Modelling of 4D Seismic Data for the Monitoring of the...

IEA Collaborative Project on Enhanced Oil Recovery 31rst Annual Workshop and Symposium

18-20 October 2010, Aberdeen, Scotland

Contact : O. Lerat - Tel: (33) 1 47 52 74 21- e-mail: [email protected]

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

O. Lerat1, F. Adjemian1, A. Auvinet1, A. Baroni1, E. Bemer1, R. Eschard1,

G. Etienne1, G. Renard1, G. Servant1, E. Bathellier2, L. Michel2, S. Rodriguez2, F. Aubin2, T. Euzen3

1 IFP Energies nouvelles

2 CGGVeritas 3 IFP Technologies (Canada) Inc.

Summary The performance of heavy-oil production by Steam-Assisted Gravity Drainage process (SAGD) can be affected by near-well reservoir heterogeneities. However, as many factors interact during thermal production such as changes in oil viscosity, fluid saturations, pore pressure, stresses..., the interpretation of 4D seismic data in terms of steam chamber geometry is neither direct nor unique.

This work focuses on the interpretation of 4D seismic data for the monitoring of the steam

chamber growth during the early months of steam injection. The study is based on a synthetic model inspired from a real field case in Athabasca (Canada). It follows a three-step approach: - 1/ Construction of a detailed initial full-field static model. The distribution of geological facies is simulated on a very fine grid by a geostatistical approach which honours all available well data. The reservoir, geomechanical and elastic properties are characterized from logs and literature at an initial stage before the start of production. - 2/ Simulation of the thermal production of heavy oil using real injection and production data. Pore pressure, temperature and saturation maps are computed by reservoir simulation in a restricted domain around a well pair. Direct coupling of both reservoir and geomechanical models allows obtaining volumetric strain and mean effective stress maps. - 3/ Generation of synthetic seismic maps at different steps of steam injection. The properties obtained from simulations allow computing new seismic velocities for each step of production according to Hertz and Gassmann formulas.

A new seismic image of the reservoir is then produced for each step. The impacts of heterogeneities, production conditions and reservoir properties are evaluated for several simulation scenarios from the beginning of steam injection to the first 6 months of production. It shows that seismic monitoring of this period can help in anticipating early changes in steam injection strategy in case of unexpected development of the steam chamber.

1. Introduction The performance of heavy-oil production by Steam-Assisted Gravity Drainage process (SAGD) can be affected by near-well reservoir heterogeneities. However, as many factors interact during thermal production such as changes in oil viscosity, fluid saturations, pore pressure, stresses, the interpretation of 4D seismic data in terms of steam chamber geometry is neither direct nor unique. Pressure and temperature variations during SAGD operations induce stress changes in the reservoir and in the surrounding media. These modifications of the stress state may imply deformations which can in turn have an impact on reservoir production. These changes also have an influence on the wave propagation into rocks and fluids and may consequently produce differences on seismic velocities and on the travel time.

This paper focuses on the simulation of SAGD production during the early months of steam injection. The objectives are to evaluate the impact of near-well reservoir heterogeneities on the steam chamber growth, and more generally to better understand the 4D seismic images acquired during thermal recovery processes.

2 O. Lerat, F. Adjemian, A. Auvinet, A. Baroni, E. Bemer, R. Eschard, G. Etienne, G. Renard , G. Servant, E. Bathellier, L. Michel, S. Rodriguez, F. Aubin, T. Euzen

IEA Collaborative Project on EOR - 31rst Annual Workshop and Symposium - 18-20 October 2010, Aberdeen, Scotland

The approach exposed here includes the generation of a synthetic model inspired from a real field case of the McMurray Fm in the Athabasca region (Canada). The workflow consists of three steps: 1/ the construction of an initial static model, 2/ the simulation of the thermal production of heavy oil with two coupled fluid-flow and geomechanical models, 3/ the production of synthetic seismic data at different steps of steam injection (1).

Fig 1: Description of the general workflow for SAGD modelling and sensitivity tests on the petroelastic model (PEM).

Step 1: the construction of a 3D detailed synthetic geological model is done on a very fine grid by a geostatistical approach. This stochastic modelling is constrained by both horizontal and vertical wells. The geological model is defined at a very fine scale (about 10m x 10m x 0.30m) in order to preserve the description of heterogeneities near the well bores. Then, it is populated with lithofacies and initial petrophysical properties (porosity and permeability) before the extraction of a SAGD well pair. Indeed, this fine-scale geological model is used to build a mechanical model for the reservoir section. Poro-elastic properties are assigned to the cells conditional to their facies and associated porosity. This assignment is based on a consistent interpretation and integration of available log data (acoustic logs, lithofacies description, porosity and mineral fractions, ...) and core data.

Step 2 consists in performing simulation for each time step of the steam injection on a SAGD well pair with a coupled fluid-flow – geomechanical model. The modelling focuses on the first six months of production, with simplified elastic and mechanical parameters and for several steam injection scenarios.

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). The evaluation of the geomechanical effects induced by reservoir production requires to couple both the multiphase fluid-flow and the geomechanical simulations. These numerical simulations need the construction of a large model which includes the surrounding formations. There are several coupling strategies of both numerical simulators. In this approach, it is proposed to limit the coupling to a one-way coupled scheme which is less cpu-time consuming than an iterative scheme.

