In order to obtain volumetric mass transfer coefficient, kLa values from the experimental dynamic oxygen absorption curves, a model of the reactor was developed based on the following assumptions:
The riser section of the reactor was assumed to extend to the dispersion height, meaning that gas bubbles in the gas-liquid separator constituted a part of the riser. In other words, no gas bubbles were present in the gas-liquid separator (or top section as it is referred to in the model). The figure below shows a representation of the reactor model:
Schematic representation of the reactor model
The governing mass balance equations for the reactor model are:
Plug flow of gas in the riser:
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Plug flow of liquid in the riser:
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Well-mixed top section:
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Plug flow of liquid in the downcomer:
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Sensor correction equation:
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With no gas in the downcomer and top section, εLD and εLT are equal to 1.
Equations (1) to (5) are subject to the following boundary conditions:
Solving the equations involved discretizing their spatial derivatives. A first-order backward-difference approximation was used, resulting in the following equations:
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The equations were solved by the Method of Lines with 50 grid points used to represent the total dispersion height in the reactor column. A FORTRAN program was written to handle this, utilizing the ODE solver DLSODE (Alan C. Hindmarsh, Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, California, United States). The volumetric mass transfer coefficient per unit volume of dispersion in the riser section of the reactor column, kLaR was changed in a loop till minimum deviation was found between a given experimental result and the model predication i.e., a best fit solution.
The volumetric mass transfer coefficient per unit volume of dispersion in the entire column was then calculated from:
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The reactor column volume, VC is the sum of the riser, downcomer and top section volumes.
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