Introduction:

This Python tutorial started from the PetroGG repository written by Mihai on GitHub:

https://github.com/petroGG/Basic-Well-Log-Interpretation

We modified his coding example with our own shaley-sand methods that we typically employ in Geolog in a python loglan.

This example is from the Gulf of Mexico where we use a typical shaley-sand interpretation. The log data includes conventional well logs along with NMR logs too. In our analysis we employ a Dual-Water method from George Coates (MRIAN) along with our own Waxman-Smits saturation method.

Normally we would load the log data directly from a Geolog Well using a loglan template specifically made for python as shown below:

However, for this notebook the conventional logs and NMR data are being loaded from the Excel Gulf_Coast_NMR.xlsx file provided in this repository.

The original PetroGG method written by Mihai gave us a good foundation in building proper depth plots, cross plots and histograms in python. We have made several additions to the original PetroGG:

• First of all, we have modified the code to use a Vshale and not Vclay as was previously used. Almost all shales have less than 100% clay volume. We have personally sampled some of the greasiest, gumbo shales to find that the maximum clay content was only about 65% according to the XRD or FTIR mineralogy data. Therefore, estimating the clay endpoint parameters for a clay point is a challenge since this 100% clay points is an imaginary points. This point does not exist in the data. Instead, we use a shale point, which can be observed in most shaly-sands data sets with a well developed shale. However, with sufficient mineralogy data from core samples or elemental log data like Schlumberger's Elemental Capture Spectroscopy (ECS), we could model the volume of clay for future applications.
• We have included two additional Saturation models suitable for shaly-sand analysis. We started with Mihai's Waxman-Smits and Dual-Water saturation models from his repository and then modified his code to employ George Coates' MRIAN Dual-Water and our own Waxman-Smits iterative model. For this application we are using Crain's Waxman-Smits saturation equation.
• We have modeled Clay Bound Water (CBW) Volume in case there are light hydrocarbon intervals with reduced Hydrogen Index (HI) affecting the well log readings. In those situations we would be using our modeled results and not the log data from the HI affected intervals.
• We calculate Qv from Swb using the Hill Shirley and Klein equation shown below.
• For this notebook we are using an integrated Conventional and NMR method in our petrophysical analysis.

NMR data has been found to be quite useful in our petrophysical analysis with numerous applications, but in this instance we are assessing reservoir quality and defining the volume of non-movable Capillary Bound Water (MBVI) from our NMR log data and comparing this to the log calculated Bulk Volume Water (BVW) to assess those intervals capable of delivering water-free hydrocarbons. The integrated approach using a combination of NMR with conventional logs provides a very holistic approach to our petrophysical analysis and interpretation. George Coates illustrated this concept with their MRIAN analysis at Numar in the mid 90's. We are using his method as well as our own Waxman-Smits techniqe in this interpretation.

One of the major benefits of these methods are to account for the conductance of the Clay Bound Water (CBW) or the CBW saturation (Swb). CBW is associated with the waters chemically bound to the shales. CBW is calculated from the difference between Total (PHIT) and Effective (PHIE) porosity. We typically start with the NMR effective porosity (MPHI for MRIL, or CMRP_3MS for CMR) as the effective porosity. In most oils and water intervals with a high Hydrogen Index, this is true. However, in light hydrocarbon, heavy oil and gas, the NMR effective porosity can be suppressed. This results in an excessive CBW volume calculated from the difference between PHIT and the NMR effective porosity. Therefore, we will call this difference calculated as CBW an apparent CBW or CBWa.

We typically use the plot of Vshale (or Swb) vs. CBWa as shown below to model CBW to determine the normal trend and segregate this trend from those intervals with light hydrocarbon. As can be seen below, there is an excellent trend with these data. However, if there was gas or heavy oil, then there could be some samples that deviated from this normal trend showing much higher CBW volumes. We would ignore those data and concentrate on the primary trend as shown below to model CBW for the entire well.

                               CBW = 0.2 * Vshale + 0

In actuality, this plot defines the porosity of shale as the CBW intercept at 100% Vsh.

The NMR data in this example from an older Numar NMR tool that was only capable of measuring an NMR effective porosity (MPHI) and NMR Bulk Volume Irreducible (MBVI); all in the effective porosity system. This tool did not have the capability to employ the PR06 activation for the measurement of the Clay Bound Water (CBW) volume where the entire NMR signal would be approaching total porosity.

