Saturday, September 26, 2009

Darcy, Percolation or Ray Tracing?

I personally believe that the subsurface migration of hydrocarbons should follow Darcy's law. However, the numerical solution is so time consuming that it is practically impossible to build models at 3D seismic resolution. Anything less is not really geologically realistic. Structure details missed by 2D seismic will significantly affect migration direction. At geological time scales, most people believe that Percolation or Ray tracing is a good approximation of the migration process, and can handle 3D seismic resolution.

However, even 3D seismic resolution is not nearly enough. Vertically migrating oil and gas is easily diverted to a different direction by the existence of a carrier bed just a few inches thick. That is beyond well-log resolution. A petroleum system analyst should be practical about this, and think about where these carriers may exist and test different scenarios. The prospects that can be charged under more scenarios are assigned lower risk and vise versa.


  1. Here are some "devils advocate" statements I hope can trigger some debate :-) How is it possible to be practical with; as the poster points out: "Vertically migrating oil and gas is easily diverted to a different direction by the existence of a carrier bed just a few inches thick." ? You could also add more than "vertically" to this. Seismic resolution is too coarse for modeling anything but a "statistical" scenario. However, resolution/scale need to enter our discussion as point 1; we are not dealing with separate Darcy, Percolation, Ray-tracing in anything but a "practical" ad-hoc way: percolation theory leads to extended Darcy as a special case, and Ray-tracing models is also based on the same percolation theory special case in that the saturation profile at the top of the carrier (and the ray simplification) follows from the same line of thought.

    1) An extended Darcy's law with relative permeability functions are what is used for "Darcy" migration. It is close to impossible in a meaningful way to derive it analytically (without making special case assumptions). At high petroleum saturations, it is probably in the ball park; you can create network-models (Navier-Stokes on a pore level) that mimic similar behavior; i.e., "numeric" percolation theory, i.e., reservoir simulations are reasonably formulated. At low saturations however, the time-scaling is can be so that the behavior is nothing like what an extended Darcy upscaling would predict; we can have very significant flux at very very low saturations and the entire behavior is strongly dependent on the details of the 3-D pore network.

    2) From 1 we could be in the situation, that only for lateral transmissions, we could do semi-realistic petroleum migration modeling with a (partly Darcy based) ray-tracer. Running a traditional (Themis type) flow model will be worse because we will always be out of scale (and we have no realistic upscaling available). The seismic-scale-"network"-models (low saturation C#) though, are similarly unlikely to ever give any realistic results (apart from "realistic looking" screen shots: you could have hand-drawn from the interpretations yourself). The models are great to show to management though, and management love to show the results to journalists and politicians ! :-) There does not exist, and there will never exist an AI (Acoustic Impedance) cube (recast to whatever "permeability" parameter) which will be even close in imaging the connectivity that will govern the true percolation at low saturation. All data cubes derived from AI cubes (remember they have all the high frequency content (that governs the network) from interpretations and 1-D wells and are simply linear extrapolations along interpretations away from wells (that also have too low resolution)) have all orders of magnitudes too high noise level for any type of realistic network models. If you smooth out the data volume, you could just as well have run a ray-tracer on the primary interpretation. (All the add-ons to these network models (e.g., compositional tracing) probably make them even worse, by adding poor thumb rules to chaos :-) )

  2. To follow up on the previous: Before discussing petroleum migration, we must address the more fundamental behaviors in the simulators; the general force balance in the system. Currently we use guesses; force balance formulations and scalings that are mostly unsubstantiated. SOMETIMES, the models can be calibrated to fit observed patterns well, but with the number of independent parameters used, you can fit statistial models just as well, so the "it fits, therefore it is right argument" should not appease anybody. We could easily be in the situation that the over-pressure patterns we are observing could be unrelated to any of the "physical phenomena" we have programmed up in the existing modeling packages.

    This topic is an interesting thread for the Petroleum System Blog: the amount of "not-well-thought-through" claims that has entered the literature regarding this (such as "pressure insensitive compaction") is alarming and an open hard debate is required.

  3. Hi TheCoalMan, if you like to post articles, email me at and I will be happy to add you as a contributor. Cheers,

  4. Very well said about the AI volume as a migration model. I agree totally.

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