Step 3 is devoted to a qualitative sensitivity analysis. Because 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 contact surface between two spherical particles and accounts for the impact of mean effective stresses on both P- and S-wave velocities. As the impact of temperature on these velocities is not well established, a simple model issued from literature will be used here. The effects of fluid

Modelling of 4D Seismic Data for the Monitoring of the Steam Chamber Growth during the SAGD Process 3


saturations on effective bulk modulus, then on velocities, are inferred from Biot-Gassmann theory. These various approaches are used to update the petroelastic model. Then maps or cubes of seismic attributes (TWT, velocities, impedances,...) are generated at different steps of production before seismic bandpass filtering (1D convolution).

2. Application to a heavy oil reservoir in Athabasca 2.1 Construction of the initial static model The case study is located in Northern Alberta (Canada) near Fort McMurray in the Athabasca oil sands province. The reservoirs are made of unconsolidated sands from the fluvio-estuarine McMurray Fm (Mannville Group, Lower Cretaceous). Reservoirs from this formation in the area exhibit a complex internal architecture which is associated with heterogeneities specific to fluvial and estuarine environments, e.g. point bar deposits and large-scale oblique stratification (IHS, inclined heterolithic stratification).

Most of the well data used to build the geological model is available in Canadian databases. The top of the McMurray is at a relatively shallow depth of 260m (TVD) in average. Its thickness is close to 50m in the area.

At a temperature of 10°C, the oil viscosity is about 2.106 cp and its density about 8 API. Production data were also obtained from the Canadian database. They consist in steam injection and oil production rates.

Reservoir zone Lithofacies interpretation

Five lithofacies (Fig. 2) were interpreted from well log data with a simple cut-off approach on the gamma-ray logs. The five classes of log responses were interpreted a posteriori by a study of their correspondence with core facies.

- Lithofacies 1: clean medium to coarse-grained sandstone facies. This lithofacies mainly corresponds (on cores) to coarse to medium-grained, massive and trough cross-bedded sandstones. Gravels and mud-clast lags are often observed. Lithofacies 1 is mostly present in Unit 2 where it corresponds to braided stacked channel deposits.

- Lithofacies 2: clean medium-grained sandstone facies. This lithofacies is finer-grained than lithofacies 1. It may also correspond on logs to sands with higher shale proportion due to the presence of thin mud-clast packets. This lithofacies is associated with channel infill sandstones of the fluvial sequences of Unit 2 and 3, and with the most sandy facies of the estuarine deposits of Unit 3. Lithofacies 2 is almost absent from Unit 4.

- Lithofacies 3: fine-grained sandstone facies. This lithofacies regroups finer and thinner sandstones with slightly higher shale content, mostly distributed as fine laminations. It occurs as fining-upward intervals at the top of channel-fills, as well as overbank deposits in Units 2 and 3. In Unit 3, this lithofacies is also associated with sandy inclined heterolithic stratification (IHS) in the estuary setting. In Unit 4, lithofacies 3 may also correspond to sandy tidal flats and small channels.

- Lithofacies 4: silty shales facies. This intermediate lithofacies is mostly associated with the main heterolithic facies associations of the reservoir, represented by the tidally influenced point bar facies, the estuarine IHS, the mud flat and fine, shaly overbank deposits. Thin sandy layers may also be a part of this lithofacies.

- Lithofacies 5: shaly facies, related to channel abandonment mud plugs, floodplain or coastal plain shales, muddy IHS, or more marine shaly facies such as distal bay deposits.



Fig. 2: Correspondence between the core synthetic log and lithofacies. Lithofacies colour code: 1=red; 2=orange; 3=yellow; 4=light green; 5=dark green.

Lithostratigraphic units

The lithostratigraphic units correspond to intervals characterized from their depositional environment and related reservoir architecture. These units are built by well-to-well correlations of main stratigraphic horizons as illustrated on Fig. 3. Four lithostratigraphic units are identified in the McMurray interval.

Fig. 3: W-E cross-section in the reservoir showing the lithostratigraphic units. Top: correlation of the main markers (colour lines), flattened on the Top McMurray. Bottom: visualization of the 4 lithostratigraphic units. From the bottom to the top, Green=Unit 1; Orange=Unit 2; Blue=Unit 3; Light green=Unit 4. The upper green interval corresponds to the Wabiskaw Mb.

Summary of the reservoir evolution The reservoir geometry observed in the case study typically corresponds to the different infill phases of a fluvial valley system during a sea-level rise. The valleys were formed during periods of base level fall, rivers incising the sediments below with a sharp basal erosion surface (Eschard & Huc, 2008). In the present case, the basal unconformity corresponds to the base of the main valley system, and the valley itself had a regional lateral extension. As the base level started to rise, high-energy braided channels filled the basal part of the valley with shales (Unit 1) then coarse-grained material (Unit 2). The base level continuing to rise, the fluvial systems changed to meandering

DevonianCarbonates

Top Wabiskaw

Top McMurrayOpen bay shales

Stacked tidal flats, Channels and bars

Tidal ravinementStacked meandering channelsWith tidal influence

Amalgamated fluvialBraided channels

Channel belt incision

Base Cretaceous unconformityUnit 1

Unit 2

Unit 3

Unit 4

Coastal plain ?

COREDESCRIPTION

RESERVOIRUNIT

DEPOSITIONALENVIRONMENT

ELECTRO-FACIES

DevonianCarbonates

Top Wabiskaw

Top McMurrayOpen bay shales

Stacked tidal flats, Channels and bars

Tidal ravinementStacked meandering channelsWith tidal influence

Amalgamated fluvialBraided channels

Channel belt incision

Base Cretaceous unconformityUnit 1

Unit 2

Unit 3

Unit 4

Coastal plain ?

