U.S. patent application number 13/779681 was filed with the patent office on 2013-09-19 for system and method for characterizing a flow property of a production well site in a reservoir.
This patent application is currently assigned to University of Southern California. The applicant listed for this patent is Ira Ershaghi, Yen Ting LIN, Antonio Ortega, Tayeb Ayatollahy Tafti. Invention is credited to Ira Ershaghi, Yen Ting LIN, Antonio Ortega, Tayeb Ayatollahy Tafti.
Application Number | 20130245952 13/779681 |
Document ID | / |
Family ID | 49158425 |
Filed Date | 2013-09-19 |
United States Patent
Application |
20130245952 |
Kind Code |
A1 |
LIN; Yen Ting ; et
al. |
September 19, 2013 |
SYSTEM AND METHOD FOR CHARACTERIZING A FLOW PROPERTY OF A
PRODUCTION WELL SITE IN A RESERVOIR
Abstract
A method and system of characterizing a flow property of a
production well site in a reservoir are provided. The method
includes identifying a plurality of injection and production well
sites in the reservoir; injecting fluid into selected injection
well sites in accordance with an injection schedule; monitoring an
output at the production well sites; determining a time delay
between the selected injection sites and the production sites based
on the monitored output using an estimated capacitance model; and
characterizing a flow property of a production well site using the
time delay and the estimated capacitance model.
Inventors: |
LIN; Yen Ting; (Los Angeles,
CA) ; Ortega; Antonio; (Los Angeles, CA) ;
Tafti; Tayeb Ayatollahy; (Los Angeles, CA) ;
Ershaghi; Ira; (Los Angeles, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
LIN; Yen Ting
Ortega; Antonio
Tafti; Tayeb Ayatollahy
Ershaghi; Ira |
Los Angeles
Los Angeles
Los Angeles
Los Angeles |
CA
CA
CA
CA |
US
US
US
US |
|
|
Assignee: |
University of Southern
California
Los Angeles
CA
|
Family ID: |
49158425 |
Appl. No.: |
13/779681 |
Filed: |
February 27, 2013 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
13738634 |
Jan 10, 2013 |
|
|
|
13779681 |
|
|
|
|
61586370 |
Jan 13, 2012 |
|
|
|
Current U.S.
Class: |
702/12 |
Current CPC
Class: |
E21B 43/20 20130101;
E21B 49/008 20130101 |
Class at
Publication: |
702/12 |
International
Class: |
E21B 49/00 20060101
E21B049/00 |
Claims
1. A method of characterizing a flow property of a production well
site in a reservoir, the method comprising: identifying a plurality
of injection and production well sites in the reservoir; injecting
fluid into selected injection well sites in accordance with an
injection schedule; monitoring an output at the production well
sites; determining a time delay between the selected injection
sites and the production sites based on the monitored output using
an estimated capacitance model; and characterizing a flow property
of a production well site using the time delay and the estimated
capacitance model.
2. The method according to claim 1, wherein the flow property
comprises a production rate of the production well site.
3. The method according to claim 1, further comprising using the
time delay in the estimated capacitance model to detect higher
permeability channels within a rock formation between the injection
well sites and the production well sites.
4. The method according to claim 3, further comprising uniformly
locating the injection and production well sites to enhance
detection of the higher permeability channel.
5. A system of characterizing a flow property in a production well,
the system comprising: a processor configured to: determine a time
delay between selected injection sites and selected production
sites based on a monitored output at the production well sites
using an estimated capacitance model, wherein fluid is injected
into selected injection well sites in accordance with an injection
schedule while an output is monitored at the production well sites;
and characterize the flow property of a production well site using
the time delay and the estimated capacitance model.
6. The system according to claim 5, wherein the flow property
comprises a production rate of a production well site.
7. The system according to claim 5, wherein the processor is
further configured to use the time delay in the estimate
capacitance model to detect higher permeability channels within a
rock formation between the injection well sites and the production
well sites.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] The present application is a Continuation-in-Part
Application of U.S. patent application Ser. No. 13/738,634 filed on
Jan. 10, 2013 which is based on and claims priority to U.S.
Provisional Patent Application No. 61/586,370, filed on Jan. 13,
2012. The entire content of which is incorporated herein by
reference.
BACKGROUND
[0002] 1. Field
[0003] The present invention relates generally to modeling
reservoir characteristics and more particularly to detection or
prediction of shale discontinuities based on reservoir flow
data.
[0004] 2. Background
[0005] A good geological model is critical to model the fluid flow
in a waterflood project. Especially when we have limited water
resources, the choices of injecting locations can become an
important issue in waterflood management. For a layered reservoir
with interlayer cross flow, the earlier depletion of the higher
permeability layer is predictable. In this situation, it may be
useful to change the injection schedule to enhance the oil recovery
in the lower permeability layer. To achieve this goal, identifying
the shale discontinuities can be helpful in modeling cross layer
fluid flow.
