MINC fracture spacing effect

Jing,

The fracture volume fraction says how much of the total volume consists of fractures; it does not say whether all this volume is in a single fracture with a large aperture, or distributed among many fractures with smaller apertures. (Make sure the continuum assumption remains valid!) If you have many fractures (small fracture spacing), the amount of surface area between the fractures and matrix is much bigger compared to a network with large fracture spacing, allowing for more fluid and heat exchange between the two continua. The size of the matrix blocks is also different (reflected by a smaller nodal distance). Surface areas and nodal distances are calculated using the so-called proximity function for a given fracture spacing and geometry (see variable TYPE). Therefore, the choice of the fracture spacing is essential and greatly impacts system behavior, even for a constant fracture volume fraction.

It might be a good exercise to set up a model consisting of a single grid block, and to play around with the MINC parameters. Choose simple geometric configurations, calculate the volumes, surface areas and nodal distances by hand, and then compare them to the values given in the TOUGH2 output file (or MESH file). This will give you the insights needed to successfully employ the MINC concept.

Stefan

Jing,

Please check again in file MINC (not file MESH).

If you have a volume fraction of, for example, 0.01, and fracture spacing is 1 m, then you have a single fracture of aperture 1 cm crossing a 1 m^3 block. The fracture-matrix interface area is then 2 m^2, right? Now assume the fracture spacing is 0.1 m, and the aperture 0.1 cm (i.e., same fracture volume fraction of 0.01), then 10 fractures cross the unit grid block, and the surface area is 20 m^2.

Hope this makes sense.

Stefan

Jing,

Please attach the input and output files of the two test cases your ran, so we can see what is going on. (I just ran a test myself with the expected results, i.e., different MINC files).

Stefan

Jing,

Please look at your output files again: There are 2205 lines with 6615 differences (as expected)!

The ELEME blocks are of course identical (also as expected, as you did not change the fracture volume fraction).

Stefan

Hello,

In TOUGH2 using MINC, how one can calculate the fracture aperture for the given volume fraction and fracture spacing for 3D grid system? 

Thanks,

Manish

Manish,

Just use the definitions of volume fraction and fracture frequency (potentially different for each set), along with some other fundamental assumptions of MINC (such as "infinitely long, parallel fractures"), account for the fracture continuum porosity (if you have gauge material), and you easily arrive at the number of fractures per unit volume (which may be less than 1) and thus aperture. I have described this before in this Forum.

Note that you usually go the other way around, i.e., you know what the apertures, fracture spacings, and infill porosities are, in which case it is straightforward to calculate the corresponding MINC parameters.

Regards,

Stefan

Hello Stefan,

If I have 4 parallel fractures with fracture spacing of 20 m and the volume fraction is 0.1 with total grid/reservoir volume as 10^6 m3 then does that mean the fracture aperture is 2 m? The concept of parallel fractures using MINC for 3D grid is very confusing to me.. I need to give parallel fractures with certain fracture spacing in y-z plane with certain aperture as an input to my model using MINC.. Is it possible through MINC? Thank you very much for your time.

Best,
Manish

Hello Stefan,

Also when you said parallel fractures, does that mean vertical parallel fractures or horizontal parallel fractures perpendicular to the wellbore? I am confused because in MINC we give fracture spacing in all direction (x,y,z), so how does it affect the nature of fractures?

Thanks,

Manish

Manish,

This may sound strange, but dual-continuum and MINC approaches are agnostic about fracture orientation!  Fracture spacing determines the proximity function, i.e., how the volumes and interface areas change as a function of distance from the fractures. As you go from the fractures inwards towards the centers of the matrix block, there is no "orientation" that can be reasonably defined. If multiple fracture sets are given (each perpendicular to the other), the fracture spacing of each set determines the shape of the matrix blocks and thus the proximity function (however, it does not matter which distance you assign to which set - please confirm this statement by shuffling the distances and checking on the resulting MINC mesh; let me know if my intuition was correct or not).

Let's say you have a single set of parallel fractures, all the geometric information (volumes, interface areas, nodal distances for each continuum) are independent of how these fractures are oriented. Next, recall that this is a continuum approach, so individual fractures "disappear", but their "average" orientation has a combined effect on the continuum permeability of the entire fracture newtor. For example, if you want all fractures of this single set to be perfectly horizontal, you have to indicate that by giving an anisotropic continuum permeability in block ROCKS, i.e., PER(1)=kx, PER(2)=ky, and PER(3)=0.0.

Your question is a good one; it shows that MINC is a rather abstract (albeit extremely practical and powerful!) concept. This may explain the large number of MINC-related questions posted to this Forum (use the Forum's Search feature to find them).

Stefan

PS: I attach an old (1983) report by Karsten (sorry for the bad quality of the copy). It has more examples of proximity functions and explains how they are generated. Specifically the one for an irregular network of randomly oriented fractures may give you the insight needed to fully understand MINC.

Thank you very much Stefan. You explained it very well. Now I think I have understood the overall idea of MINC methdology to model fractures. Even the document was really helpful.

Regards,
Manish

Hi Stefan, 

I'm almost there with the understanding of the MINC principle. I just need one more clarification, Should a person take into consideration the size discretised grid when deciding the fracture spacing or no need of such consideration ? 

Regard

Nathan   

Nathan,

The fact that you ask this question tells me that you are correctly grasping the MINC concept!

The answer is: No, there is no fundamental need to consider fracture spacing when deciding on grid resolution. This means you can have grid blocks that are smaller than fracture spacing, i.e., geometrically there are many grid blocks that are not intersected by a fracture at all! This may seem nonsensical, but recall that discretization is just a way to solve the governing equations using a numerical scheme. In MINC, these are continuum equations, and you may want to have a fine grid to resolve steep gradients.

Consider this: an analytical solution (e.g., Theis equation) corresponds to having an infinite number of infinitely small  grid blocks, and the pressure drawdown can be calculated with at any point (i.e., with infinite resolution). Nobody claims that this is nonsensical because Darcy's law cannot be applied to the sub-pore scale (i.e., that there are points in the analytical solution that do not contain any pores, or do not contain any solid). The same is true for the numerical discretization of the MINC continuum equations.

Having said all this, the key decision that needs to be made is whether fluid flow through the fracture network can be appropriately described by a continuum equation on the scale of interest. So: scale has to be considered, but not that of the grid block size.

Sorry for the long answer.

Have fun MINCing away!

Stefan

Stefan Finsterle 

Thank you Stefan .

Now i understand