To make up microseismic

I am not a proponent of making up fictitious data, but for the purposes of demonstrating technology, why not? This post is the third in a three-part follow-up from the private beta I did in Calgary a few weeks ago. You can check out the IPython Notebook version too. If you want more of this in person, sign up at the bottom or drop us a line. We want these examples to be easily readable, especially if you aren't a coder, so please let us know how we are doing.

Start by importing some packages that you'll need into the workspace,

%pylab inline

import numpy as np
from scipy.interpolate import splprep, splev
import matplotlib.pyplot as plt
import mayavi.mlab as mplt
from mpl_toolkits.mplot3d import Axes3D

Define a borehole path

We define the trajectory of a borehole, using a series of x, y, z points, and make each component of the borehole an array. If we had a real well, we load the numbers from the deviation survey just the same.

trajectory = np.array([[   0,   0,    0],
                       [   0,   0, -100],
                       [   0,   0, -200],
                       [   5,   0, -300],
                       [  10,  10, -400],
                       [  20,  20, -500],
                       [  40,  80, -650],
                       [ 160, 160, -700],
                       [ 600, 400, -800],
                       [1500, 960, -800]])
x = trajectory[:,0]
y = trajectory[:,1]
z = trajectory[:,2]

But since we want the borehole to be continuous and smoothly shaped, we can up-sample the borehole by finding the B-spline representation of the well path,

smoothness = 3.0
spline_order = 3
nest = -1 # estimate of number of knots needed (-1 = maximal)
knot_points, u = splprep([x,y,z], s=smoothness, k=spline_order, nest=-1)

# Evaluate spline, including interpolated points
x_int, y_int, z_int = splev(np.linspace(0, 1, 400), knot_points)

plt.gca(projection='3d')
plt.plot(x_int, y_int, z_int, color='grey', lw=3, alpha=0.75)
plt.show()

Define frac ports

Let's define a completion program so that our wellbore has 6 frac stages,

number_of_fracs = 6

and let's make it so that each one emanates from equally spaced frac ports spanning the bottom two-thirds of the well.

x_frac, y_frac, z_frac = splev(np.linspace(0.33, 1, number_of_fracs), knot_points)

Make a set of 3D axes, so we can plot the well path and the frac ports.

ax = plt.axes(projection='3d')
ax.plot(x_int, y_int, z_int, color='grey',
        lw=3, alpha=0.75)
ax.scatter(x_frac, y_frac, z_frac,
        s=100, c='grey')
plt.show()

Set a colour for each stage by cycling through red, green, and blue,

stage_color = []
for i in np.arange(number_of_fracs):
    color = (1.0, 0.1, 0.1)
    stage_color.append(np.roll(color, i))
stage_color = tuple(map(tuple, stage_color))

Define microseismic points

One approach is to create some dimensions for each frac stage and generate 100 points randomly within each zone. Each frac has an x half-length, y half-length, and z half-length. Let's also vary these randomly for each of the 6 stages. Define the dimensions for each stage:

frac_dims = []
half_extents = [500, 1000, 250]
for i in range(number_of_fracs):
    for j in range(len(half_extents)):
        dim = np.random.rand(3)[j] * half_extents[j]
        frac_dims.append(dim)  
frac_dims = np.reshape(frac_dims, (number_of_fracs, 3))

Plot microseismic point clouds with 100 points for each stage. The following code should launch a 3D viewer scene in its own window:

size_scalar = 100000
mplt.plot3d(x_int, y_int, z_int, tube_radius=10)
for i in range(number_of_fracs):
    x_cloud = frac_dims[i,0] * (np.random.rand(100) - 0.5)
    y_cloud = frac_dims[i,1] * (np.random.rand(100) - 0.5)
    z_cloud = frac_dims[i,2] * (np.random.rand(100) - 0.5)

    x_event = x_frac[i] + x_cloud
    y_event = y_frac[i] + y_cloud     
    z_event = z_frac[i] + z_cloud
    
    # Let's make the size of each point inversely proportional 
    # to the distance from the frac port
    size = size_scalar / ((x_cloud**2 + y_cloud**2 + z_cloud**2)**0.002)
    
    mplt.points3d(x_event, y_event, z_event, size, mode='sphere', colormap='jet')

You can swap out the last line in the code block above with mplt.points3d(x_event, y_event, z_event, size, mode='sphere', color=stage_color[i]) to colour each event by its corresponding stage.

A day of geocomputing

I will be in Calgary in the new year and running a one-day version of this new course. To start building your own tools, pick a date and sign up:

    

Workshop? Talkshop

Day 4 of the SEG Annual Meeting. I attended the workshop entitled Geophysical data interpretation for unconventional reservoirs. It was really about the state of the art of seismic technologies for shale gas exploration and exploitation, but an emergent theme was the treatment of the earth as an engineering material, as opposed to an acoustic or elastic medium.

Harvey Goodman from Chevron started the workshop by asking the packed room, "are there any engineers in the room?" Hilariously, a single lonesome hand was raised. "Well," he said "this talk is for you." Perhaps this wasn't the venue for it; so much for spreading cross-disciplinary love and the geophysical technical vernacular. 

Mark Zoback from Stanford presented decades worth of laboratory measurements on the elastic/plastic properties of shales. Specifically the concentrations of illite and TOC on mechanical stiffness and creep. When it came to questions, he provided the most compentent and cogent responses of the day: every one was gold. Your go-to guy for shale geomechanics.

Marita Gading of Statoil presented some facinating technology called Source Rock from Seismic (we mentioned this on Monday)—a way to estimate total organic carbon from seismic for basin modeling and play evaluation. She listed the factors controling acoustic properties of shales as

1. organic content;
2. compaction or porosity;
3. lithotype and mineral composition;
4. seismic to microscale anisotropy.

She showed an empirically derived acoustic impedance transform coupled with more interpretive methods, and the results are compelling. It's not clear how well this might work in ancient shales onshore, but it has apparently worked for Statoil in younger, offshore basins.

Galen Treadgold from Global Geophysical gave a visually stunning presentation showing the value of expansive data sets in the Eagle Ford shale. He showed 1000 km² of 3D seismic that had been stitched together, highlighting the need to look at a regional picture. Patchwork data fails to give the same clarity of variation in mechanical stratigraphy.

The session shifted to the state of microseismic technology and 'getting beyond the dots'. Speakers from rival companies MicroSeismic, ESG Solutions, and Pinnacle described how microseismic waveforms are now being used to resolve moment tensors. These provide not only the location and magnitude but also the failure characteristic of every single event. While limited by uncertainty, they may be the way to get the industry beyond the prevailing bi-wing paradigm.

The session was a nice blend of disciplines, with ample time for question and answer. I struggle though to call it a workshop, it felt like a continuation of the huge number of talks that have been going on in the same room all week. Have you ever been to a stellar workshop? What made it great? 

More from our SEG 2011 experience.