Modeling the Impact of Subseismic Scale Fractures on
Macroscale Block properties and flow performance
Yongshe Liu and André G. Journel
Stanford Center for Reservoir Characterization
May, 2004
Abstract
In this paper, a method to simulate subseismic scale fractures and evaluate their
impact on flow performance is proposed. A representative panel is retrieved for each
geologically distinct reservoir unit. Small scale fractures are then simulated within
the panel and their impact on flow simulation block effective properties is assessed.
The resulting statistics are then extended to the entire unit and simulation of flow
performance is performed over that unit. As expected, the simulated fracture porosity
has little impact on the total effective porosity, but the simulated fracture
permeability has a significant impact on the total effective permeability and flow
performance. The impact of fractures on fluid flow is studied for both primary
depletion and water injection.
1
1. Introduction and major Results
Subseismic scale fractures, more precisely joints (Helgenson and Aydin, 1991), are
prevalent in most reservoirs, whether clastic or carbonate, yet their impact on macroscale
permeability is poorly known although expected to be significant. This study suggests a
workflow for simulating such fracture characteristics, and evaluates their impact on flow
simulation-scale block porosity and permeability then on flow performance. If, as
expected, fracture porosity has little impact on the total effective porosity, the fracture
permeability has a significant impact on effective permeabilities, both in terms of
anisotropy and magnitude, with a consequent significant impact on flow performance and
recovery results.
Since simulation over the whole reservoir of all elementary subseismic scale fractures is
not possible - this would require discretizing a medium size 3D reservoir with some 109
cells – the approach proposed is to limit that fine scale simulation to a few representative
panels, say, one panel per major and significantly different reservoir unit. The
characteristics of the fractures (orientation, aperture, spacing, length) are simulated in
great detail at spacing 2.5m.×2.5m.×4m. within each such panel, then averaged into
effective porosities and permeabilities for the blocks constituting each panel (in this case
study, there are 12×12×10=1,440 blocks per panel). The spatial statistics (histograms,
correlation coefficients and variograms) of these calibration blocks are then retrieved, and
they are used to simulate directly the block effective properties over the entire reservoir
unit represented by the panel considered.
In short, the full 3D reservoir numerical model accounting for small scale fractures is
built as an assemblage of a not too large number (<106) of blocks effective properties.
These block effective properties are geostatistically simulated from block-scale spatial
statistics derived from calibration data. These calibration block effective properties can
be simulated over a very limited number (<5) of representative panels, each panel being
representative of a geologically distinct reservoir unit. The fine scale simulation of
fractures geometry and characteristics is limited to within these panels, and averaged into
2
the calibration block effective properties. The flowchart of Figure 1 summarized the
proposed workflow, explained in greater detail in section 3 of this paper.
Major Results
The channel facies, within which fractures are simulated, are divided into two sub-facies:
good channel sand and border channel sand, the latter including channel border and
levee. Each sub-facies is studied separately given their specific characteristics and the
data available.
The sub-seismic scale fracture aperture and fracture spacing are simulated within a
calibration panel and the resulting fracture total effective porosities are retrieved. As
expected, the fractures increase only slightly the total porosity.
The fracture permeability is simulated using Parsons’ relation (Parsons, 1966), resulting
in the histograms on the top row of Figure 2, to be compared with the original histograms
of matrix permeability on the 2nd row. The impact of fracture on the total permeability is
significant. The crossplots of fracture permeability vs. fracture porosity show log-log
relationship (Figure 3).
The impact of fractures on flow is studied for two simulation scenarios: primary
depletion and water injection. For the primary depletion scenario under low rate control,
cumulative oil production is unaffected by the fractures, see Figure 4, case 1. This is not
any more the case with a higher rate control case (Figure 4, case 2). The results are
significantly different in the case of bottom hole pressure (BHP) control, see Figure 4,
case 3. This demonstrates the potential impact of small scale fractures on production at
the early stage of depletion. The fractured model can lead to longer production times at
the constant target rate, although with a sharper production decrease rate when the BHP
reaches its constraint (Figure 4b and e).