COREDESCRIPTION

RESERVOIRUNIT

DEPOSITIONALENVIRONMENT

ELECTRO-FACIES



channels overlying the braided channels (Unit 3). Then, the sea progressively invaded the valley and the effect of the tidal action can be seen in the upper part of the valley with the deposition of heterolithic sandstones and mudstones in estuarine channels and tidal flats (Unit 4). Marine sediments were then deposited as the sea-level rise continued, depositing the marine shales of the base of the Wabiskaw Mb. When the relative sea-level rise slowed, an overall progradation of a delta plain sealed the valley, facies being more and more proximal upward (Upper part of the Wabiskaw Mb.).

Geostatistical modelling

The geological grid built for the reservoir zone contains about 5.106 cells, with a 10m x 10m x 0.5m definition. The four lithostratigraphic units are modelled independently with a stochastic approach. The geostatistical modelling of the distribution of lithofacies is based on the truncated Gaussian method (Galli et al., 1993, Doligez et al., 1999).

The main geostatistical parameters which are used in the truncated Gaussian method are the vertical proportion curves, the matrix of proportions and the variograms, which are all commonly computed from wells. Any additional data may be used to better constrain the simulations, such as interpretative geological maps or information derived from seismic maps or cubes (Doligez et al., 1999 and 2003). Nowadays, 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 beginning of the reservoir characterization workflow (Lerat et al., 2007; Roggero et al., 2007).

However, in the present case, as seismic information was not available, geostatistical parameters were computed from well data only. To avoid any bias in the lithofacies quantification, only vertical wells were considered for the computation of lithofacies proportions. Horizontal well information was introduced in the well database to be honoured by the stochastic realizations.

Simulation results Fig. 4 illustrates the simulation results along a W-E vertical section across the reservoir, and in

3D. Each unit was simulated independently with its own geostatistical parameters. The sharp contacts between the units are well depicted, as well as the changes in the

lithofacies distribution and proportions: - Erosion of the basal shales by the braided channel sands, - Onlap of the meandering fluvial system of Unit 3 over Unit 2, - Tidal ravinement surface at the bottom of Unit 4.

The model restitutes the upward increase of lithofacies 4 and 5 from Unit 2 to Unit 4. Laterally, the expected massive sandbodies associated with the braided system reservoir is correctly handled. Note that the well control permits to reproduce the westward degradation of reservoir facies in Unit 2.

Fig. 4: Lithofacies stochastic model. Left: Close-up view of the reservoir showing the simulation results for the four units. Right: Geostatistical simulation results (seed 10). The four reservoir units are displayed. See Fig. 2 for lithofacies colour codes

Overburden zone Materials

In this section, "material" refers to classes of rock with specific physical properties characterized for the geomechanical and petroacoustic simulations. In the reservoir interval, the materials match the

W E

1-Green (basal shales) 2-Orange (braided fluvial)

3-Blue (meandering fluvial)4-Upper McMR (tidal/estuarine)



lithofacies in terms of lithology. Consequently, there are five materials in the reservoir zone (Materials 1 to 5).

In the overburden zone and according to the lack of data for this interval, the number of materials is limited to three. These materials were easily identified thanks to the gamma-ray and the resistivity logs.

- Material 6 corresponds to low gamma-ray values, interpreted as sandstones, - Material 7 is an intermediate material made of shaly sandstone or alternations of sandstones

and shales, - Material 8 corresponds to high gamma-ray values, interpreted as shales.

The characterization of materials in terms of initial geomechanical and petroacoustic properties was achieved at the full-field scale. However, all physical properties are presented in the modelling section for the local SAGD model.

Table 1: Correspondence between lithofacies and materials

Layering

Using the same methodology used for the reservoir zone, eleven layers were identified from well-to-well correlations in the overburden interval.

Two layers are made of Material 1, three are defined as Material 3, and six layers correspond to Material 2. The overburden layering is summarized in Fig. 5. Together with the reservoir section, the full-field model comprises 5 550 000 cells.

Fig. 5: Layering of the overburden and distribution of the 3 materials within this interval. In the reservoir section, the 5 lithofacies are directly assigned to materials for the geomechanical modelling.

2.2 Coupled reservoir - geomechanical modelling

SAGD reservoir modelling

The local SAGD grid is defined as a tartan grid, with a grid refinement in the direction perpendicular to the well paths (Fig. 6). Cell size varies in the radial direction (X) from 1m to 2.5m. The axial direction (Y) is represented by 41 cells 20m long. In the vertical direction (Z), there are 71 layers in the reservoir interval and 11 layers in the overburden interval.

Lithofacies Material1: Clean medium to coarse-grained sandstone 1: Clean medium to coarse-grained sandstone

2: Clean medium-grained sandstone facies 2: Clean medium-grained sandstone facies

3: Fine-grained sandstone facies 3: Fine-grained sandstone facies

4: Silty shales facies 4: Silty shales facies

5: Shales 5: Shales

6: Sandstones

7: Shales and Sands

8: Shales

Overburden

Reservoir

RESERVOIR71 layers

MNVL3: 4 layers

MNVL2: 1 layerMNVL1: 1 layerUpper MNVL: 1 layerJLFU: 1 layerGDPD: 1 layerSHALE: 1 layerSURFACE: 1 layer

Material 6

Material 8Material 7

Material 1



Overburden

ReservoirOVE

RB

UR

DEN

(~26

0m th

ick)



Fig. 6: Local SAGD model. The grid is defined as a tartan grid in the X direction.

