Seismic petrophysics: Part 1

We never seem to have enough data to analyze the complexity of the subsurface. The geologist would love to have hundreds of cores, but the manager will let him have just one. The geophysicist's dream is to acquire a new 3D with long offsets, complete azimuth coverage, and 5-m bins, but she is more likely to be stuck with a couple of 2D lines.

The idea in this tutorial is to show how to create new data starting from what is available so we can make deductions, analyze alternative scenarios, and decide whether a certain variation in lithologic properties would have an impact on seismic. Specifically, I will show how to create new well-log data. In doing so, I hope to demonstrate how easily this kind of work can be done by all practitioners who dislike “black-box” approaches.

The goal is to create an abstraction of the reservoir rock under study to investigate alternative and plausible scenarios, e.g., a change in pore fluids or in some lithologic property such as porosity. The workflows I will show are:

• Import well-log data and create a lithology curve log.
• Augment data through fluid-replacement modeling.
• Describe the reservoir through simple statistics.
• Create synthetic data sets that represent different scenarios.

There is also some data-loading and data-management overhead to take care of, so we will focus only on the first item in this article.

All Python code and data used here is available at GitHub. Please take a minute to look at them and perhaps follow along by running the code yourself.

Import well-log data

To handle well-log data, I use a Python library called Pandas, which makes it very easy to manage and inspect large, complex data sets. For example, we can load a sample data set with

>>> import pandas as pd

>>> logs = pd.read_csv(‘qsiwell2.csv’)

The term logs refers to a DataFrame, a “container” we can use for all sort of things, such as investigating the depth range or average velocity:

>>> print “depth min {0:.2f} m”.format(logs.DEPTH.min())

>>> print “depth max {0:.2f} m”.format(logs.DEPTH.max())

>>> print “Vp average {0:.2f} m/s”.format(logs.VP.mean()) depth min 2013.25 m depth max 2640.53 m Vp average 2977.10 m/s

Pandas also allows us to have a quick glance at all the logs loaded by simply calling logs.describe(), which will output a table such as this:

Stats	$V_{P}$	$V_{S}$	rho	phi
count	4117	4117	2701	2701
mean	2977	1371	2.22	0.29
std	449	297	0.06	0.03
min	1440	689	2.04	0.11
25%	2594	1141	2.18	0.28
50%	3036	1415	2.22	0.30
75%	3251	1595	2.26	0.31
max	4431	2428	2.54	0.38

Create a lithofluid-class log

What I do first is calculate a lithofluid-class log (LFC) in which I separate groups of data identified by similar lithologic and/or pore-fluid content. The values of the LFC log will be assigned following these rules:

0: Undefined 1: Brine sand 2: Oil sand 3: Gas sand 4: Shale

First I need to create the “flag” logs brine_sand, oil_sand, gas_sand and shale (these are logs made of 1 or 0, i.e., True or False in Python) using cutoff values on $V_{sh}$ (shale volume) and $S_{w}$ (water saturation):

>>> sand_cutoff = 0.20

>>> brine_sand = ((logs.VSH <= sand_cutoff) & (logs.SW >= 0.9))

>>> oil_sand = ((logs.VSH <= sand_cutoff) & (logs.SW < 0.9))

>>> shale = (logs.VSH > sand_cutoff)

Notice that we cannot define gas_sand just yet (occurrence of gas sands) because the in situ log did not record any gas sand. We will deal with that in the next tutorial, on fluid replacement.

These flag logs are then used to create the LFC log:

>>> import numpy as np

>>> temp_lfc = np.zeros(np.shape(logs.VSH))

>>> temp_lfc[brine_sand.values] = 1

>>> temp_lfc[oil_sand.values] = 2

>>> temp_lfc[shale.values] = 4

>>> logs[‘LFC'] = temp_lfc

To see how many samples each facies is made of:

>>> string = “brine sst={0}, oil sst={1}, shale={2}”

>>> data = (np.count_nonzero(brine_sand), np.count_nonzero(oil_sand), np.count_nonzero(shale))

>>> print string.format(*data) brine sst=706, oil sst=134, shale=1128

Pandas also allows us to do quick graphical inspection of the data. For example, Figure 1 shows the way to draw $I_{P}$ histograms for all the available classes.

logs.IP.hist(bins=50, by=logs.LFC)

For a comprehensive look at the data available, we plot everything in one panel, applying a color convention for the lithofluid classes (Figure 2).

The same data are shown in a crossplot domain that should be familiar to geophysicists, i.e., acoustic impedance ($I_{P}$) versus ${\frac {V_{P}}{V_{S}}}$ (Figure 3). The colors are the same as in Figure 2, but what about that red? It indicates gas sands — but so far, we don't have gas sands in here. In the next tutorial, I will show how to synthesize gas sands and create an additional gas_sand class.

A look ahead

In this tutorial, we have laid the foundations for the real work. In * Part 2, we will look at applying Gassmann's equation to our logs to perform fluid-replacement modeling (FRM). Starting with the original data we have looked at in this tutorial, we will continue our work and replace oil with brine, then transform all the fluid to oil and to gas (Figure 4). This will let us examine the relationship between impedance and ${\frac {V_{P}}{V_{S}}}$ with the new, synthetic data. From there, we can do some statistical cleaning and analysis for a complete interpretation.

• 

  Figure 1  Histograms showing the distribution of P-wave impedance ($I_{P}$) values for lithofluid (a) class 1 = brine sand, (b) class 2 = oil sand, and (c) class 4 = shale.

• 

  Figure 2  Various logs, with the new lithofluid-class log at right.

• 

  Figure 3  Crossplot showing ${\frac {V_{P}}{V_{S}}}$ versus P-wave impedance for the logs in Figure 2. Colors indicate the lithofluid class shown in Figure 2.

• 

  Figure 4  Crossplots showing ${\frac {V_{P}}{V_{S}}}$ versus P-wave impedance after fluid replacement.

See also

• Seismic petrophysics: Part 2

External links

• IPython Notebook — includes all the code
• Madagascar workflow - reproducible using Madagascar open-source software
• Corresponding author: Alessandro Amato del Monte alessandro.admgmail.com

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