Porosity Permeability (Poro-Perm) Log-Linear Regression in Python - Petrophysics

Permeability is one of the key reservoir properties we as petrophysicists attempt to derive as part of our workflow. As well logging tools do not provide a direct measurement for permeability, we have to infer it through relationships with core data from the same field or well, from empirically derived equations or NMR data.
One common method of deriving permeability is to plot core porosity (on a linear scale) against core permeability (on a logarithmic scale) and observe the trend.
From this, a regression can be applied to the porosity permeability (poro-perm) crossplot to derive an equation. This can subsequently be used to predict a continuous permeability from a computed porosity in any well.
In this week's video, I demonstrate the application of linear regression within Python to derive a poro-perm relationship. However, when doing this we need to account for permeability being logarithmically scaled and porosity being linearly scaled.
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[@kushwantsingh8690]

Hi Andy. What's the difference between the CKHG and CKHL perm values? Can you shed some light? Cheers

[@joaovictorfernandes9829]

Congratulations on the channel. Here is shown a high quality content of Petrophysics.
Andy, I would like to propose a mental exercise:
Imagine a situation where you have wells situated in a mature field where common logging data such as:
GR, ILD, NPhi, RHOb, SP and DTco. Nothing else, no core data or the ability to get them.
Apart from the basic conventional petrophysical analysis, with the calculation of VSh, Porosity and Water saturation by the Archie equation (or other models), what else you could do to improve and work with this data, generating results that improve and facilitate evaluation or even generate interesting results? i.e, what to apply (Machine Learning, Neural Networks, Fuzzy Logic, Rock Typing, or any other methodology...) - and in order to acquire which new properties - only with these conventional logs, without the need for core data, that can generate interesting results? It's possible? What would you do with this data and in this specific case?

[@AndyMcDonald42]

Thanks João.
To answer your question, the first thing I would do is find out what the end goal is of the client/project and then try to work towards that. Otherwise it is wasted time.
If this is just theoretical and about what you can obtain from just these curves, then there are numerous things we can do.
- Basic Deterministic Interpretation to get VCL, PHIE, PHIT, SWE, SWT etc.
- Probabilistic Interpretation - Mineral volumes and standard petrophysical outputs
- Log Derived Saturation Height Models
- Rock Typing (HFUs) using established workflows such as Lucia and Pitmann
- Rock Typing through clustering algorithms or Self Organising Maps
- Permeability Prediction based on standard equations
- Rock Mechanics
- Rock Physics
- Seismic properties
I am sure this list is not endless, and there is much more we can do with the basic data.
ML can be applied, however, you would have to determine what the end goal is. Based on the curves provides, you can't predict permeability as you have no reference. Nor can you predict DTS, again due to no reference.
Also, what you can derive would depend on if you have access to the raw logging data (acoustic waveforms, raw counts, spectral GR components etc).
Hope that helps :)

[@joaovictorfernandes9829]

@@AndyMcDonald42 Man, that definitely helped.
I will try to execute these suggestions to my model. I already have a good development of the basic petrophysical interpretation but I feel I need to add something more to my model. Your suggestions fit like a glove.
Thank you!