American Oil and Gas Reporter - December 2019 - 60

SpecialReport: Stimulation & Completion Technology

Model Predicts Number Of Frac Stages
· How many perforations per cluster?
· What is the spacing between clusters?
This new methodology can predict
the number of fracture stages and optimize
completion strategies in Wolfcamp wells.
The pool of independent (or input) variables considered in the model to predict
fracture stages (the dependent variable)
include county, depth, reservoir type,
overlap between horizontal wells' drainage
volumes, volume of injected fluid per
stage, true vertical depth, proppant volumes, gas yield, cumulative oil and cumulative natural gas, estimated ultimate
recoveries of both oil and gas, and initial
30-day and 60-day production rates for
both oil and gas.
The model relates the 30-day IP of oil
to the number of fracture stages for horizontal wells. According to the concept,
stages vary by county and reservoir, and
also according to 23 distinct completion
variables used in developing the model.
The parameters ranged from completed
feet of lateral to cluster spacing, average
proppant concentration, gas-to-oil ratio
and initial reservoir pressure.

Wade Baustian,
Ahmed Alzahabi
Ahmed Kamel
and A. Alexandre Trindade
MIDLAND-The industry continues
to work toward optimizing horizontal
well completion designs to effectively
develop the Permian Basin Wolfcamp
Shale. Many completion variables directly
impact the performance of Wolfcamp
horizontal wells, including fracture stages
per well, fracture type, average water requirements, proppant type, fluid type,
proppant size, average pump rate, hydraulic
horsepower per stage, pounds/foot of
proppant per stage, number of clusters,
cluster spacing and lateral length (completed interval).
Relationships among these variables
were studied with the help of advanced
multivariate regression (supervised machine learning) techniques, which allow
for the group-wise inclusion/exclusion
of factor variables. The analysis was performed on 201 horizontals in the Wolfcamp
play (A through D benches) with available
data. The analysis identified key parameters that could be used to predict the
number of fracture stages. Three additional
models were introduced to answer the
following questions:
· How many clusters per fracture
stage?

Optimizing Completion Designs
For years, the industry has employed
zipper fracturing, modified zipper fracturing
and sequential fracturing approaches for

FIGURE 1
Predicted versus Actual Number of Stages

Observed

10
10

40
Predicted

60 THE AMERICAN OIL & GAS REPORTER

stimulating unconventional reservoirs.
These placement methods activate more
natural fractures and may increase production from shale reservoirs. On the other
hand, some operators prefer the engineering
design of fracture stage placement based
on equal spacing. With any of these approaches, multivariate regression can analyze the relationships among variables.
The number of fracture stages has increased with time in all shale gas and
tight oil plays along with increases in the
proppant and fluid volumes, lateral lengths,
and fluid injected and proppant pumped
per foot of lateral. In fact, proppant volume
per foot in horizontal wells has increased
500% during the past eight years, fluids
have increased 800%, and average lateral
lengths have doubled. The 12-month cumulative production per 4,500 feet of
lateral doubled during the same period.
The industry's Wolfcamp completion
designs continue to optimize each of
these variables. The number of fracture
stages is a key aspect of the completion
design that impacts other variables, such
as proppant and fluid volumes. The workflow involves two main stages.
The first stage is to develop a userfriendly model to predict fracture stages
using a multivariate linear regression for
the four outputs (stages, perforations,
clusters and spacing) to fit the data using
the "group lasso" method. This relatively
new approach was devised for multitask
machine learning applications, where
strong correlation exists among the outputs,
while also incorporating shrinkage and
model selection.
The second stage entails testing the
model using in-sample test data and publicly available information. While the
global model was fitted to the four outputs,
this article focuses only on the results of
the model for frac stages.
Predictive Model
The model shows relatively good insample predictions, as shown in Figure 1,
which display the actual observed values
of outputs on the y-axis versus their model-predicted values on the x-axis. The
model multiplies the model coefficients
(B values) with their corresponding inputs
to produce the output.
Figure 2 shows pairs plot of stages by
county and reservoir (colored according
to reservoir). From the clear separation

American Oil and Gas Reporter - December 2019

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