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ABSTRACT
Pressure transient testing techniques such as pressure
buildup, pressure drawdown, and constant rate injection
have been used in petroleum industry for well
performance evaluation and reservoir characterization.
Conventional method of analysis usually assumes that
permeability and compressibility of the reservoir
formation are constant or a function of pore pressure.
This assumption has limitations when applied to an oil
sands reservoir because of the unconsolidated deformable
nature of oil sands. Three injection tests were conducted
in an oil sands reservoir at a depth of about 500 m.
History matching of the field injection data using a fully
coupled reservoir-geomechanical simulator demonstrates
that the permeability and compressibility of oil sands are
interrelated and effective stress dependent.
INTRODUCTION
The basic principle of pressure transient testing
techniques, which are prevalent in petroleum industry, is
to create and observe changing wellbore pressures.
Appropriate and comprehensive interpretation of recorded
well testing data provides information into reservoir
properties such as permeability and compressibility.
Conventional analysis is based on the principle of mass
conservation, assuming that the permeability, porosity and
compressibility of fluid are dependent on the pore pressure
only. This simplified assumption has limitations when
applied to an oil sands reservoir because oil sands will
deform subjected to fluid injection and withdrawal,
thereby causing changes in pore pressure and total
stresses. Therefore, in order to interpret the well testing
data in oil sands reservoir, coupled diffusion-deformation
analysis, which considers the principle of mass
conservation and equilibrium, should be used.1,2,3 In this
paper, a history matching of the pore pressure responses of
three injection tests in an oil sands reservoir was carried
out using a fully coupled reservoir-geomechanical
This paper is to be presented at the 1999 CSPG and Petroleum Society Joint Convention, Digging Deeper, Finding a Better Bottom Line,
in Calgary, Alberta, Canada, June 14 18, 1999. Discussion of this paper is invited and may be presented at the meeting if filed in
writing with the technical program chairman prior to the conclusion of the meeting. This paper and any discussion filed will be considered
for publication in Petroleum Society journals. Publication rights are reserved. This is a pre-print and subject to correction.
THE PETROLEUM SOCIETY PAPER 99-30
Analysis of Well Testing in an
Oil Sand Reservoir
R.C.K. Wong, Y. LiUniversity of Calgary
K.C. YeungSuncor Energy Inc.
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simulator. This exercise provides some estimate on the
flow (permeability) and deformation response of oil sands
subjected to water injection.
INJECTION TESTS
Three injection tests were conducted in a cased well at
Burnt Lake, Alberta. The well was completed with a
diameter of 178 mm. The perforation zone is 5 m in the
middle of the oil sands layer, which is 21 m thick, and has
an overburden of 505 m. The overlying and underlying
formations of the oil sands layer can be considered
impermeable because it is capped and underlain by shale
layers of 3 to 5 m. The oil sands layer has an initial pore
pressure of 3.3 MPa and its in situ porosity is 33%. The
void ratio of oil sands layer is 0.4893, which is the ratio of
the volume of void to the volume of solid.
In each test, cold water was injected into the oil sands
formation through the tubing at a controlled rate for some
interval, and then the well was shut in allowing the bottom
hole pressure to decay to its initial insitu state. The
bottom hole pressure was monitored during the injection
and shut-in periods. The injection rate was increased from
test 1 to test 3. The injection rates of three tests are
presented in Figure 1. The bottom hole pressures
monitored during the well testing are shown in Figure 3.
FULLY COUPLED MODEL
A fully coupled reservoir-geomechanical simulator
ABAQUS4
was used in this study to carry out the history
matching analysis of the injection tests. The simulator
solves the equilibrium and continuity equations
simultaneously in each time increment using finite
element method to model the single-phase, fully saturated
fluid flow through porous media. The porous medium
theory applied in ABAQUS is based on the conventional
effective stress principle, with compressibilities of solid
grain and fluid phases allowed in the continuity equations.
Displacements and pore pressure are calculated at each
node of all finite elements. The total stresses are back
calculated using the constitutive law and principle of
effective stress.4
In the simulation, axisymmetric elements were used,
assuming radial flow in the homogeneous oil sands layer.
Figure 2 shows the configuration of reservoir model. The
finite element model contains 2459 nodes and 780
elements. All nodes along the right vertical boundary and
left vertical boundary are allowed to move vertically only.The nodes at the bottom base are restrained to any
displacements. The top boundary surface is free to deform.
