modelling of 4d seismic data for the monitoring of steam ... · june 2010, volume 49, no. 6 21...

June 2010, Volume 49, No. 6 21

Modelling of 4D Seismic Data for the Monitoring of Steam Chamber Growth During the SAGD Process

O. Lerat, F. Adjemian, A. Baroni, G. Etienne, G. Renard, IFPE. Bathellier, E. Forgues, F. Aubin, CGGVeritas

T. Euzen, IFP Technologies (Canada) Inc.

IntroductionThe performance of heavy oil production by SAGD is affected

by reservoir heterogeneities. However, because many factors in-teract during thermal production, such as changes in oil viscosity, fluid saturations, pore pressure and stresses, the interpretation of 4D seismic data, in terms of steam chamber geometry, is not direct.

Pressure and temperature variations during SAGD operations in-duce stress changes in the reservoir and in the surrounding media.

AbstractThis paper presents an integrated workflow for the interpreta-

tion of 4D seismic data to monitor steam chamber growth during the steam-assisted gravity drainage recovery process (SAGD). Superimposed on reservoir heterogeneities of geological origin, many factors interact during thermal production of heavy oil and bitumen reservoirs, which complicate the interpretation of 4D seismic data: changes in oil viscosity, fluid saturations, pore pressure, and so on.

The workflow is based on the generation of a geological model inspired by a real field case of the McMurray formation in the Athabasca region. The approach consists of three steps: the construction of an initial static model, the simulation of thermal production of heavy oil with two coupled fluid-flow and geome-chanical models and the production of synthetic seismic maps at different stages of steam injection.

The distribution of geological facies is simulated on a fine grid using a geostatistical approach, which honours all available well data. The reservoir’s geomechanical and elastic properties are characterized by logs and literature at an initial stage before the start of production. Production scenarios are run to obtain pore pressure, temperature, steam and oil saturations on a de-tailed reservoir grid around a well pair at several stages of pro-duction. Direct coupling with a geomechanical model produces volumetric strain and mean effective stress maps as additional properties. These physical parameters are used to compute new seismic velocities and density for each stage of production ac-cording to Hertz and Gassmann formulae. Reflectivity is then computed, and a new synthetic seismic image of the reservoir is generated for each stage of production.

The impacts of heterogeneities, production conditions and res-ervoir properties are evaluated for several simulation scenarios from the beginning of steam injection to 3 years of production. Results show that short-term seismic monitoring can help in an-ticipating early changes in steam injection strategy. In return, long-term periods allow the behaviour of the steam chamber to be monitored laterally and in the upper part of the reservoir. This study demonstrates the added value of 4D seismic data in the context of steam-assisted heavy oil production.

These modifications of the stress state may imply deformations that can, in turn, have an impact on reservoir production. These changes also have an influence on wave propagation into rocks and fluids and may consequently produce differences on seismic veloc-ities and on the travel time.

The objectives of this work are to evaluate the impact of reser-voir heterogeneities on steam chamber growth and to improve the interpretation of 4D seismic data in steam-assisted production. The study is based on a heavy oil field of the Canadian Athabasca Mc-Murray formation. Two periods of SAGD production are studied in detail: the early steam injection and later on when the steam chamber develops laterally and vertically toward the top of the reservoir.

Simulation WorkflowThe workflow consists of three steps: the construction of an in-

itial static model of the full reservoir, the simulation of the thermal production of heavy oil in a well pair with a fluid-flow model coupled explicitly with a geomechanical model and the modelling of seismic data at different stages of steam injection (Figure 1).

Step 1The construction of a 3D detailed geological model is done on a

fine grid using a geostatistical approach. This stochastic modelling is constrained by both horizontal and vertical wells. The geological model is defined at a fine scale in order to preserve the descrip-tion of heterogeneities near the well bores. The model is populated with lithofacies and initial petrophysical properties (porosity and permeability) before the extraction of a SAGD well pair. This fine scale geological model is also used to build a mechanical model for the reservoir section. Poro-elastic properties are assigned to the cells according to the facies and associated porosity. This as-signment is based on a consistent interpretation and integration of

InitialGeological

Model

InitialGeological

Model

InitialGeological

Model

faciesΦ

K(initial)

Sagd PilotFluid-Flow Simulation

KΦKΦ

PT

SatPT

Sat Sagd PilotFluid-Flow Simulation

KΦKΦ

PT

SatPT

Sat

Geo-mechanical

Model

mechanicalproperties,constitutive laws

σε

Geo-mechanical

Model


σε

Geo-mechanical

Model


σε

TWT Velocities

Impedances

Maps of Attribute

Differences

TWT Velocities

Impedances

Maps of Attribute

Differencest3t2t1t0

t3t3t2t2t1t1t0t0

Sat, P, TStresses

Petro-ElasticParams

t3t2t1t0

t3t3t2t2t1t1t0t0

t3t2t1t0

t3t3t2t2t1t1t0t0

Sat, P, TStresses

Petro-ElasticParams

SensitivityTests

on PEM

SensitivityTests

on PEM

SensitivityTests

on PEM

Step 1:Initial

static model

Step 2:SAGD well pair

dynamic simulations

Step 3:Generation of synthetic seismic

cubes & sensitivity study

FIGURE 1: General workflow applied to the synthetic McMurray reservoir model.

