Figure
1.96
Estimating distance
to a
noflow
boundary.
from which:
At
x
 YI.
45 hoursStep 5. Calculate the distance
L
from the well to the fault byapplying Equation
1.5.59:
L
_
/0.000148ftAf
~
V
<i>m
I
0.000148(30) (17.45)V (0.15) (0.6) (17 xlO
6
)
Qualitative interpretation of buildup curves
The Horner plot has been the most widely accepted meansfor analyzing pressure buildup data since its introduction in
1951.
Another widely used aid in pressure transient analysisis the plot of change in pressure
Ap
versus time on a loglog
scale.
Economides (1988) pointed out that this loglog plotserves the following two purposes:(1) the data can be matched to type curves;(2) the type curves can illustrate the expected trends inpressure transient data for a large variety of well andreservoir systems.The visual impression afforded by the loglog presentationhas been greatly enhanced by the introduction of the pressure derivative which represents the changes of the slope ofbuildup data with respect to time. When the data producesa straight line on a semilog plot, the pressure derivative plotwill, therefore, be constant. That means the pressure derivative plot will be flat for that portion of the data that can becorrectly analyzed as a straight line on the Horner plot.Many engineers rely on the loglog plot of
Ap
and itsderivative versus time to diagnose and select the properinterpretation model for a given set of pressure transientdata. Patterns visible in the loglog diagnostic and Hornerplots for five frequently encountered reservoir systems areillustrated graphically by Economides as shown in Figure1.97. The curves on the right represent buildup responsesfor five different patterns, a through e, with the curves onthe left representing the corresponding responses when thedata is plotted in the loglog format of
Ap
and
(AtAp^)
versus
time.
The five different buildup examples shown in Figure1.97 were presented by Economides (1988) and are brieflydiscussed below:Example a illustrates the most common response—thatof a homogeneous reservoir with wellbore storage andskin. Wellbore storage derivative transients are recognized as a hump in early time. The flat derivative portionin late time is easily analyzed as the Horner semilogstraight line.Example b shows the behavior of an infinite conductivity,which is characteristic of a well that penetrates a naturalfracture. The
\
slopes in both the pressure change andits derivative result in two parallel lines during the flowregime, representing linear flow to the fracture.Example c shows the homogeneous reservoir with a single vertical planar barrier to flow or a fault. The level ofthe secondderivative plateau is twice the value of the levelof the firstderivative plateau, and the Horner plot showsthe familiar slopedoubling effect.Example d illustrates the effect of a closed drainagevolume. Unlike the drawdown pressure transient, thishas a unitslope line in late time that is indicative ofpseudosteadystate flow; the buildup pressure derivativedrops to zero. The permeability and skin cannot be determined from the Horner plot because no portion of the dataexhibits a flat derivative for this example. When transientdata resembles example d, the only way to determine thereservoir parameters is with a type curve match.Example e exhibits a valley in the pressure derivative thatis indicative of reservoir heterogeneity. In this case, thefeature results from dualporosity behavior, for the caseof pseudosteady flow from matrix to fractures.Figure 1.97 clearly shows the value of the pressure/pressure derivative presentation. An important advantage ofthe loglog presentation is that the transient patterns havea standard appearance as long as the data is plotted withsquare log cycles. The visual patterns in semilog plots areamplified by adjusting the range of the vertical axis. Withoutadjustment, many or all of the data may appear to lie on oneline and subtle changes can be overlooked.Some of the pressure derivative patterns shown are similar to those characteristics of other models. For example,the pressure derivative doubling associated with a fault(example c) can also indicate transient interporosity flowin a dualporosity system. The sudden drop in the pressure derivative in buildup data can indicate either a closedouter boundary or constantpressure outer boundary resulting from a gas cap, an aquifer, or pattern injection wells.The valley in the pressure derivative (example e) could indicate a layered system instead of dual porosity. For thesecases and others, the analyst should consult geological, seis
mic,
or core analysis data to decide which model to use inan interpretation. With additional data, a more conclusiveinterpretation for a given transient data set may be found.An important place to use the pressure/pressure derivative diagnosis is on the well site. If the objective of the test is todetermine permeability and skin, the test can be terminatedonce the derivative plateau is identified. If heterogeneitiesor boundary effects are detected in the transient, the testcan be run longer to record the entire pressure/pressurederivative response pattern needed for the analysis.