[0006] In the past few decades, many different methods have been
developed to estimate the parameters for layered reservoir. Seismic
crosshole tomography (Chapman and Pratt, 1992) can provide very
high resolution results if enough sensors are installed. Tracer
tests (Vasco et al. 1999) are also widely used to investigate the
flow property in the reservoir.
[0007] However, all of the above methods require additional cost
and may interrupt the daily operation. Seismic crosshole testing
usually takes a long period of time and has difficulty in
characterizing the flow property directly. Tracer tests can map the
inter-well flow property conveniently, but usually are not
repeatable.
SUMMARY
[0008] An aspect of an embodiment of the present invention is to
provide a method of characterizing a flow property of a production
well site in a reservoir. The method includes identifying a
plurality of injection and production well sites in the reservoir;
injecting fluid into selected injection well sites in accordance
with an injection schedule; monitoring an output at the production
well sites; determining a time delay between the selected injection
sites and the production sites based on the monitored output using
an estimated capacitance model; and characterizing a flow property
of a production well site using the time delay and the estimated
capacitance model.
[0009] An aspect of an embodiment of the present invention includes
a system of characterizing a flow property in a production well.
The system includes a processor configured to: (a) determine a time
delay between selected injection sites and selected production
sites based on a monitored output at the production well sites
using an estimated capacitance model, wherein fluid is injected
into selected injection well sites in accordance with an injection
schedule while an output is monitored at the production well sites;
and (b) characterize the flow property of a production well site
using the time delay and the estimated capacitance model.
[0010] Other aspects of embodiments of the present invention
include computer readable media encoded with computer executable
instructions for performing any of the foregoing methods and/or for
controlling any of the foregoing systems.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] Other features described herein will be more readily
apparent to those skilled in the art when reading the following
detailed description in connection with the accompanying drawings,
wherein:
[0012] FIG. 1 is a flow chart illustrating steps of a method in
accordance with an embodiment of the invention;
[0013] FIG. 2 is a schematic representation of an injector/producer
relationship in a multilayer reservoir having a shale
discontinuity, according to an embodiment of the present
invention;
[0014] FIG. 3 is a schematic illustration of a flow in an
injector/producer relationship illustrating Fermat's principle in
determining the location of shale discontinuities, according to an
embodiment of the present invention;
[0015] FIGS. 4a-4c illustrate a testing scenario in a simulated
application of a method in accordance with an embodiment of the
invention;
[0016] FIG. 5a illustrates injection rates, according various
embodiments of the present invention
[0017] FIG. 5b illustrates measured production rates corresponding
to the injection rates shown in FIG. 5a;
[0018] FIG. 5c illustrates an estimated FIR and a CM to determine a
time delay constant for the simulated method, according to an
embodiment of the present invention;
[0019] FIG. 6a illustrates an initial structure, according to an
embodiment of the present invention;
[0020] FIG. 6b illustrates an output of the algorithm, according to
an embodiment of the present invention;
[0021] FIG. 6c illustrates the simulated reservoir structure,
according to an embodiment of the present invention;
[0022] FIG. 7 shows a comparison between the estimated CM to
predict the production rate and the measurements, according to an
embodiment of the present invention;
[0023] FIG. 8a shows the relative well locations for the injector
and the producer wells;
[0024] FIG. 8b shows an estimate probability map for a pilot area,
upper side;
[0025] FIG. 9a shows the relative well locations for the injector
and producer wells;
[0026] FIG. 9b shows an estimate probability map for a pilot area,
lower side; and
[0027] FIG. 10 depicts the estimated probability map for the whole
field with a known fault, according to an embodiment of the present
invention.
DETAILED DESCRIPTION
[0028] In accordance with an embodiment of the present invention,
injection and production data are used to estimate high
permeability channels. This may be extended to the 3D case to
identify the shale discontinuities which causes cross layer flow.
The present method may be implemented without stoppage in
production schedules.
[0029] In particular, the inventors have determined that it may be
difficult to identify shale discontinuities, particular in a
layered reservoir with large permeability contrast. In order to
overcome this difficulty, the inventors have investigated use of
flow rates as an indicator. In particular, because the shale
discontinuities provide channels for the fluid to flow between
different layers, when an injection rate is changed, and producers
in the same layer are shut-in, it should be possible to detect
changes in production in different layers. By controlling injection
schedule design and including shut-in for producers, well-pair
response time in a 3D layered reservoir may be estimated.
[0030] With the injection/production data, a capacitance model (CM)
may be used to characterize the flow property for each well-pair.
Specifically, the model can be viewed as a virtual streamline
approach to explain the production according to the interaction
between well-pairs. In CM, a `time delay` constant is introduced to
characterize the time delay effect of the injection signal at the
producers. This "time delay" constant is associated with the cross
layer travel path, which is determined by the location of shale
discontinuities. In this regard, the injector and producer are
treated as the transmitter and receiver, respectively, and use the
time delay constant as the travel time for each well-pair. One
special property of this problem is that shale discontinuities may
have very different flow properties. This approach may be referred
to as "high contrast travel time tomography."
