Re: [Opm] Solving a linear eigenvalue problem with OPM

[Atgeirr Rasmussen]

Hi Rodrigo,

Thanks for your kind words!

The problem you describe looks interesting, and I hope that we can help you 
towards a solution.
First I must admit that I have very limited experience with solving eigenvalue 
problems numerically
(I have not done that in 20 years…) which limits how useful tips I can give.

I think that some sort of eigenvalue solver exists in dune-istl (on which we 
base our linear algebra),
but I have no idea if it would be fit for your purpose, I think Markus Blatt 
would be a better person to
answer that.

Finally, I agree that you could probably reuse the matrix created in the 
upscaling code for your purpose.
You can find it in the IncompFlowSolverHybrid class (opm-upscaling module, at 
opm/porsol/mimetic/IncompFlowSolverHybrid.hpp),
the matrix is stored in the class after it's built:

(lines 936-937)

Dune::BCRSMatrix   S_;// System matrix
Dune::BlockVector  rhs_;  // System RHS

Hope that helps you along!

Atgeirr



26. okt. 2017 kl. 17.54 skrev 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"). 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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[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"
). 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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