To make up microseismic

December 18, 2013 Evan Bianco

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: