[Opm] Solving a linear eigenvalue problem with OPM

[Rodrigo Piccinini]

Hello

First, thanks for sharing OPM. I've compiled it in Debian Stretch and I'm
running some of the tutorials.
It is a great tool!

I'm writing to ask for guidance through OPM code as I'm interested in
studying the application of diffusion equation eigenvalues to the
characterization of heterogeneous reservoirs.
The basic idea is to compare eigenvalues of 3D reservoir models with
eigenvalues obtained from extended well tests.

The problem I'd like to solve with OPM (possibly by modifying some of the
code) is the linear eigenvalue problem that results after applying
separation of variables to the linear diffusion equation. In latex code,
that would be:

\nabla k(x) / \mu \cdot \nabla \Psi = \lambda w(x) \Psi ,

where k(x) is the permeability tensor, \mu is the fluid viscosity and w(x)
is a weight scalar function (e.g., porosity times compressibility). At
boundaries, Neumann boundary conditions apply and
\lambda and \Psi are the eigenvalues and the eigenfunctions, respectively.
I'm  considering single phase flow only.

I believe some suitable code may exist in opm-upscaling module.

If I'm successful at this task, I'd like to compare the computed
eigenvalues with ones extracted from an extended well test performed at
Petrobras. Maybe that can help integrate the well test data into the
reservoir model. The eigenvalues from the well test are being extracted
with a method introduced by two Shell engineers ("A New Method for
Estimating Average Reservoir Pressure: The Muskat Plot Revisited"
<https://www.onepetro.org/journal-paper/SPE-102730-PA>). I expect to make
it a phd project for myself, but I'd like to make some tries before looking
for a university.

Sorry for the long message and thanks in advance.

--
Rodrigo
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