Note: Descriptions are shown in the official language in which they were submitted.
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METHODS, SYSTEMS AND DEVICES FOR MODELLING RESERVOIR PROPERTIES
FIELD
[0001] The present application relates to the field of reservoir
modelling, and particularly
to methods, systems and devices for modelling unconventional oil reservoir
production
based on collected physical data.
BACKGROUND
[0002] Hydrocarbon exploration involves trade-offs between the number
and spacing of
wells (and associated costs) and the geological and commercial risk based on
available data
which may impact production forecasting and resource development planning.
[0003] Type curves can be used to estimate reservoir production for new
wells by
averaging existing wells. However, in some instances, type curves may be
difficult to adjust
for differences, and may not account for subtle changes across an area or over
time.
[0004] Simulations can also be used to model reservoir properties;
however, simulations
may require large amounts of input data which may be expensive to obtain, and
are
expensive from both a time and computational resource perspective.
[0005] Methods, systems and devices which can reduce computational
requirements
and/or input data requirements are desirable.
SUM MARY
[0006] In accordance with one aspect, there is provided a method of
modelling
hydrocarbon production rates for a subterranean formation. The method
includes: obtaining,
by at least one processor, production data for at least one well in the
subterranean
formation; based at least in part on geological data for the subterranean
formation, identify,
at the at least one processor, a range of potential values for each of a
plurality of
parameters, the plurality of parameters including at least one parameter
representative of
geological characteristics of the subterranean formation, and fracture
parameters; where
each set of values including a selection from each of the ranges for the
plurality of
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parameters defining a potential subterranean formation model, and where sets
of values
including different combinations of values for the plurality of parameters
define a set of
potential subterranean formation models; matching at least a portion of the
set of potential
subterranean formation models to the production data for the at least one well
by iteratively:
inputting, by the at least one processor, a set of parameter values selected
from the ranges
of potential values to an analytical fracture model to generate a production
model for the
subterranean formation for the particular subterranean formation model defined
by the
inputted set of values, the production model a function of a stimulated area
value; determine
at least one stimulated area value for the production model, and comparing
production
values for the production model with the production data for the at least one
well to generate
an error value; and selecting parameter values for inputting in a subsequent
iteration based
on a machine learning algorithm and past error values to reduce a number of
analyzed
subterranean formation models that do not fit the production profile;
identifying production
models which fit the production profile from the production data within a
defined error
threshold; with the identified production models which fit the production
profile from the
production data for the at least one well in the subterranean formation,
selecting a range of
stimulated area values from a subset of the identified models having the
lowest generated
error values; and based on a frequency distribution of the stimulated area
values from the
subset of the identified models having the lowest productivity value error
scores, creating a
forecast production model for at least a portion of the subterranean resource,
the forecast
production model having input parameters representative of geological
characteristics of at
least the portion of the subterranean formation, and an input parameter
associated with the
stimulated area value and limited to the selected range.
[0007] In accordance with another aspect, there is provided a system for
modelling
hydrocarbon production rates for a subterranean formation. The system includes
at least one
processor configured for: obtaining production data for at least one well in
the subterranean
formation; based at least in part on geological data for the subterranean
formation, identify a
range of potential values for each of a plurality of parameters, the plurality
of parameters
including at least one parameter representative of geological characteristics
of the
subterranean formation, and fracture parameters; where each set of values
including a
selection from each of the ranges for the plurality of parameters defining a
potential
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subterranean formation model, and where sets of values including different
combinations of
values for the plurality of parameters define a set of potential subterranean
formation
models; matching at least a portion of the set of potential subterranean
formation models to
the production data for the at least one well by iteratively: inputting a set
of parameter values
selected from the ranges of potential values to an analytical fracture model
to generate a
production model for the subterranean formation for the particular
subterranean formation
model defined by the inputted set of values, the production model a function
of a stimulated
area value; determine at least one stimulated area value for the production
model, and
comparing production values for the production model with the production data
for the at
least one well to generate an error value; and selecting parameter values for
inputting in a
subsequent iteration based on a machine learning algorithm and past error
values to reduce
a number of analyzed subterranean formation models that do not fit the
production profile;
identifying production models which fit the production profile from the
production data within
a defined error threshold; with the identified production models which fit the
production
profile from the production data for the at least one well in the subterranean
formation,
selecting a range of stimulated area values from a subset of the identified
models having the
lowest generated error values; and based on a frequency distribution of the
stimulated area
values from the subset of the identified models having the lowest productivity
value error
scores, creating a forecast production model for at least a portion of the
subterranean
resource, the forecast production model having input parameters representative
of
geological characteristics of at least the portion of the subterranean
formation, and an input
parameter associated with the stimulated area value and limited to the
selected range.