22 Journal of Canadian Petroleum Technology

available log data (acoustic logs, lithofacies description, porosity and mineral fractions, etc.) and core data.

Step 2This step consists of performing simulation for a selection of

time periods of steam injection on the SAGD well pair, while cou-pling a fluid-flow model with a geomechanical one. The modelling focuses on the first 6 months of production and on a later period comprised between 1 – 3 years, with a simplified elastic and me-chanical model.

A detailed SAGD model is extracted from the geological grid and imported in the fluid-flow reservoir model for the simulations. The grid is downscaled to better describe the evolution of the steam chamber in the direction perpendicular to the well pair axis (metric cell size in this direction). Evaluation of the geomechanical effects induced by reservoir production requires coupling both the mul-tiphase fluid-flow and the geomechanical simulations. These nu-merical simulations require the construction of a large model that includes the surrounding formations. There are several coupling strategies for both numerical simulators. In a previous work, direct coupling was chosen [Lerat et al.(1)]. It is proposed here to perform an explicit coupling scheme with an update of the reservoir perme-abilities at chosen steps of simulation.

Step 3This step is devoted to the modelling of 4D seismic surveys. Be-

cause there are three main sources of stress dependency of wave velocities (changes in porosity with stress, the existence of grain contacts and the presence of cracks), a stress-sensitive rock physics model is required. The Hertz-Mindlin’s contact theory is used as a first approach. This model is based on the evolution of the con-tact surface between two spherical particles and accounts for the impact of mean effective stresses on both P- and S-wave veloci-ties. As the impact of temperature on these velocities is not well established, a simple model issued from literature is used here. The effects of fluid saturations on effective bulk modulus, then on vel-ocities, are inferred from the Biot-Gassmann theory. These various approaches are used to update the petroelastic model. Then maps or cubes of seismic attributes (travel time, velocities, impedances, etc.) are generated at different stages of production before seismic bandpass filtering (1D convolution).

In this paper, the workflow is applied to a field located in Northern Alberta’s Athabasca oil sands. The reservoirs are made

of unconsolidated sands from the fluvio-estuarine McMurray for-mation (Mannville Group, Lower Cretaceous).

Reservoirs from this area exhibit a complex internal architec-ture associated with heterogeneities specific to fluvial and estu-arine environments. In the study area, the top of the McMurray is at a relatively shallow depth of 260 m on average. Its thickness is close to 50 m.

At a temperature of 10°C, the oil viscosity is approximately 2×106 cP and its density approximately 8ºAPI. Production data available for this study consist of steam injection and oil produc-tion rates [for further details, see Lerat et al.(1)].

Step 1: Construction of the Geological Model

Definition of LithofaciesFive lithofacies were interpreted from well-log data with a

simple cutoff approach on the gamma ray logs (Figure 2). The five classes of log responses were interpreted a posteriori by a study of their correspondence with core facies (Figure 3):

• Lithofacies 1: clean medium- to coarse-grained, massive to trough crossbedded sandstone facies, mostly present in braided stacked channel deposits.

• Lithofacies 2: medium-grained sandstone facies. This lith-ofacies is associated with fluvial and estuarine channel-fill sandstones.

• Lithofacies 3: fine-grained sandstone with fine shaly lam-inations. It occurs as fining-upward intervals at the top of channel fills, as well as overbank deposits. It is also associ-ated with sandy inclined heterolithic stratification (IHS) in the estuary setting or with sandy tidal flats in the upper part of the McMurray formation.

• Lithofacies 4: silty shales facies. This lithofacies is asso-ciated with the main heterolithic facies associations of the reservoir, represented by the tidally-influenced point bar fa-cies, the estuarine IHS, the mud flat and fine, shaly overbank deposits.

FIGURE 2: Correspondence between the core sedimentological description and lithofacies. From left to right: track 1 = Gamma Ray log; track 2 = sonic, neutron, density logs; track 3 = core sedimentological description; track 4 = lithofacies log (colour code: 1 = red; 2 = orange; 3 = yellow; 4 = light green; 5 = dark green). Lithostratigraphic units and main sedimentary environments are also displayed.

FIGURE 3: Core photographs, Unit 2. A: Lithofacies 1, massive, oil-saturated sandstone; B: Lithofacies 2, tabular crossbedded sandstone; C: mud clast breccia (undifferentiated from Lithofacies 3 and 4 on logs); D: Lithofacies 4, fine-grained, heterolithic ripple-bedded sandstone; E: Lithofacies 5, floodplain shales.


• Lithofacies 5: shaly facies related to channel abandonment mud plugs, floodplain or coastal plain shales, muddy IHS or distal bay deposits.

Lithostratigraphic UnitsThe lithostratigraphic units correspond to intervals character-

ized by their depositional environment and related reservoir archi-tecture. These units are built by well-to-well correlations of the main stratigraphic surfaces. Four lithostratigraphic units are iden-tified in the McMurray interval:

• Unit 1: discontinuous shale interval overlying the basal un-conformity and interpreted as a coastal plain environment. This unit is not a reservoir.

• Unit 2: coarse-grained sands deposited by high-energy braided channels. This is the main reservoir unit.

• Unit 3: medium- to fine-grained sandstones and sand/shale alternations interpreted as meandering channel facies asso-ciation. This unit has poorer reservoir quality than Unit 2.

• Unit 4: medium- to fine-grained heterolithic sandstones and mudstones from estuarine channels and tidal flats. The res-ervoir quality of this unit is poor. However, sandy channels may be connected, acting as drains for fluids.

Geostatistical ModellingThe geological grid built for the reservoir zone contains ap-

proximately 5.106 cells, with a 10 m×10 m×0.5 m definition. The four lithostratigraphic units are modelled independently with a stochastic approach (Figure 4), based on the truncated Gaussian method [Galli et al.(2) and Doligez et al.(3)].

The main geostatistical parameters used in the truncated Gaussian method are vertical proportion curves, the matrix of pro-portions and variograms, which are all commonly computed from wells and additional data if available. In the present study, 50 vertical wells and 16 well pairs were used to build the stochastic model.

Interpretative geological maps or information derived from seismic maps or cubes could have been used in this modelling ap-proach [Doligez et al. (3,4)]. Currently, 3D and 4D seismic data are of the highest importance for reservoir characterization and for fluid-flow history matching, and should be integrated from the start of the reservoir characterization workflow [Lerat et al.(5) and Roggero et al.(6)].

However, in the present case, because seismic information was not available, geostatistical parameters were computed from well data only.

Step 2: Reservoir and Geomechanical Modelling

MethodologyReservoir and mechanical simulations are explicitly coupled

with an update of the permeability field in the reservoir area. Seven coupling periods were defined during the first 3 years of oil pro-duction, respectively, after 2 and 4 months of the warm-up phase;

then after 1, 2, 6, 18 and 36 months of production. Reservoir simu-lation is performed until one of the coupling steps is reached; at this timestep, temperature and pressure fields are extracted and in-terpolated toward the finite element grid in order to perform mech-anical calculations.

Mechanical results (i.e., stresses and strains) are used to com-pute the new permeability field for the following period. Per-meability evolution depends on volumetric strains as stated by Touhidi-Baghini(7). These data are also mandatory for 4D seismic processing (see Step 3 in this paper).

Reservoir and geomechanical computations are made on a local SAGD grid representing one well pair (Figure 5). The reservoir model thickness is approximately 50 m on average, with a 20 m – 25 m net pay. The producer well is placed just above the Devonian limestone and the injector well lies 5 m above the producer. The well pair length in the reservoir is 820 m.

Cell size varies in the radial direction (X) from 1 m – 2.5 m (Figure 6). The axial direction (Y) is represented by 41 cells, which are 20 m long. In the vertical direction (Z), there are 71 layers in the reservoir interval and 11 layers in the overburden interval. The numerical simulation of the selected well pair is constrained by the production history of both wells: steam injection rate in the injec-tion well and the total liquid rate (oil+water) in the producer.

Mechanical properties corresponding to each lithofacies have been set according to constitutive laws deduced from a review of literature on similar rocks in equivalent conditions. As a conse-quence, Chalaturnyk’s(8) results were mainly used in this study. Dif-ferent settings of thermal expansion coefficient (α) were chosen: in sandstones, α is constant and positive, whereas it evolves with temperature in shales. This implies a radically different response to thermal and pressure loading, which has already been investi-gated, but this paper focuses on monitoring applications. Consti-tutive models were set as follows: overburden materials (6, 7 and 8) behave as perfectly elastic materials, whereas they are elasto-plastic in the reservoir (materials 1 to 5, with strain hardening for materials 4 and 5). Note that in the reservoir, materials correspond to lithofacies with mechanical properties.

The next sections present first the global results from the res-ervoir modelling, followed by an illustration of the mechanical responses to thermal and pressure changes in the reservoir. Both results are used in Step 3 in order to analyze amplitude maps for 4D monitoring.

ReservoirThe results of the reservoir computations are presented in

Figure 7 and 8. �ithout any modification to the set of param- and 8. �ithout any modification to the set of param-eters, calculations were performed over the full history of the field

W E

Unit 1 - Basal shales Unit 2 - Braided fluvial

Unit 3 - Meandering fluvialUnit 4 - Tidal/Estuarine

~ 50 m

200 m

Lithofacies 1Lithofacies 1 Lithofacies 3Lithofacies 3Lithofacies 2Lithofacies 2 Lithofacies 4Lithofacies 4 Lithofacies 5Lithofacies 5

FIGURE 4: Lithofacies geostatistical model and lithostratigraphic units (full-field model).

