American Oil and Gas Reporter - January 2015 - 166

Production Technology

Method Models Decline Curves, EURs
By Babafemi Ogunyomi,
Dong Song,
Natalie-Nguyen La,
Larry W. Lake
and C. Shah Kabir
AUSTIN, TX.-Traditional empirical
decline curve analysis methods have significant limitations in forecasting well
and reservoir production performance
and estimating ultimate recovery in unconventional production.
A University of Texas study performed
statistical and model-based analyses on
production data from hydraulically fractured horizontal wells in a liquid-rich
North American shale play. The research
resulted in a new method to mitigate the
limitations with conventional decline
curve methods.
The production data were carefully
analyzed to identify the flow regimes
and understand the overall decline behavior. Following this step, model-based
analysis was performed using a parallelflow model (sum of exponential terms),
and a logistic-growth model. After the
model-based analysis, the study statistically
analyzed the model parameters and cross
plotted them against available reservoir
and well completion parameters for correlations.
Based on the conclusion from the
cross plots and statistical analysis, design-of-experiments and numerical-reservoir simulations were employed to develop
functions that related the model parameters to reservoir/well completion properties.
All the models used in the study fit the
oil rate data very well and resulted in realistic estimates of EUR. The cross plots of
model parameters and reservoir/well completion properties indicate some relationship
between them, which were developed
using statistical design of experiments
(DOE) and flow simulations. The models
developed through this work can be applied
to obtain reasonable estimates of EUR
from production data in unconventional
oil reservoirs.
Objectives And Workflow
Most decline curve methods have two
main limitations. First, because they are
derived empirically, model parameters are

not functions of reservoir and well completion properties. Second, they may yield
unrealistic (nonphysical) values of estimated ultimate recovery because boundary-dominated flow may not develop early
enough in unconventional reservoirs. Over
the past few years, several empirical
models have emerged to address the second
limitation, but they are challenged by the
time to transition from infinite-acting flow
to the boundary-dominated flow.
This study had three main objectives:
* Understand the decline behavior
and characteristics of oil wells by analyzing
field production data (rate and wellhead
pressures);
* Investigate the existence of a relationship between empirical model parameters and reservoir and/or well completion properties; and
* Demonstrate the use of the relationship identified or developed in the
second step in rate forecasting (this study
explored the applications of both the logistic growth and parallel [sum of exponential] models).
The dataset contained data from 80
liquids-rich horizontal shale wells of varying lengths and completion properties
that had been on production from 50 to
1,500 days. Average water cuts were between 10 and 30 percent. The high-frequency production data were reported on
a daily basis.
The primary steps in the workflow included:
* Analyzing oil rate and wellhead
pressure data to identify the predominant
flow regime and signatures from this
dataset;
* Performing model-based data analysis by fitting noisy oil rates to empirical
models to estimate the model parameters;
* Analyzing and cross plotting the
model parameters obtained in the second
step against available reservoir and well
completion properties (This analysis
identifies the existence of any relationship
between the empirical model parameters
and the reservoir/well completion properties) and
* Using DOE and numerical reservoir
flow simulations to develop relationships
between model parameters and
reservoir/well completion properties.
The original work presents the theo-

166 THE AMERICAN OIL & GAS REPORTER

retical basis for identifying flow regime
(Ogunyomi et al. [2014] SPE 170899),
but a few key observations were made
from log-log plots of rate versus time
and tubinghead pressure (THP) versus
time (THP was used as a proxy for the
flowing bottom-hole pressure) for all the
wells in the dataset.
First, the rate-time log-log plots showed
slopes of 0.5, 1.0, 1.5, and exponential
declines in no particular order. In general,
however, the wells exhibited "power law"
behavior with 0.5 being the predominant
slope observed.
Second, in most of the wells, the plot
of THP versus time showed the existence
of at least two time scales that were not
necessarily the result of operational
changes such as shut-ins or operating
pressure changes at the surface. This conclusion was made after observing a 0.5
slope followed by an exponential curve
and then constant THP. The exponential
curve defines the fracture boundary, and
constant THP indicates flow from the
reservoir matrix.
Model-Based Analyses
Parallel-flow (sum of exponential
terms) and logistic-growth empirical models were fitted to production rate and cumulative production data to obtain the
model parameters. The existence of any
relationships between the model parameters and reservoir/well completion properties were investigated by cross plotting
them against available reservoir/completion
properties.
The parallel-flow model is based on
the concept that when a horizontal well
is hydraulically fractured, the reservoir
rock is broken into discrete blocks, each
of which makes independent flow contribution to the fractures. The flow from
each block has an exponential decline,
which is consistent with boundary-dominated flow. Logistic growth models are
often used to model population, market
penetration of new products and technologies, etc. Over the past few years,
however, logistic growth models also are
being applied to forecast production in
unconventional reservoirs.
In estimating the model parameters
with the parallel-flow model, the number
of exponential terms was set initially to

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