Thermal Rock Physics of Heavy-Oil Sandstones

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SPE-171096-MS
Thermal Rock Physics of Heavy-Oil Sandstones
Paul Perdomo (Baker Hughes Inc.), Claudio Rabe (Universidade Federal Fluminense and Baker Hughes Inc.),
Fredy Artola (Universidade Federal da Bahia), and Jose Cherrez (Independent Oil and Gas Consultant)
Copyright 2014, Society of Petroleum Engineers
This paper was prepared for presentation at the SPE Heavy and Extra Heavy Oil Conference - Latin America held in Medellin, Colombia, 24–26 September 2014.
This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been
reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its
officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to
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Abstract
This study investigates whether thermally induced changes from steam assisted gravity drainage (SAGD) operations in a
heavy oil sandstone reservoir are observable using seismic methods. Thermally induced changes can include stress changes,
changes in characteristics arising from shear heating of heavy oils, and changes in fluid saturation and density driven by
thermal heating. These variations are important to understand if seismic monitoring in “real time” is used for project
optimization. The SAGD process injects steam from a "steam chamber" that grows vertically and horizontally in the
reservoir and overburden. The heat from the steam reduces the viscosity of the heavy oil which enablesit to flow down into
the producer well (where expectations of recovery can reach approximately 40% of oil in place).
This study presents an analysis of the changes that are expected in seismically observed characteristics such as velocity
(compressional and shear velocities) and seismic acoustic impedance. Variations of the rock and fluid properties from steam
injection in a heavy oil sandstone reservoir were calibrated with ultrasonic laboratory testing using high temperatures (up to
150°C). A 2D synthetic seismogram using results from, logs, images (borehole and laboratory (PVT, thin section)) was
evaluated for time-lapse modeling. The outputs from reservoir simulation (pressure, saturation and temperature) were used to
calculate the variation in acoustic impedance and the fluid substitution was evaluated using Gassmann’s equation.
The results indicate that massive variation in fluid saturation, density, effective horizontal stresses and generation of shear
dilation zones from thermally-induced volume changes affect seismic parameters. Variations in the horizontal stresses
reached inside the steam chamber can be as great as 8%, and affect the seismic response by increasing acoustic impedance
contrast by approximately 4.5%.
Introduction
Reserves of heavy oils have increased in importance because of the reduction of the reserves of light oil and rising oil prices.
The world's largest reserves of heavy oil are in Canada and Venezuela. To produce these heavy oils, their viscosity must be
reduced, and one method to reduce it is through heat transfer by steam injection. The steam injection not only alters the
properties of heavy oils, but also the properties of the rock, and leads to the question of how thermal variations affect
reservoir properties. The heavy oil reservoirs can suffer thermal impact during steam injection such as thermal expansion,
softening and mechanical rock failure; previous investigations indicated (Samier, 2007) high values of effective normal stress
and increased shear failure during stimulation. Therefore, a geomechanic model of the reservoir was created, which couples
the fluid data set to the seismic (in order to understand the dimensions of the steam chamber and its steam front along the
stimulation process). Because the conventional flow simulators do not take into account the geomechanic effects on the
stimulation process, a better understanding on how the rock matrix affects the gravitational segregation, fluid phase changes
and thermal expansion in the reservoir is necessary. The geomechanic model of the reservoir is constructed using
petrographic, petrophysical and rock mechanical laboratory data.
Time-lapse seismic interpretation is the process of linking differences between seismic surveys (base and monitor) that have
endured changes in saturation, pressure and temperature in the reservoir. It is used for the propagation of mechanical and
thermal properties of rocks and fluids and seismic simulation (time-lapse 4D), and to investigate whether seismic data is a
useful technique for monitoring a SAGD process. The synthetic model was generated containing data from real seismic,
velocity and density logs of The Faja del Orinoco Belt. The steam-assisted gravity drainage (SAGD) is a method to
economically increase the recovery factor of the large accumulations of heavy oil from The Faja del Orinoco Belt.
The Faja del Orinoco Belt comprises 55,314 km2with an area of 11,593 km2currently in production (includes Guárico,
Anzoátegui and Monagas states). The Faja del Orinoco Belt comprises an estimated 186 billion barrels. 1,360 billion barrels