[0031] After determining a time delay constant, the problem of
finding the shale discontinuities can be modeled as a cross-hole
travel time tomography. Travel time tomography aims to reconstruct
an interior velocity model based on measured first-arrival times
between transmitters and receivers. The velocity model captures the
physical properties of the region where the signal transmission
occurs. The transmitted signal can be a seismic wave, an acoustic
sound wave, and even a fluid pressure wave. This technique can
characterize large scale elastic media, in applications such as
seismic geophysical exploration and acoustic tomography, in the
atmosphere's surface or the ocean layers. However, the geophysical
problem is different from many other transmission tomographic
reconstruction problems (X-Ray CT, Positron Emission Tomography CT,
etc.) where the straight-line trajectory assumption is commonly
used. Indeed, in the geophysical problem, the acoustic trajectory
may bend severely if the local velocity variation is high. Instead
of using the straight line trajectory assumption, travel paths can
be characterized by Fermat's principle, where the travel time
observed corresponds to the path traversed in the shortest time,
where the time can be obtained as a path integral of the slowness
(reciprocal of velocity) function integrated along the travel
path.
[0032] In many geophysical applications, it is very common to have
heterogeneous structures where the velocity contrast is high, e.g.,
an area may have twice the velocity than other areas. Example
scenarios where this situation can be encountered arise in
different applications, e.g., using seismic waves to find permeable
fracture zones in ground-water flow, monitoring the water/oil
saturation in vegetable oil bio-remediation projects, etc.
Different from the case that the velocity distribution only has
small variation, the travel path in high velocity contrast media
not only bends severely but is almost dominated by these high
velocity structures that form high transmissive channels. Because
the straight line travel path approximation is not valid, the
reconstruction of the velocity model becomes a nonlinear inverse
problem. Furthermore, conventional reconstruction methods are based
on iterative linearized algorithms to approximate the travel path.
Given that in many practical situations, only sparse measured
travel time data is available, these methods suffer from problems
due to low ray-coverage and severe path bending in the high
contrast velocity medium.
[0033] Water-flooding is used as a technique in enhanced oil
recovery (EOR). Water is injected in a controlled manner in order
to provide pressure support that can slowly sweep oil into the
production wells. During this process, the permeability
(measurement of ability to transmit fluid) of open fractures can be
orders of magnitude higher than that of surrounding tight rocks,
providing fast pathways for the flow. Thus, travel time through a
fracture (which could be modeled as a line in 2D or a plane in 3D)
is much faster than through surrounding rocks. The flow properties
of the reservoir are dominated by these highly `transmissive`
fracture structures. If a fracture is close to both an injection
well and a production well, most water will directly flow through
the fracture and thus fail to displace oil in other areas which is
called "water cycling" and thus significantly reduces the
efficiency of oil recovery. Therefore, understanding these
fractures is useful in flow characterization to enhance oil
recovery.
[0034] In one embodiment, high velocity structures (HVS) in a
relatively slow homogeneous background are determined. The
velocities are considered discrete which calls for solving a
`discrete` travel time tomography problem. For example, a reservoir
can be modeled as a layered structure, where each layer having a
different hydraulic conductivity.
[0035] Object-based models can be used to represent the HVS. For
example, objects can be pre-defined convex polygons, and the
geometrical shape of HVS is represented by a combination of these
fundamental objects. This allows an arbitrary shape to be
represented with convex objects, and prior information about the
HVS can be input into the object-based models. For instance, in the
fracture characterization problem, the geometrical shape of
fractures can be approximated by lines in 2D models or planes in 3D
models. The shape of the convex fundamental object can be defined
as a `line`. As a result, a small number of objects is sufficient
to approximate the shape of HVS, which reduces the dimensionality
and uncertainty of the problem. Furthermore, the travel path
tracking procedure can be simplified by only considering the
shortest time path between objects instead of all grids in the
spatial domain. This approach can reduce the number of unknown
variables to the object parameters and avoids the `lack of path
coverage` problem arising in grid-based models which provides a
more stable result in inversion.
[0036] In order to estimate the velocity model with the measured
travel time, a nonlinear inverse problem may be solved. In inverse
problems, the estimated velocity model (the solution) may not be
unique to the given measurements. One popular approach to handle
the non-uniqueness of the solution is to apply a regularization to
favor certain properties in the model. The regularization methods
can lead to solutions that balance the data-fitting and
model-penalty.
[0037] In another embodiment, an alternative approach is to
estimate the probability distribution for the model space according
to the data-fitting. This gives a full description of the relative
probabilities of the different models so that all likely solutions
may be considered.
[0038] In one embodiment, the Bayesian approach may be selected to
estimate the probability density map for the model parameter space.
Due to the large dimension of the model parameter space, an
accelerated random walk algorithm is provided to explore the model
space. In one embodiment, based on the Hamiltonian Monte Carlo
method (HMC), an additional friction term can be added in the
simulation of dynamic system. The samples are more likely to fall
into local minimum and achieve efficient sampling on high
probability regions. The HVS property can then be used to
approximate the neighboring probability distribution. The results
are presented as a probability map showing where the high velocity
objects are more likely to appear in the underlying structure of
the system.