Initial constant pore pressure (3.3 MPa for test 1, 3.75
MPa for test 2, 3.8 MPa for test 3) are maintained at the
nodes of elements in the oil sands layer on the right
vertical boundary. The no flow condition is applied to the
nodes of elements at the top and bottom of the oil sands
layer. The injection rate is imposed to the corresponding
sides of elements in the perforation zone at the wellbore.
In this paper, the overburden and underburden are
assumed to be linear elastic with Youngs modulus, E = 1
GPa and Poissons ratio, = 0.3. They are assumed to be
impermeable so that no injected water will diffuse into
these formations. Porous non-linear elastic model is
applied to simulate the oil sands behavior,
vp
p
e
=
+
)ln()1(
0
0
(1)
where,
straincvolumetri
stresseffectivemean
stresseffectivemeanofvalueinitial
ratiovoidinitial
modulusbulkclogarithmi
0
0
=
=
=
=
=
v
p
p
e
Equation (1) states that the volume change of the oil sands is
dependent on the effective stress instead of pore pressure
only.
Base on the experimental data5, the value of lies in a
range of 0.012 0.024. Figure 4 shows the void ratio versus
effective stress and porosity versus effective stress
relationships for e0 = 0.4893, p0 = 7 MPa, = 0.012 and
0.024. The porosity increases with decreasing effective
stress.
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The bitumen in oil sands is relatively immobile as
compared to water because of its low viscosity of 30,000
cp at reservoir temperature of 12o
C. Hence, it is assumed
that the flow occurred during injection tests is a single-
phase water flow. The effective permeability to water of
oil sands as a function of void ratio (or porosity) isassumed to follow the laboratory data5, and shown in
Figure 5. It is shown that there is a significant increase in
permeability when void ratio exceeds 0.61 (or porosity
exceeds 0.38).
The simulation procedure involves two steps: (1)
applying in situ stresses to the formation, and (2) injecting
water in the perforation zone. The total in situ stresses are
assumed to be isotropic.
ANALYSIS RESULTS
The objective of history matching analysis is to
determine a set of oil sands properties which will match
the pore pressure responses monitored during the injection
tests. It has been shown6 that the pore pressure responses
are sensitive to the bulk compressibility and permeability.
Different combination of bulk compressibility and
permeability will yield different pore pressure results. The
bulk compressibility is defined as the reciprocal of the
bulk modulus. The logarithmic bulk modulus = 0.012and laboratory data of permeability shown in Figure 5 are
used as input parameters for the base case study. Then, the
relationships (void ratio versus permeability and volume
change versus effective stress) are varied to match the
pore pressure responses. Based on the work by Wong et
al,5 the range of bulk modulus is narrower than the range
of effective permeability to water if there is no shear
dilation induced. The effective permeability value could
vary within an order of magnitude, depending on the
reservoir quality of the test specimen. Hence, the
logarithmic bulk modulus is limited to a range of 0.012 -
0.024, whereas the permeability value is varied until a
reasonable match is achieved.
Figure 3 compares the pore pressures monitored in the
three injection tests and obtained from the simulation
calculations. A same logarithmic bulk modulus ( =
0.024) was used in the simulations. However, two
different relationships of permeability versus void ratio,
which are shown in Figure 5, were required to be input in
the simulations to give good matching.
Based on the laboratory data
5
, in order to have a goodmatching in the pore pressure buildup phase, the effective
permeability value has to be increased. Matching the pore
pressure decay portion requires to decrease the in situ
effective permeability. To have an overall good matching,
the effective permeability values used in the simulations
are much higher than the laboratory values. The effective
permeability values have to be increased if low
logarithmic bulk modulus ( = 0.012) is used. This
discrepancy between the simulation and laboratory values
might be due to the difference in bitumen saturation in the
reservoir formation and test specimen.
It is also found that the effective permeability values
used in simulation of low injection rate tests 1 and 2 are
higher than those used in high injection rate test 3. It could
be attributed to the fact that some of bitumen might be
displaced by high rate injection and the total mobility be
decreased.
Simulation results of three tests on development of the
total and effective radial, tangential and vertical stresses at
the wellbore are plotted in Figures 6 and 7, respectively.