For the water injection scenario, if both the injector and producer are located in a sandy
and well connected channel area, the fluid moves faster along the high-permeability
3
fractured channels. Although the fractured model is produced at a lower oil production
rate, it still leads to an earlier breakthrough, see the top graph of Figure 5. The oil sweep
efficiency for the fractured model is not as good as for the matrix model, resulting in a
lower cumulative oil production (middle graph of Figure 5). The BHP of the matrix
model increases faster because of the lower permeability of the matrix model (bottom
graph of Figure 5).
2. The Stanford V reservoir
Stanford V is a large 3D synthetic numerical model of a fluvial reservoir (Mao and
Journel, 1999). It includes 3 major units (layers). Each unit is discretized into
100×130×10 blocks informed with multiple petrophysical properties. The physical size of
each block is 25m×25m×1/10th of the unit thickness, which average is 200m. The ten
stratigraphic sub-units of each unit in the vertical direction are called sublayers. Our
study will focus on the sole unit 1. The original facies types, porosity, permeability,
velocity, density and impedance models are given in Figure 6. These models are
considered as the matrix models.
Select and densify a representative panel
The fracture calibration study is limited to a representative panel of size 12×12×10=1440
blocks. Figure 7 gives the facies distribution over the ten horizontal stratigraphic sections
of unit 1. Fracturation is deemed limited to the 3 sand facies, good channel sand, border
channel and levee. The physical size of the panel selected is 300m×300m×about 200m
(the vertical thickness varies from 125 m. to 405 m.).
Because the original Stanford V block size (25m.×25m.×20m.) is much larger than the
small scale of the fractures, we had to densify the block properties. Each block is
discretized into 10×10×5 cells, with each cell size being about 2.5m×2.5m×4m. The total
number of cells in the panel is thus 1440×500=720,000. The initial block matrix
properties (facies, porosity, permeability, etc) are directly copied into the cell scale
4
without any further interpolation. These are now considered as the cell matrix properties
as opposed to the fracture properties to be simulated.
3. Fracture characteristics simulation
In this study, we assume the micro-scale fractures to have constant orientation, their
planes being vertical and along the major channel orientation. The fracture lengths are set
to be equal to the local cell thickness (4m.). The fractures are thus terminated by the 10
sublayer surfaces. Fracture aperture and fracture spacing remain to be simulated.
Fracture aperture simulation in the panel
Fracture aperture, that is the fracture width, is related to confining pressure, lithologies
and grain size. Generally, the aperture decreases as the pressure increases. Stanford V is a
shallow reservoir with depth varying from 150 m to 600 m. The aperture range of such
shallow buried fractures is from 1.0×10-3 cm to 0.5 cm (Nelson, 2001). The distribution
of fracture aperture is typically log-normal. Therefore, we chose for aperture a lognormal distribution with mean 0.01 cm and standard deviation 0.004 for good channel
sand, and a log-normal distribution with mean 0.02 cm and standard deviation 0.006 for
border channel and levee.
The fracture aperture variogram model is based on the channel spatial geometry within
the panel. The major channel orientation ( hx ) was taken for direction of maximum
continuity. The variogram model retained for fracture aperture is spherical:
2
2
2 

 h x   h y   hz  

γ = 0.05 + 0.95 × sph 
 + 
 +
  220   125   50  


(1)
with long range 220 in the major channeling direction hx .
Next using Sequential Gaussian Simulation (Deutsch and Journel, 1998, pp. 144-146), we
simulated fracture aperture within good channel sand and border channel separately. The
resulting fracture aperture models and histograms are shown in Figure 8.
5
Fracture spacing simulation
Fracture spacing is affected by several geological parameters: composition, grain size,
porosity and bed thickness. Generally, the fracture spacing increases as porosity and layer
thickness increase (Nelson, 2001). Based on published sand fracture statistics (Bogdanov
1947, Wu 1994), we chose for fracture spacing a log-normal distribution with mean 0.1
m and standard deviation 0.03 for good channel sand, and a log-normal distribution with
mean 0.08 m and standard deviation 0.03 for border channel. The same variogram used
for fracture aperture, see expression (1), was retrieved.
