What I have found so far and what I usually do is defining the optimum gridblock size in a reservoir model by running multiple cases with fine and then coarser gridblock sizes then find a compromise between simulation accuracy and run time.
I am not sure if there is a method to pre-define the optimum gridblock size that does not result in large reduction of accuracy without the need of making multiple runs (maybe based on governing equations of reservoir simulation). I am more interested in areal since vertical is governed by heterogeneity mostly. The issue raises again when trying to use paeudo relative permeability to reduce number of gridblocks. Here, I am not trying to eliminate a geological aspect and I am aware simulation is governed by geological aspects and data, but for the same homogenous model, the more gridblocks (the finer the model), the slower the fluid front is simulated. Example, injecting water in one gridblock that is two gridblocks away from producer will result in faster breakthrough than the model has 20 gridblocks between producer and injector. One method used is the pseudo modelling, however that is also time consuming (closed loop).
Please let me know if you are aware of such a method/fast guess. Many thanks in advance.
Hi,
You're looking for "representative elementary volume":
https://en.wikipedia.org/wiki/Representative_elementary_volume
It will largely depend on what information you're trying to simulate and the method of simulation you are using. Typically in oil reservoir the cell size is determined by the same one on the seismic model (mainly due to seismic inversion procedures since, although you can "guess" at finer grids you can't really access it's quality because you don't have a seismic analogue).
If this is not the case you may want to try to understand what is the fundamental vertical and horizontal size for your case study (I'm assuming regular grids).
* If your variable is largely determined by geology you want at least to have a cell size with the minimum vertical size of the thinnest geological layer.
* If it's largely determined by fracturing you want to look for the minimum size a relevant fracture may occupy.
* if it's largely determined by other variable try seeing the minimum size of the bodies of that variable (check the formula you are using right now to see what variables are relevant).
Notice however that some methods (specifically in interpolation and estimation) are themselves less accurate even if you have a very fine grid (so accuracy is determined by more than just the cell size). A good example is kriging that uses a variogram model which is an average of the behavior of a variable in "X" direction. Since it's averaged you can't really expect it to calculate values that go outside the prediction of the model.
Hope it helps.
grid size and computational time has a trade-off relation. If you make more coarse grid, computational time is less and vice versa. Optimum can be obtained by conducting simulation with various grid sizes and correlate the results with some available data. If matches then that would be the optimum grid with optimum utilization of computational time.
Shib,
Many thanks for your answer. Any general formula's available rather than the trial method? I am currently using your method but thinking if there is a formula to defines optimum gridblock size (based on run time and accuracy) using computational flow governing equations. The issue again rises when trying to use pseudo curves to mimic the impact of upscaling (long run time plus time consuming for defining the representative pseudo curves).
Thanks again.
Dear Khaldoon,
Well, selecting the proper grid from the many available choices can be quite a challenge. Till date, I am not sure if there is any research paper on specific equations to choose proper grid is available that you looking for. Yet, this is a very interesting query you raised --it is a nice research problem. Probably we need to define self organized algorithm which will choose optimum grid as any optimization method does.
Please let me know if you identify any approach to solve this.
Thanks
Thanks Shib,
Maybe it is something we can collaborate together and work on.
I am currently trying to find a solution to bench-marking to reduce the range of estimated RF.
https://www.researchgate.net/post/Bench-marking_as_a_fast_way_of_field_development_appraising_bidding_decisions_for_different_development_schemes_of_reservoirs
Thanks again,
Dear Khaldoon
No rule of thumb to detect the optimum gridblock size but there are some significant parameters that assign the minimum and the maximum number of grids.
The parameters are : Availability of data (the most significant factor), Number of wells, Quality of data, degree of heterogeneity of reservoir and boundary conditions
Best Wishes
Omar
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