Fig. 7 clearly shows that the upper injection well is going through low quality reservoir at its heel while the lower production well is entering similar low reservoir quality at its toe. It can be suspected that both extremities of the SAGD well pair will have a low injectivity or productivity with a difficulty for steam to be injected or effluents to be produced on these extremities. The impact of low quality reservoir at both ends of the well pair is evaluated in this section.

Fig. 7: View of the reservoir model around one well pair, showing reservoir heterogeneity (in dark and light green). Block size is 820m x 100m x 50m.

There are mainly two periods in the performance of the SAGD process implemented in a very high viscosity oil or bitumen reservoir.

Period 1: warm-up phase. In a first period, hot steam is circulated independently in each well in order to heat the reservoir by conduction in its close vicinity. Heat liquefies the oil during a few months until a hydraulic path is created between the two wells, and then, the effluents can flow easily to the lower production well, this start-up phase lasts four months. In the reservoir model used to simulate the process, steam circulation in the wells is not implemented. Therefore, it is simulated by defining a constant temperature of 220°C in all the grid cells of a well.

Period 2: production phase. As soon as the hydraulic path exists between the two wells, steam is continuously injected in the reservoir by the upper well at a steam bottom hole quality of 0.8 (steam volume/hot water/total water volume) and oil and water continuously produced in the lower well. A steam trap control process has been activated in order to prevent the breakthrough of steam in the lower production well. Steam trap control consists in monitoring the temperature difference between the two wells. This constraint has been defined to range between 20°C and 35°C. This second phase lasts six months after the warm-up phase. Table 2 summarizes the main input data for the reservoir model.



Table 2: Main data for fluids and rock properties.

Data Value UnitInitial reservoir pressure (at -312 m) 20 Bar Initial reservoir temperature (at -312 m) 10 °C Horizontal permeability 3000 (sands)

0,005 (mudstones) mD

Vertical permeability 1000 (sands) 0,001 (mudstones) mD

Porosity 34 (sands)

20 (mudstones) 10 (shales)

%

Rock compressibility 2,54 E-04 Bar-1 Rock heat capacity 2.04 E+06 J m-3 °K-1 Rock thermal conductivity 1.7 W m-1 °K-1 Surface density of the residual oil 1,008 g cm-3 Oil coef. of compressibility 2,17 E-04 Bar-1 Oil coef. of thermal expansion 8,50 E-04 °C-1 Irreducible water saturation 15 % Initial oil saturation 85 % Residual oil saturation 10 %

The numerical simulation of the selected well pair is constrained by the production history of both wells: steam injection rate in the injection well and the total liquid rate (oil+water) in the producer. Another constraint has been set in the two wells, a maximum BHP (bottom hole pressure) of 50 bars in the injection well, and a minimum BHP of five bars in the production well.

Fig. 8 exhibits simulation results over six months (left) and for the full history of the well pair (i.e. six years, right) in good agreement with field data without any modification of the set of data.

0

5000

10000

15000

20000

25000

30000

35000

40000

0 50 100 150 200 250

Time from start of steam injection (days)

Cum

ulat

ive

oil p

rodu

ctio

n (m

3)

water

oil

- Field data- Simulation

Reservoir simulation with PumaFlow

0

100000

200000

300000

400000

500000

600000

0 500 1000 1500 2000 2500Time from start of steam injection (days)

Cum

ulat

ive

oilp

rodu

ctio

n (m

3 )

oil

water

- Simulation- Field data

Time from start of steam injection (days)

Fig. 8: Oil and water production after six months (left) and after six years (right)

The evolution of several parameters along the various grid cells of the injection and production well are shown for various times in Fig. 9.

0123456789

101112

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

Perc

ent s

team

rate

inje

cted

in th

ew

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)

heel toe

Well pair profile Fig. 9: Profile of steam rate versus time in the injection well, expressed in percent of the total rate of the well.



The profiles of the two wells are shown below each curve to visualize in a better way the low quality reservoir areas (in red). This figure clearly shows the sections along the well were there is good or very low steam injection. The evolution in time indicates an equilibration between the various zones where steam is injected and, at the same time, the start of steam injection in sections where initially low to poor injection was possible.

Geomechanical modelling

Constitutive laws for geomechanical simulations are deduced from a literature review on similar rocks, in equivalent conditions and used to model the mechanical behaviour of the media.

Mechanical properties of the model were essentially taken from Chalaturnyk (1996). The author had made several mechanical tests in laboratory on sandstones and shales of the UTF (Underground Test Facility) site, and was able to give drained static parameters. Although the UTF reservoir is 160m deep, compared to 300m in our field case, the same intrinsic parameters were kept for both sites (dilation angle, Poisson coefficient, ...), while the strength parameters of the sandstones and the shales (Young modulus, cohesion, friction angle, ...) were adjusted – almost always increased - in this reservoir, located deeper. For materials 7 and 4, which represent shaly sandstones to silty shales (Table 1), an average value of each parameter was chosen between the sandstones (Materials 1 and 6) and the shales (Materials 5 and 8).

Table 3 gives the values of all mechanical parameters chosen to define the behaviour of the different materials in the finite element software.

Table 3: Mechanical parameters used in mechanical simulations.

