Bacterial transport in porous media: New aspects of the mathematical model

2005 ◽  
Vol 260 (1-3) ◽  
pp. 53-62 ◽  
Author(s):  
Tushar Kanti Sen ◽  
Dipankar Das ◽  
Kartic C. Khilar ◽  
G.K. Suraishkumar
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Bacterial Transport ◽  
Transport In Porous Media ◽  
The Mathematical Model

BASIC MATHEMATICAL MODELS AND AN APPROXIMATE METHOD OF FILTRATION THEORY

2021 ◽  
pp. 25-31
Author(s):  
Alla A. Mussina
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Mathematical Models ◽  
Heterogeneous Porous Media ◽  
Effective Management ◽  
Filtration Theory ◽  
New Device ◽  
Scientific Papers ◽  
The Mathematical Model ◽  
Inhomogeneous Liquids

The article defines the basic concepts of filtration theory and provides an overview of the existing mathematical models of inhomogeneous liquids in porous media. The paper considers the Stefan problem. The number of scientific papers devoted to the study of porous structures has recently increased. This is primarily due to the fact that the prob-lems of oil and uranium production have been identified, and the solution of environmental problems is overdue. Therefore, a new device is needed to develop models of liquid filtration. With the advent and development of computer technology, it has become easier to solve problems that require numerical methods for their solution. Understanding the movement of fluids and the mechanism of dissolution of rocks under the action of acids in heterogeneous porous media is of great importance for the extraction and production of oil and the effective management of these processes. The article examines the mathematical model of the theory of isothermal filtration. Possible variants of the solva-bility of the model are shown. The research scheme consists of the output of a mathematical model, the formulation of the problem, one variant of the solution of the problem, the algorithm of the numerical method of solving the problem.

Asymptotic Model of Free Convection Flow on a Vertical Surface in Porous Media with Newtonian Heating

2015 ◽  
Vol 756 ◽  
pp. 469-475
Author(s):  
Anna A. Bocharova ◽  
Irina V. Plaksina ◽  
Andrey A. Obushnyy
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Free Convection ◽  
Vertical Surface ◽  
Momentum Equation ◽  
Convection Flow ◽  
Asymptotic Model ◽  
Free Convection Flow ◽  
Energy Equations ◽  
The Mathematical Model

The mathematical model based on system of momentum and energy equations for free convection flow along a vertical surface in porous media under boundary conditions of the third sort is solved analytically using the method of matched asymptotic expansions. The region of validity for boundary layer model and expansions for stream function and temperature with parameter of perturbations were defined. The dependence of characteristic flow from governing dimensionless parameters and was analyzed numerically. The influence of viscous and convective terms of momentum equation in the proposed mathematical model significantly increases the rate of heat transfer on plate in porous media in comparison with Darsy flow model.

scholarly journals Modeling and Analysis of Magnetic Nanoparticles Injection in Water-Oil Two-Phase Flow in Porous Media under Magnetic Field Effect

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mohamed F. El-Amin ◽  
Ahmed M. Saad ◽  
Amgad Salama ◽  
Shuyu Sun
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Porous Media ◽  
Magnetic Nanoparticles ◽  
Additional Term ◽  
Flow In Porous Media ◽  
Phase System ◽  
Two Phase ◽  
The Mathematical Model ◽  
Nanoparticles Suspension

In this paper, the magnetic nanoparticles are injected into a water-oil, two-phase system under the influence of an external permanent magnetic field. We lay down the mathematical model and provide a set of numerical exercises of hypothetical cases to show how an external magnetic field can influence the transport of nanoparticles in the proposed two-phase system in porous media. We treat the water-nanoparticles suspension as a miscible mixture, whereas it is immiscible with the oil phase. The magnetization properties, the density, and the viscosity of the ferrofluids are obtained based on mixture theory relationships. In the mathematical model, the phase pressure contains additional term to account for the extra pressures due to fluid magnetization effect and the magnetostrictive effect. As a proof of concept, the proposed model is applied on a countercurrent imbibition flow system in which both the displacing and the displaced fluids move in opposite directions. Physical variables, including water-nanoparticles suspension saturation, nanoparticles concentration, and pore wall/throat concentrations of deposited nanoparticles, are investigated under the influence of the magnetic field. Two different locations of the magnet are studied numerically, and variations in permeability and porosity are considered.

scholarly journals A SIMPLIFIED OXIDATION MODEL FOR TWO-PHASE FLOW IN POROUS MEDIA

