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Establishing Patterns Correlation
from Time Lapse Seismic
Jianbing Wu(1), Andre G. Journel(1) and Tapan Mukerji(2)
(1) Stanford Center for Reservoir Forecasting
(2) Stanford Department of Geophysics
April 23, 2003
Abstract
The extensive spatial coverage of seismic data provides a unique source of infor-
mation widely used for surface and facies modeling, faults detection, more generally
static heterogeneities modeling. The advent of 4D time-lapse seismic surveys opens
a new dimension – the possibility of monitoring fluid flow hence production. Dis-
counting the favorable cases in which fluid displacement canbe seen directly from
time lapse seismic data, the preliminary challenge is to establish a correlation be-
tween saturation changes and seismic data changes. Becauseof the low resolution
of seismic data, one should not expect any useful point-to-point correlation; instead,
in the general case one might expect correlations between spatial patterns of seismic
time differences and corresponding spatial patterns of saturation changes.
This preliminary study aims at developing a general methodology to establish
such pattern correlations, hence preparing the way for a systematic utilization of time
lapse seismic surveys beyond trivial visual observation. The exhaustively known
Stanford V reservoir, over which both flow simulation results and repeated synthetic
seismic surveys are available, is used to explore such correlations.
1
1 Introduction
4D seismic surveys, possibly with permanent downhole sensors, are being considered
to monitor production through observing changes in reservoir state. Time differences of
seismic attributes are related to changes in pore fluids and pore pressure because bulk den-
sity and bulk moduli change during the drainage of the reservoir. Maps of seismic time
difference can be used to detect fingering, monitor fluid movement, improve recovery and
locate new wells (Nur, 1989; Anderson, 1998; Lumley, 1999; Guerin, 2000). Clear suc-
cess stories are presently limited to clastic reservoirs, shallow reservoirs and reservoirs
where gas flow allows a greater density differentiation. There has been also some suc-
cessful applications to carbonate reservoir (Hirsche, 1997; Talley, 1998; Weathers, 1998).
In the best case, correctly processed time lapse seismic data can point out to fluid move-
ment through mere visual inspection without any need for correlation statistics. These
clear success stories may have led to dismissing the potential of 4D seismic surveys in
less favorable cases, deep layers for example. In such unfavorable cases, there may still
be some influence of fluid saturation changes on the seismic data, but detection of such
weak relation would need filtering and correlation tools beyond mere visual inspection
(Sønneland, 1997).
A wider utilization of 4D seismic surveys for monitoring production would have to
settle with lesser expectation: water or gas fronts may not be seen deterministically yet
may have a detectable influence, if only tenuous and stochastic, on the seismic attributes.
Seismic time differences would only influence (perhaps in a stochastic fashion) the fluid
transfer calculations as performed through a flow simulator. Time lapse seismic data could
then be systematically considered as a covariate data whosecorrelation would vary from
quasi perfect (present best cases) to none. The intermediary cases are the object of this
study.
A preliminary requisite to using any covariate data is to establish its correlation with
the primary variable being estimated. There are, however, many ways one spatially dis-
tributed variable, sayy(u), may be dependent on another one, sayz(u), besides the trivial
point-to-point correlation calling for the 2 variables to be colocated at the same location
of coordinates vectoru:
- first, the 2 variables may be defined on different volume supports and have different
space and time resolution. Typically, the vertical resolution of seismic data is lesser
than the vertical discretization of numerical reservoir models, those used to predict
2
flow movement.
- it may be that only specific spatial patterns of the covariate y(u) carry a relation
with either the primary variablez(u) itself or some of itsz-spatial patterns.
In the previous discussion, the covariatey(u) may be a time difference of seismic
amplitudes measured at locationu, z(u) could be the corresponding time difference in
water saturation defined over a flow simulator block co-centred atu.
The unique (because extensive) and potentially valuable time lapse seismic informa-
tiony(u) should not be dismissed just because, from a few calibrationwells, the colocated
correlation{y(u), z(u)} was found to be poor or very poor.
An eye-opener:
Figure 1 gives nine horizon (stratigraphic) sections of a 3Dcube of seismic amplitude
time difference, and Figure 2 gives the corresponding 9 horizon sections of the water
saturation time difference. The pattern correlation between the 2 series of figures is clear,
yet the 3D point-to-point correlation between the two time difference variables is quasi
zero (-0.11). In real practice, one may have the time lapse seismic maps of Figure 1 but
will not have access to the “true” water saturation difference maps of Figure 2, and one
would rely on calibration correlation from well data where both seismic amplitude and
water saturation data are available; were that correlationfound to be poor (-0.11) one may
have dismissed wrongly the time lapse seismic information of Figure 1.
As will be explained in detail in the following text, the results of Figures 1 and 2 were
obtained by forward simulating the reflection seismic data and simulating water flood over
a layer of the synthetic clastic (fluvial channels) StanfordV reservoir. The time lapse is 2
years of production from a given set of vertical wells. Both simulations (seismic reflection
and water saturation) made use of the exhaustively known petrophysical properties of that
reservoir.
From the same 3D cube of time differences (seismic amplitudeand water saturation
vertical difference), but using principal components of these 2 difference variables de-
fined over a spatial moving window, the correlation was increased to 0.71, a value more
reflective of the excellent visual correspondence seen between Figures 1 and 2. Our goal
is to detect such pattern correlation between difference variables, model it and use it to
improve the traditional flow-based prediction of fluid movements.
3
2 Setting the experiment: The Stanford V reservoir
The Stanford V reservoir is a large 3D data set modeling a clastic reservoir made up of
meandering fluvial channels with crevasse splays and leviesin a mud background, see
Figure 3. This data set was built through a sequence of geostatistical simulations generat-
ing first the layers geometry, the meandering channels and associated facies within each
layer, then populating each facies with petrophysical properties (porosity, permeability,
initial saturation, velocity and density), see Mao (1999),Mao and Journel (1999).
The Stanford V reservoir comprises 3 layers, each with a different net to gross and
varying channel directions. Layer 2 was retained for this study. Figure 4 gives a schematic
vertical cross section of that layer, which is discretized by a 3D grid with100× 130× 10
nodes. The vertical coordinate of that grid is stratigraphic subdividing the layer thickness
at each horizontal location(x, y) into 10 stratigraphic sublayers,j = 1, · · · , 10. The
porosity field over these 10 sublayers is shown in Figure 3. Table 1 gives the average
porosity, permeability values: note the significant porosity 0.07 in mud, the mud facies
thus contributes significantly to oil saturation and final recovery. The overall net to gross
ratio (proportion of channel+crevasse) is 0.53.
Flow simulation:
To maximize sensitivity of the seismic time lapse data, the reservoir is assumed shal-
low (top depth at 600m, see Figure 4, with light oil density at45APIo. The initial pressure
is set at 1000psi at 180oF . Water viscosity is 0.325 cP and GOR was set at 850 scf/STB.
The initial water saturations are:
Sw = 0.15 in sandstone and crevasse
Sw = 0.30 in mudstone
This corresponds to a water-wet mudstone which, globally, contributes a substantial amount
of oil.
Two different relative permeability curves for sand+crevasse and mud were consid-
ered, see Figure 5.
One injector is located in the SW corner at grid node (10,10),and one producer in
the NE corner at grid node (90, 120). The water injection rateis 40,000STB/day. Dur-
ing production no gas is emitted from the oil phase. The Eclipse simulator was run for
water flooding over a total period of 20 years starting Jan.1,2000. Breakthrough occurs
4
at the end of 2013. Figure 6 gives the oil saturation field on Dec.29, 2013 just before
breakthrough. Comparing Figures 3 and 6, note the water penetration in mud.
Warning: Figure 6 as well as all other flow simulation results shown inthis report is exact.
These exact recovery figures were calculated from the reference petrophysical fields and
would not be available in the real practice of prediction. Actual prediction will have to
consider an estimated (or simulated) petrophysical model built from whatever information
is available, typically well log data, geological interpretation and most important seismic
data, in particular time lapse seismic data.
Seismic data simulation
The original reference velocity field was generated assuming 100% brine saturation
(Mao, 1999). It has thus to be corrected to account for the initial oil saturation: this was
done using Gassmann substitution (Mavko, Mukerji and Dvorkin, 1998). The density
and bulk moduli of the proper mixture of oil and brine at initial condition (prior to water
injection) was then generated. Last, from the resulting velocity and density fields the am-
plitude seismic traces were forward simulated using a normal incidence 1D convolution
model with Fresnel zone lateral averaging, see Wu (2003) forgreater details.
Figure 7 shows the scattergrams of P wave velocity vs. porosity for each facies when
the reservoir is saturated with 100% brine and 100% oil, respectively. These scattergrams
indicate that the seismic survey is capable of distinguishing the P wave velocity difference
between a brine saturated rock and an oil saturated rock.
The incident wave frequency is 60Hz, the wavelength is about60m, the mean depth
to the center of Layer2 is set at 850m, hence the diameter of the Fresnel zone is 225m.
The Fresnel zone used for forward seismic simulation is a225m × 225m square.
This seismic data simulation was repeated at different times during the 20 years pro-
duction period to mimic 4D surveys attempting to track the changes in water (brine) sat-
uration. The 3 time instants discussed hereafter are:
- Jan.1, 2000: initial conditions before water injection
- Jan.2, 2004: before water breakthrough
- Dec.29, 2014: after water breakthrough
Figure 8a gives the 3 facies distribution (channel, crevasse, mud) over the first NS
vertical section at x=1. Figure 8b gives the same section of the seismic amplitude 3D
5
cube. The vertical axis is time. The survey data is Jan.1, 2000. From Figure 8b it would
be difficult to retrieve the facies distribution of Figure 8a, the reason being that seis-
mic impedances and amplitudes vary within the same facies because of the within-facies
petrophysical variability.
Note: Here we only consider normal incidence seismic amplitude.It is possible that with
pre-stack seismic (e.g. AVO, near & far-offset impedance) some of the facies distribution
could have been better revealed.
3 Point-to-point Correlation
We attempted a direct point-to-point correlation between the two previously generated
seismic amplitude and water saturation fields on Jan.1, 2000. Not surprisingly, that cor-
relation came out very low at -0.06.
Indeed seismic amplitude and water saturation are defined onvery different volume
supports. Seismic amplitude is an average of reflectivity coefficients over a large Fresnel
zone, here of dimension9×9 grid nodes, i.e. of size225m×225m in average. In addition,
seismic amplitude records vertical impedance contrast. Consequently, we would expect
better correlation between seismic amplitude and a vertical contrast of spatially averaged
saturation values:
- average first the water saturation data over a 3D moving window approximating the
seismic Fresnel zone. That average is porosity-weighted:
Sw(u) =
∑L
l=1 φl × Swl∑L
l=1 φl
(1)
whereL = 243 is the number of grid nodes of the9 × 9 × 3 window centred at
locationu = (i, j, k) in stratigraphic coordinates;φl andSwl are the nodel porosity
and saturation values.
- next, define the vertical saturation contrast as:
dSw(i, j, k) = Sw(i, j, k) − Sw(i, j, k − 1) (2)
wherek is the vertical stratigraphic coordinate, increasing withdepth.
Figure 9 gives the seismic amplitude fieldseis(u) as recorded on Jan.1, 2000 (prior
to water injection) over the 9 stratigraphic surfacesk = 1, · · · , 10. Figure 10 gives the
6
corresponding 9 surfaces of water saturation vertical difference. The overall 3D colocated
correlation (in stratigraphic coordinate) is now -0.20, asopposed to the previous -0.06.
However that -0.2 correlation still does not reflect the visual patterns correlation seen on
the 2 figures.
Note that neither Figure 9 or 10 involve any time lapse (difference). Figure 10 only
displays vertical contrast in water saturation measured the same day, here Jan.1, 2000.
4 Spatial pattern correlation
Because the point-to-point correlation (-0.20) does not render justice to the visual (pat-
tern) correlation seen between Figures 9 and 10, we have to define a better correlation
tool, yet one which is not too case-specific and could be applied to a whole range of
reservoir heterogeneities and seismic surveys.
The goal here is not so much to detect spatial patterns withina 3D seismic cube, but to
define a measure able to correlate fuzzy spatial patterns between 2 cubes, say the seismic
cube and the water saturation one. There are many classification tools (Duda 2001), but
their primary goal is to detect patterns independently of correlation. As an initial choice
we have focused on principal component analysis (PCA) and canonical analysis (CA)
(Michael 1984, Jolliffe 1986, Caers et al. 2003) for the following reasons:
- they are general, well understood, tools easy to apply
- they only involve linear combinations of data, i.e. statistics up only to order 2,
variance and covariance, which are easy to infer
- PCA is based on a variance analysis, defining linear combinations of data which
contribute maximally to that variance. Considering the spatial variance of attributes
within a given 3D template, one could argue that the first principal component (PC)
is a ”good”, or at least a general, summary of patterns existing within that template.
Correlating PC’s, defined on seismic vs. saturation data, could allow capturing
some of the patterns correlation
- CA is an even more direct approach: it aims at defining pairs of linear combinations
(one for seismic, one for saturation) that are maximally correlated.
The general idea is to define spatial templates, one for seismic data, one for saturation
data, then to define within each template a linear combination of the data which would
7
maximizes the cross-correlation seismic vs. saturation. PCA has the added advantage that
each linear combination contributes maximally to the within-template variance.
Template sizes: Because seismic data are already averaged over a Fresnel zone, here
9 × 9 grid nodes corresponding to225m × 225m in average, the seismic template needs
only extend vertically. In depth coordinate we retain a vertical column template of size
(1 × 1) × 7 centred on each grid node locationu, see Figure 11a.
To appromixate the seismic Fresnel zone, we consider for saturation data a full 3D
template of size(5 × 5) × 3, see Figure 11b. To reduce the actual dimension of these
templates, the 25 saturation data of each of its horizon sections are averaged into 3 values:
the central value, the average of the 8 first aureola values, the average of 16 outer aureola
values. Thus a saturation template comprises3× 3 = 9 values, as opposed to 7 values for
the seismic template.
Data tables: The two 3D cubes of seismic and saturation data, at a given date say Jan.1,
2000, are scanned with the two previous templates generating two large data tables,
- of sizeN rows× 7 columns for seismic
- of sizeN × 9 for saturation, whereN is the number of template centers. Here
N = 477, 310.
The mean and variance of each column of these tables are calculated and the correspond-
ing column values are standardized to mean zero and unit variance.
The covariance matrix is calculated from each standardizeddata table; that matrix is
of size (7 × 7) for seismic, (9 × 9) for saturation.
Finally, PCA and/or CA is performed using these covariance matrices.
Output of PCA are:
- the percent contribution of each of the PC’s (7 for seismic,9 for saturation) to the
within-template variance.
- the linear combination weights (also called PC loads) defining each PC:
PCi =n∑
α=1
λ(i)α
Vα (3)
wherePCi is theith PC,λ(i)α are then weights,n is the number of dataVα in each
template (n = 7 for seismic,n = 9 for saturation).
8
- the 3D cube of PC-values, one cube per PC, from which PC-mapsand sections can
be plotted, see Figure 12.
Output of CA are:
- the weights for the pair of linear combinations which display the largest cross cor-
relation seismic vs. saturation:
CCseis =7∑
α=1
aαseisα (4)
CCSw =9∑
α=1
bαSwα
whereCCseis andCCSw are the1st canonical components of seismic and saturation
with maximum cross-correlation,aα andbα are the weights applied to the within-
template dataseisα andSwα, respectively.
- the 3D cube of CC values, one for seismic, one for saturation.
Application to 3D correlation (no time lapse)
PCA was applied to the data recorded on Jan.1, 2000, more precisely the 3D cube
of seismic amplitudeseis(i, j, k) and the corresponding 3D cube of vertical saturation
differencedSw(i, j, k) = Sw(i, j, k) − Sw(i, j, k − 1).
The1st seismic PC explains 84% of the within-template variance, while the1st satu-
ration difference PC explains only 59% of its template variance. The overall 3D point-to-
point correlation between these two first PC is 0.39, a value more reflective of the patterns
correlation seen between Figures 9 and 10. Those pattern correlations are less visually
clear on the two series of PC maps shown in Figures 12 (1st seismic PC) and 13 (1st
Sw-difference PC). Recall, however, that PC patterns on Figure 12 and 13 are “order 2
patterns”, being patterns of PC values which are already patterns summaries.
The same PCA was repeated on the data recorded on Jan.1, 2004.The resulting 3D
point-to-point correlation between the first PC’s of seismic amplitude and water saturation
vertical difference was found to be 0.32, an equally high value.
In preliminary conclusion, it appears that PCA succeeds to recognize some of the
patterns correlation existing between seismic attribute and vertical difference of spatially
averaged water saturation. That observation should be now checked on time difference of
both seismic and saturation data.
9
Application to 4D correlation (time lapse data)
The previous PCA and CA were repeated on now time lapse (difference) data. More
precisely,
- the 3D seismic data used is now a time difference of seismic amplitude:
δseis(i, j, k, t2, t1) = seis(i, j, k, t2) − seis(i, j, k, t1) (5)
- the 3D saturation data is the corresponding time difference of water saturation ver-
tical difference:
∆sw(i, j, k, t2, t1) = dSw(i, j, k, t2) − dSw(i, j, k, t1) (6)
with dSw(i, j, k, t) = Sw(i, j, k) − Sw(i, j, k − 1).
The reasons for using the vertical differencedSw instead ofSw in Eq.(6) are:
- 3D seismic amplitude shows the vertical contrast of water saturation, the variable
Sw itself does not carry such vertical contrast information.
- The overall 4D point-to-point correlation betweenδseis and water saturation time
differenceδsw is very poor around -0.07, and the pattern (first PC’s) correlation is
also poor around 0.3. That water saturation time differenceδsw is defined directly
from Sw as:
δsw(i, j, k, t2, t1) = Sw(i, j, k, t2) − Sw(i, j, k, t1)
The time lapse here considered is:t2 =Jan.1, 2004,t1 =Jan.1, 2000.
The1st seismic PC explained 53% of the within-template variance, while the1st sat-
uration PC explains 48% of its template variance. The overall 4D (actually 3D for time
difference) correlation between these two first PC’s is 0.78. This large correlation value
is a good omen for using time lapse seismic to monitor water saturation changes. Figures
14 and 15 gives the maps of these two first PC’s values over the 9stratigraphic reservoir
surfaces, these maps clearly show high visual correlationsbetween the seismic time lapse
and water saturation difference time lapse. The next best correlation is between the sec-
ond δseis PC and the second∆sw, which is a low -0.25, hence only the first PC’s were
retained.
10
Canonical analysis (CA) was applied to the two previous setsof time lapse data. The
resulting first pair of canonical components,CCseis(u) andCCsat(u), features a high
cross correlation of 0.82. The corresponding two series of CC maps are shown on Figures
16 and 17.
Pattern correlation between seismic and water volume
Because amplitude shows a vertical impedance contrast, which is a function of both
porosity and water saturation, one should look for the relationship between seismic am-
plitude and the water volume defined as the product of porosity φ and water saturation
Sw:
V ol(i, j, k) = Sw(i, j, k) × φ(i, j, k)
• 3D correlation Similar to the previous 3D correlation without time lapse, PCA
was applied to the 3D cube of seismic amplitude and the corresponding 3D cube of
vertical water volume difference defined as
dV ol(i, j, k) = V ol(i, j, k) − V ol(i, j, k − 1) (7)
The1st PC of water volume difference explains only 51% of its template variance,
and its point-to-point 3D correlation with the1st PC of seismic amplitude is 0.75, a
value much higher than the corresponding correlation between the two first PC’s of
water saturation difference and seismic amplitude. Figure18 shows the first PC of
water volume difference over 9 stratigraphic surfaces, to be compared with Figure
12.
The same PCA was repeated on the corresponding data recordedon Jan.1, 2004.
The resulting 3D correlation between the two first PC’s is 0.53, still an high value.
• 4D correlation PCA and CCA were repeated on the time lapse data of seis-
mic amplitude and water volume difference. The time difference of water volume
vertical difference is defined as:
∆V ol(i, j, k, t2, t1) = dV ol(i, j, k, t2) − dV ol(i, j, k, t1) (8)
with the vertical differencedV ol(i, j, k, t) at timet defined as in Eq.(7).
The previous time lapse step is considered witht2 =Jan.1, 2004,t1 =Jan.1, 2000.
The1st water volume PC explains 50% of its template variance. The point-to-point
11
4D correlation between the first two PC’s of seismic and watervolume is 0.70, a
value similar to the 4D correlation (0.78) found between thefirst two PC’s of seis-
mic and water saturation. Figure 19 gives the first PC of watervolume difference
over 9 stratigraphic surfaces.
CA was repeated on those two sets of time lapse data. The resulting first pair of
canonical components,CCseis(u) andCCV ol(u), features a equally high correla-
tion 0.78. The corresponding two series of CC maps are shown on Figures 20 and
21.
5 Conclusions
Because of their different resolution (different support volumes) the point-to-point corre-
lation between saturations and seismic time lapse might be low, although there may be
significant correspondence between spatial patterns of thetwo time lapse variables. A
spatial pattern, although immediately visible to the eye, is a complex statistical concept
involving multiple-points in space. Correlation between multiple-point data events is not
yet well understood nor does it exist any established measure for it.
The idea is to summarize a multiple-point data event, as defined within a fixed tem-
plate of points, by a few linear combinations of these point values. Traditional correla-
tion measures can then be applied to such linear combinations. The linear combinations
should be indicative of the within-template spatial patterns, and should display signifi-
cant cross-correlation between saturations and seismic time lapse variables. The linear
combinations provided by principal component analysis (PCA) comes to mind: by def-
inition, the first few principal components (PC’s) or linearcombinations explain a large
part of the within-template spatial variance. Because of that large variance contribution,
it is conjectured that PC’s are summaries of potential spatial patterns existing within the
template area. Another, more direct, approach is canonicalanalysis (CA) which seeks at
determining the two linear combinations (one for saturation, one for seismic time lapse)
with maximum cross-correlation independently of their respective within-template vari-
ance contributions.
Both PCA and CA were applied to the synthetic clastic Stanford V reservoir, where
both seismic and reference water saturation time lapse dataare available and pattern cor-
respondences are visually evident. The two sets of data (seismic and saturation) were
analyzed through the filters of their respective templates,vertical for seismic, 3D mim-
12
icking the Fresnel zone for saturation. Although the original point-to-point correlation
between the two time lapse variables was insignificant around 0.1, correlation of the two
first PC’s (one for seismic one for saturation) is high around0.7, a value more reflective of
the excellent visual patterns correspondence. Canonical analysis increases that correlation
up to almost 0.8.
In real practice, such proxies for spatial patterns correlation could be established from
simulated reservoirs on which 4D seismic is forward simulated. Such correlation could
be used to estimate or simulate time lapse saturation valuesusing observed PC’s or CC’s
values of seismic time lapse data. Geostatistics provides tools for estimating/simulating
a variable such as water saturation, conditional to linear combinations of another variable
(seismic time lapse data). This aspect of the study can now beaddressed, because we
have shown that, indeed, principal and/or canonical components do carry multiple-point
pattern information.
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13
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14
Porosity permeability (md) initial Sw
Channel sand 0.27 648
Crevasse 0.24 5210.15
Mudstone 0.07 1.5 0.3
All layer 0.17 314 N/G:0.53
Layer thickness [min=60m, max=283m], mean=152m
Depth to top of layer [min=612m, max=886m], mean=727m
Depth to bottom of layer [min=692m, max=1097m], mean=879m
Table 1: Stanford V, Layer 2, statistics
15
−5
0
5
x 10−4Section z=2
20 40 60 80100
20
40
60
80
100
120
−5
0
5
x 10−4Section z=3
20 40 60 80100
20
40
60
80
100
120
−5
0
5
x 10−4Section z=4
20 40 60 80100
20
40
60
80
100
120
−5
0
5
x 10−4Section z=5
20 40 60 80100
20
40
60
80
100
120
−1
−0.5
0
0.5
1
x 10−3Section z=6
20 40 60 80100
20
40
60
80
100
120
−1
−0.5
0
0.5
1
x 10−3Section z=7
20 40 60 80100
20
40
60
80
100
120
−1
−0.5
0
0.5
1
x 10−3Section z=8
20 40 60 80100
20
40
60
80
100
120
−1
−0.5
0
0.5
1
x 10−3Section z=9
20 40 60 80100
20
40
60
80
100
120
−1
0
1
x 10−3Section z=10
20 40 60 80100
20
40
60
80
100
120
Figure 1: Seismic amplitude time lapse (Jan.1, 2000 – Jan.1,2002) along stratigraphic
sections.
16
−0.4
−0.2
0
0.2
0.4
Section z=2
20 40 60 80100
20
40
60
80
100
120
−0.4
−0.2
0
0.2
0.4
Section z=3
20 40 60 80100
20
40
60
80
100
120
−0.4
−0.2
0
0.2
0.4
Section z=4
20 40 60 80100
20
40
60
80
100
120
−0.4
−0.2
0
0.2
0.4
Section z=5
20 40 60 80100
20
40
60
80
100
120
−0.4
−0.2
0
0.2
0.4
Section z=6
20 40 60 80100
20
40
60
80
100
120
−0.4
−0.2
0
0.2
0.4
Section z=7
20 40 60 80100
20
40
60
80
100
120
−0.5
0
0.5Section z=8
20 40 60 80100
20
40
60
80
100
120
−0.5
0
0.5Section z=9
20 40 60 80100
20
40
60
80
100
120
−0.5
0
0.5Section z=10
20 40 60 80100
20
40
60
80
100
120
Figure 2: Water saturation difference time lapse (Jan.1, 2000 – Jan.1, 2002) along strati-
graphic sections.
17
Figure 3: Reference porosity field with vertical stratigraphic coordinate.
