American Oil and Gas Reporter - April 2016 - 77

SpecialReport: Drilling Technology
structing a decision tree is a classification
and regression tree (CART). In a classification context, binary CART models
recursively partition a dataset using splits
on predictor values. At each branch in
the tree, a predictor and threshold assign
one set of observations to go down the
left path and sends the others down the
right path.
The predictor and threshold are chosen
to maximally separate the category labels
of observations between the two paths.
While this splitting could continue until
each observation is in its own terminal
node, trees typically are pruned to earlier
splits so that terminal nodes contain multiple training observations.
For the Wolfcamp dataset, the top 25
percent and bottom 25 percent of producing wells were identified, and the 50
percent in the middle were removed. A
decision tree was built to separate the
top and bottom groups (Figure 3).
The first split at the top of the tree
checks whether less than 1.405 million
pounds of proppant was used. If so, a
well observation moves down the left
path. In not, it goes right. Subsequent
splits work in the same way, until the observation eventually reaches a terminal
node that contains a prediction.
Decision trees are easy to interpret.
Not only do they indicate which predictors
are influential in determining the response
category, but they also identify critical
values at which these categories change.
In this case, there are two general paths
to obtaining a top 25 percent producing
well. For wells using lower amounts of
proppant, the goal is to have a longer
lateral and greater vertical depth. For
wells using larger amounts of proppant,
the goal is to have greater vertical depth
and a lateral that is not too long.
Fundamentally, decision trees partition
the predictor space into blocks of similar
observations. In a scatter-plot of two predictors, this appears as vertical and horizontal segmentations of the plot. Unfortunately, 2-D views can show only so
much when multiple predictors are involved in the tree.
Figure 4 shows how 3-D visualization
can lead to a better understanding of how
the top 25 percent of wells compare with
the bottom 25 percent. In this case, the
bottom 25 percent (yellow triangles) form
a distinct cluster at low proppant levels
and short lateral lengths. The remaining
wells are mixed with the top 25 percent
wells (blue circles), but tend toward higher

FIGURE 4
3-D CART Analysis of Top 25 Percent
And Bottom 25 Percent of Producing Wells

depths and lower proppant levels.
Variable Importance
In some applications, the objective
may not be to build a predictive model
for a given response, but to identify the
drivers of that response from among a
large set of predictors. For the Wolfcamp
dataset, the aim may be to identify operational characteristics of horizontal wells
that tend to correlate with higher performance. With fewer predictors to focus
on, a screening exercise could guide the
development of simpler predictive models
or make experimental designs feasible
with a smaller number of runs.
There are many approaches to measuring variable importance. An easy approach not tied to a particular model is

JARED SCHUETTER is an applied
statistician and principal research scientist at Battelle Memorial Institute. He
specializes in several interrelated fields
that include exploratory data analysis,
clustering and classification algorithms,
pattern recognition, machine learning,
data mining, image processing, and
computer vision. Schuetter's involvement
in these areas includes algorithm work,
data visualization, and implementation
in software. He holds a Ph.D. in statistics
from Ohio State University.
SRIKANTA MISHRA is a senior research leader ("institute fellow") at
Battelle Memorial Institute. He is responsible for developing and managing
a technology portfolio related to reservoir modeling and data analytics for
geological carbon storage, shale gas
development, and improved oil recovery
projects. Mishra has served as an associate editor of the "Journal of Petroleum Science & Engineering." He holds
a Ph.D. in petroleum engineering from
Stanford University.

called R2-loss. It works for any regression
model, and the reasoning is that if an influential predictor is removed from a
model, the model's accuracy will fall
dramatically. Alternatively, if a superfluous
predictor is removed from the model,
there should be little to no impact on accuracy.
Model fit can be assessed using an R2
measure to compare the sum of squared
differences between the true and predicted
responses with the overall sum of squares,
which is proportional to the variance of
the responses. That is, it measures how
much of the variability in the response is
explained by the model. A larger loss in
R2 indicates a predictor with higher influence on the response.
When measuring variable importance,

MING ZHONG is a data scientist
working on advanced analytics at Shell.
He has data mining experience in different business sectors, from the pharmaceutical to the financial and banking
industries. Zhong holds a master's in
physics and a Ph.D. in statistics from
Texas A&M University.
RANDY LAFOLLETTE is director
of applied reservoir technology in the
pressure pumping production enhancement product line at Baker Hughes in
Tomball, Tx. He is a subject matter expert in geoscience and petroleum engineering for the company. With 38 years
of industry experience, LaFollette is a
2015-16 Society of Petroleum Engineers
distinguished lecturer in data mining
in unconventional plays. He also has
developed and taught short courses on
hydraulic fracturing for the American
Association of Petroleum Geologists.
LaFollette holds a B.S. in geological
science from Lehigh University.

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