A mathematical model which simulates the previously reported experimental results on permeability decrease of porous media is proposed. In the model, the silica deposition rate is proportional to the product of the degree of supersaturation of dissolved silica in geothermal water with respect to amorphous silica solubility and the surface area of porous media exposed to the water. In addition, the effect of the previously deposited silica on silica deposition should be considered because it accelerates the silica deposition. Unknown deposition rate coefficients, and ß2, are determined using trial and error method so as to fit the measured flow rates. The calculated profiles for the amount of deposited silica and permeability are then compared with the experimental data. The optimum values for the deposition rate coefficients are obtained by assuming that a very small quantity of excess silica in the water can deposit along the porous media. For instance, at the inlet of the porous media, it is only 2 ppm, although the concentration of excess silica in the water is as high as 201 ppm. The deposition rate coefficients determined are (ß1 = 3.5 x 10 -4cm/s and ß2 =4.0x10 3 ~ 5.0 x l03.
|Number of pages||22|
|Journal||journal of the geothermal research society of japan|
|Publication status||Published - 1987|
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