FIGURE 5: Vertical cross section across the reservoir showing the well pair placement. Well toe to the right of the figure. Vertical exaggeration: ×3.

FIGURE 6: Local SAGD reservoir model. Left: layering; right: detail showing the grid definition.


(i.e., 6 years). Figure 7 exhibits simulation results, which concur well with field data.

The evolution of steam injection rates along the various grid cells of the injection and production wells are shown for various times in Figure 8. The profiles of the two wells are shown below the curves and in Figure � to better visualize the low-quality reser-Figure � to better visualize the low-quality reser- to better visualize the low-quality reser-voir areas. These illustrations clearly show the sections along the well where there is good or low steam injection. The evolution in time indicates a balance between the various zones where steam is injected and, at the same time, the start of steam injection in sec-tions where initially low to poor injection was possible.

GeomechanicsFigure 10 presents the extension of the steam chamber after 6

and 36 months of production. The 3D envelope corresponds to a minimum value of 100°C, which means that every cell inside this domain has a temperature ranging from 100°C – 280°C. This figure clearly shows a high degree of heterogeneity of temperature

distribution along the well pair, especially for short durations. In-deed, at 6 months, the steam chamber development seems to be confined vertically from sections one to 11. These sections co-incide with the presence of heterogeneities at the heel of the well (see Figure �). From sections 11 to 41, the vertical development of steam is no longer limited, except in section 26 where a shale bed is located right between the wells and therefore limits oil produc-tion as well as steam injection. The limitation in the steam chamber development disappears with longer production times (Figure 10, right) because steam can propagate in several directions and there-fore bypass impermeable shale beds of limited extent.

Geomechanical computation results can also be presented in terms of stress evolution. These results are visualized for section 23 in Figure 11 (see also Figure 12 for location of points). The stress path is different from point to point, especially when the considered location is away from the steam chamber (point C). It can therefore be inferred that it will impact 4D seismic monitoring because of the changes in seismic velocities over time.

Step 3: Modelling of Synthetic 4D Seismic Surveys

Initial Synthetic Seismic Survey

The aim is to estimate seismic parameters (density, compres-sion velocity and shear velocity) of the saturated rocks, from ini-tial mechanical and reservoir parameters in coherence with the well-log data.

Reservoir simulation with Puma Flow

OIL

WATER- Simulation- Field data

Reservoir simulation with Puma Flow

0

100000

200000

300000

400000

500000

600000

0 500 1000 1500 2000 2500

Time From Start of Steam Injection, days

Cum

ulat

ive

Oil

Pro

duc

tio

n, m

3

OIL

WATER

- Field data

- Simulation

FIGURE 7: Cumulated oil and water production for the well pair.

0

1

2

3

4

5

6

7

8

9

10

11

12

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Section Number

Per

cent

Ste

am R

ate

Inje

cted

in t

he W

ell

Date 5/7/00 (time 5 days)Date 10/7/00 (time 10 days)Date 20/7/00 (time 20 days)Date 30/7/00 (time 30 days)Date 30/8/00 (time 61 days)Date 1/10/00 (time 92 days)Date 1/11/00 (time 122 days)Date 1/12/00 (time 153 days)Date 1/1/01 (time 183 days)

FIGURE 8: Profile of steam rate vs. time in the injection well, expressed in percent of the total well rate. Red cells are non-reservoir.

FIGURE 9: Distribution of heterogeneities in the reservoir (top) and on selected sections (bottom).

FIGURE 10: Steam chamber extent after 6 months (left) and 36 months (right) of production.


Concerning the well data, the interpreted logs used are density, total porosity, saturation, P-sonic, materials and gas indicator. No S-sonic log was available for this study.

The basic idea is that the seismic properties of the oil saturated rocks are related to the seismic properties of heavy oils, which de-pend on density, composition, temperature and gas/oil ratio. At the initial stage, before the warm-up phase, only water and oil components are present in our fluid model, with heavy oil being considered almost a solid because of its high viscosity. Another challenge is that the determination of seismic parameters requires dynamic mechanical parameters (Young’s modulus, Poisson’s ratio), whereas mechanical parameters used in mechanical mod-elling are static.

Static to Dynamic Elastic Properties

A three-step approach is then carried out. First, in the static do-main, the bulk and shear moduli are derived from Young’s mod-ulus and Poisson’s ratio. Next, the two moduli of the dry rock are converted from the static domain to the dynamic domain, with the help of well-log data. Finally, the saturated rock elastic and seismic parameters are computed using a rock physics model in the dy-namic domain.