1.6
Interference
and
Pulse Tests
When the flow rate is changed and the pressure response isrecorded in the same well, the test is called a singlewell test. Examples of singlewell tests are drawdown, buildup,injectivity, falloff and steprate tests. When the flow rate ischanged in one well and the pressure response is recordedin another well, the test is called a multiplewell test.
SLOPE
= 650
psi/cycleSLOPE
= 1300
psi/cycle
Previous Page
aWell with WellboreStorage and Skin
in
a
Homogeneous ReservoirbWell with InfiniteConductivity VerticalFracture
in
a
Homogeneous ReservoircWell with WellboreStorage and skin
in
a
Homogeneous Reservoirwith One Sealing FaultdWell with WellboreStorage and skin
in
a
Homogeneous Reservoirwith Closed OuterBoundaryeWell with WellboreStorage and skin
in
a
Dual Porosity Systemwith PseudoSteadyState Flow from Matrix
to
Fractures
Figure 1.97
Qualitative interpretation
of
buildup curves (After Economides, 1988).
Log

LogDiagnostic PlotHomer Plot
WELLBORE'STORAGE
RADIAL FLOWLINEAR FLOWTRANSITIONRADIALFLOW
.WELLBORESTORAGERADIALFLOWSEALINGFAULTWELLBORESTORAGENOTLOWBOUNDARYRADIAL FLOW(TOTAL SYSTEM)RADIAL FLOW(IN FISSURES)WELLBORE' STORAGEPSEUDOSTEADY STATEFLOW FROM MATRIXTOHS6URES
Figure
1.98
Rate history and pressure response
of a
twowell interference test conducted
by
placing
the
active well
on
production
at
constant rate.
Examples of multiplewell tests are interference and pulsetests.Singlewell tests provide valuable reservoir and
well
characteristics that include
flow
capacity
kh,
wellbore conditions,
and
fracture length as examples of these important properties. However, these tests do not provide the directional
nature
of reservoir properties (such as permeability in the
A:,
y,
and
z
direction) and have inabilities to indicate the degreeof
communication
between the test
wells
and adjacent
wells.
Multiplewell tests are run to determine:
ã
the presence or lack of communication between the test
well
and surrounding
wells;
ã
the mobilitythickness product
kh/'\i\
ã
the porositycompressibilitythickness product
(f)C
t
h;
ã
the fracture
orientation
if intersecting one of
the
test
wells;
ã
the permeability in the direction of the major and minoraxes.
The
multiplewell test requires at least one active (producing or injecting)
well
and at least one pressure observation
well,
as shown schematically in Figure 1.98. In an interfer
ence
test, all the test
wells
are shutin until their wellborepressures stabilize. The active
well
is
then
allowed to pro
duce
or inject at constant rate and the pressure response in
the
observation
well(s)
is observed. Figure 1.98 indicates
this
concept with one active
well
and one observation
well.
As the figure indicates, when the active
well
starts to pro
duce,
the pressure in the shutin observation
well
begins torespond after some time lag that depends on the reservoirrock and fluid properties.Pulse testing is a form of interference testing. The pro
ducer
or injector is referred to as the pulser or the active
Figure
1.99
Illustration
of
rate history
and
pressureresponse
for a
pulse test (After Earlougher,
R.
Advancesin
Well
Test Analysis) (Permission
to
publish
by the SPE,
copyrightSPE
1
1977).
well
and the observation
well
is called the responder. Thetests are conducted by sending a series of shortrate pulsesfrom the active
well
(producer or injector) to a shutin observation well(s). Pulses generally are alternating periods of
production
(or injection) and shutin, with the same rateduring each production (injection) period, as illustrated inFigure 1.99 for a twowell system.
