I do not think this would be possible since whatever is measured in shales of nm ior even sub-nm permeability is an apparent permeability or apparent diffusion coefficient in a two-phase flow experiment. In a single phase experiment what you measure is permeability of course (so e.g. water through water-saturated pore space).

You can consult the papers from Alexandra Amann-Hildenbrand and Bernhard Krooss at RWTH Aachen University. They have thought about all this in a large number of papers.

Andreas is right in the sense that you cannot decouple the different effects in single phase.  However, I disagree is that you do not measure permeability, you measure the pressure response and interpret it as apparent permeability at that particular condition. Theoretically if you do many experiments at different pressures with various non-reactive gases ( to avoid adsorption) it may be possible to separate the effects. As far as i know nobody has done it yet.

Dear Andreas,

Thank you for your answer. I'm working on single phase apparent permeability modeling willing to conduct related experiment and find the answer. For  diffusion coefficient measurement of pulverized sample, it may be assumed that only diffusion flow happened at very low pressure in tight rock particles. So I thought for intact core in pulse-decay, the pressure change with time may be able to represent diffusion flow only in very similar condition. 

And I will read Dr. Alexandra Amann's work and get more ideas. Thanks again.

Dear Carlos,

Thank you for your response. I agree with you that if we do pulse-decay at certain condition, the diffusion coefficient may be interpreted by pressure data in some way. Because we cannot simply use only Darcy flow to account for this tight rock gas transport  most of the time. I will keep thinking if there's any smart way we can do this.

I do agree with Carlos that an apparent permeability can be measured within any two-phase flow experiment but I am not sure about the absolute permeability in such a scenario when the pressure-driven transport velocity is similar to the concentration driven one. This is what I actually wanted to say in my first response but it was not clear, sorry for this. This is the case, or at least presumably the case, in shales of nano-Darcy permeability where the gas permeability in the two-phase system is even 1-2 orders of magnitude lower. We tried this and I have attached a talk I gave last year on behalf of Sandra Amann from Aachen University. In the slides from slide 17 you can see that for a gas test where gas was injected in a water-saturated shale, you can calculate either apparent diffusion coefficient or apparent permeability. Flow rates are so slow that you can't really know if the system is concentration or pressure driven or both.

Nevertheless, far what you are planning Yi, I do not think that in a simople pulse-decay experiment you will be able to get any information on diffusional transport. Diffusion is concentration driven at dp=0. There are many papers in the literature that address diffusional transport in shale like from Marc Fleury from IFP, Elke Jacops from SCK-CEN or Bernhard Krooss from Aachen Univ.

Dear Andreas,

That material is very informative. I may start to think of some way other than single phase pulse-decay to  get apparent diffusion coefficient. Thanks again.

I wasn't very clear in my single phase comment.

I was thinking  in gas pulse decay in an very low permeability core which is filled  with air  or Nitrogen and the pulse is performed with other gas (e.g. methane, He, etc) so there is a pressure and concentration gradient ( darcy flow +  diffusion) . Most samples have been exposed to air for a long time changing the original gas composition then a pulse decay test (including GRI) is done  with a bottled gas (different from the one in the pore space).

I think this is a challenging topic. To avoid confusion, I guess it is important when speaking about diffusion to specify what type of diffusion we are referring to. In tight rock formation and in particular with the pulse-decay exp., Knudsen diffusion  is more relevant than molecular diffusion. Knudsen diffusion is driven by density gradient while molecular diffusion is driven by mole-fraction gradient (or concentration). Therefore, if we assume no computational variation in the gas, molecular diffusion is zero. Knudsen diffusion will be dominant. I don't think CO2 molecular-diffusion coefficient is relevant for this particular experiment.

This paper may give some insights:

  Understanding Shale Gas Flow Behavior Using Numerical Simulation 

by Sun et al.

http://dx.doi.org/10.2118/167753-PA