18
top
stratigraphiccoordinates
s=0
s=1
613m
692m887m
1097m
283m
60m
depth(true coordinates)
0m
600m
1100m
Reservoirenvelope
Layer 2
i
12
4950
top of layer
bottom of layer
bottom of reservoir envelope
top of reservoir envelope
th(x,y,j)
dz=10m
P1(x,y,i1)
P2(x,y,i2)
10sub-layersz(x,y,j)
z(x,y,i)
Figure 4: Vertical section of the reservoir model.
19
a). mudstone
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
krw kro
rela
tive
perm
eabi
lity
water saturation
b). channel+crevasse
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
krw kro
rela
tive
perm
eabi
lity
water saturation
Figure 5: Relative permeability curves.
20
3-D oil saturation cube Oil saturation at layer 1
East
Nor
th
0.0 2500.000.0
3250.00
0.1500
0.2500
0.3500
0.4500
0.5500
0.6500
0.7500
0.8500
Oil saturation at layer 2
East
Nor
th
0.0 2500.000.0
3250.00Oil saturation at layer 3
East
Nor
th
0.0 2500.000.0
3250.00Oil saturation at layer 4
East
Nor
th
0.0 2500.000.0
3250.00
Oil saturation at layer 5
East
Nor
th
0.0 2500.000.0
3250.00Oil saturation at layer 6
East
Nor
th
0.0 2500.000.0
3250.00Oil saturation at layer 7
East
Nor
th
0.0 2500.000.0
3250.00
Oil saturation at layer 8
East
Nor
th
0.0 2500.000.0
3250.00Oil saturation at layer 9
East
Nor
th
0.0 2500.000.0
3250.00Oil saturation at layer 10
East
Nor
th
0.0 2500.000.0
3250.00
Figure 6: Oil saturation field on Dec. 29, 2013 before breakthrough.
21
Figure 7: Scattergrams of P velocity vs. porosity when saturated with 100%brine and
100% oil, in each of the 3 reservoir facies.
22
a). Facies distribution in NS vertical section at x=1
500 1000 1500 2000 2500 3000
0.45
0.5
0.55
0.6
0.65
0.7
0.75
distance
time
blue: mudstonered: crevassegreen: sandstone
b). Seismic amplitude in same section
time
distance0 500 1000 1500 2000 2500 3000
0.45
0.5
0.55
0.6
0.65
0.7
0.75
Figure 8: Facies and amplitude in North-South section at x=1.
23
Section z=2
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
Section z=3
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
Section z=4
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
0.02
Section z=5
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
Section z=6
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
Section z=7
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
Section z=8
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
Section z=9
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=10
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Figure 9: Seismic amplitude values over 9 stratigraphic surfaces (Jan.1, 2000, prior to
water injection).
24
b). Seismic amplitude in same sectionSection z=2
20 40 60 80100
20
40
60
80
100
120
−0.05
0
0.05
Section z=3
20 40 60 80100
20
40
60
80
100
120
−0.05
0
0.05
Section z=4
20 40 60 80100
20
40
60
80
100
120
−0.05
0
0.05
Section z=5
20 40 60 80100
20
40
60
80
100
120
−0.05
0
0.05
Section z=6
20 40 60 80100
20
40
60
80
100
120
−0.05
0
0.05
Section z=7
20 40 60 80100
20
40
60
80
100
120
−0.05
0
0.05
Section z=8
20 40 60 80100
20
40
60
80
100
120
−0.05
0
0.05
Section z=9
20 40 60 80100
20
40
60
80
100
120
−0.05
0
0.05
Section z=10
20 40 60 80100
20
40
60
80
100
120
−0.05
0
0.05
Figure 10: Vertical difference of spatially averaged watersaturation (Jan.1, 2000, prior to
water injection).
25
(b) Water saturation template
(a) Seismic template
X
Y
Z
W2(u,1),W2(u,2),W2(u,3)
W2(u,4),W2(u,5),W2(u,6)
k-1
k
k+1W2(u,7),W2(u,8),W2(u,9)
W1(u,1)W1(u,2)
W1(u,7)
k-3k-2
k+3
Z
X
Y
u(i,j) i+2i-2
j+2
j-2
W(u,1): value at
W(u,2): mean value over
W(u,3): mean value over
Figure 11: Moving templates considered for PCA and CCA. a) Vertical template for
seismic amplitude; b) 3D template for water saturation timedifference.
