Petroleo

PROCEEDINGS. “Twenty-Seventh Workshop on Geothermal Reservoir Engineering
Stanford University, Stanford, California, January 28-30, 2002
SGP-TR-171

DECLINE CURVE ANALYSIS FOR NATURALLY FRACTURED
RESERVOIRS WITH TRANSIENT INTERPOROSITY FLOW
Héctor Pulido B. 1,2, Fernando Samaniego V.2, Jesús Rivera R.2 , Rodolfo Camacho V.1,2 and César Suárez A.3
1. PEMEX; 2. National University ofMexico; 3. Michoacán University.
ABSTRACT
Constant producing pressure solutions that define
declining production rates with time, for a naturally
fractured reservoir, with transient interporosity flow are
presented. The solutions for the dimensionless flow rate
are based on a model presented by Cinco-Ley,
Samaniego and Kucuk. In this work the model was
extended to include constant producingpressure in both
infinite and finite systems. The results obtained for a
finite no flow outer boundary are new and surprising.
Similarly to Da Prat et al.1, it was found that the flow rate
for conditions of fracture skin greater than 10, shows
initially rapid decline, becomes nearly constant for a
period, and then a final decline in rate takes place.
The same criterion established by Da Pratet al.1 for the
estimation of the outer radius of a reservoir, re , requiring
that the almost constant flow rate period be reached by
the data is applicable to the present transient interporosity
flow model. However, the estimation of re from this
method is higher for fixed values of the ω and λ
parameters. A field example is presented to illustrate the
method of type curve matching for anaturally fractured
reservoir with transient interporosity flow.
The values of ω and λ are determined from the best
match and this is particularly important for the case of
production forecasting by numerical simulation. The
results show that the initial decline could be a key factor
in deciding whether to complete or abandon a well, and
for a practical viewpoint, given an initial valuefor the
flow rate, it is important to know the time required to
deplete the two porosity system.
INTRODUCTION
Naturally Fractured Reservoirs (NFR) consist of
heterogeneous porous media where the openings (fissures
and fractures) vary considerably in size. Fractures and
openings of large size generate vugs and interconnected
channels, whereas the fine cracks form block systems
which are themain body of the reservoir.
In the past, the analysis of short time flow rate data to
obtain reservoirs parameters was not a common
technique, mainly due to the difficulties in obtaining
accurate measurements of the flow rate as compared to
high resolution pressure measurements. However, the
advent of new production tools, like the real time flow
meter (see Kucuk and Ayestaran2, Stewartet al.3), has
made possible the analysis of simultaneously measured
pressures and flow rates in a transient well test. The

advantage of incorporating the measured flow rate, is that
the type curve matching technique is improved, giving
more information regarding the uniqueness as to the type
of reservoir being dealt with, i.e., fractured, multi layer,
composite, etc. In a fracturedformation we may have
wells initially producing at a high rate where in some
cases, production starts to decline after a few hours
without any clear explanation. Therefore, analyzing the
transient flow rate behavior in a well completed in a
fractured formation will add more information that will
result in a more complete evaluation analysis. From an
engineering and economic viewpoint, theinitial decline
could be a key factor in deciding whether to complete or
abandon a well.
NFR have been studied extensively in the petroleum
literature. One of the first such studies was published by
Pirson4 in 1953. Pollard5 presented one of the first
pressure models available for interpretation of well test
data; however, the graphical technique proposed is
susceptible to error caused by...