1 2 3 4 5 6 7 8λ (W/moC) 1.736 1.8 1.85 2 2.5 1.73 1.73 2

ρdry (kg/m3) 1900 1900 1950 2000 2100 1660 1920 2180

ρwet (kg/m3) / / / / / 2030 2200 2370

PHI (%) 34 34 34 20 10 37 28 19

kh (mD) 3000 3000 3000 0.005 0.005 / / /

kv (mD) 1000 1000 1000 0.001 0.001 / / /

PHIeff (%) 34 34 34 20 10 / / /

MATERIALS

α (oC-1) 3,0 10 -5 2,0 10 -5 2,0 10 -5 - 2,0 10 -5 - 0,5 10 -5 3,0 10 -5 3,0 10 -5 - 2,0 10 -5

ρdry (kg/m3) 1900 1900 1950 2000 2100 1660 1920 2180

ρwet (kg/m3) / / / / / 2030 2200 2370

E (MPa) 1300 1300 1250 1000 1100 1200 1000 1000

ν 0.30 0.30 0.3 0.25 0.4 0.3 0.3 0.4

ϕ (° ) 60 60 55 45 40 50 40 35

ψ (° C) 15 15 15 0 0 15 5 0

C (MPa) 0.5 0.5 0.5 1 1.25 0 0.75 1.25

E is the Young's modulus, ν the Poisson's coefficient, ρwet the wet density, α the thermal expan-sion coefficient, κh the hydraulic conductivity, ϕ the friction angle, ψ the dilation angle and C0 the initial cohesion. Thermal expansion coefficient and strain hardening laws are implemented by discrete value tables. Expansion coefficient was set positive for sandstones and variable with temperature for reservoir shales (Material 5) and shaly sandstones (Material 4) as shown in Fig. 10. This means that when the thermal expansion coefficient is positive (like for sandstones), a competition occurs between thermal stresses and steam injection effects. Indeed, effective stress increases with temperature whereas it decreases as pore pressure rises. But when the coefficient is negative (like for shales), the effects of heating and steam injection cumulate.

-2.5E-05-2.0E-05-1.5E-05-1.0E-05-5.0E-060.0E+005.0E-061.0E-051.5E-052.0E-052.5E-05

0 50 100 150 200 250 300

Temperature (°C)

α (°C-1)

Fig. 10: Variation of the thermal expansion coefficient with temperature for lithofacies 4 and 5.



The cohesion parameter of the reservoir sandstones (Materials 1, 2, and 3) is different from zero, even if this rock is known to be unconsolidated. In fact, the grains have been deformed during the geological loading and are classified as "locked grains" (Li and Chalaturnyk, 2003). Their geometry gives them a fictive cohesion that remains lower than the shale one, but different from zero.

Mechanical parameters were introduced in the geomechanical simulator for each material and were used to define the constitutive law. 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).

The main results of the reservoir geomechanical response to temperature and pore pressure loading, extracted from the reservoir model, are interpreted in terms of mean effective stress (σ'moy), maximal total strain (εtotmax) and yield criterion which indicates when the plasticity is reached. Initial pore pressure in the reservoir is uniform and equals to 1.8 MPa, initial temperature is also uniform and equals to 12°C, and mean effective stress in the reservoir is about 4.8 MPa. Six coupling steps have been chosen for geomechanical simulations (Table 4).

Table 4: Chosen dates for reservoir – geomechanical one-way coupling

Step 1 03/01/2000 balancing with gravity Step 2 05/01/2000 second month of warm-up phase Step 3 07/01/2000 end of warm-up phase Step 4 08/01/2000 first month of production Step 5 09/01/2000 second month of production Step 6 01/01/2001 sixth month of production

Fig. 11 presents the extension of the steam chamber after six months of production. The 3D envelope corresponds to a minimum value of 100°C; it means that every cell inside this domain has a temperature ranging from 100°C to 280°C. This figure clearly shows a high degree of heterogeneity of temperature distribution along the well pair. From sections A to B, steam chamber development seems to be confined vertically. These sections coincide with the presence of heterogeneities at the heel of the well (see Fig. 7). From Section B to D, the vertical development of steam is no longer limited, excepted in section C where a shale bed is located right between the wells and therefore limits oil production as well as steam injection.

The colour range corresponds to pore pressure evolution which is also presented on this figure. It can be noticed that the maximum pore pressure (7.1 MPa) is localized between sections A and B. These pressures are located around the injector well, right above the shale inclusion. From section B to D, mean pore pressure (4.7 MPa) is equally distributed around the well pair and forms a 40 m diameter cylinder.

AB

C D

AB

C D

Fig. 11: 3D envelope corresponding to a minimum temperature of 100°C. A, B, C, D represents vertical sections Section cuts for visualization of the mechanical effects inside the reservoir.

Geomechanical computations results are presented in terms of mean effective stress and total strains values in Fig. 13, Fig. 14 and Fig. 15. These results are presented for one section located between points A and B (on the left) and a second section located between points B and C (on the right) on Fig. 11 and Fig. 12.

Fig. 13 shows that high effective stress is developed principally in the sandstones of Lithofacies 1. Indeed, its thermal expansion coefficient is the higher (3.10-5°C-1), and the results show that the



thermal effect gets ahead of the overpressure induced by the steam injection (that tends to decrease σ' moy). Minimal σ' moy is about 1.0 MPa and appears in the shale material because pore pressure and temperature growth act in the same way, that is to reduce the effective stress. The minimum effective stress location corresponds exactly to the shale material, i.e. near the injection well (on the right) and near the top of the reservoir (on the left).