First step: The static domain refers to displacements at low fre-quencies. Quasi-static mechanical processes usually lead to softer mechanical parameters than in seismic processes. The Poisson’s ratio is assumed to remain constant between static and dynamic domains. This is reasonable because this coefficient quantifies the ratio of vertical and horizontal relative deformations induced by a stress. Because the bulk modulus on shear modulus ratio depends only on Poisson’s ratio:

KG

= +−

2 13 1 2

( )( )

νν

........................................................................................ (1)

where K is the bulk modulus, G the shear modulus and ν the Pois-son’s ratio, this modulus ratio remains invariable from the static to dynamic domains. The dynamic dry bulk modulus was chosen equal to the dry static bulk modulus, multiplied by a constant A to be determined for each material:

K AKdrydynamic

drystatic=

................................................................................. (2)

Second step: Gassmann’s equation [Gassmann(�)] was applied in the case of a full water saturation. After computation of the sat-urated bulk modulus and density, P-velocity could be estimated as a function of A for each material. The bulk modulus on shear mod-ulus ratio [Equation (1)] is helpful to estimate the dynamic shear modulus, which is the same for dry and saturated rock, from the dynamic bulk modulus.

The density vs. porosity crossplots of the water-saturated log data allowed density to be checked (Figure 13 and 14), whereas the velocity vs. porosity crossplot enabled the A constants to be cali-brated. These constants were found to be greater than one, as ex-pected, in the range of 2.5 – 5.

Third step: In order to compute the density and the P- and S-velocities of the oil-water saturated material, the heavy oil elastic properties have to be determined. The heavy oil is viscous (8° – 10°API) initially at reservoir temperature (10°C) and pressure (2 MPa). Consequently, the oil shear modulus cannot be neglected. The oil density was set to 1008 kg/m3 and the oil bulk modulus to 2.7 GPa, according to Batzle and �ang(10). The shear modulus was drawn on the results of a 7°API oil [Batzle et al.(11)] and a value of 0.5 GPa was chosen. The generalized Gassmann’s equations [Ciz and Shapiro(12)] were handled under the simplifications of a homo-geneous grain rock, and a uniform macroscopic fluid distribution. They consist of two similar equations to compute the saturated bulk modulus and the saturated shear modulus:

M MM M

Msaturated dry

dry rock

flui

− −− −

= −−( )1 1

1 12

φ dd rock dry rockM M Mfor M K G

− − − −−( )+ −( )=

1 1 1 1 ,

..... (3)

where K is the bulk modulus, G the shear modulus and φ the po-rosity. The P- and S-velocities were then derived from the saturated bulk and shear modulus, and the saturated density. The computed density and P-velocity were checked on crossplots (materials in in-tervals free of gas) for 0.15 and 0.6 water saturations. In contrast, the P-velocity values initially obtained by standard Gassmann’s

0.0E+00 1.0E+06 2.0E+06 3.0E+06 4.0E+06 5.0E+06 6.0E+06 7.0E+06 8.0E+06 9.0E+06

0.0E+00 2.0E+06 4.0E+06 6.0E+06 8.0E+06 1.0E+07 1.2E+07 1.4E+07

q- p' (Pa)

C

A B

Mean Effective Stress, Pa

Dev

iato

ric

Str

ess,

Pa

FIGURE 11: Stress paths in section 23 in the deviatoric-mean effective stresses plane.

FIGURE 12: Section 23 of the steam chamber after 6 months of production. The displayed property is temperature.

Den

sity

, g/c

m3 3000

2800

2600

2400

2200

2000

1800

1600

5000

4000

3000

2000

1000

Velo

city

, m/s

0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6

PHINS PHINS

FIGURE 13: Water-saturated data crossplots for materials 1 to 3 (sandstones). Density vs. porosity (left), velocity vs. porosity (right). x indicates calculated parameters for Materials 3.

Den

sity

, g/c

m3 3000

2800

2600

2400

2200

2000

1800

1600

5000

4000

3000

2000

1000

Velo

city

, m/s

0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6

PHIDSS PHIDSS

FIGURE 14: Water-saturated data crossplots for material 5 (shale). Density vs. porosity (left), velocity vs. porosity (right). x indicates calculated parameters for Materials 5.


equations did not fit these velocity vs. porosity crossplots (approxi-mately 1�0 m/s and 170 m/s lower).

Initial Full Seismic Model

Each material was assigned the elastic properties corresponding to the initial water saturation set to 0.15 in the reservoir sands ma-terials, and set to 1 in all other materials. The 3D full model was then populated with density, P- and S-velocities. In the overburden, the P- to S-velocities ratio is in a 2.5 – 3.1 range, whereas in the reservoir it falls between 2.0 and 3.0.