[0039] In one embodiment, the HVS properties can be used to
simplify the path tracking step, which allows the Hamiltonian Monte
Carlo (HMC) sampling process to be more efficient. Furthermore, the
monotonicity of the travel time as a function of high velocity
object size can be exploited to approximate the probability
distribution in the space of model parameters.
[0040] In one embodiment, the high contrast travel time tomographic
reconstruction algorithm described above can be implemented in the
geophysical context and applied in petroleum or gas fields.
Understanding the heterogeneous structure of oil and gas reservoirs
can provide information to sweet spot mapping, drilling, production
forecasting and operation efficiency optimization. In enhance oil
recovery (EOR) process, fluids such as water, gas, or chemicals are
injected to increase the amount of oil that can be extracted from
the reservoir. The water-flood process is a process where water is
used as the injected fluid. Water injection provides pressure
maintenance in the reservoir while displacing part of residual oil
to production wells. To maximize operation efficiency of the
water-flood, steps may be taken to uniformly "push" the residual
oil where the presence of high permeability channels affect the
horizontal and vertical sweep efficiency. For example, the
water-flood process can be applied to a tight fractured reservoir.
In "tight" fractured reservoir, fractures provide conduits for the
fluid flow and these conduits provide fast pathways for the
injected fluid. Hence, these pathways dominate the sweep efficiency
in water-flood.
[0041] For example, if a high permeability channel is in close
proximity to one injection-production well-pair, most injected
water may flow through this channel and may fail to sweep the oil
in other regions. This phenomenon is called "water cycling", which
decrease the sweep efficiency and increase the water cut (the ratio
of water produced compared to the volume of total liquids
produced). To optimize the water-flood efficiency, it is desirable
to identify the locations of these high permeability channels in
the reservoir by appropriate changes in injection rates in
different wells.
[0042] The seismic cross-hole tomography method provides very
detailed geophysical structures. However, in this method, it can be
difficult to use the seismic velocity to infer the flow property
directly. Other methods use tracer tests which measure the
diffusion process between the injector-producer pairs and provide
the flow permeability distribution in a direct way. A common aspect
of these methods is that they all require additional equipments and
may interrupt daily operations. Seismic cross-hole testing requires
inducing seismic waves and deploying sensors to monitor the
reflected waves. In tracer tests, chemicals or radioactive
materials are injected and concentration response is monitored to
map inter-well flow properties. In addition, repeating the testing
in the same area is complicated and one needs to wait a long time
for the tracer concentration to return back to background
levels.
[0043] In a water-flood field, the injection/production data is the
most abundant data source and there is freedom to control the
injection rates. Thus, the injection rate can be changed while
monitoring the change in production wells. The estimated response
time between well pairs enables a user to infer the structure of a
reservoir using travel time tomography. In one embodiment, to
estimate the travel time, the water-flood reservoir can be modeled
as a linear system by considering water injection rates as inputs
and total fluid production rates as outputs. For example, in pulse
testing, sensitive differential pressure gauges can be used to
monitor the resulting pressure response at adjacent wells.
[0044] In another embodiment, the reservoir can be treated as a
multi-input and multi-output system and estimate all the inter-well
response by the production rates. By using a capacitance model
(CM), the relation between the injection-production response and
the "time delay" constant can be built. The relation between the
injection-production response and the time delay is approximately
proportional to the pressure wave propagation time. Therefore, the
time delay can be estimated from the injection/production data. The
obtained time delay can be used as the travel time between well
pairs. This procedure has the benefit of being able to be applied
without additional cost or significantly affecting daily
operation.
[0045] In tight fractured reservoirs, fractures can be viewed as
high permeability channels where the permeability contrast is
relatively high, about 10.sup.5 times permeable than the host rock
formation. In this case, the travel time for the pressure wave to
propagate through the high permeability channels can be considered
almost negligible. The travel time data is restricted to the
injection-production well-pair locations sparsely located in the
field. The reconstructed result is related to the density of travel
ray-path. Thus, the reconstructed reservoir image resolution is
fundamentally limited by the spatial distribution of well
locations.
[0046] Based on these conditions, the high permeability channels in
a reservoir can be characterized by solving a high contrast travel
time tomography problem with sparse data. If the grid model is used
and the conventional iterative least square methods are applied,
the reconstruction results would be poor. To identify these high
permeability channels an object-based model which employs "lines"
as fundamental objects can be used to represent fractures in
2D.
[0047] To estimate the travel time from historical data, a physical
model is used to describe the injection/production response. The
capacitance model can be used to characterize the system response,
where the time delay constant in CM is related to the control
volume. When the flow passes through a homogeneous region, the
control volume can be assumed to be proportional to the travel
path. By definition, the travel time is the travel path divided by
the local velocity. The time delay constant is proportional to the
control volume divided by the productivity index. In a tight
fractured reservoir, a simple reservoir model with embedded high
permeability channels in a homogeneous background may be used.