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of oil in-situ are in the fields of Boyacá, Junín, Ayacucho, and Carabobo.
Statement of Theory and Definitions
The integrated reservoir model involves flow, temperature, geomechanics and seismic data, with influences of the
overburden, 4D time-lapse geomechanics. The flux-deformation model takes into account the influence of overburden and
side layers according to the tensions generated in the reservoir (as boundary conditions).
This geomechanics model includes horizontal tectonic forces (and overburden stresses), rock properties, a pore pressure
profile, a failure criterion and a hardening criterion.
Description and Application of Equipment and Processes
Seven geomechanical reservoir models were constructed and included a dataset of the fluid and rock properties from The
Faja del Orinoco Belt. Table 1 presents the geomechanical and vertical spacing between well parameters. In all cases, the
overburden stress is 2,500 psi at the top of the reservoir. The value of the maximum horizontal stress is 1,957.8 psi and the
minimum horizontal stress is 1,899.1 psi (with its respective axis system and cell numbers on each axis shown in Fig. 1). The
data was obtained from laboratory analysis (Rabe et al 2013).
Table 1. Rock parameters
Fig. 1. Stress boundary conditions and simulation grid
In the simulations, two types of rocks stiffness systems are used. In the first one, the rock is ductile (less resistant and more
compressive); in the second one, the rock is more brittle (more resistant and less compressive).
The brittle rock (more resistant and less compressive) and the ductile rock (less resistant and more compressive ) were chosen
to know the answers of these kinds of rock when subjected to the SAGD process. The modulus of elasticity may vary with
the minimum horizontal effective stress (Li and Chalaturnyk, 2009).

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The total volume analyzed in the model, considering well pairs inside, is 2,175 ft x 665 ft x 98 ft., and was chosen by
PDVSA (Petróleos de Venezuela SA) according to the equipment injection, steam pressure and well pairs design available in
the region. The number and reservoir cells in the study were evaluated by several numerical iterations (until reaching the
convergence). The chosen time step is one monthl for calculating flow-geomechanics simulations. That is enough to evaluate
small variations in the pore pressure changes and saturations.
The numerical flux-deformation simulator employs the adaptive implicit method (AIM) to solve the equations of the pressure
and saturation system. The AIM is an approach between the fully implicit method and Implicit Pressure and Explicit
Saturation method (IMPES), enabling the reservoir cells that lie in regions with high instability to be implicitly solved while
the reservoir cells that lie in regions with low instability are solved using the IMPES method.
Heat losses are calculated by the analytical method (solution considering Vinsome and Westerveld’s approach of the
temperature equation) (Westerveld and Vinsome, 1980).
The mean reservoir pressure, FPR is defined by Equation 1:



HCPV
PHCPV
FPR (1)
where:


gw SSPVHCPV



1
Absolute permeability can be updated by simple empirical relationships (Samier and Gennaro, 2007), and in this case, by
considering the horizontal stress distribution. Table 2 shows the permeability multipliers based on the maximum and
minimum horizontal stresses. The steam injection rate was kept constant (1881 STBD) and maximum production rate was
kept constant what?(1200 STB/d) to compare results. All simulations also took into account the total production rate (water,
gas and oil).
Table 2. Permeability multipliers as a function of the maximum and minimum horizontal stresses
Table 3 shows the fluid and rock properties for the construction of a SAGD model.
Table 3. Reservoir model and rock and fluid properties

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Fig. 2 shows the vertical spacing between wells: 14, 28 and 42 ft (reservoir simulations, not shown in this paper, concluded
that these spacings are the best well pairs separation for optimum production) and Fig. 3 shows the workflow used. The type
of coupling between the simulated flow and geomechanical simulation is explicit; the porosity is the coupling parameter (i.e.
the input porosity simulator is not the same output porosity recalculated in each step because of stress variations).
Fig
.
2
. Vertical spacing between wells
Fig
.
3
.
Workflow
Equation 2 is implemented for the model of conservation of mass rock:
 
PC
C
Crb
bc
r









 1(2)
where:
 
nn AAA  1
Adelta

Presentation of Data and Results
Seismic Modelling
The purpose of the fluid substitution and stress simulations is to model seismic properties (seismic velocities), evaluate the
density of a saturated rock at a given reservoir condition (i.e. pressure, temperature, porosity, salinity and mineral type) and
evaluate the fluid saturation with steam injection stimulation (Kumar, 2006). The seismic velocity of an isotropic material
can be calculated using equations referenced by Gassmann (1951).
The fluid properties (density and incompressibility modules) were calculated using the equations of Batzle and Wang (1992)
that model the properties as a function of pressure, temperature and characteristics related to their chemical compositions. It
is assumed that the fluid properties calculated according to Batzle and Wang (1992) are good approximations as
demonstrated by Vasquez and Dillon (1993). The compressional and shear velocity variations for fluid substitution were
calculated using Gassmann’s equations (1951).
The absolute change in acoustic impedance was calculated for the two rock types after 9 years of continuous steam injection,
and taking into account the three possible well spaces (14, 28 and 42 ft). The same variation of acoustic impedance was
expressed in percentage form (Fig. 4,Fig. 5, and Fig. 6).
Acoustic Impedance Variation
The Gassmann equations were used to perform fluid substitution (Gassmann, 1951). The values of pressure, temperature, oil,
gas and water saturation for the initial time and the time of abandonment (9 years) were taken from simulations of flow-
thermal-geomechanics. Equations from Batzle and Wang (1992) were used to calculate the seismic properties of fluids.
Table 4 shows the initial conditions for fluid substitution using the Gassmann equation.