For the same reason, maximal total strain is the highest (+ 1.1 %) for the sandstone materials, because there is a conjugate effect of temperature and pore pressure rises. Whereas minimum strain (near zero in several cells) is observed in the shale material cells, because temperature increase counteracts the effect of pore pressure increase. In that case, elastic and plastic strains (positive values) balance exactly the thermal strains which are negative.

Fig. 15 shows that thermal and pressure loading generate yielding of shale lithofacies (Material 5) in both sections, where temperature increase is sufficient to reach a negative value of the thermal expansion coefficient (see also Fig. 10).

Fig. 12: Distribution of lithofacies in the two cross-sections. White dots indicate the intersection with the well pair. See Fig. 2 for colour codes.

Fig. 13: Mean effective stress at the end of the production period (step 6).

Fig. 14: Maximal total strain at the end of the production period (step 6).

Fig. 15: Yield criterion (plasticity in red) at the end of the production period (step 6).

2.3 4D seismic modelling Base synthetic survey

The aim is to estimate seismic parameters (density, compression velocity and shear velocity) of the saturated rocks, from initial mechanical and reservoir parameters in coherence with the well log data. Mean values of all mechanical and reservoir parameters assigned to materials were presented above in Table 3.

Concerning the well data, interpreted logs used are density, total porosity, saturation, P-sonic, lithofacies and gas indicator. The lack of S-sonic log in Canadian databases is a detrimental source of uncertainty. The basic idea is that the seismic properties of the oil saturated rocks are related to seismic properties of heavy oils which depend on density, composition, temperature and



gas/oil ratio. At the initial time, only water and oil components are present in our fluid model, but heavy-oil is considered near like a solid due to its high viscosity. Moreover, the main issue is that the determination of seismic parameters requires dynamic mechanical parameters (Young’s modulus, Poisson’s ratio), whereas mechanical parameters used in mechanical modelling are static.

Static to dynamic elastic properties

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

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

)1()21(3)1(2

νν

−+

=GK

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

)2(staticdry

dynamicdry KAK =

Second Step: Gassmann’s equation (Gassmann, 1951) was applied in the case of a full water saturation. After computation of the saturated bulk modulus and density, P-velocity could be estimated as a function of A for each material. The bulk modulus on shear modulus ratio (Equation 1) is helpful to estimate the dynamic shear modulus (the same for dry and saturated rock) from the dynamic bulk modulus. The density vs. porosity cross-plot of the water-saturated log data allowed to check density (Fig. 16), whereas the velocity vs. porosity cross-plot led to calibrate the A constants, which were found greater than one as expected, in the range 2.5 - 5. Porosity and associated dynamic dry properties of each material are presented in Table 5. Note that the dry density values of Materials 1, 2 and 3 have been slightly decreased in order to be consistent with density logs in the water saturated zones of the selected wells. Nevertheless, material densities are only taken into account for the equilibrium of the mechanical structure in the geomechanical simulation, and thus will not mainly affect final results.

xx

xx

xx

xx

Fig. 16: Water saturated data cross-plots. Density vs. porosity (left), velocity vs. porosity (right). Lithofacies 1 2 3 (top), lithofacies 5 (bottom): x indicates calculated parameters for Materials 3 (top) and 5 (bottom).



Third step: In order to compute the density, 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) at the initial time because of temperature (10°C) and pressure (2 MPa) in the reservoir. 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 Wang, 1992. The shear modulus was drawn on the results of a 7° API oil (Batzle and Hofmann, 2006) and a value of 0.5 GPa was chosen. The generalized Gassmann’s equations (Ciz and Shapiro, 2007) were handled under the simplifications of a homogeneous grain rock, and a uniform macroscopic fluids repartition. They consist in two similar equations to compute the saturated bulk modulus and the saturated shear modulus:

( ))3(,

)()( 1111

21111 GKMfor

MMMMMM

MMrockdryrockfluid

rockdrydrysaturated =

−+−

−−= −−−−

−−−−

φ

where K is the bulk modulus, G the shear modulus and φ the porosity. 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 cross-plots (lithofacies in intervals free of gas) for 0.15 and 0.6 water saturations. In contrast, the P-velocity values initially obtained by standard Gassmann's equations did not fit these velocity vs. porosity cross-plots (about 190 m/s and 170 m/s lower)

Table 5: Materials with corresponding lithofacies, porosity and associated dynamic

dry properties (density, bulk modulus, shear modulus).

Material Lithofacies porosity(v/v)

ρdry(Kg/m3)

Kdry(GPa)

Gdry(GPa)

Reservoir zone1 1 0,34 1800 2.708 1.252 2 0,34 1800 2.925 1.353 3 0,34 1850 3.854 1.7794 4 0,20 2150 2.867 1.725 5 0,10 2300 8.617 1.864

Overburden zone6 1 2 3 0,37 1660 2.6 1.27 4 0,28 1920 4 1.8468 5 0,19 2180 6.667 1.428

Initial full seismic model Each material has been assigned the elastic properties corresponding to the initial water saturation set to 0.15 in the reservoir sands materials, and set to 1 in all others materials. The 3D full model is 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. In the reservoir zone (Fig. 17), the high P-velocities of the water saturated shales are visible in the right and left parts, and the average P-velocities of the near oil saturated sands in the middle bottom part. The S-velocities seem to discriminate more the oil sands from the water shales, but this interpretation is not proven as no S-sonic is available to check it.