Thus, if the productivity index in high permeability channels is
higher than the background, the time delay constant inside the high
permeability channels can be ignored. The time delay constant is
proportional to the travel time in the high contrast reservoir
model.
[0048] The capacitance model provides a powerful tool to evaluate
the water-flood performance by treating the injection/production as
the system input/output and uses signal processing techniques to
estimate the unknown system parameters, which relates to reservoir
physical properties. The mathematical formulation for one
injection-production well pair in CM can be expressed by the
following equation (1).
.tau. q t + q ( t ) = i ( t ) - .tau. * J p wf t ( 1 )
##EQU00001##
[0049] Where i(t) is the injection rate and q(t) is the total
production rate. P.sub.wf represents the flowing bottom hole
pressure (BHP) and J stands for the productivity index. In the case
where the reservoir is mature and the bottom-hole pressure is
fixed, then it is possible to approximate the j-th well production
rates based on only the contribution from injectors by using the
following equation (2).
q j ( t ) = i .intg. t 0 t - ( t - ) / .tau. ij .tau. ij I i ( ) (
2 ) ##EQU00002##
[0050] The discrete form of equation (2) can be written as equation
(3).
q ( t ) = k ( 1 .tau. - ( k / .tau. ) [ t - k ] ) ( 3 )
##EQU00003##
[0051] Where t is equal to 1, 2, . . . , N. For multiple
injection-production well pairs, additional parameters l.sub.ij for
inter-well connectivity, which represent flow distribution from
injector i to different producers j. The j-th well production rate
is the sum of flow from different injector wells i. This can be
expressed by the following equation (4).
q j ( t ) = i k l ij ( 1 .tau. - ( k / .tau. ) [ t - k ] ) ( 4 )
##EQU00004##
[0052] By using equation (4), a linear multi-input multi-output
(MIMO) system can be used to model the relation between
injection/production rate. The impulse response is controlled by
the "time delay constant" .tau..sub.ij between each
injector-producer pair which is defined by the total
compressibility c.sub.t, the productivity index J, and the pore
volume Vp which are associated with the control volume between
injector i and producer j pair. The time delay constant
.tau..sub.ij between each injector-producer pair can be expressed
by the following equation (5).
.tau. ij = ( c t V p J ) ij ( 5 ) ##EQU00005##
[0053] From above, it is clear that if there is an area with higher
productivity index J, the time delay constant will be much smaller.
This implies that if the time delay constant for a specific
well-pair is very small, it is probable that a majority of the flow
path is through a high permeability layer.
[0054] For a homogeneous reservoir, the control volume is roughly
proportional to the distance between the injector and producer.
When a cross-layer flow in a layered reservoir is considered, the
travel path will be the path with the least time cost in accordance
with Fermat's principle. This implies that the flow will take
advantage of the higher permeability layer.
[0055] A total control volume can be modeled as the cascade of
several small control volumes, e.g., for example two control
volumes which can be two different layers. Each control volume is
proportional to a line segment which represents the flow path
through the control volume. Therefore, the time-delay constant
between a well pair will be the summation of two parts: the time
delay constant of the first layer (e.g., upper layer) and the time
delay constant of the second layer (e.g., lower layer). Each is
given by the ratio of flow path in different layers, which is
determined by the location of the shale discontinuities because
they provide the entries for the fluid to travel through different
layers.
[0056] In order to get a reliable estimate of the parameters for
CM, a Pseudo-Noise (PN) sequence may be used as the injection
schedule. By using PN sequence as the input, it may be possible to
achieve the lowest covariance for the parameter estimation. In
addition, by using PN sequences as inputs, lowest average
cross-correlation between inputs may also be achieved.
[0057] When the injection rate in the lower permeability layer is
changed, usually it is possible to detect the change of production
even for the producers located in the higher permeability layer.
However, in some instances, it may be difficult to detect this
cross-layer flow if the injection rate in the high permeability
layers is changed. This is because the high permeability layer
provides a fast pathway for the fluid so only a small amount will
flow through the shale discontinuity to the low permeability layer.
Therefore, when designing the injection schedule it may be useful
to shut-in the producers in the same layer to force the fluid to
flow through different layers. In this situation, the cross layer
flow can be detected by monitoring the change of production.
[0058] The algorithm to identify the shale discontinuities with
cross-layer time delay constant can be referred as the "high
contrast travel time tomographic reconstruction". One of the issues
with this approach is that the sensor locations may be limited in
the injectors/producers, and the flow velocity contrast of the
shale discontinuities may be very high. If the conventional grid
based inversion method is used, the result may result in a blurred
image and it may be difficult to identify the shale
discontinuities.
[0059] As such, instead of using the grid based method, an
object-based representation of the shale discontinuities may be
chosen. The reconstruction algorithm will modify the object
parameters for the shale discontinuities to match the measured
delay time constant. It can be described as a `Forward-Backward`
iterative procedure.
