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Dear Community

I'm doing my first steps in COMSOL modeling. The problem to solve is the simulation of transient, radial gas flow through a piece of radial rock sample. The governing physical phenomena is flow through porous media obeying Darcy's law, so I'm using the Earth Science module. The rock sample has a borehole in its centre (with radius rw), where gas is entering. Gas leaves the core through its outer mantle (i.e. @ radius R). Gas enters the core form a finite volume vessel ("in") connected to the central borehole having a changing pressure of p_in, and flows out from the core into a vessel ("out") having a changing pressure of p_out. This "out" vessel is connected to the outer mantle of the rock sample. So the in- and outflow bondary conditions can be described as follows, i.e. gas inflow and outflow velocities depend on two ODEs as follows:

@ r = rw: p = p_in, and C1 * d(p_in) / dt = v_in
@ r = R: p = p_out and C2 * d(p_out) / dt = v_out

Here v_in and v_out are in- and outflux velocities respectivelyThey could also be expressed with spatial derivatives of the pressure @ r=rw and r=R boundaries. C1 and C2 are known constants.

I'm using COMSOL V4.0, and a 1D axialsymmetric model. All parameters are known, my problem is how to specify the above boundary conditions at the inflow surface (which is the wall of the central borehole @ r = rw) and the outflow bondary (which is the outer mantle of the core sample, i.e. r = R)? I have to add two ODEs to these boundaries, which express that the in- and outflow gas velocities at these surfaces are proportional to the pressure change rates of the "in" and "out" vessels respectively.

The rock sample is regarded as homogeneous and isotropic. I've derived the analytical solution already, and I would like to compare it with the numerical solution, and later on I would like to extend the problem to heterogeneous, anisotropic cores, which cannot be solved analytically, but numerically only.

Any help, advice or an example giving me the first push how to solve this problem would be gratefully acknowledged.

best regards

Andras

P.S.: I coud not upload a ppt file from the assembly to the website, I could e-mail it privately.