Fig. 17: Elastic model (reservoir zone). Top: P-velocity in m/s, Bottom: S-velocity in m/s.

The block of the three elastic parameters, namely P-velocity, S-velocity and density, was

converted from depth to time domain with the velocity law derived from the P-velocity model. As high frequencies have to be handled, the time sampling rate was chosen equal to 1ms. The reflectivity coefficients were first derived from the P-impedances (expressed as density multiplied by P-velocity) in 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 Fig. 18 shows the seismic section for one line extracted from the 3D model. The 3D seismic results of the full-field model are presented in Fig. 19.

materials

Fig. 18: 1D seismic modelling (reservoir zone). Top: Materials, Bottom: reflectivity coefficients convolved by a 80 Hz Ricker.



Fig. 19: 3D view of the full-field model. Left: Materials, right: Reflectivity coefficients convolved by a 80 Hz Ricker.

Synthetic monitor surveys The evolution of physical parameters has been computed thanks to the coupled reservoir-geomechanical model:

- The fluid flow simulation led to temperature, saturation and pore pressure evolution in the reservoir only,

- The geomechanical simulation led to stress and strain evolution in the reservoir and in the overburden.

The evolution of those physical parameters drives the mechanical parameter modification (bulk modulus, shear modulus and density) that pilots wave velocities and reflectivity changes. In the present workflow, seismic velocities are computed using the initial data and the process described below.

Updating density, bulk and shear moduli The stress dependency of the dry bulk modulus is taken into account through the Hertz relation

(Mindlin, 1949) expressed as:

)4()( 00

Hertz

drydry KK ⎟⎠⎞

⎜⎝⎛=

σσσ

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 0.13-0.16 range. The dry shear modulus is taken constant (no Hertz effect for modelling) but the fluid shear modulus has to be calculated if pores contain viscous oil. The temperature dependency of the oil shear modulus can be approximated by:

)5(

)(1

)(

TG

GTG

oil

oiloil

ηω ×+

=

where Goil is the oil shear modulus at infinite viscosity, ω the seismic pulsation, η the oil viscosity and T the temperature.

At the initial temperature of 10°C the oil viscosity is around 2200000 cp, this viscosity falls to about 15400 cp when the temperature rises to 40°C, and to about 10 cp for a temperature of 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.

Fluid and saturated rock density are computed with no dependency with temperature, more precisely only porosity and saturation dependency is taken into account.

According to equation (3), the new saturated bulk and shear modulus are computed in terms of

new saturation, new temperature, new porosity and new stress. P- and S-wave velocities can thus



be calculated, as well as acoustic impedance that can be derived along 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 time domain, and convolved with a chosen wavelet (Ricker with a central frequency of 80 Hz).

Qualitative sensitivity analysis to reservoir conditions The methodology described above has been applied to generate seismograms for a selection of

simulation steps (see Table 4). As shown on the following illustrations, the seismograms are clearly affected by the simulation conditions.

Fig. 20 displays six time-seismograms for P-wave computed on a vertical section in the vicinity

of the well pair. Large amplitude variations can be observed in the reservoir.

step 1 step2

step 3 step 4

step 5 step 6

Fig. 20: P-wave seismogram in a vertical section parallel to the well paths. Vertical axis is time (300 ms), horizontal length: 900 m. See Table 4 for the definition of steps.



Seismograms shown on Fig. 21 illustrate the model sensitivity: - The increase in porosity clearly affects the P-wave computation for the step 3: the porosity

considered in the new computation is 30% higher than in the reference, - The effect of the increase of gas saturation (20% higher) is negligible due to the low gas

saturation in the chosen period, - The modification of the Hertz coefficient (0.13 in the modified computation, 0.16 in the

reference one) does not affect P-wave results.

step 3 step 3 with porosity +30%

step 3 step 3 with steam saturation +20%

step 3 (Hertz = 0 .16) step 3 (Hertz = 0.13)

Fig. 21: P-wave seismogram in a vertical section parallel to the well paths, illustrating some sensitivity tests for step 3. See Table 4 for the definition of steps.

From the mechanical and reservoir simulation results, the evolution of seismic velocities has been computed through the petroelastic model (PEM) presented in this section. This PEM allows describing the physical dependence of mechanical parameters. The model being populated with velocities, 1D seismograms have been generated. Differences of P-wave depth seismograms are computed for five steps for a horizontal slice chosen in the vicinity of the injection well (Fig. 22).



Each slice represents the cumulative difference of P-wave between a given step (Steps 2 to 6) and the initial state of the model before the start of production operations (Step 1). A high contrast is observed along the well path from Step 2 (second month of warm-up phase) to Step 6 (six months of production). Other areas affected by 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 to develop harmoniously, which induce local changes in pressure, temperature, steam saturation and stresses.

Fig. 22: Difference in P-wave depth seismograms at 314.5 meter depth.

3. Conclusions and perspectives This study is based on a fully integrated approach which involves geology, geophysics, reservoir and geomechanics. This methodology implies the construction of a fine-scale initial static model, including reservoir and overburden areas, designed before the start of thermal operations. In the reservoir area, specific care has been devoted to ensure the consistency of the initial petroelastic model (PEM) with the geological model as also with the fine-scale mechanical model, since there is a strong link between lithofacies, porosity, static and dynamic mechanical moduli. A SAGD well pair has been extracted and modelled with a coupled reservoir – mechanical approach at different steps of production. For each step, elastic parameters were assigned to the model using the PEM. Finally, the impact of physical parameters was evaluated by comparing maps of seismic attributes produced at different times.