The NMR Capillary Bound Irreducible Water (MBVI) is calculated from the NMR T2 distribution by partitioning this T2 distribution into the Capillary Bound Water (MBVI) region vs. the Free Fluid (MFFI) region based on an NMR T2 cutoff. The MFFI pore volume is associated with the larger pores with movable fluid where MBVI has the smaller pores with Capillary Bound Water that is a non-movable fluid. This partition point is called the T2 Cutoff, and for this clastic well the T2 Cutoff was 33ms. In Carbonate formations the T2 Cutoff is typically > 100ms due to the lower killing-strength in carbonate rock.

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Saturation Models:

Since we have an estimated volume of CBW and Clay Bound Water Saturation (Swb = CBW/PHIT), we can use the CBW volume to account for the conductivity of the CBW region and calculate Qv for our shaley-sand saturation models.

Dual-Water saturations are from the George Coates' (1) MRIAN analysis method developed at Numar to integrate conventional and NMR log data for a robust interpretation.

George Coates and the team at Numar developed a Dual-Water saturation model that was near fool-proof and this was a part of their MRIAN analysis. They employed Dual-Water saturations and uses a variable 'w' for the electrical properties. They also accounted for an excess porosity calculated in the shales using RPHICLAY which discounted total porosity in the shales.

Waxman-Smits saturation model using the Hill, Shirley and Klein equation(2) to calculate Qv from Swb as shown below:

            Qv = Swb/(0.6425/((Fluid_Density*Salinity(kppm))**0.5) + 0.22) 

We are using both the standard iterative approach to Waxman-Smits and the option to use the Waxman-Smits equation provided by Crain in lieu of this iterative approach.

Usually we are using a standard iterative approach to Waxman-Smits, but in this instance we are using the option provided by Crain in lieu of this iterative approach. PetroGG has layed a foundation in this Pandas DataFrame such that the iterative approach to Waxman-Smits is creating a 'bug' that we are trying to overcome. In Geolog we have overcome this issue by using a level-by-level processing where the iteritive approach works well. Please contact us at craig@cbpetro.com to obtain the entire Geolog project with the python Geolog loglan. Of course, you would need Geolog. In the near future, we will re-write this entire code to read in a las file of the conventional logs with NMR data and apply the level-by-level approach where we can use the Waxman-Smits interative.

Experience has shown that Waxman-Smits method is a bit more flexible to use in shaley-sand interpretations in that we can model the Waxman-Smits cementation exponent m* to vary with Vsh calibrated to Swb according to the trends observed in the wet intervals. A Cross Plot of Vsh vs. m*_apparent (MNA) is shown below. The apparent m* increases as Vsh (or Swb) increase. This can best be observed in the wet intervals. m*_apparent goes quite high in the hydrocarbon bearing intervals and should not be used for the m* vs. Vsh or Swb trend. The m* at a Vsh (or Swb) of 0 (y-intercept) is the Archie m. m* increases with increased Vsh (or Swb). We have also found that a wrong Rw can lead to an unrealistic y-intercept to give us feedback as to our choice of Rw too.

In the plot above, we calculated the initial, apparent m* using the following equation used on the y-axis:

    m*_apparent = log10(Rw/(RT*(1+Rw*B*Qv)))/log10(PHIT)

The plot above shows m*_apparent vs. Vsh. We are useing water saturations on the color z-axis. The wet trend (dark blue sample points) are rather well defined with a y-intercept of approximately 1.9 at zero Vhs with a slope of 1.8. The y intercept at zero Vsh could be considered the Archie 'm' for the clean rock. This slope and intercept define the Waxman-Smits m* over the range of Vsh from 0 to 1. As Vsh (or Swb) increase, so does m*.

   m* = slope * Vsh + m_archie

Finally, for our interpretation we typically compare our log analysis based Bulk Volume Water in the effective porosity system (BVWe) to MBVI, that is also in the effective porosity system, to determine what intervals have hydrocarbon saturations at irreducible water saturation with no movable water. When BVWe is higher than MBVI, as indicated by the cyan colored fill below in the next to the last track, then we expect movable water depending on the relative permeability and mobility of these fluids.

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1. Coates, G.R., Gardner, J.S., and Miller, D.L., 1994, "Applying pulse-echo NMR to shaly sand formation evaluation", paper B, 35th Annual SPWLA Logging Symposium Transactions, 22 p.

2. Hill, H.J., Shirley, O.J., Klein, G.E.: “Bound Water in Shaley Sands - Its Relation to Qv and Other Formation Properties”, Log Analyst, May-June 1979.

3. Dacy, J., Martin, P.: "Practical Advances in Core-Based Water Saturation Analysis of Shaly Tight Gas Sands", SCA, SCA2009-29, 2009.