The blocks of the three elastic parameters, namely P-velocity, S-velocity and density, were converted from the depth to time do-main with the velocity law derived from the P-velocity model. The reflectivity coefficients were first derived from the P-impedances (expressed as density multiplied by P-velocity) in the time domain. Next, the reflectivity coefficients were convolved with a wavelet in order to compute the synthetic seismic data. Convolution was performed by a Ricker wavelet (80 Hz peak frequency) and Figure 15 shows the seismic section for one line extracted from the 3D model. The 3D seismic results of the full-field model are presented in Figure 16.

Synthetic 4D Seismic SurveysThe evolution of physical parameters during steam injection was

computed thanks to the coupling of the reservoir and geomechan-ical models. These changes were used to dynamically update the seismic velocities, both in the overburden and in the reservoir:

• Temperature, saturation and pore pressure evolution, com-puted by the fluid-flow simulation, were taken into account in the reservoir only.

• Stress and strain evolution, computed by the geomechanical simulation, was taken into account in both the reservoir and the overburden regions.

The evolution of these physical parameters drives the modifi-cation of mechanical parameters (dry modulus, fluid modulus and density) that pilot saturated modulus. The evolution of both satu-rated modulus [see Equation (3)] and density pilots wave velocities

and reflectivity changes. In the present workflow, seismic veloci-ties are computed using the initial data and the following described process.

Updating Dry Bulk and Shear Moduli

The stress dependency of the dry bulk modulus is taken into ac-count through the Hertz relation [Mindlin(13)] expressed as:

K Kdry dry

Hertz

( )σ σσ

=

0

0....................................................................... (4)

where K is the dynamic dry bulk modulus, σ the mean effective stress with the superscript 0 indicating initial parameters and the Hertz coefficient being in the 0.05 – 0.5 range. The dry shear mod-ulus is also stress-dependent, with a Hertz coefficient being in the 0.03 – 0.5 range [relation similar to Equation (4)].

Updating Fluid Moduli

Fluid moduli are computed through a harmonic mean of each component (oil, water and vapour) with respect to their relative saturations.

Bulk moduli for water and vapour are taken dependent on pres-sure and temperature, whereas oil bulk modulus is assumed to be constant. However, an oil shear modulus dependent on tem-perature is considered to account for the evolution of oil viscosity during SAGD.

The temperature-dependency of the oil shear modulus can be approximated by:

G TG

G

T

oiloil

oil

( )

( )

=

+×

1ω η

......................................................................... (5)

where Goil is the oil shear modulus at infinite viscosity, ω the seismic pulsation, η the oil viscosity and T the temperature [Ciz and Shapiro(12)].

At the initial temperature of 10°C, the oil viscosity is approxi-mately 2×106 cP. This viscosity falls to approximately 15,400 cP when the temperature rises to 40°C, and to approximately 10 cP when the temperature reaches 200°C. The fluid shear modulus is equal to the oil shear modulus if pores contain viscous oil and to zero in the other cases.

Updating Density

Dry rock density is taken as constant, whereas fluid densities were computed with dependency on pressure, temperature and sat-uration. The evolution of porosity is taken into account for the sat-urated rock density computation, which involves both dry rock and fluid densities.

Updating Velocities

According to Equation (3), the new saturated bulk and shear modulus are computed in terms of new saturation, new tempera-ture, new porosity and new stress. P- and S-wave velocities can thus be calculated, as well as acoustic impedance that can be derived along the vertical axis to obtain the reflectivity. In these relations the dependence of the reflectivity and of the impedance relative to location is implicit. The reflectivities are then computed in the time domain, and convolved with a chosen wavelet (Ricker wavelet with a central frequency of 80 Hz).

Lessons Learned for Short- and Long-Term Monitoring

The petroelastic model (PEM) previously presented allows the physical dependence of mechanical parameters to be described

FIGURE 16: 3D view of the full-field model. Left: Materials. Right: Reflectivity coefficients convolved by a 80 Hz central frequency Ricker wavelet.

FIGURE 15: 1D seismic modelling (reservoir zone). Top: Materials. Bottom: reflectivity coefficients convolved by a 80 Hz central frequency Ricker wavelet.


during SAGD production. The model populated with velocities is used to generate 1D seismograms (Figure 17).

Short-Term Monitoring (0 – 6 Months)The evolution of the PEM over production time is highlighted

by differences of P-wave depth seismograms, which are computed for four timesteps for a horizontal slice chosen in the vicinity of the injection well (Figure 18). Each slice represents the cumulative difference of P-wave between a given production date (t1=after 2 months of warm-up; t2=first month of production; t3=second month of production; t4=after 6 months of production) and the initial state of the model before the start of production operations (t0). These differences are noted respectively Δt1, Δt2, Δt3 and Δt4. A high con-trast is observed along the well path since the start of steam injec-tion. Other areas showing major changes are located at the heel and the toe of the injection well, which are highly heterogeneous. In these areas, the shale beds prevent the steam chamber from de-veloping harmoniously, inducing local changes in pressure, tem-perature, steam saturation and stresses.