Because fracture spacing is related to layer thickness, the fracture spacing simulation was
made conditional to the thickness data by using the co-located cell thickness as secondary
data (Goovaerts, 1997, pp. 235-241). Sequential Gaussian Simulation (SGS) with
colocated cokriging was performed with a positive 0.6 correlation coefficient between
fracture spacing and cell thickness. Figure 9 shows the cell thickness model, the
simulated fracture spacing and histogram for the two sand facies.
Upscale fracture aperture and spacing
The cell fracture aperture and spacing are upscaled into block values. A cell volumeweighted arithmetic average is used:
N
F B = ∑ Fi C × viC
(2)
i =1
where F B is the fracture aperture (or spacing) at the block scale, F C is the previously
simulated fracture aperture (or spacing) at the cell scale, N is the number of cells and viC
is the cell volume. The upscaled fracture aperture and spacing models and their
histograms for the two sand facies are shown in Figure 10 and 11.
Extend simulation to entire unit
The previous statistics obtained within the calibration panel are extended to the entire
unit. Block scale fracture aperture was simulated within each of the 2 sand facies using
Sequential Gaussian Simulation (SGS). Block scale fracture spacing is simulated using
colocated co-kriging conditional to the layer thickness. As a result, in each block over the
6
entire reservoir unit we have now a simulated fracture aperture and fracture spacing
values.
4. Effective block properties simulation
The block effective properties (porosity and permeability) are retrieved from the original
matrix values and the previously simulated block scale fracture characteristics.
Porosity
The block fracture porosity is simply calculated as:
φf =
e
D+e
(3)
where φ f is the fracture porosity, e is the fracture aperture and D is the fracture spacing.
The total effect porosity φ t is then obtained by combining the matrix porosity φ m and
fracture porosity φ f :
φ t = φ f + (1 − φ f )φ m
(4)
Generally, the fracture porosity is less than 0.5%. Because the fracture aperture is so
small, the average fracture porosity values in the two facies (0.1% for good channel sand
and 0.29% for channel and levee) are much smaller than the matrix porosity (28.7% for
good channel sand and 25.5% for border channel), recall from Figure 2. Consequently,
the total porosity distributions are almost identical to the distributions of matrix porosity.
Thus Equation (4) reduces to:
φ total ≈ φ matrix
(5)
Although the fracture porosity is negligible compared to the matrix porosity, its
simulation is necessary to condition the simulation of fracture permeability and other
fracture properties.
7
Permeability
Parsons’ equation is used to calculate the cell fracture permeability (Parsons, 1966):
e 3 cos 2 α
k f = km +
12 D
(6)
where k f is the fracture permeability, k m is the matrix permeability and α is the angle
between the axis of the pressure gradient and the fracture planes, e and D are as defined
in expression (3).
There are several assumptions underlying this equation. First, it is suitable only for
laminar flow between smooth and parallel plates. Second, fluid flow across any
fracture/matrix surface is assumed not to alter the flow within either the fracture or the
matrix system. Third, the fracture distribution is assumed homogeneous as for its
orientation, length and spacing. Fourth, the surface roughness is small relative to the
fracture spacing. In our study, the cell size is small, so fracture properties within it can be
considered as homogeneous. We assume the other conditions to be satisfied also. In
addition, we assume the angle α equal to 0 corresponding to a constant fracture
orientation, thus the pressure gradient is parallel to fracture planes. The effective fracture
permeability can then be obtained from e and D through equation (6). The fracture
aperture appears as a cubed term in this expression, which indicates that a small increase
of fracture aperture will increase fracture permeability dramatically.
Permeability was then simulated as follows (see the right column of Figure 1).
1. Simulate the cell fracture permeability within the panel, using expression (6).
2. Uspscale the cell fracture permeability into block fracture permeability using a
geometric average to get the distribution of fracture permeability, see the
histograms of upscaled permeability for both facies on the top of Figure 12.
3. Cross plot fracture permeability versus the corresponding fracture porosity, and find
the correlation, see the bottom graphs of Figure 12.
4. From the statistics obtained in steps 2 and 3, simulate the fracture block
permeability over the entire reservoir unit, using colocated cokriging conditional on
the previously simulated block scale fracture porosity.