SPE SPE-171096-MS 5
Table 4. Initial fluid replacement to the Gassmann equation conditions
Fig.4. Acoustic impedance variations (gm/cm3·m/s) and temperature (˚F) after 9 years of steam injection for the
more resistant rock and vertical separation of 14 ft between wells
Fig. 5 Horizontal sections: acoustic impedance variation after 9 years of steam injection for the more resistant
rock and a vertical separation of 14 ft between wells

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(a)
(b)
(c)
Fig. 6. Histograms of the percentage of change of acoustic impedance for the more resistant rock and a vertical spacing of (a)
14 ft, (b) 28 ft and (c) 42 ft
Temperature has a similar behavior to the variation of acoustic impedance behavior because the region with the highest
temperature gradient corresponds to the region which has undergone a greatest displacement of oil, gas and water, and
therefore, the greatest variation of oil, gas and water saturation.
In more resistant and less compressive rock, the maximum percentage variation of acoustic impedance was -4.5 % (between
monitor and base), being predominant the value of 0.75 % for the three vertical separations (Fig. 6). The value of the initial
acoustic impedance is 5288 gm/cm3m / s.
Frequency values for the vertical spacing of 14 ft, 28 ft and 42 ft indicate respective variations of approximately 6 %, 7.5 %
and 10 % (out of 23,142 cells). Variation in the acoustic impedance of -4.5 % means a larger volume of oil being drained
from the reservoir, and therefore, a greater volume of the steam chamber.
(a)
(b)
(c)
Fig. 7 shows the histograms of the percentage of change of acoustic impedance for the less resistant rock and a vertical
spacing of (a) 14 ft (b) 28 ft and (c) 42 ft
In less resistant and more compressive rock, the maximum percentage variation of acoustic impedance rock was -4.5%
(between the monitor and base), being predominant the value of 0.75% for the three vertical separations (Fig. 7). The value
of the initial acoustic impedance is 5,288 gm/cm3 m / s.
Frequency values for the vertical spacing of 14 ft, 28 ft and 42 ft (4%, 5% and 7% (of 23,142 cells), respectively) for the
percentage change in acoustic impedance from -4.5% mean a greater volume of oil being drained from the reservoir, and
therefore, a greater steam chamber.
(a)
(b)
(c)
Fig. 8. Histograms of the absolute values of the differences in acoustic impedance between the less resistant and more
resistant to rock vertical spacing between wells: (a) 14 ft (b) 28 ft and (c) 42 ft
The absolute change in acoustic impedance between the more resistant and less compressive rock, and less resistant and more
compressive rock, is approximately 10 gm/cm3m / s, a low value (a frequency of approximately 40% of 23,142 cells for
three vertical well spacing). There are marginal values around 100 gm/cm3m / s, but with a lower frequency of 1% (possibly
because of high values in the oil and gas saturation). The Gassmann equation is highly sensitive to the incompressibility of
the dry rock (dry bulk) (Artola and Alvarado, 2005).

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Conclusions
•The temperature has a similar behavior to the variation of acoustic impedance behavior, because the hottest region
corresponds to the region which has undergone the greatest displacement of oil, and therefore, the greatest variation of oil
saturation.
•The percentage variation of acoustic impedance was approximately 4.5% .The main reason for this low variation is because
of the high incompressibility of the rock.
•Variations of seismic reservoir properties were not significant; therefore, no substantial differences between the base and
monitor in the synthetic seismograms were found.
Acknowledgements
We appreciate PDVSA for allowing these results to be published, PUC-Rio and GTEP for the opportunity to study a PhD in
petroleum geomechanics, ANP and CAPES for financial support and UFBA for allowing Dr. Artola to dedicate to this study.
Nomenclatures
A
Parameter
CASE 1 More resistant and less compressive rock with yield model and permeability variation
CASE 2 Less resistant and more compressive rock with yield model and permeability variation
CASE 1A More resistant and less compressive with yield model
CASE 2B Less resistant and more compressive with yield model
CASE 1C More resistant and less compressive without yield model
CASE 2D Less resistant and more compressive without yield model
CASE 3 More resistant and less compressive with yield model with stress rotation
HCPV Hydrocarbon Pore Volume
C-M Mohr-Coulomb
HYP
Hyperbolic Model
bc
CTotal Compressibility
r
CRock Matrix Compressibility
b

Volumetric Strain

Delta
FRP
Mean Reservoir Pressure
nn AA ,
1Steps nand n+1


,Porosity
P
Pressure
g
SGas Saturation
o
SOil Saturation
w
SWater Saturation
STBD Stock Tank Barrel per Day
p
VCompressional Wave Velocity
s
VShear Wave Velocity
T
Temperature
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8 SPE SPE-171096-MS
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