Kamal
(1983) provided an excellent
review
of interfer
ence
and pulse testing and summarized various methods thatare used to analyze test data. These methods for analyzing
interference
and pulse tests are presented below.
1.6.1 Interference testing
in
homogeneous isotropicreservoirs
A reservoir is
classified
as homogeneous when the porosity and thickness do not change significantly with location.An isotropic reservoir indicates that the permeability is
the
same throughout the system. In these types of reservoirs, the type curve matching approach is perhaps the most
convenient
to use when analyzing interference test data in
a
homogeneous reservoir system. As
given
previously by
Equation
1.2.66,
the pressure drop at any distance
r
from anactive
well
(i.e., distance between an active
well
and a shutinobservation
well)
is expressed as:
A
>(r,/)
=
A>=___JEI—^
j
Earlougher (1977) expressed the above expression in adimensionless form as:
PiP(r
f
t)
Ul.2QBn
_ 1
\(l\ ( *№% \ (lV]
kh
2 [V 4 /
V0.0002637*f/
V*W J
From
the definitions of the dimensionless parameters
PD,
fo, and ro, the above equations can be expressed in a
TimeTimeTime
pressure response
in
the observation
well
FmaoFPee
Lag
TimeTime
Re
a
Av
W
Re
aPsnW
Pee
a
Ovo
W
dimensionless form as:
*.
=
>[=£]
[1.6.1]
with the dimensionless parameters
as
defined by:
=
[P
1
PJrJ)]Hh
PD
~ U1.2QBnrr
D
=
—
r
w
_ 0.0002637fr
where:
p(r, t) —
pressure
at
distance
r
and time
t,
psi
r
=
distance between the active well and
a
shutinobservation well
t
=
time, hours
p\
=
reservoir pressure
k
=
permeability, mdEarlougher expressed in Equation 1.6.1
a
type curve formas shown previously
in
Figure
1.47 and
reproduced
for
convenience as Figure
1.100.
To analyze
an
interference test by type curve matching,plot the observation well(s) pressure change
Ap
versus timeon tracing paper laid over Figure 1.100 using the matchingprocedure described previously. When the data is matched tothe curve, any convenient match point is selected and matchpoint values from the tracing paper and the underlying typecurve grid are read. The following expressions can then
be
applied to estimate the average reservoir properties:
k
=
ri4i.2QfiMirfoi
[162]
L
*
JLA/>J
MP
O0002637
m T
t
1
c^
UJLfo/vgj
MP
where:
r
=
distance between the active and observation wells,
ft
k
=
permeability, mdSabet (1991) presented an excellent discussion on the useof the type curve approach in analyzing interference test databy making use of test data given by Strobel et al. (1976). Thedata,
as
given by Sabet,
is
used
in
the following example
to
illustrate the type curve matching procedure:
Example
1.42
An
interference test was conducted
in a
dry gas reservoir using two observation wells, designatedas Well 1 and Well 3, and
an
active well, designated as Well
2.
The interference test data
is
listed below:ã Well 2
is
the producer,
Q
g
=
12.4 MMscf/day;ã Well 1
is
located
8
miles east of Well 2, i.e.,
r
12
=
8
miles;ã Well 3 is located
2
miles west of Well 2, i.e., r
23
=
2 miles.
Flow rate Time Observed pressure
(psia)
Q
t
Welll Well
3
(MMscf/day)
(hr)
P
1
Ap
1
p
3
Ap
3
0.0
24
2912.045 0.000 2908.51
0.00
12.4
0
2912.045 0.000 2908.51
0.00
Figure 1.100
Dimensionless pressure for
a
single well
in
an infinite system,
no
wellborn storage, no skin.Exponentialintegral solution (After Earlougher, R. Advances
in
Well Test Analysis) (Permission
to
publish
by
the SPE,copyright SPE, 1977).