8
Finally, we combine the matrix permeability (histogram shown in the middle row of
Figure 2) with the fracture permeability to get the block total permeability, see
histograms at the bottom of Figure 2. The average fracture permeabilities (1.19 Darcy for
good channel sand and 11.24 Darcy for border channel) are much larger than the matrix
permeabilities (0.432 mD for good channel sand and 0.353mD for border channel).
Therefore, the fractures will be the dominant flow conduit. The crossplot of fracture
permeability vs. fracture porosity has been shown in Figure 3.
Fractures cause spatial anisotropy of permeability. For open fracture, the permeability is
much higher along the fracture planes. Here we assume the effective permeability across
the fracture plane to remain equal to the matrix permeability because the fracture aperture
is so small, of the order of the size of matrix pore (Nelson, 2001). Fracture permeability
is also related to the angle α between the axis of the pressure gradient and the fracture
planes; that angle was here considered constant, recall discussion of expression (6)..
Seismic Velocity (not developed here)
The impact of fractures on seismic velocity was studied using Hudson’s Model (Hudson,
1981). The main result is that fractures cause an anisotropy of seismic velocity and a Swave splitting. These two impacts could make possible the detection of such fractures
from seismic data.
5. Impact on flow simulation
In this section, two production scenarios, primary depletion and water injection, are
studied to evaluate the impact of the previously simulated small scale fractures.
Primary depletion
A dead oil model was considered, with typical PVT relations for oil and water. The initial
pressure at the top of the reservoir is set at 4000 psi. The well is located in block (33, 39),
see Figure 13. The net to gross ratio at the well location is 0.7, see the top graph of Figure
13. Several continuous channels intersect this well, see the bottom two graphs of Figure
9
13. In the original matrix model, the average porosity and permeability of this well are
0.27 and 217 md. In the fractured model, the well porosity and permeability increase to
0.31 and 2567 md. The fractures result in a small increase of porosity, but a large
increase of permeability. We assume the fracture planes to be in the y-z general direction
of channeling. Therefore, in the fractured model, the permeability in the y and z
directions are the fractured effective permeability, the permeability in the perpendicular x
direction is left equal to the original matrix permeability.
Flow simulations are run for the 3 following cases using the Eclipse simulator
(GeoQuest, version 22-01):
• Case 1: relatively low well oil production rate control: 1000 stb/day;
• Case 2: relatively high well oil production rate control: 4000 stb/day;
• Case 3: Bottom Hole Pressure constraint: BHP =1000 psi.
The resulting production curves: cumulative oil production, oil production rate and BHP,
for these 3 cases, were shown in Figure 4. As stated previously, the cumulative oil
production curves corresponding to the fracture model and the matrix model for case 1
are almost identical (Figure 4a); they are different for case 2 (Figure 4d) and significantly
different for case 3 (Figure 4g). The reason is that the fractures increase considerably the
permeability in the channels, thus fluid moves much more easily along the fractured
channels than along matrix channels. As production proceeds, the pressure at the well
location drops. Away from the well, the pressure drop is slower. With the higher fracture
permeability, the pressure difference between the well and the remainder of the reservoir
is smaller; it thus takes a shorter time to reduce that pressure difference in the fractured
model than in the matrix model. If the well produces at low rate, the impact of the high
permeability model in the early stage (say the first three years) is negligible, see Figure
4a. If the well produce at a high rate, that impact becomes significant, see Figure 4d. If a
constant BHP is imposed, the oil production rate in the fractured model is much higher
than that in the matrix model in the early stage, see Figure 4g and h. This will result in a
cumulative oil production very different between fractured model and matrix model.
10
From Figure 4b and e, we can see that the fractured model can produce over a longer
period at the constant rate, ending into a sharper production decrease rate than the matrix
model when the BHP reaches its constraint. This is favorable for oil production.
Figure4c, f and i give the pressure curves for the 3 production scenarios. In the first 2
cases, the pressure of the matrix model has to drop faster to maintain the target oil rate.
