Mathematical modeling of water purification in a bioplato filter

A mathematical model of filtration taking into account clogging and suffusion in the bioplato filter system in the two-dimensional case was built. The constructed mathematical model takes into account the physical effects of the dynamic change of porosity and the dependence of the filtration coefficient on the concentration of contaminants, which is not in the known analogues

Transport of Turbulence Across Permeable Interface in a Turbulent Channel Flow: Interface-Resolved Direct Numerical Simulation

Turbulence transportation across permeable interfaces is investigated using direct numerical simulation, and the connection between the turbulent surface flow and the pore flow is explored. The porous media domain is constructed with an in-line arranged circular cylinder array. The effects of Reynolds number and porosity are also investigated by comparing cases with two Reynolds numbers ($$Re\approx 3000,6000$$ R e ≈ 3000 , 6000 ) and two porosities ($$\varphi =0.5,0.8$$ φ = 0.5 , 0.8 ). It was found that the change of porosity leads to the variation of flow motions near the interface region, which further affect turbulence transportation below the interface. The turbulent kinetic energy (TKE) budget shows that turbulent diffusion and pressure transportation work as energy sink and source alternatively, which suggests a possible route for turbulence transferring into porous region. Further analysis on the spectral TKE budget reveals the role of modes of different wavelengths. A major finding is that mean convection not only affects the distribution of TKE in spatial space, but also in scale space. The permeability of the wall also have an major impact on the occurrence ratio between blow and suction events as well as their corresponding flow structures, which can be related to the change of the Kármán constant of the mean velocity profile.

A new theory for membrane efficiency coefficient of compacted clay

A new method for calculation the membrane efficiency coefficient w of compacted clay is proposed in this paper. The influence of fixed negative charge on the surface of clay minerals is considered. What’s more, the change of porosity during deformation is considered. Based on the chemical potential of specimens, the true ion concentration in pore-water is obtained. Based on the true ion concentration in pore water, the disjoining pressure considering fixed negative charge inside soils and the change of void ratio is proposed. A new calculation method for the membrane efficiency coefficient of compacted clay is established. The test data of w considering different porosity are calculated and the calculated results are compared with the traditional calculation methods. The new calculation methods of w provide a more physical-based theory for environmental geotechnical engineering.

Degenerate equations in a diffusion–precipitation model for clogging porous media

In this article, we consider diffusive transport of a reactive substance in a saturated porous medium including variable porosity. Thereby, the evolution of the microstructure is caused by precipitation of the transported substance. We are particularly interested in analysing the model when the equations degenerate due to clogging. Introducing an appropriate weighted function space, we are able to handle the degeneracy and obtain analytical results for the transport equation. Also the decay behaviour of this solution with respect to the porosity is investigated. There a restriction on the decay order is assumed, that is, besides low initial concentration also dense precipitation leads to possible high decay. We obtain nonnegativity and boundedness for the weak solution to the transport equation. Moreover, we study an ordinary differential equation (ODE) describing the change of porosity. Thereby, the control of an appropriate weighted norm of the gradient of the porosity is crucial for the analysis of the transport equation. In order to obtain global in time solutions to the overall coupled system, we apply a fixed point argument. The problem is solved for substantially degenerating hydrodynamic parameters.

Investigating Permeability of Coal Samples of Various Porosities under Stress Conditions

Among the numerous factors that have an impact on coal permeability, coal porosity is one of the main parameters. A change in the mechanical stress applied to coal results in a change of porosity. The main objective of the conducted research was to answer the following question: is a decline in coal permeability a direct effect of a decrease in coal porosity, and does mechanical stress result solely in a porosity change? A study of coal porosity under mechanical stress conditions was conducted using a uniquely constructed measurement stand. The coal samples used were briquettes prepared from a granular coal material (middle-rank coal of type B—meta bituminous, upper carboniferous formation) from the “Zofiówka” coal mine, in Poland. In order to describe coal permeability, the Klinkenberg equation was used, as it takes into consideration the slippage effect, typical of porous media characterized by low permeability. On the basis of the obtained results, it was established that the values of the Klinkenberg permeability coefficient decrease as the mechanical stress and the corresponding reduction in porosity become greater. As the briquette porosity increased, the Klinkenberg slippage effect: (i) disappeared in the case of nitrogen, (ii) and was minor for methane. The briquettes used were characterized by various porosities and showed that mechanical stress results mainly in a change in coal porosity, which, in turn, reduces coal permeability.

Optical strain measurement for the modeling of surgical meshes and their porosity

The porosity of surgical meshes makes them flexible for large elastic deformation and establishes the healing conditions of good tissue in growth. The biomechanic modeling of orthotropic and compressible materials requires new materials models and simulstaneoaus fit of deformation in the load direction as well as trannsversely to to load. This nonlinear modeling can be achieved by an optical deformation measurement. At the same time the full field deformation measurement allows the dermination of the change of porosity with deformation. Also the socalled effective porosity, which has been defined to asses the tisssue interatcion with the mesh implants, can be determined from the global deformation of the surgical meshes.

Estimation of Sand Production Rate Using Geomechanical and Hydromechanical Models

This paper aims to develop a numerical model that can be used in sand control during production phase of an oil and gas well. The model is able to predict not only the onset of sand production using critical bottom hole pressure inferred from geomechanical modelling, but also the mass of sand produced versus time as well as the change of porosity versus space and time using hydromechanical modelling. A detailed workflow of the modelling was presented with each step of calculations. The empirical parameters were calibrated using laboratory data. Then the modelling was applied in a case study of an oilfield in Cuu Long basin. In addition, a sensitivity study of the effect of drawdown pressure was presented in this paper. Moreover, a comparison between results of different hydromechanical models was also addressed. The outcome of this paper demonstrated the possibility of modelling the sand production mass in real cases, opening a new approach in sand control in petroleum industry.

Determination of Sintering Activity of Sodium-Potassium Feldspar

The aim of the article is to describe the sintering activity of industrially milled sodium potassium feldspar to determine of optimal firing temperature during fast firing typical for e.g. production of dry pressed ceramic tiles. The change of porosity, flexural strength, firing shrinkage and mineralogical composition in dependence on the firing temperature (1120 1210 °C) were determined on the test samples made from dry granulate prepared from the pure feldspar. Tested alkali sodium potassium feldspar is characterized by low sintering temperature (1190 °C) during fast firing (heating rate 10 °C/min). During the sintering process, feldspar gradually disappears in phases first of all potassium feldspar (microcline), sodium feldspar (albite) we can find in the fired body at firing temperature 1180 °C.

Effect of ZrO2 Coating on the Properties of Porous Silicon Nitride

The powder of 3molY2O3-ZrO2 as the coating material sprayed on the surface of porous silicon nitride which porosity is more than 50% by Plasma Sprayed. The microstructure of the coating and the matrix was analysised. The performance change of porosity, strength and insulation, before and after spray, were researched.