American Oil and Gas Reporter - January 2015 - 170

Production Technology
the parameters for both the empirical logistic-growth and parallel-flow models,
were estimated by fitting them to wells
rate and cumulative production data. Regression analysis was performed on each
parameter in the empirical model and all
variables to identify reservoir/completion
properties with the strongest effects on
each empirical model parameter. As an
example, fracture half-length was found
to have a strong effect on the value of the
carrying capacity in the logistic-growth
model.
Once a list of variables with the
strongest influences on each model parameter was identified, the study performed
a full factorial DOE with these variables
for each model parameter, the numerical
reservoir model was built to generate
data, and the previous step was repeated.
Using regression analysis, a functional
relationship was developed between each
of the model parameters and the reservoir/well completion properties. The relationship then was validated with synthetic
examples.

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Results And Conclusions
Both models used in the study can
predict EUR, and because both methods
require numerical fitting of model parameters, neither offers a clear advantage.
Although both models result in good fits,
the logistic-growth model does not have
physically meaningful parameters (except
for the carrying capacity) and does not
fit the data quite as well as the parallelflow model. The parallel-flow model has
more parameters (four for the two-compartment model, as opposed to three for
the logistic model). The logistic-growth
model also does not have the multiple
scales that are such a prevalent feature of
the data, and this may be a limiting factor
in its application.
As noted, analysis with the parallelflow model clearly indicates the existence
of multiple time scales in the wells' production profiles. The parallel-flow model
is based on the concept that the reservoir
contains multiple independently declining
reservoir elements (compartments) that
have different and unique time constants
(declining characteristics). Therefore,
when two or more reservoir compartments
are present, there are two or more terms
in the parallel-flow model. The observed
time scales also highlight the importance
of high-frequency data.
Most analysis techniques ignore ear-

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170 THE AMERICAN OIL & GAS REPORTER

ly-time production data because of wellbore effects (wellbore storage or skin
and frac fluid flow back) and noise,
thereby missing the first time scale and
only analyzing data that are dominated
by production from the second time scale.
While it is possible that these phenomena
affect early-time production only, it does
not eliminate the possibility of analyzing
early-time data to estimate reservoir element/compartment dimensions (this could
be the fracture or fracture network that
account for early-time flow).
University of Texas researchers have
developed a rate/time relation capable of
modeling flow from a double-porosity
model that typically exhibits two or more
time scales. That model is valid also for
both early- and late-time transient and
boundary-dominated flow.
Analyzing the model parameters for
the logistic growth and parallel flow models shows some correlation with reservoir
and well completion properties. In an
ideal situation, properties such as well
spacing and volumes of injected fluid
and sand can be used to define a well's
drainage volume. It seems reasonable to
use carrying capacity as a constraint on
recoverable reserves from a well.
Based on the results of these analyses,
production performance from wells in
unconventional oil reservoirs should be

American Oil and Gas Reporter - January 2015

Table of Contents for the Digital Edition of American Oil and Gas Reporter - January 2015