The workflow is applied to a synthetic model of a heavy oil reservoir, inspired from a real field case in Athabasca (Canada). The study focuses on the early production period (six months) to monitor the steam chamber development. In terms of reservoir simulation, the equilibration in the development of the steam chamber is an important result shown by the various profiles of fluid repartition along the wells. It is necessarily due to gravity that monitors the process and imposes a fair repartition of the steam along the well pair. This means that heterogeneities have a huge impact on the repartition of fluid injected and produced along the well pair. However, gravity stabilizes the fluid repartition as time goes on.

The most interesting knowledge for a SAGD operator, that could hopefully be inferred from a permanent seismic monitoring interpretation, 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 the steam chamber development all along the well and not only in some limited sections.

When aiming to monitor a steam chamber growth with time-lapse seismic, it is necessary to study the impact of stresses and strains on the PEM because of the stress-sensitivity behaviour of



oil-sands. The reservoir-geomechanics coupled approach shows that heterogeneity distribution has a huge impact on mechanical results. From this study, it can also be inferred that the thermal expansion coefficient has as critical influence on the shale behaviour. This would be even more visible if transport parameters were modified after mechanical computations. Indeed, further studies would imply a higher degree of coupling where permeabilities and/or porosities of the media are updated according to strain evolution. A second remark would concern the lack of data in terms of mechanical properties, as uncertainties on the mechanical results must be expected.

The synthetic seismic data illustrates the changes that occur during the modelling of the SAGD production process. High contrasts in seismic attributes are observed from the very beginning of production operations. Changes in physical conditions can be monitored even for these early periods with a permanent seismic monitoring survey. However, as pressure, temperature, viscosity, saturations,... effects are coupled, the seismic signature needs to be investigated quantitatively. Further work on this model will consist in a quantitative interpretation of the synthetic monitor surveys together with an uncertainty study on the PEM parameters following the experimental design approach.

Acknowledgement The authors would like to thank IFP Technologies (Canada) Inc. for the help, contacts and valuable information provided for this study.

References Batzle M. and Hofmann R [2006] Heavy oils – seismic properties. The Leading Edge, pp 750-756. Batzle, M., and Wang, Z. [1992] Seismic properties of pore fluids. Geophysics, 57, pp 1396-1408. Chalaturnyk, R.J. [1996] Geomechanics of SAGD in Heavy Oil Reservoirs. PhD dissertation;

Department of civil Engineering, University of Alberta. Ciz, R., and Shapiro, S. A. [2007] Generalization of Gassmann equations for porous media

saturated with a solid material. Geophysics, 72, A75-A79 Doligez, B., H. Beucher, F. Geffroy, and R. Eschard [1999] Integrated reservoir characterization:

improvement in heterogeneous stochastic modelling by integration of additional external constraints. in R. Schatzinger and J. Jordan, eds., Reservoir Characterization – Recent Advances: AAPG Memoir, no. 71, pp 333-342.

Doligez, B., P. Gomel, B. Andrieux, F. Fournier, and H. Beucher [2003] Use of seismic to constrain geostatistical reservoir models: a quantitative approach using proportions of facies. AAPG annual meeting, paper no. 78165.

Eschard, R. and Huc, A.Y. [2008] Habitat of Biodegraded Heavy Oils: Industrial Implications. Oil & Gas Science and Technology – Rev. IFP, Vol. 63 (2008), No. 5, pp. 587-607

Galli, A., H. Beucher, G. Le Loc'h, B. Doligez, and groupe Heresim [1993] The pros and cons of the truncated gaussian method, in M. Armstrong and P.A. Dowd, eds, Geostatistical simulations, Kluwer Academic Publishers, pp 217-233.

Gassmann, F. [1951] Elastic waves through a packing of spheres: Geophysics, 16, pp 673-685. Lerat, O., Nivlet, P., Doligez, B., Roggero, F., Berthet, P., Lefeuvre, F., and Vittori, J. [2007]:

"Construction of a Stochastic Geological Model Constrained by 3D High Resolution Seismic Data - Application to the Girassol Field, Offshore Angola". SPE 110422, SPE Annual Technical Conference and Exhibition, 11-14 November 2007, Anaheim, California, U.S.A

Li, P. and Chalaturnyk, R.J. [2003] Discussion of SAGD and Geomechanics. JCPT, vol.42, n° 9, pp 37-39.

Mindlin, R. D. [1949] "Compliance of elastic bodies in contact". J. Appl. Mech., Vol. 17, 259-268 Roggero, F., Ding, D. Y., Berthet, P., Cap, J., Schreiber, P.E. [2007] Matching of Production

History and 4D Seismic Data - Application to the Girassol Field, Offshore Angola. SPE 109929, SPE Annual Technical Conference and Exhibition, 11-14 November 2007, Anaheim, California, U.S.A.

Sarzalejo S. and Hart B.S. [2006] Stratigraphy and lithologic heterogeneity in the Mannville Group (southeast Saskatchewan) defined by integrating 3-D seismic and log data. Bulletin of Canadian Petroleum Geology, V. 54, pp 138-151.

Modelling of 4D Seismic Data for the Monitoring of the...

Documents

Transcript of Modelling of 4D Seismic Data for the Monitoring of the...