Modeling sonic log from resistivity log

Hi

I'm working with data from an old borehole, which means I haven't got a lot of logs to work with.

I have tried generating a P-wave log from both the deep and the medium induction logs in HRS 9.
When I compare the velocities with interval velocities from adjacent boreholes, the log based on the medium induction log is the best match in the sandy intervals and the log based on the deep log is the best match in the shaly intervals.

So my question is; how do you choose which induction log to use for this kind of transformation?

Kind regards

Kris,

Interesting question and I must admit that I haven't used this technique. Is the mud intrusion accounted for in HRS 9?

Can you share details on the equations/algorithm?

As far as I know the intrusion isn't accounted for. The equation is Faust's:

Vp = γ(dRt)^1/6

Vp = P wave velocity
γ = 882,265
d = depth
Rt = resistivitet

However I decided to follow a different approach, and therefore estimated the porosity from the resistivities measured by the lateral log (with Archies equation), and the estimated the P wave velocity from the porosity.

Dear Kris_10,

I am joining this discussion at quite a late stage and not even sure if it is still active.
I have not done much work on deriving compressional sonic log from resistivity logs.
However, in your case, it looks like a combination effect of mud filtrate invasion and shale alternation when using the Faust equation to derive compressional sonic log from induction resistivity logs.
In the case of sandy intervals, the medium induction is more affected by mud filtrate invasion, which I presume to be water base mud. Therefore, the medium induction gives you the best match, since the flushed zone is now water bearing.
In the shaly intervals, there may be shale alteration due to drilling process in the near wellbore area. That my be the reason the deep induction is giving you a better match, since the medium induction is now more affected by near wellbore shale alteration.
Please note that I am just speculating and that I may be wrong.

As you have done, you can back calculate the sonic log using a porosity from suitable resistivity logs. However, here you are assuming that the invaded zone is fully flushed with mud filtrate, which is water. Therefore, the invaded zone is 100% water bearing.
This may not be true in the case of hydrocarbon bearing zones, especially gas bearing intervals.
Although water and oil have densities which are relatively similar, gas has a very low density and if the invaded zone is not fully flushed with mud filtrate, you computed sonic log may not be very accurate due to the lower gas density still present in the invaded zone.

Another thing is that when you are deriving a porosity log from a laterolog curve (I believe it would be the deep laterolog), you need to know the formation water resistivity Rw and the cementation factor m. If you already know these values, it should be alright.
Again, if you are using Archie's equation, you may end up with less accurate sonic log values in shaly sands, because of the conductive clay present in the sands.
There is another equation to compute sonic log from a resistivity log, but I cannot remember it offhand. I will have to dig up my reference materials and get back to you later, if you are still interested.

Regards,

Ko Ko Kyi

Dear Ko Ko Kyi

There is no evidence of hydrocarbons, so I'm assuming that the formations are water saturated.

Yes, it's a deep laterolog (18 feet). I'm assuming m = 2 in Archies equation, and I have estimated Rw from core measurements of the porosity together with the measured resistivity in the same depth (Rw = Ro*phi^2). Of course there could be some uncertainties here, since the measured resistivity may not be representative of the exact same depth of the porosity measurement.

I have also calculated the effective porosity, where I have accounted for the shale volume. I then found that the P-wave log in this case, seems to be most accurately estimated by the Raymer-Hunt-Gardner transformation.

I'm very interested in the other equation, if you can find it.

Kind regards,
Kris

Hello community!
This is my first post here!

I am interesting in this subject also, I have used Faust equation to model a sonic log and after to create a time-depth curve to calibrate with seismic data. Usually we have this situation for old wells which was logged only with resistivity devices. From my point of view there are two question marks related to this problem:
1. Determining the equation's coefficients from crossploting of neighboring wells (with sonic and resistivity logs available) or using the default parameters.
2. Which type of resistivity we shall use in equation? We can have:
- short/long normal resistivity devices (most of the cases)
- laterologs (msfl/lls/lld)
- induction (sfl/ilm/ild)

Other option for sonic modeling is Smith equation which converts transit time from resistivity:
DT=k1*R^k2
where k=91, k2=-0.15

My questions are what are the default coefficients for Faust eq. for cases where Z is in meters, and what resistivity we shall use in equation?

Any comments are welcome.

Dear Listmember,

I am not an expert in Rock Physics, but I would like to make the following comments:

1) I believe the best approach is to derive the coefficients for Faust equation from nearby wells. Then you will have better match in your compuation of Vp from resistivity logs. You may not get a good match if you use the default parameters. As far as I know, Young's Modulus Y will also change according to the type of formation, e.g. limestone or sandstone, etc.

2) Use the deep resistivity (LLD or ILD) to compute the Vp. The objective is to obtain Vp from an unaltered formation, which is far away from the wellbore. The shallow reading resistivities, such as MSFL, LLS, SFL and ILM will be affected by formation alteration and mud filtrate invasion to a certain extent. Furthermore, you should not use the Long Normal, as it is an old type of resistivity log from the ES (Electrical Survey). The Long Normal needs a lot of corrections to derive something close to true formation resitivity, as it is affected by many factors. Schlumberger has published several correction charts for the Long Normal. The Short Normal is a very shallow reading log (usually about 16 inches) and should not be used for interpretation.

Regarding your question about the units of measurements for Y in the Faust equation, I believe it could be Mega Pascales. However, don't take my word for it.

Regards,

Ko Ko Kyi

Hi

Does anyone of you know an equation for calculation of Rw, based on salinity, temperature and pressure?

Kind regards