A method of mass transfer calculation in a back-flow model

1980 ◽  
Vol 45 (8) ◽  
pp. 2164-2170
Author(s):  
Josef Vrba
Keyword(s):  
Mass Transfer ◽  
Nonlinear Equations ◽  
Flow Model ◽  
Back Flow ◽  
Number Of Iterations

Instead of solving a set of N nonlinear equations (as has been proposed by the author and his coworker), the problem may be solved iteratively as a linear one. The proposed method converges rapidly and the number of iterations is practically constant regardless of the number of stages in countercurrent cascade N and the degree of nonlinearity of equilibrium formula. The method proved to be suitable for computation on desk-top calculator.

Difference Schemes for Three Kinds of Nonlinear Flow Model in Low Permeability Porous Media

2015 ◽  
Vol 723 ◽  
pp. 125-130
Author(s):  
Tang Wei Liu ◽  
Hong Zhi Lu ◽  
Xiang Ping Zou
Keyword(s):  
Nonlinear Equations ◽  
Flow Model ◽  
Finite Difference Methods ◽  
Nonlinear Flow ◽  
Low Permeability ◽  
Order Difference ◽  
Discrete Equations ◽  
Forward Difference ◽  
Difference Methods ◽  
Rectangle Formula

This paper discusses three kinds of typical one-dimensional nonlinear equations coming from low permeability reservoir seepage models with different boundary conditions. The several finite difference methods including forward difference method and second central order difference quotient method are used for the respective discrete process of three models. With these difference methods, the discrete schemes of models are obtained. Then the corresponding nonlinear discrete equations are deduced. While dealing with the boundary condition, the mid-rectangle formula is used. Finally, integrated discrete equations of three nonlinear equations are formed. The results should be meaningful for the numerical simulation of non-Darcy flow model of the low-permeability oil wells.

Oxygen absorption into Ellis liquid in a bead column

1989 ◽  
Vol 54 (7) ◽  
pp. 1795-1799
Author(s):  
František Potůček ◽  
Jiří Stejskal
Keyword(s):  
Mass Transfer ◽  
Transfer Coefficient ◽  
Mass Transfer Coefficient ◽  
Flow Model ◽  
Oxygen Absorption ◽  
Correlation Equations ◽  
Dimensionless Groups ◽  
Vertical Row ◽  
Newtonian Liquids

Liquid side mass transfer coefficient was measured for absorption of oxygen in non-Newtonian liquids. The experiments were carried out in a laboratory absorption bead column in which the liquid flowed over a single vertical row of spheres without vertical spaces between elements and/or with spaces of 0.2 cm between elements. The results were described by correlation equations involving dimensionless groups modified for Ellis flow model.

Ozone mass transfer in water treatment: hydrodynamics and mass transfer modeling of ozone bubble columns

2001 ◽  
Vol 1 (2) ◽  
pp. 123-130 ◽  
Author(s):  
M.G. El-Din ◽  
D.W. Smith
Keyword(s):  
Mass Transfer ◽  
Steady State ◽  
Liquid Phase ◽  
Plug Flow ◽  
Axial Dispersion ◽  
Bubble Columns ◽  
Algebraic Equations ◽  
Mixed Flow ◽  
Back Flow ◽  
Linear Algebraic Equations

Most of the mathematical models that are employed to model the performance of bubble columns are based on the assumption that either plug flow or complete mixing conditions prevail in the liquid phase. Although due to the liquid-phase axial dispersion, the actual flow pattern in bubble columns is usually closer to being mixed flow rather than plug flow, but still not completely mixed flow. Therefore, the back flow cell model (BFCM), that hypothesises both back flow and exchange flow to characterise the liquid-phase axial dispersion, is presented as an alternative approach to describe the hydrodynamics and mass transfer of ozone bubble columns. BFCM is easy to formulate and solve. It is an accurate and reliable design model. Transient BFCM consists of NBFCM ordinary-first-order differential equations in which NBFCM unknowns (Yj) are to be determined. That set of equations was solved numerically as NBFCM linear algebraic equations. Steady-state BFCM consists of 3 × NBFCM non-linear algebraic equations in which 3 × NBFCM unknowns (qG,j, Xj, and Yj) are to be determined. Those non-linear algebraic equations were solved numerically using Newton–Raphson technique. Steady-state BFCM was initially tested using the pilot-scale experimental data of Zhou. BFCM provided excellent predictions of the dissolved ozone profiles under different operating conditions for both counter and co-current flow modes.

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