[0008] In accordance with another aspect, there is provided a computer-
readable medium
or media having stored thereon computer-readable instructions which when
executed by at
least one processor configured the at least one processor for: obtaining, by
the at least one
processor, production data for at least one well in the subterranean
formation; based at least
in part on geological data for the subterranean formation, identify, at the at
least one
processor, a range of potential values for each of a plurality of parameters,
the plurality of
parameters including at least one parameter representative of geological
characteristics of
the subterranean formation, and fracture parameters; where each set of values
including a
selection from each of the ranges for the plurality of parameters defining a
potential
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subterranean formation model, and where sets of values including different
combinations of
values for the plurality of parameters define a set of potential subterranean
formation
models; matching at least a portion of the set of potential subterranean
formation models to
the production data for the at least one well by iteratively: inputting, by
the at least one
processor, a set of parameter values selected from the ranges of potential
values to an
analytical fracture model to generate a production model for the subterranean
formation for
the particular subterranean formation model defined by the inputted set of
values, the
production model a function of a stimulated area value; determine at least one
stimulated
area value for the production model, and comparing production values for the
production
.. model with the production data for the at least one well to generate an
error value; and
selecting parameter values for inputting in a subsequent iteration based on a
machine
learning algorithm and past error values to reduce a number of analyzed
subterranean
formation models that do not fit the production profile; identifying
production models which fit
the production profile from the production data within a defined error
threshold; with the
identified production models which fit the production profile from the
production data for the
at least one well in the subterranean formation, selecting a range of
stimulated area values
from a subset of the identified models having the lowest generated error
values; and based
on a frequency distribution of the stimulated area values from the subset of
the identified
models having the lowest productivity value error scores, creating a forecast
production
model for at least a portion of the subterranean resource, the forecast
production model
having input parameters representative of geological characteristics of at
least the portion of
the subterranean formation, and an input parameter associated with the
stimulated area
value and limited to the selected range.
[0009] Many further features and combinations thereof concerning
embodiments
described herein will appear to those skilled in the art following a reading
of the present
disclosure.
DESCRIPTION OF THE FIGURES
[0010] In the figures,
[0011] Fig. 1 is a cross sectional view of an example geological
formation and well;
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[0012] Fig. 2 is an example system to which aspects of the present
disclosure may be
applied;
[0013] Figs. 3 is a perspective sectional view of an example horizontal
well portion with
fractures;
[0014] Figs. 4 is a top view of an example horizontal well portion with
fractures;
[0015] Figs. 5, 6 and 7 are flowcharts illustrating aspects of example
methods for
modelling reservoir properties;
[0016] Figs. 8 and 9 is are stimulated area vs. error value plots;
[0017] Fig. 10 shows an example geographic map showing different
production forecasts
for different portions of a resource; and
[0018] Fig. 11 shows a graph showing examples of different probabilistic
forecasts of
production rates.
DETAILED DESCRIPTION
[0019] In hydrocarbon development, accurate estimations of rates of
production can help
provide information regarding the value and/or viability of a
project/resource. These
estimations may also guide the number, location and/or orientation of wells.
Due to the high
cost of development, there can be significant financial incentives to properly
describe
uncertainty in outcomes so informed decisions can be made as much as possible.
In some
examples, it may be important to keep the cost and amount of time spent
acquiring the
information low.
[0020] In some embodiments, aspects of the present disclosure may
provide analytic
devices, systems and methods for modelling resource production which are
computationally
less intensive or less time consuming than a complex simulation. In some
embodiments,
aspects of the present disclosure may have a higher degree of confidence in
their models
than a type curve or other similar model.
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[0021] In some embodiments, aspects of the present disclosure may
provide devices,
systems and methods for modelling resource production based on incomplete or
less
information than would be necessary for other processes.
[0022] In broad embodiments, aspects of the disclosure may, in some
instances, provide
a practical method for spatially modelling value to target areas of highest
potential
investment return.
[0023] Fig. 1 illustrates a cross-sectional view of a subterranean
resource or geological
formation 110 which may include a number of different layers of materials
having different
physical characteristics as illustrated in Fig. 1 by the lines in the
formation. It should be
understood that these lines are illustrative only and that geological
formations may have any
number of layers or types of material which may not have distinct delineations
but may be
gradual or may contain mixtures or combinations of different material. There
may also be
lateral and/or vertical variations in the types of material contained within
any of the
geological formations.
[0024] In evaluating the subsurface or subterranean formations, in some
examples, data
is collected from one or more wells 100 drilled into or around the formations.
In some
examples, the wells are exploratory wells, production wells or wells for any
other purpose.
The wells may include vertical wells 100, horizontal wells 105, or any wells
of any direction
or structure, and/or any combination thereof.
[0025] In some examples, data collected from the well(s) 100 can include or
can be used
to create logs of the geologic formations penetrated by the well(s). The data
can be collected
from core samples or by measurements taken by devices in the borehole.
[0026] In some examples, the well data collected or generated from well
measurements
can include, but are not limited to, gamma ray logs, bulk density logs,
neutron density logs,
induction resistivity logs, and/or well core or image data.