From Figure 6, the total stresses increase during injection.
The higher the injection rate is, the larger the changes in
total stresses are. In high injection rate test 3, the total
radial stress becomes the minor principal stress. The
increase in total radial stress is about 2 MPa. This implies
that the injection pressure could be higher than the initial
insitu confining stress without causing fracturing because
of the increase of total stress.
From Figure 7, the effective stress decreases during theinjection period and rebounds to its initial values during
the shut-in period. The effective radial stress has a
minimum value of 1.9 MPa in test 3. The void ratio
interpolated from the relationship shown in Figure 3 is
about 0.52, which is the maximum void ratio induced in
the three injection tests. It can be inferred from Figure 5,
the maximum effective permeability induced in test 3 is
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about 8.7 md. This interpretation suggests that the high
rate injection does not cause significant volume dilation
and thus the permeability enhancement. When the
effective confining stress is reduced to values lower than 1
MPa, the void ratio increases at a larger rate and
significant dilation may occur.
Additional simulations were conducted to investigate
the effect of bulk modulus and permeability on the pore
pressure, total and effective stresses at the wellbore. The
results are shown in Figures 8 to 10. In general, decreases
in bulk compressibility and permeability values cause
increase in pore pressure and total stresses. However, the
changes in effective stresses are less significant than the
changes in total stresses and pore pressure because the net
effect is reduced.
CONCLUSIONS
From the numerical simulation of 3 injection tests in oil
sands reservoir, following conclusions can be drawn.
The injection induces increases in pore pressure
and total stress. It is necessary to use coupled
reservoir-geomechanical model to analyze well
testing data.
The pressure response near the wellbore is
sensitive to porous elastic properties and
permeability. To achieve a good matching of field
data, non-linear relationships among void ratio,
permeability and effective stress must be used in
the simulation.
Due to the increase of total stresses during
injection, it may be possible to increase injection
pressure exceeding the initial overburden stress
without causing fracturing.
The model considering multi-phase flow would
be required under the condition of high rate injection
which would induce bitumen movement. In addition,
shear dilation mechanism should be considered in the
simulation if high pressure injection is used.
ACKNOWLEDGEMENTS
The authors wish to acknowledge financial and technical
supports provided by Alberta Department of Energy
(ADOE) and Suncor Energy Inc.
REFERENCE
1. M.A. Biot, General theory of three-dimensional
consolidation, J. Appli. Phys., 12, 155-164, 1941.
2. K. Terzaghi, Theoretical soil mechanics, John Wileyand Sons, New York, 1943.
3. Y. Li, R.C.K. Wong and K.C. Yeung, Analysis of
transient pressure response near a horizontal well a
coupled diffusion-deformation approach, SPE 50385,
1998 SPE International Conference on Horizontal
Well Technology, Calgary, Alberta, Canada,
November, 1998.
4. ABAQUS/Standard, Users manual, Version 5.5,
Hibbitt, Karlsson & Sorensen, Inc., 1995.
5. R.C.K. Wong, W.E. Barr, N.M. To and R. Paul,
Stand-up times of Athabasca oil sands in the bore
hole mining process, Proc. of the 44th Canadian
Geotechnical Conference, Calgary, Alberta, Canada,
Vol. 2, 57.1-57.3, 1991.
6. J. Hasubek, Poroelastic analysis in tunnel and well
testing, MSc. Thesis, University of Calgary, Calgary,
Alberta, 1998.
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Figure 1. Injection rates
Overburden layer
Oil sands layer
Underburden layer
505m
21m
100m
500m
vertical
tangential
radial
Perforation
zone, 5m
wellbore
Figure 2. Configuration of reservoir model
0
5
10
15
20
25
30
0 10 20 30 40 50 60
Time (Hour)
Injectionrate
(m
3/day)
test 1
test 2
test 3
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Figure 3. History matching of pressure responses
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Figure 4. Void ratio (porosity) versus effective stress
Figure 5. Permeability versus void ratio
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Figure 6. Total stress development
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Figure 7. Effective stress development
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Figure 8. Effect of bulk modulus and permeabilityon pore pressure
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Figure 9. Effect of bulk modulus and permeabilityon total stress
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Figure 10. Effect of bulk modulus and permeability
on effective stress