Water injection
We consider 2 cases to study the impact of fracture on water injection. These 2 cases
correspond to different locations for the producer and injector. In case 1, the producer
(45,126) and the injector (33, 39) are located in sandy locations with respective net-togross ratios of 60% and 70%. In case 2, the producer (34, 126) and the injector (26, 33)
are located in shaly areas with respective net-to-gross ratios of 30% and 40%. In both
cases, the water injection rate is set equal to the oil production rate.
In the first case, the BHP constraint set at 2,000 psi. The oil rate for matrix model is
4,000 stb/day and the oil rate for fractured model is 3,000 stb/day. The production curves
were given in Figure 5. The reason for the early breakthrough of the fracture model is
that the fluid can easily move along the fractured high-permeability channels.
Consequently, the oil sweep efficiency for the fractured model is not as good as for the
matrix model, and the resulting cumulative oil production is lower (middle graph of
Figure 5). The BHP of the matrix model increases faster because of the low permeability
of the matrix model (bottom graph of Figure 5).
In the second case, the BHP constraint set at 2,000 psi and the target oil production rate
set at 2,000 stb/day. Figure 14 shows the production curves. As expected, the BHP of the
matrix model drops slightly faster (bottom graph of Figure 14). The BHP pressure does
not increase as those in the first case (Figure 15 bottom graph) because the BHP of the
producer can not quickly response to the water injection due to the relatively low
permeability around the injector and the producer wells. The target oil rate of the matrix
model can not be maintained shortly before the 5th year (red curve in the top graph of
11
Figure 14) due to the low permeability around producer in the matrix model. The
fractured model can produce at the target rate for a longer time but has an earlier
breakthrough time (about the 12th year) than the matrix model (about the 14th year). This
causes only slight difference in the cumulative oil production curves (middle graph of
Figure 14). Figure 15 shows the water saturation of the two models at level K=10 in the
6th year. We find that the water tends to flow along the channels, faster in the fractured
model. The water saturation map displays more local heterogeneity (fingers) in the
fractured model.
6. Conclusions
A workflow has been proposed to simulate the impact on flow performance of subseismic
scale fractures. A representative calibration panel for each different reservoir is selected,
then fracture aperture, spacing and permeability at small scale is simulated, then
upscaled. The panel statistics are extended through simulation to the entire reservoir unit
yielding the block effective properties needed for flow simulation.
As expected, the contribution of fracture porosity is negligible. The fracture porosity,
however, contributes as conditioning data for the simulation of fracture permeability. The
contribution of the simulated fracture permeability is now significant. The fractures result
in higher total permeability and a fracture anisotropy. Along the fracture plane, the
effective permeability is significantly increased.
The significant increase in fracture permeability in sand along the direction of channeling
has major impact on fluid flow and hydrocarbon recovery. In a primary depletion
scenario, the fractured mode leads to greater productivity under a high oil rate control. In
a water injection scenario, the fracture impact depends on whether the injector-producer
intersect a channel conduit or not, with in the first case faster breakthrough and less oil
recovery (poorer sweep).
12
The impact of small scale, subseismic fractures thus could not be ignored. This study
proposes a workflow for their study.
Acknowledgements
The authors wish to acknowledge the contribution of Professor Atilla Aydin from the
Geomechanics program in the Department of Geological and Environmental Sciences,
Professor Lou Durlofsky in the Petroleum Engineering Department, Dr Tapan Mukerji in
the Geophysics Department, Dr. Guillaume Caumon from Ecole de Geologie in Nancy,
France, and Joe J. Voelker, PhD candidate in the Petroleum Engineering Department.
References
1. Parsons, R. W., 1966, “Permeability of Idealized Fractured Rock,” Society of
Petroleum Engineering Journal, pp. 126-136.
2. Huitt, J. L., 1956, “Fluid Flow in Simulated Fractures”, AICbE Journal, Vol. 2, 259.
3. Nelson, R. A., 2001, Geologic Analysis of Naturally Fractured Reservoirs, Gulf
Professional publishing, 64-75 pp.
