Most of the theoretical work on decline-curve analysis with nonlaminar flow
in the reservoir considers either a dry gas or liquid flow in a homogeneous
system. The purpose of this work is to analyze decline curves considering the
non-Darcy flow effect in the reservoir for a slightly-compressible-liquid flow
in dual-porosity systems at constant wellbore pressure.
The transient and boundary-dominated flow periods are examined by means of
computer results generated with a finite-difference simulator. Analytical
expressions of velocity and wellbore rate are presented for the first time in
this paper. These equations contain the laminar-flow solution as a particular
case. A method is proposed to identify the presence of inertial effects by
plotting d[log(q)]/d[log(t)] against log(t).
The method for area calculation under laminar conditions produces a good
approximation for a reservoir under nonlaminar flow. However, the presence of
inertial effects distorts the shape of decline curves, resulting in erroneous
estimates of wellbore and reservoir parameters by type-curve analysis with
laminar decline curves.
The utility of the methodology presented in this work is illustrated with
Most of the existing techniques available in the literature for determining
productivities and reservoir parameters are based on two main assumptions:
applicability of Darcy’s law and constant inner-boundary condition, either
constant production rate or constant bottomhole flowing pressure. Neither of
these assumptions is frequently fulfilled.
In a naturally fractured formation, we may have wells initially producing at
a high rate and, in some cases, production declines after a few hours.
Analyzing the transient flow-rate behavior will add more information to produce
a more complete evaluation. From an engineering viewpoint, the initial decline
could be a key factor in deciding whether to complete or abandon a well. In
homogeneous systems, this decline is the only one observed, but for fractured
reservoirs, the initial decline does not always represent the final state of
At present, most of the reports on constant-bottomhole-pressure tests found
in the literature assume that only one phase flows in porous media and that
Darcy’s law is applicable to both homogeneous and fractured reservoirs.
In cases in which Darcy’s law is not valid, there are some works that
consider different kinds of tests as well as different reservoir types. Refs.
10 and 11 showed that inertial effects could be important in systems with
slightly-compressible-liquid flow, providing analytical solutions for both
transient and boundary-dominated flow. Nevertheless, there are no analytical
expressions to analyze flow-rate responses for constant-bottomhole-pressure
tests in naturally fractured reservoirs with non-Darcy flow. These expressions
are relevant if we take into consideration that inertial effects are expected
to occur mainly in the fracture system. The objective of this paper is to
present new analytical expressions for non-Darcy liquid flow in dual-porosity
systems produced at constant bottomhole pressure.
© 2005. Society of Petroleum Engineers
View full textPDF
- Original manuscript received:
1 April 2002
- Revised manuscript received:
28 July 2005
- Manuscript approved:
13 September 2005
- Version of record:
15 December 2005