[0060] FIG. 1 is a flow chart illustrating steps of a method for
determining the time delay constant, according to an embodiment of
the present invention. In the forward step, a time delay is
calculated based on the current or initial locations of shale
discontinuities based on a current or initial reservoir model, at
S10. At S12, a test is performed to determine whether or not a
difference between the time delay and a measured time delay is
small enough, i.e., smaller than a set threshold (e.g. smaller than
1% to 5% of the measured value). If the calculated result fits the
measurement (i.e., the difference between the measurement and the
current estimate is small or smaller than the set threshold), then
the selected current reservoir model can be considered as a
solution and the algorithm is stopped, at S14. If not, the
`backward` step is performed to update the locations of shale
discontinuities (i.e., the initial reservoir model is updated)
based on the difference of the current predicted response time with
the measurements, at S16. Therefore, if the difference is greater
than the set threshold, the method includes updating the initial
reservoir model based on the difference, calculating the time delay
based on the updated reservoir model; and determining whether or
not a difference between the time delay based on the updated
reservoir model and the measured time delay is smaller than the
threshold. This loop procedure can be repeated until convergence
between the calculated time delay and the measured time delay is
achieved. That is, the loop procedure is repeated until the
difference between the calculated time delay and the measured time
delay is smaller than the set threshold.
[0061] The detail of the "forward" step can be described as
follows. With the current location of shale discontinuities, the
flow travel path can be calculated by Fermat's principle. The shale
discontinuities act as entry points to the different layers, and
the time delay constant can be approximated by the cascade of
different layers which is proportional to the travel distance
inside. In this case, the time delay constant is well defined by
the locations of shale discontinuities.
[0062] FIG. 2 is a schematic representation of an injector/producer
relationship in a multilayer reservoir having a shale
discontinuity, according to an embodiment of the present invention.
Injector well 10 and producer well 12 provided within rock
formation 13 are separated by distance L. As illustrated in FIG. 2,
there two shale layers 14A and 14B. Shale layer 14A has a lower
permeability and shale layer 14B has a higher permeability. As
shown in FIG. 2, there is a shale discontinuity 16 between shale
layer 14A and shale layer 14B, the discontinuity corresponding to a
fracture in the rock formation 13 where fluid flow (indicated
schematically by the arrows) is privileged. For example, if it is
assumed that the flow velocity of the layer (shale layer 14A)
having lower permeability is equal to 1 (VL=1) and the flow
velocity of the layer (shale layer 14B) having a higher
permeability is 10 (VH=10), the flow path can be separated as two
segments belonging to the two different layers 14A and 14B and the
delay time can be calculated using the following equation (6).
Travel time=L.sub.1/1+L.sub.2/10, with L.sub.1+L.sub.2=L (6)
where L represents the geometrical distance between the
injector-producer well 10 and 12, and the ratio of two segments is
controlled by the location of shale discontinuities. The distance
L1 corresponds to the distance traversed by the injected fluid
through layer 14A. The distance L2 corresponds to the distance
traversed by the injected fluid through layer 14B. The travel time
within the discontinuity or fracture 16 is considered small
relative to the travel times of fluid flow within the layers 14A
and 14B. Therefore, the travel time within fracture 16 is not taken
into account when calculating the total travel time using equation
(6).
[0063] FIG. 3 is a schematic illustration of a flow in an injector
well and producer well relationship illustrating Fermat's principle
in determining the location of shale discontinuities, according to
an embodiment of the present invention. Injector well 20 and
producer well 22 provided within rock formation 23 are separated by
distance L. As illustrated in FIG. 3, there are two types of shales
24A and 24B. Shale 24A has a lower permeability and shale 24B has a
higher permeability. As shown in FIG. 3, there is a shale
discontinuity 26 between shale 24A and shale 24B, the discontinuity
corresponding to a fracture in the rock formation 23. In this model
of the earth, the relationship between the various shales (i.e.,
shales with various permeabilities) and the position of the
discontinuity is not as straight forward as in the example shown in
FIG. 2. Therefore, in order to determine an appropriate model that
provides an estimate of the travel time and thus the location of
the discontinuity, the backward step in the loop S16 is performed.
In the `backward` step, the locations for the shale discontinuities
26 is updated base on the mismatch of the measured and predicted
time delay constant .tau.. Time delay constant .tau. is the sum of
time delay .tau.(1) within shale 24A and time delay .tau.(2) within
shale 24B. Time delay .tau.(1) is proportional to the traversed
length L1 within shale 24A and inversely proportional to the flow
velocity within shale 24A. Similarly, time delay .tau.(2) is
proportional to the traversed length L2 within shale 24B and
inversely proportional to the flow velocity within shale 24B.
[0064] Because the shale discontinuities are represented by objects
with parameters, we can formulate the updating as a parameter
estimation problem. Current object parameter can be expressed by
the following equation (7).
.theta. = Arg min .theta. T ( .theta. ) - t ( 7 ) ##EQU00006##
[0065] where T(.theta.) is the calculated response time based on
current object parameters .theta. and t is the measurement. A
gradient search is used to find the optimal parameters to represent
the location of the shale discontinuities.