Figure 1� and 20 represent two selected transverse sections, 11 and 23, at an initial stage before production and after 6 months of production, respectively. The model is defined in the time domain. In the upper display the injection well crosses a shale bed on sec-tion 11. As a result, after 6 months, there are limited changes in the initial seismogram and fluid saturations. On the contrary, sec-tions with good reservoir facies (e.g., section 23) allow the steam chamber to develop, which can be identified on the corresponding seismogram.

Long-Term MonitoringThe steam chamber growth is also affected by heterogeneities at

longer periods of steam injection. Figure 21 displays sections 11

and 23 extracted from the model after 3 years of steam injection. On the P-wave seismograms, the perturbation resulting from pro-duction extends to the top of the reservoir on section 23. On sec-tion 11 the changes are also visible on the seismograms, but they are not as well expressed.

These observations concur with the distribution of oil satura-tion, which shows a symmetrical development on section 23. The blue range corresponds to 0.5 – 0.65 oil saturation. This range has a V-shaped geometry corresponding to the development of the up-ward steam chamber. In this area of the reservoir, oil is mobilized and percolates by gravity toward the producing well. In the orange range, steam saturation is approximately 0.7 and residual oil sat-uration is approximately 0.1. The contrast in fluid content between the blue and orange clearly affects the synthetic seismic response.

The top of the steam chamber is blocked by reservoir heterogen-eity (green lithofacies). However, it can be seen that in this model the oil saturation decreases along a vertical “chimney” above the steam chamber, caused by steam and heat transfers in 3D.

These observations can be compared to those of section 11. The impact of near-well heterogeneities discussed in Figure 20 is no longer visible because the steam propagated across the small-scale shale bed after some time. However, compared to section 23, the V-shaped steam chamber development of section 11 is stopped by a thicker and continuous shale bed. This heterogeneity locally af-fects the efficiency of the recovery process.

ConclusionsThis study is based on a fully integrated approach involving

geology, geophysics, reservoir and geomechanics. The method-ology implies the construction of a fine scale initial static model, including reservoir and overburden areas, designed before the start of thermal operations. A SAGD well pair was extracted and mod-elled with a coupled reservoir/mechanical approach at different pe-riods of production. For a selection of production stages, elastic parameters were assigned to the model using the petroelastic model (PEM). The impact of physical parameters was evaluated by comparing maps and cubes of seismic attributes produced at different times.

The workflow is applied to a field case in Athabasca, Alberta. The study focuses on the early production period (6 months) and

FIGURE 17: Synthetic P-wave seismograms in time. Top: t0= initial stage before steam injection. Bottom: t4= after 6 months of production.

FIGURE 18: Maps showing difference in P-wave seismograms, computed on a horizontal slice, in depth. See text for details.


longer periods (3 years) to monitor development of the steam chamber.

In terms of reservoir simulation, the equilibrium in the devel-opment of the steam chamber is an important result shown by the various fluid distribution profiles along the wells. It is necessarily gravity that controls the process and imposes a regular distribution of the steam along the well pair. This means that heterogeneities have a huge impact on the distribution of fluid injected and pro-duced along the well pair. However, gravity stabilizes the fluid dis-tribution as time goes on.

The most interesting knowledge for an SAGD operator, that could hopefully be inferred from a permanent seismic monitoring interpretation during the early injection stages, is how the steam would be distributed along the injection well in the first few weeks or months of steam injection. This knowledge, if effective, would help to monitor the injection in order to optimize steam chamber

development all along the well and not only in some limited sections.

During longer periods of production, the reservoir-scale het-erogeneities can impact the production by limiting upward steam chamber growth. However, paths and drains in the upper part of the reservoir may allow the steam to propagate in low pay areas or in thief zones.

The synthetic seismic data illustrates the changes that occur during the modelling of the SAGD production process. High con-trasts in seismic attributes are observed from the beginning of pro-duction operations.

The relative impact of pressure, temperature, saturations, etc., on the synthetic seismic data can be discussed in the heterogeneous regions of the reservoir. �hen the injection well is located below a shale layer, the temperature field cannot develop above the hetero-geneity except by conduction. Above the shale layer, oil is heated

FIGURE 19: Synthetic SAGD model in time at the initial stage: sections 11 and 23. Top: lithofacies distribution; Middle: P-wave seismogram; Bottom: oil saturation.

FIGURE 20: Synthetic SAGD model in time after 6 months of production: sections 11 and 23. Top: lithofacies distribution; Middle: P-wave seismogram; Bottom: oil saturation.


by conduction, but is not produced as the heterogeneity blocks the flow. This generates a local overpressure; hence a local decrease in the mean effective stress, which impacts the petroelastic model. The contrast on the synthetic seismogram is emphasized by the presence of gaseous water in these heterogeneous regions.

Changes in physical conditions can be monitored even during these early periods with a permanent seismic monitoring survey. However, because the effects of pressure, temperature, viscosity, saturations, etc., are coupled, the seismic signature needs to be in-vestigated quantitatively.

