[Numpy-discussion] Interpolation question

Andrea Gavana andrea.gavana at gmail.com
Mon Mar 29 18:57:29 EDT 2010

```HI Friedrich & All,

On 29 March 2010 23:44, Friedrich Romstedt wrote:
> 2010/3/29 Andrea Gavana <andrea.gavana at gmail.com>:
>> If anyone is interested in a follow up, I have tried a time-based
>> interpolation of my oil profile (and gas and gas injection profiles)
>> using those 40 interpolators (and even more, up to 400, one every
>> month of fluid flow simulation time step).
>>
>> I wasn't expecting too much out of it, but when the interpolated
>> profiles came out (for different combinations of input parameters) I
>> felt like being on the wrong side of the Lala River in the valley of
>> Areyoukidding. The results are striking. I get an impressive agreement
>> between this interpolated proxy model and the real simulations,
>> whether I use existing combinations of parameters or new ones (i.e., I
>> create the interpolation and then run the real fluid flow simulation,
>> comparing the outcomes).
>
> I'm reasoning about the implications of this observation to our
> understanding of your interpolation.  As Christopher pointed out, it's
> very important to know how many gas injections wells are to be
> weighted the same as one year.
>
> When you have nice results using 40 Rbfs for each time instant, this
> procedure means that the values for one time instant will not be
> influenced by adjacent-year data.  I.e., you would probably get the
> same result using a norm extraordinary blowing up the time coordinate.
>  To make it clear in code, when the time is your first coordinate, and
> you have three other coordinates, the *norm* would be:
>
> def norm(x1, x2):
>    return numpy.sqrt((((x1 - x2) * [1e3, 1, 1]) ** 2).sum())
>
> In this case, the epsilon should be fixed, to avoid the influence of
> the changing distances on the epsilon determination inside of Rbf,
> which would spoil the whole thing.
>
> I have an idea how to tune your model:  Take, say, the half or three
> thirds of your simulation data as interpolation database, and try to
> reproduce the remaining part.  I have some ideas how to tune using
> this in practice.

This is a very good idea indeed: I am actually running out of test
cases (it takes a while to run a simulation, and I need to do it every
time I try a new combination of parameters to check if the
interpolation is good enough or rubbish). I'll give it a go tomorrow
at work and I'll report back (even if I get very bad results :-D ).

>> As an aside, I got my colleagues reservoir engineers playfully
>> complaining that it's time for them to pack their stuff and go home as
>> this interpolator is doing all the job for us; obviously, this misses
>> the point that it took 4 years to build such a comprehensive bunch of
>> simulations which now allows us to somewhat "predict" a possible
>
> :-) :-)
>
>> I wrapped everything up in a wxPython GUI with some Matplotlib graphs,
>> and everyone seems happy.
>> The only small complain I have is that I
>> wasn't able to come up with a vector implementation of RBFs, so it can
>> be pretty slow to build and interpolate 400 RBFs for each property (3
>> of them).
>
> Haven't you spoken about 40 Rbfs for the time alone??

Yes, sorry about the confusion: depending on which "time-step" I
choose to compare the interpolation with the real simulation, I can
have 40 RBFs (1 every year of simulation) or more than 400 (one every
month of simulation, not all the monthly data are available for all
the simulations I have).

> Something completely different: Are you going to do more simulations?

110% surely undeniably yes. The little interpolation tool I have is
just a proof-of-concept and a little helper for us to have an initial
grasp of how the production profiles might look like before actually
running the real simulation. Something like a toy to play with (if you
can call "play" actually working on a reservoir simulation...). There
is no possible substitute for the reservoir simulator itself.

Andrea.

"Imagination Is The Only Weapon In The War Against Reality."
http://xoomer.alice.it/infinity77/

==> Never *EVER* use RemovalGroup for your house removal. You'll
regret it forever.
http://thedoomedcity.blogspot.com/2010/03/removal-group-nightmare.html <==

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