We have a vertical pipe, let say 1000 m long; near the bottom the pipe has openings through which in communicates with a porous medium, obeying Darcy's law, let say of permeability 10^-13 m^2.
At t < 0, everything is filled with fluid (water with suitable salts and suspended solids to have the right density) at hydrostatic equilibrium; the pore pressure in the porous medium is maintained at constant pressure P0 far from the pipe. (see the picture).
At t = 0 and for a duration of about 2 sec, a source of gas is turned on at the bottom of the well (in practice by burning a suitable chemical; there is other hardware such as a cable in the pipe, but let's neglect that); let's take a point source with constant rate over 2 sec, producing about 10 kg of a perfect gas during that time. Some of the gas will go into the porous medium, and some will raise up the well by buoyancy. The question is: how much goes up, and how much goes in the porous medium, what are the gas flow rates versus time. Also of interest is the evolution of pressure along the pipe.
The problem can be done approximately, I believe, with analytical methods, but I am interested in doing it numerically, so that it can later be extended to more coplex geometries (inclined pipe, detailed geometry of openings between pipe and porous media, finite rigidity pipe) or to more complex physics (the gas is hot, and one could look at how it is cooled down).
Андрюша, а ты хорошо знаешь английский язык, или просто прикалываешься? Мне интересно, есть ли в Америке форумы примерно нашего уровня на космическую тему, и о чем они там говорят?
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