[0066] FIGS. 4a-4c illustrate a testing scenario in a simulated
application of a method in accordance with an embodiment of the
invention. A two layer reservoir model with high permeability
contrast was built and a commercial simulator (CMG) is used to test
the method. The testing case was a line drive with 5 injectors and
5 producers. Three of the injectors/producers are in the low
permeability layers, and the two other injectors/producers are in
the high permeability layers. A simple shale discontinuity was
placed and high permeability assigned to it to simulate the effect.
For the reservoir model configuration, a high permeability channel
is simulated. In the simulation, the high permeability channel
connects injector well 5 with producer well 3. A pulse testing is
applied in the simulation. The pulse testing uses a step or square
function or wave as the change of injection rate. The injection
rate is changed each time so the response can be easily estimated
from the change of production rate. The travel time is defined by
the time to reach 90% of the final change of the production rate.
FIG. 4a shows the configuration of injector wells I2 and I4
relative to production wells P2 and P4 in the first layer. FIG. 4b
shows the configuration of injector wells I1, I3 and I5 relative to
producer wells P1, P3 and P5 in the second layer. FIG. 4c
illustrates the shale layers and their respective permeabilities
(shown on the scale strip) within the rock formation and the
relative position of the 5 injector wells I1 through I5 and 5
producer wells P1 through P5.
[0067] A PN sequence was used as the injection schedule and the
producers in the same layer were shut-in for the testing period.
The changes of production can be measured for the producers located
in different layers. A time delay constant was retrieved in CM by
injection/production data, and used to identify the location of
shale discontinuities as shown in FIGS. 5a-5c.
[0068] FIG. 5a depicts two plots with two different injection
rates. FIG. 5b depicts two plots with two production rates
corresponding to the two injection rates shown in FIG. 5a. FIG. 5c
represents a plot of an estimated FIR and a CM to determine a time
delay constant for the simulated method. The plot represents a
correlation between injection and production as a function of time
(the horizontal or x-axis representing time and the vertical or
y-axis representing the normalized response). As it can be noted,
the average time delay to obtain a change of production at the
production site is in this case about 5 to 6 days.
[0069] To apply the method in a real field, one of the useful
parameters is the sampling frequency. Another useful parameter is
accuracy of the data. Usually it is possible to obtain reliable and
frequent injection data, but production rates are obtained from the
well-test, which can performed periodically, e.g., on a weekly
basis. This factor tends to limit the time-resolution when the time
delay constant is measured. For example, assuming the time delay
constants for the well-pairs are 1 and 4 days, when injection rates
are increased, it is possible to measure almost the same changes in
production rate if it is measured by well-test. To deal with this
problem, it is possible to use an inferred production value
provided by a controller pump which provides more frequent
production data.
[0070] FIG. 6a illustrates an assumed initial structure of the high
permeability channel or discontinuity, according to an embodiment
of the present invention. The assumed initial structure is used in
the initial model to estimate an initial time delay. FIG. 6b
illustrates an output of the algorithm, according to an embodiment
of the present invention. FIG. 6b depicts the position of the high
permeability channel or shale discontinuity obtained through
refining the initial model until the difference between the
estimate time delay and the measured time delay is relatively small
and below a certain threshold. FIG. 6c illustrates the simulated
reservoir structure, according to an embodiment of the present
invention. The scale strip next to the graph provides a scale of
the permeability of the rock formation. The bar within the graph
indicates the position of the discontinuity. A good match is
obtained between the measurement and the calculated position or
location of the discontinuity (fault) as well as the direction of
the discontinuity (fault).
[0071] A field experiment under water-flood in an oil field is
performed. The field is considered to be a tight fractured
reservoir. In the experiment, a pilot area with 12 injection wells
is considered. The well installation is a line-drive and roughly
parallel to the direction of fractures which are estimated from
seismic survey.
[0072] Two types of systems in the oil field are used to provide
the well production data. One is the "well-test" data, which
accumulates a three phase production rate of one specific well for
a short period of time. However, many wells share the same
separation facility. Therefore, these wells are tested
sequentially. This limits the sampling rate of the production
rates, because the sampling period is the sum of the testing period
for all production wells. In this case, one measurement point every
two weeks is taken which makes our production rate sparsely sampled
in the well-test data.
[0073] The other data source is the pump-of-control (POC) data,
which measures the pump load change in every stroke. If the number
of strokes counted is multiplied by the load change, the
theoretical total daily production can be calculated. To get a
reliable data with high sampling rate, the POC data is used and the
pumping efficiency is calibrated with the well-test data. After
calibrating with the pumping efficiency, the POC data would be able
to provide a daily production rate. However, we do observe unusual
low production rate, which might be outliers due to the power
outage or loss of transmission. Thus, in the linear model
estimation we choose l.sub.1 instead using l.sub.3 norm as the
error metric, which is more balance between fitting good data
points and outliers.
