudi Arabia, receive high annual solar radiation and have relatively high humidity levels. This study is focused on the simulation and modeling of the water absorption capacities of three anhydrous salts under different relative humidity environments: copper chloride (CuCl2), copper sulfate (CuSO4), and magnesium sulfate (MgSO4), to produce atmospheric drinking water in water-scarce regions. By using a mathematical model to simulate water absorption, this study attempts to compare and model the results of the current computed model with the laboratory experimental results under static and dynamic relative humidities. This paper also proposes a prototype of a system to produce atmospheric water using these anhydrous salts. A sensitivity analysis was also undertaken on these three selected salts to determine how the uniformity of their stratified structures, thicknesses, and porosities as applied in the mathematical model influence the results.

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