4. Aziz, K., Settari, A., 2002, “ Petroleum Reservoir Simulation”, Calgary.
5. Mao, S. & Journel, A., 1999, “Generation of a reference petrophysical/seismic data
set: the Stanford V Reservoir”, in ’Report 12, Stanford Center for Reservoir
Forecasting’, Stanford, CA.
6. Helgeson, D.E., Aydin, A., 1991, “Characteristics of Joint Propagation Acrss
interfaces in Sedimentary rocks”, Journal of Structure Geology, Vol. 13, No.8, pp.
897 to 911.
7. Deutsch, C.V., Journel, A.G., 1998, “GSLIB: Geostatistical Software Library and
User’s Guide,” 2nd ed., Oxford Press, NY.
13
8. Goovaerts, P., 1997, “Geostatistics for Natural Resources Evaluation,” publ, Oxford
Press, N.Y.
9. Alvarez, A. L., 2000, “fractured Reservoirs: Concepts and Case Studies,”, MS thesis,
The University of Texas at Austin, TX.
10. Wu, H., Pollard, D. D., 1994, “An Experimental Study of the Relationship between
Joint Spacing and Layer Thickness,”, Journel of Structure Geology.
11. Renshaw, C. E., Polland, D. D., 1994, “Numerical Simulation of Fracture Set
Formation:
A
Fracture
Mechanics
Model
Consistent
with
Experimental
Observations,” Journel of Geophysical Research, Vol. 99, No. B5, pp. 9359-9372.
14
Retrieve a typical panel (2 facies)
(300m×300m × single unit total thickness)
Simulate cell FA and FS.
(2.5m × 2.5m × 4m)
Calculate cell perm.
within the panel
Upscale to get
block FA and FS
Simulate
block por.
in the panel
Average to get
effective block
frac. perm
Get statistics of block
FA and FS in panel
Get correlation
between por. and
perm in panel
Simulate block FA
and FS in the unit
Simulate block frac.
perm. collocated with
frac. por
Simulate frac. por.
within the unit
Calculate total effective
block perm. in the unit
Calculate total effective
block porosity in the unit
Figure 1: Workflow for simulating effective fracture porosity and permeability
FA: fracture aperture, FS: fracture spacing
15
Good channel sand
no.=13131
mean=1.19 D
std=1.25
Matrix
no.=13131
mean=1.63 D
std=1.31
Border channel
Fracture
Fracture
no.=13131
mean=0.432D
std=0.398
Matrix
Total
Total
no.=26821
mean=11.24 D
std=10.85
no.=26821
mean=0.353 D
std=0.357
no.=26821
mean=11.60D
std=10.84
Figure 2: Histograms of fractured, matrix and total permeability
16
Good channel sand
Correlation coefficient: 0.912
Log. of fracture permeability (Darcy)
Logarithm of fracture porosity
Border channel
Correlation coefficient: 0.912
Log. of fracture permeability (Darcy)
Logarithm of fracture porosity
Figure 3: Crossplots of fracture permeability vs fracture porosity for two facies
17
Case 1: oil rate control (1,000 stb/day)
1200
(b) Oil production rate
(a) Cumulative oil production
1000
2000000
WWOPR(STB/day)
Culmulative oil production (STB)
2500000
1500000
Fractured
Matrix
1000000
500000
800
600
Fractured
Matrix
400
200
0
0
0
1
2
3
4
5
6
Time(year)
7
8
0
9
4500
1
2
3
4
5
6
7
8
9
Time(year)
(c) Bottom Hole Pressure
4000
3500
Fractured
Matrix
BHP(psi)
3000
2500
2000
1500
1000
500
0
0
1
2
3
4
5
6
7
8
9
Time(year)
2500000
4500
(d) Cumulative oil production
(e) Oil production rate
4000
2000000
3500
WOPR(STB/day)
Culmulative oil production (STB)
Case 2: oil rate control (4,000 stb/day)
1500000
Frcture
Matrix
1000000
3000
Fracture
Matrix
2500
2000
1500
1000
500000
500
0
0
0
1
2
3
4
Time(year)