26
Section z=2
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=3
20 40 60 80100
20
40
60
80
100
120
−5
0
5
10Section z=4
20 40 60 80100
20
40
60
80
100
120
−5
0
5
10
Section z=5
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=6
20 40 60 80100
20
40
60
80
100
120
−5
0
5
10Section z=7
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=8
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=9
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=10
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Figure 12: First PC of seismic amplitude over 9 stratigraphic surfaces (Jan.1, 2000).
27
b). Seismic amplitude in same sectionSection z=2
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=3
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=4
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=5
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=6
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=7
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=8
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=9
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=10
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Figure 13: First PC values of water saturation vertical difference over 9 stratigraphic
surfaces (Jan.1, 2000).
28
Section z=2
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10Section z=3
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10Section z=4
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=5
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10
Section z=6
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10
Section z=7
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10
Section z=8
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10
Section z=9
20 40 60 80100
20
40
60
80
100
120
−10
0
10
Section z=10
20 40 60 80100
20
40
60
80
100
120
−10
0
10
Figure 14: First PC of seismic amplitude time lapse over 9 stratigraphic surfaces
(Jan.1, 2000 – Jan.1, 2004).
29
b). Seismic amplitude in same sectionSection z=2
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10
Section z=3
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10
Section z=4
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10
Section z=5
20 40 60 80100
20
40
60
80
100
120
−10
0
10
Section z=6
20 40 60 80100
20
40
60
80
100
120
−10
0
10
Section z=7
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10
Section z=8
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10
Section z=9
20 40 60 80100
20
40
60
80
100
120
−10
0
10
Section z=10
20 40 60 80100
20
40
60
80
100
120
−20
−10
0
10
20
Figure 15: First PC values of water saturation vertical difference time lapse over 9 strati-
graphic surfaces (Jan.1, 2000 – Jan.1, 2004).
30
Section z=2
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=3
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=4
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=5
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=6
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=7
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=8
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=9
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
0.02Section z=10
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
0.02
Figure 16: First CC of seismic amplitude time lapse over 9 stratigraphic surfaces
(Jan.1, 2000 – Jan.1, 2004).
31
b). Seismic amplitude in same sectionSection z=2
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=3
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=4
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=5
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=6
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=7
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=8
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=9
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=10
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
0.02
Figure 17: First CC values of water saturation vertical difference time lapse over 9 strati-
graphic surfaces (Jan.1, 2000 – Jan.1, 2004).
32
b). Seismic amplitude in same sectionSection z=2
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=3
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=4
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=5
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=6
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=7
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=8
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=9
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Section z=10
20 40 60 80100
20
40
60
80
100
120
−5
0
5
Figure 18: First PC values of water volume vertical difference over 9 stratigraphic sur-
faces (Jan.1, 2000).
33
Section z=2
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10
Section z=3
20 40 60 80100
20
40
60
80
100
120
−10
0
10
Section z=4
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10
Section z=5
20 40 60 80100
20
40
60
80
100
120
−10
0
10
Section z=6
20 40 60 80100
20
40
60
80
100
120
−10
0
10
Section z=7
20 40 60 80100
20
40
60
80
100
120
−10
0
10
Section z=8
20 40 60 80100
20
40
60
80
100
120
−10
−5
0
5
10
Section z=9
20 40 60 80100
20
40
60
80
100
120
−10
0
10
Section z=10
20 40 60 80100
20
40
60
80
100
120
−20
−10
0
10
20
Figure 19: First PC of water volume difference time lapse over 9 stratigraphic surfaces
(CCA on seismic and water volume vertical difference, Jan.1, 2000 – Jan.1, 2004).
34
Section z=2
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=3
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=4
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=5
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=6
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=7
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=8
20 40 60 80100
20
40
60
80
100
120
−0.01
−0.005
0
0.005
0.01
Section z=9
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
0.02
Section z=10
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
0.02
Figure 20: First CC of seismic amplitude time lapse over 9 stratigraphic surfaces
(CCA on seismic and water volume vertical difference, Jan.1, 2000 – Jan.1, 2004).
35
b). Seismic amplitude in same sectionSection z=2
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=3
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=4
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=5
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=6
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
0.02
Section z=7
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=8
20 40 60 80100
20
40
60
80
100
120
−0.01
0
0.01
Section z=9
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
0.02
Section z=10
20 40 60 80100
20
40
60
80
100
120
−0.02
−0.01
0
0.01
0.02
Figure 21: First CC values of water volume vertical difference time lapse over 9 strati-
graphic surfaces (CCA on seismic and water volume vertical difference, Jan.1, 2000 –
Jan.1, 2004).
36
