# Estimating the permeability tensor of an oil field by remote sensing

I work a lot with numerical methods to solve multiphase flow in porous media for oil applications. In our field, we often use Darcy's law which states that the flux is negatively proportional to the pressure gradient by a factor called the permeability. In general, permeability is not a constant, but a tensor. This implies that a pressure gradient in one direction may induce flow in an orthogonal direction as well.

In a laboratory, permeability tensors are obtained by inducing controlled pressure gradients and measuring the resulting flow. In an oil field, we can certainly induce pressure gradients, but it is much more difficult to control all the parameters. Is there a way to sense a permeability field using remote sensors and geophysical inversion?

## 1 Answer

I remember a comment on this by Rodney Calvert in the video lecture version of his SEG Distinguished Instructor Lecture "Insights and Methods for 4D Reservoir Monitoring and Characterization": http://shop.seg.org/OnlineStore/ProductDetail/tabid/177/Default.aspx?ProductId=1842

The comment was referring to the possibility of observing a pressure change front moving through the reservoir (as opposed to a fluid staturation change front) if one were to perform very closely repeated time lapse seismic surveys (down to probably days instead of months between surveys) AND in the very early stages of development. Costly of course but it would allow far superior well placement in complex reservoirs.

There's some reference to this in Chapter 2 of the book: http://library.seg.org/doi/book/10.1190/1.9781560801696

but if I recall, the comment in the video lecture was far more specific. It is worht a try, the course is great to take anyways.

UPDATE

Following comments below and a review of some reference material. The problem of permeability is that this is a multiscale property. You get different estimates (and different relationships, for example to porosity) at different scales (e.g. pore, lamina, bed, geobody, formation, and reservoir scales). The challenge is to link permeability at all scales and it is compound mainly by two facts: 1) at some scales you measure permeability statically, at other scales dynamically; and 2) at some scales permeability is not well captured/represented by any measurement (for example bedset scale, which is larger than core scale but often not well captured by wireline log data).

My advice to you would be to get this book by Patrick Corbett, the go-to guy in the field: http://library.seg.org/doi/book/10.1190/1.9781560801597. It is about 90 pages and it guides you through the whole process, with measurements, modeling, testing at all scales, topped by an excellent example of integration at all scales in chapter 6. I worked through the book and several of the reference papers 3 years ago, for personal knowledge, and it was great.

From a quick review last night I'd say one very important tool is Petrotyping, as defined in the book. The full work is in reference paper Corbett and Potter, 2004, Society of Core Analysts paper SCA2004-30. This paper defines Hydraulic Units as representative volume elements where geological, petrophysical, hydraulic properties are predictable and different from those in other units. Each unit is defined by a Flow Zone Indicator (FZI) (defined in the paper). A relationship is intorduced in the paper relating permeability to porosity via FZI. With this relationship a set of lines of constant FZI can be used as a template in a porosity (decimal) - permeability (log) plot to assess Global Hydraulic Elements in the reservoir. A Global Hydraulic Element is an element where the relationship between porosity and permeability is unique. If you are lucky your reservoir (for example a chalk reservoir, one of the examples in Corbett's book) has a single Global Hydraulic Element, in essence a single rock type of uniform properties. In this case you could go relatively easily from a static geomodel of reservoir facies modeled at the reservoir scale (and constrained with seismic inversion for acoustic impedance or porosity, ideally stochastically) to permeability at the scale of your lab measurements - you would be using also well tests (drill stem tests, production tests) and Lorentz plots. In the case of a developed field you may also integrate dynamic simulations and time laps (4D) seismic data (linekd to saturation and/or geomechanic changes introduced in the reservoir by production).

If there are multiple GHEs, then the work of predicting at core plug scale, upscaling, validating with dynamic testing, and extending to the reservoir scale is more complicated (but still possible).

I really recommend the book.

• I suspect that not many companies do this in practice. What is the traditional approach to determining the permeability of the field?
– Paul
Apr 21, 2014 at 16:42
• Agreed. BUt wouldn't it be awesome? As to conventional approach, I have some reference at home. I'll get back to you by tomorrow. Apr 21, 2014 at 16:55
• Seismic investigations for permeability. You can get to porosity but the relationship porosity-permeability is non linear and scale dependent - tricky. It looks like there is some interest in using seismic attenuation and dispersion but methodology is not mainstream yet. 2 reference papers: Rubino et al. Dynamic permeability of heterogeneous porous rocks having strong permeability fluctuations. SEG Expanded Abstracts 2012 p. 1-5. Korneev et al. Seismic imaging of oil production rate, SEG Expanded Abstracts 2004 p. 1476-1479. Tomorrow I will get you reference on methods based on core and logs. Apr 22, 2014 at 14:21
• I just remembered about this more recent paper about analysis of seismic attenuation to estimate permeability: csegrecorder.com/articles/view/… Apr 29, 2014 at 20:41
• Check this video from Mark Zobak's free Reservoir Geomechanics course (Stanford University): youtube.com/watch?v=OaC9oEVzATc Sep 20, 2018 at 19:34