This SAGD model could be improved by calibrating and opti-mizing the reservoir model to the real field seismic data at the ini-tial stage before steam injection, using the base seismic survey, and during production using the 4D seismic data. Another enhance-ment could be to integrate the observation well data (temperature) in the reservoir history match process. This second point would

enable the control of evolution of the steam chamber geometry during production. However, neither the seismic nor the observa-tion well data were available for this study.

Further work on this model will consist of a quantitative inter-pretation of the synthetic monitor surveys together with an uncer-tainty study on the PEM parameters following the experimental design approach.

SI Metric Conversion Factors

˚API 141.5/(131.5 + ˚API) = g/cm3

cP×10-3 = Pa·s

ReFeReNCeS 1. Lerat, O., Adjemian, F., Auvinet, A., Baroni, A., Bemer, E., Eschard,

R., Etienne, G. et al. 200�. 4D Seismic Modelling Applied to SAGD Process Monitoring. Presented at the 15th European Symposium on Improved Oil Recovery, Paris, 27–2� April.

2. Galli, A., Beucher H., Le Loc’h G., Doligez B., and Heresim group. 1��3. The Pros and Cons of the Truncated Gaussian Method. In Geo-statistical Simulations, ed. M. Armstrong and P.A. Dowd, 217-233. Dordrecht, The Netherlands: Quantitative Geology and Geostatistics, Kluwer Academic Publishers.

3. Doligez, B., Beucher, H., Geffroy, F., and Eschard, R. 1��. Inte-grated reservoir characterization: improvement in heterogeneous stochastic modeling by integration of additional external constraints. In Reservoir Characterization: Recent Advances, ed. R.A. Schatz-inger and J.F. Jordan, No. 71, 333–342. Tulsa, Oklahoma: AAPG Memoir, AAPG.

4. Doligez, B., Gomel, P., Andrieux, B., Fournier, F., and Beucher, H. 2003. Use of Seismic to Constrain Geostatistical Reservoir Models: A Quantitative Approach Using Proportion of Facies. Paper 78165 presented at the AAPG Annual Convention, Salt Lake City, Utah, USA, 11–14 May.

5. Lerat, O., Nivlet, P., Doligez, B., Lucet, N., Roggero, F., Berthet, P., Lefeuvre, F., and Vittori, J. 2007. Construction of a Stochastic Geological Model Constrained by High-Resolution 3D Seismic Data—Application to the Girassol Field, Offshore Angola. Paper SPE 110422 presented at the SPE Annual Technical Conference and Exhibition, Anaheim, California, USA, 11–14 November. doi: 10.2118/110422-MS.

6. Roggero, F., Ding, D.Y., Berthet, P., Lerat, O., Cap, J., and Sch-reiber, P.E. 2007. Matching of Production History and 4D Seismic Data—Application to the Girassol Field, Offshore Angola. Paper SPE 10��2� presented at the SPE Annual Technical Conference and Exhibition, Anaheim, California, USA, 11–14 November. doi: 10.2118/10��2�-MS.

7. Touhidi-Baghini, A. 1��8. Absolute Permeability of McMurray Formation Oil Sands at Low Confining Stresses. PhD dissertation, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Alberta.

8. Chalaturnyk, R.J. 1��6. Geomechanics of SAGD in Heavy Oil Res-ervoirs. PhD dissertation, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Alberta.

�. Gassmann, F. 1�51. Elastic waves through a packing of spheres. Geo-physics 16 (4): 673–685. doi:10.11�0/1.1437718.

10. Batzle, M. and �ang, Z. 1��2. Seismic properties of pore fluids. Geophysics 57 (11): 13�6–1408. doi:10.11�0/1.1443207.

11. Batzle, M., Hofmann, R., and Han, D-H. 2006. Heavy oils—seismic properties. The Leading Edge 25 (6): 750–756. doi:10.11�0/1.2210074.

12. Ciz, R. and Shapiro, S.A. 2007. Generalization of Gassmann equa-tions for porous media saturated with a solid material. Geophysics 72 (6): A75–A7�. doi:10.11�0/1.2772400.

13. Mindlin, R.D. 1�4�. Compliance of Elastic Bodies in Contact. J. Appl. Mech. 16 (1�4�): 25�–268.

This paper (200�-0�5) was accepted for presentation at the 10th Canadian International Petroleum Conference (the 60th Annual Technical Meeting of the Petroleum Society), Calgary, 16-18 June, 200�, and revised for pub-lication. Original manuscript received for review 30 March 200�. Revised paper received for review 31 March 2010. Paper peer approved 5 April 2010 as SPE Paper 138401.

FIGURE 21: Synthetic SAGD model in time after 3 years of production: sections 11 and 23. Top: lithofacies distribution; Middle: P-wave seismogram; Bottom: oil saturation.

modelling of 4d seismic data for the monitoring of steam ... · june 2010, volume 49, no. 6 21...

Documents