0
5
1
2
3
4
5
6
Time(year)
4500
4000
(f) Bottom Hole Pressure
3500
Fracture
Matrix
BHP(psi)
3000
2500
2000
1500
1000
500
0
0
1
2
3
4
5
Time(year)
120000
2500000
(g) Cumulative oil production
(h) Oil production rate
100000
2000000
Fractured
Matrix
80000
STB/day
1500000
1000000
Fractured
Matrix
60000
40000
500000
20000
0
0
0
1
2
3
4500
Time (year)
4
5
0
0.5
1
1.5
2
(i) Bottom Hole Pressure
4000
Matrix
2.5
3
3.5
4
Time(year)
Fracture
3500
3000
BHP(psi)
Culmulative oil production (STB)
Case 3: BHP control (1,000 psi)
2500
2000
1500
1000
500
0
0
1
2
3
4
5
Time(year)
Figure 4: Primary depletion production curves for three scenarios
18
4.5
5
Well Oil Production Rate
4500
4000
3500
WOPR
3000
2500
2000
matrix
fractured
1500
1000
500
0
0
1
2
3
4
5
6
7
8
9
10
9
10
Time(year)
Culmulative oil production
14000000
Culmulative Oil production (stb)
12000000
matrix
fractured
10000000
8000000
6000000
4000000
2000000
0
0
1
2
3
4
5
6
7
8
Time(year)
Bottom Hole Pressure
4500
4000
3500
BHP
3000
2500
matrix
fractured
2000
1500
1000
500
0
0
1
2
3
4
5
6
7
8
9
10
Time(day)
Figure 5: Water injection production curves (wells in sandy area)
19
Facies
Porosity
Permeability
Velocity
Density
Impedance
Figure 6: Original Stanford V matrix property models
20
k=1
k=5
k=9
k=2
k=3
k=6
k=4
k=7
k=8
k=10
Good channel sand
Channel border
Levee
Shale
Crevasse
Figure 7: Horizontal facies sections of unit 1
21
Border channel
Good channel sand
no.=144,000
mean=0.01 cm
std=0.004
no.=257,000
mean=0.02cm
std=0.006
Figure 8: Simulated cell fracture apertures and corresponding histograms
22
Border channel
Good channel sand
Collocated cell thickness
Simulated fracture spacing
no.=257,000
mean=0.082m
std=0.035
no.=144,000
mean=0.104m
std=0.033
Figure 9: Simulated cell fracture spacing and corresponding histograms
23
Good channel sand
Border channel
no.=514
mean=0.02cm
std=0.005
no.=288
mean=0.01cm
std=0.0035
Figure 10: Upscaled block fracture aperture
Good channel sand
Border channel
no.=514
Mean=0.08m
std=0.032
no.=288
mean=0.1m
std=0.029
Figure 11: Upscaled block fracture spacing
24
Good channel sand
Border channel
no.=288
mean=1.15D
std=1.15
no.=514
mean=11.04D
std=9.59
Fracture permeability
Fracture permeability
Log. of fracture permeability
Correlation coefficient: 0.87
Correlation coefficient: 0.91
Logarithm of fracture porosity
Figure 12: Histograms of upscaled block fracture perm and crossplot of fracture
permeability vs porosity
25
Producer facies
N/G=0.875
Producer location (33,39)
Fractured effective perm
sub-layer 10
Producer location (33,39)
Fractured effective perm
sub-layer 5
Figure 13: Producer location for the primary depletion scenario
26
Well Oil Production Rate
2500
WOPR(std/day)
2000
1500
Fractured
Matrix
1000
500
0
0
2
4
6
8
10
12
14
Time(year)
Cumulative Oil Production
12000000
fractured
matrix
8000000
6000000
4000000
2000000
0
0
2
4
6
8
10
12
14
Time(year)
Bottom Hole Pressure
4500
4000
Fractured
3500
matrix
3000
BHP(psi)
FOPT(std/day)
10000000
2500
2000
1500
1000
500
0
0
2
4
6
8
10
12
14
Time(year)
Figure 14: Production curves of water injection (wells in shaly area)
27
Fractured model
Matrix model
Water saturation at level K=10 in 6th year
Facies slice at K=10
Figure 15: Water saturation and facies slices at level K=10
28