2002 ◽  
Vol 1 (2) ◽  
pp. 09
Author(s):  
J. C. Da Mota ◽  
A. J. De Souza ◽  
D. Marchesin ◽  
P. W. Teixeira
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Wave Structure ◽  
Thermal Recovery ◽  
Flow In Porous Media ◽  
Low Temperature Oxidation ◽  
Two Phase ◽  
Temperature Oxidation ◽  
Physical Effects ◽  
The Mathematical Model

This paper describes a simplified mathematical model for thermal recovery by oxidation for flow of oxygen and oil in porous media. Some neglected important physical effects include gravity, compressibility and heat loss to the rock formation, but heat longitudinal conduction and capillary pressure difference between the phases are considered. The mathematical model is obtained from the mass balance equations for air and oil, energy balance and Darcy's law applied to each phase. Based on this model some typical features in low temperature oxidation concerning the wave structure are captured. Numerical simulations showing saturations and temperature profiles are reported.

scholarly journals Water-In-Oil Emulsions through Porous Media and the Effect of Surfactants: Theoretical Approaches

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 620 ◽  
Author(s):  
Josue F. Perez-Sanchez ◽  
Nancy P. Diaz-Zavala ◽  
Susana Gonzalez-Santana ◽  
Elena F. Izquierdo-Kulich ◽  
Edgardo J. Suarez-Dominguez
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Theoretical Study ◽  
High Viscosity ◽  
Dispersed Phase ◽  
Interaction Energies ◽  
Theoretical Approaches ◽  
Heavy Crude ◽  
Oil Emulsions ◽  
The Mathematical Model

The most complex components in heavy crude oils tend to form aggregates that constitute the dispersed phase in these fluids, showing the high viscosity values that characterize them. Water-in-oil (W/O) emulsions are affected by the presence and concentration of this phase in crude oil. In this paper, a theoretical study based on computational chemistry was carried out to determine the molecular interaction energies between paraffin–asphaltenes–water and four surfactant molecules to predict their effect in W/O emulsions and the theoretical influence on the pressure drop behavior for fluids that move through porous media. The mathematical model determined a typical behavior of the fluid when the parameters of the system are changed (pore size, particle size, dispersed phase fraction in the fluid, and stratified fluid) and the viscosity model determined that two of the surfactant molecules are suitable for applications in the destabilization of W/O emulsions. Therefore, an experimental study must be set to determine the feasibility of the methodology and mathematical model displayed in this work.

scholarly journals A SIMPLIFIED OXIDATION MODEL FOR TWO-PHASE FLOW IN POROUS MEDIA

2002 ◽  
Vol 1 (2) ◽  
Author(s):  
J. C. Da Mota ◽  
A. J. De Souza ◽  
D. Marchesin ◽  
P. W. Teixeira
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Wave Structure ◽  
Thermal Recovery ◽  
Flow In Porous Media ◽  
Low Temperature Oxidation ◽  
Two Phase ◽  
Temperature Oxidation ◽  
Physical Effects ◽  
The Mathematical Model

This paper describes a simplified mathematical model for thermal recovery by oxidation for flow of oxygen and oil in porous media. Some neglected important physical effects include gravity, compressibility and heat loss to the rock formation, but heat longitudinal conduction and capillary pressure difference between the phases are considered. The mathematical model is obtained from the mass balance equations for air and oil, energy balance and Darcy's law applied to each phase. Based on this model some typical features in low temperature oxidation concerning the wave structure are captured. Numerical simulations showing saturations and temperature profiles are reported.

Bacterial transport in porous media: Evaluation of a model using laboratory observations

1992 ◽  
Vol 28 (3) ◽  
pp. 915-923 ◽  
Author(s):  
George M. Hornberger ◽  
Aaron L. Mills ◽  
Janet S. Herman
Keyword(s):  
Porous Media ◽  
Bacterial Transport ◽  
Transport In Porous Media

On the equation describing the transient flow of a compressible liquid through deformable porous media

1978 ◽  
Vol 56 (6) ◽  
pp. 691-695
Author(s):  
B. S. BačlićF ◽  
D. P. Sekulić
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Porous Media ◽  
Transient Flow ◽  
A Priori ◽  
Nonlinear Partial Differential Equation ◽  
Compressible Liquid ◽  
Deformable Porous Media ◽  
The Mathematical Model

The effect of the linearized treatment of the equation describing the transient flow of a compressible liquid through elastic porous media is studied analytically in this paper. It is shown that if there is a need for a simplified description based on the linearization of the original nonlinear partial differential equation, then it has to be done in an optimal sense. However, even then the mathematical model may degenerate for certain boundary conditions and some values of parameters defining the dependence of fluid and media properties on pressure. This fact is illustrated by the help of a simple example of transient filtration in a semi-infinite Hookeian medium. The reliability and adequateness of the a priori linearized equation is discussed.

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