[0074] To estimate the CM parameters, the direct approach is chosen
in this case. The reason is because the input data length is
limited (about 90), and thus, the multi-stage approach is not
suitable because the unknown parameters in FIR model will be much
larger than the measured data. From a previous discussion in the
above paragraphs, it is established that the direct estimation uses
fewer unknown variables but needs to solve a nonlinear
optimization. Therefore, the estimated CM might be a solution in a
local minimum and not represent the system well. To verify the
estimated CM, cross-validation is used which divides the measured
data into two parts. The first part is the training data, which is
used to estimate the CM parameters. The second part is the testing
data, where estimated CM is used to predict the production rate and
compare with the measurements. If the error is too high, the
estimated CM is determined to be not accurate and the non-linear
optimization is re-run. FIG. 7 shows a comparison between the
estimated CM to predict the production rate and the measurements,
according to an embodiment of the present invention.
[0075] Following the same principle in numerical simulation, the
travel time is only used when the inter-well connectivity is
greater than 10%. The pilot area is separated into upper and lower
side and the travel time between well pairs inside each region is
estimated. The reason why the estimation for the well pair is not
performed for the whole field is that that solving for the whole
field needs a greater number of variables. In the line drive
water-flood, it can be assumed the flow only comes from the nearby
two rows of injectors. Hence, solving two smaller fields is
selected instead.
[0076] FIG. 8a shows the relative well locations for the injector
and the producer wells. FIG. 8b shows an estimate probability map
for pilot area 1, upper side. It can be noted that the estimated
high permeability is roughly parallel to the installation of the
wells which is consistent with the prior information of fracture
direction. FIG. 9a shows the relative well locations for the
injector and producer wells. FIG. 9b shows an estimate probability
map for pilot area 1, lower side. Similar to FIG. 8b, it can also
be noted that the estimated high permeability is roughly parallel
to the installation of the wells which is consistent with the prior
information of fracture direction.
[0077] The estimate travel time results for the upper part of pilot
area is shown in FIG. 8b, and the lower part is shown in FIG. 9b.
In the upper part, two reliable production rate measurements are
obtained, and the travel time used are t_(1,1), t_(3,2), t_(4,2),
t_(5,1), t_(5,2), t_(6,1), t_(7,1), t_(7,2), t_(8,1), t_(8,2), a
total of 8 well pairs. The result shows in the upper side, the
estimated high permeability channels are close to production well 2
and roughly parallel to the installation of wells. This is
consistent with the fact that the well production is a 24 hours
run, high production well, which implies that there are high
permeability channels nearby. In the lower part, one production
well is present and the estimated travel time are t_(7,3), t_(9,3),
t_(10,3), t_(11,3), and t_(12,3) where there are fewer measured
travel times to estimate the high permeability map. The result in
two areas are then combined and compared with the known fault
location. The result shows the appearance probability of high
permeability channels in the fault zones is very low, and roughly
parallel to the well installation which agrees with the seismic
survey. FIG. 10 depicts the estimated probability map for the whole
field with a known fault, according to an embodiment of the present
invention. The position of the known fault is indicated on the
probability map. The results show the permeability channel has a
very low appearance probability in the fault zone consistent with
the prior survey.
[0078] The "time delay constant" can be used in a CM method to
detect high permeability channels. The method uses the
injection-production. The method uses the change of injection as
the active probing and detect the field changes in real-time
without altering the average daily production. In order to apply
this to real field data, some practical issues are noted. First,
the data sampling period and quality can play an important role.
Usually, a reliable daily injection rate data is obtained. However,
production rates are often obtained from bi-weekly well-test data.
This may reduce the time resolution of estimated travel times. The
POC data calibrated with well-test data can be used to get the
daily production rate. In addition, in practical applications, the
distribution of well locations is related to spatial resolution.
For example, in an extreme case where one injector-producer pair is
in the horizontal direction, any high permeability channel exactly
in the vertical direction will not affect the lag time. Therefore,
the high permeability channels may not be visible in this
situation. In order to detect the high permeability channel in any
arbitrary direction, the wells can be uniformly located in the
field and to cover all angles.
[0079] As will be appreciated, the method as described herein may
be performed using a computing system having machine executable
instructions stored on a tangible medium. The instructions are
executable to perform each portion of the method, either
autonomously, or with the assistance of input from an operator. In
an embodiment, the system includes structures for allowing input
and output of data, and a display that is configured and arranged
to display the intermediate and/or final products of the process
steps. A method in accordance with an embodiment may include an
automated selection of a location for exploitation and/or
exploratory drilling for hydrocarbon resources. Where the term
processor is used, it should be understood to be applicable to
multi-processor systems and/or distributed computing systems.
[0080] Those skilled in the art will appreciate that the disclosed
embodiments described herein are by way of example only, and that
numerous variations will exist. The invention is limited only by
the claims, which encompass the embodiments described herein as
well as variants apparent to those skilled in the art. In addition,
it should be appreciated that structural features or method steps
shown or described in any one embodiment herein can be used in
other embodiments as well.
* * * * *