[0027] In some examples, the geological formation may include
hydrocarbon-bearing
layers having low permeability such as shale or tight sandstone. Such
formations may be
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suitable for hydrocarbon extraction using hydraulic fracturing technologies.
In some
instances, such unconventional plays may have large spatial variability, may
involve multiple
hydrocarbon fluids phases, and/or may have uncertainties in fracturing areas
and
permeability.
[0028] As such, in some instances, traditional techniques for conventional
oil well drilling
may be unsuitable for these unconventional resources.
[0029] The embodiments of the devices, systems and methods described
herein may be
implemented in a combination of both hardware and software. These embodiments
may be
implemented on programmable computers, each computer including at least one
processor,
a data storage system (including volatile memory or non-volatile memory or
other data
storage elements or a combination thereof), and at least one communication
interface.
[0030] Program code may be applied to input data to perform the
functions described
herein and to generate output information. The output information may be
applied to one or
more output devices. In some embodiments, the communication interface may be a
network
communication interface. In embodiments in which elements may be combined, the
communication interface may be a software communication interface, such as
those for
inter-process communication. In still other embodiments, there may be a
combination of
communication interfaces implemented as hardware, software, and combination
thereof. In
some examples, devices having at least one processor may be configured to
execute
software instructions stored on a computer readable tangible, non-transitory
medium.
[0031] The following discussion provides many example embodiments.
Although each
embodiment represents a single combination of inventive elements, other
examples may
include all possible combinations of the disclosed elements. Thus if one
embodiment
comprises elements A, B, and C, and a second embodiment comprises elements B
and D,
other remaining combinations of A, B, C, or D, may also be used.
[0032] The technical solution of embodiments may be in the form of a
software product.
The software product may be stored in a non-volatile or non-transitory storage
medium,
which can be a compact disk read-only memory (CD-ROM), a USB flash disk, or a
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removable hard disk. The software product includes a number of instructions
that enable a
computer device (personal computer, server, or network device) to execute the
methods
provided by the embodiments.
[0033] The embodiments described herein are implemented by physical
computer
hardware, including computing devices, servers, receivers, transmitters,
processors,
memory, displays, and networks. The embodiments described herein provide
useful physical
machines and particularly configured computer hardware arrangements. The
embodiments
described herein are directed to electronic machines and methods implemented
by
electronic machines adapted for processing and transforming electromagnetic
signals which
represent various types of information. The embodiments described herein
pervasively and
integrally relate to machines, and their uses; and the embodiments described
herein have no
meaning or practical applicability outside their use with computer hardware,
machines, and
various hardware components. Substituting the physical hardware particularly
configured to
implement various acts for non-physical hardware, using mental steps for
example, may
substantially affect the way the embodiments work. Such computer hardware
limitations are
clearly essential elements of the embodiments described herein, and they
cannot be omitted
or substituted for mental means without having a material effect on the
operation and
structure of the embodiments described herein. The computer hardware is
essential to
implement the various embodiments described herein and is not merely used to
perform
steps expeditiously and in an efficient manner.
[0034] Fig. 2 shows an example system 200 include one or more devices
205 which may
be used to model or predict hydrocarbon production rates. In some examples, a
device 205
may be a computational device such as a computer, server, tablet or mobile
device, or other
system, device or any combination thereof suitable for accomplishing the
purposes
described herein. In some examples, the device 205 can include one or more
processor(s)
210, memories 215, and/or one or more devices/interfaces 220 necessary or
desirable for
input/output, communications, control and the like. The processor(s) 210
and/or other
components of the device(s) 205 or system 250 may be configured to perform one
or more
aspects of the processes described herein.
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[0035] In some examples, the device(s) 205 may be configured to receive
or access data
from one or more volatile or non-volatile memories 215, or external storage
devices 225
directly coupled to a device 205 or accessible via one or more wired and/or
wireless
network(s) 260. In external storage device(s) 225 can be a network storage
device or may
be part of or connected to a server or other device.
[0036] In some examples, the data may be accessed from one or more
public databases.
Such data can, in some examples, include less well characteristic and / or
production data
than may be available for well data from an internal source. For example, well
production
data may be provided as an aggregate of multiple wells or for an area without
any
information as to the number or size of fractures. In another example, well
production data
may be provided over time in less granular time periods. In some embodiments,
the
methods, devices, and systems described herein may generate models which
account for
such unknown(s).
[0037] In some examples, the device(s) 205 may be configured to receive
or access data
from sensors or devices 230 in the field. These sensors or devices 230 may be
configured
for collecting or measuring well, seismic or other geological and/or physical
data. In some
examples, the sensor(s)/device(s) 230 can be configured to communicate the
collected data
to the device(s) 205 and/or storage device(s) 225 via one or more networks 260
or
otherwise. In some examples, the sensors or devices 230 may be connected to a
local
computing device 240 which may be configured to receive the data from the
sensors/devices
230 for local storage and/or communication to the device(s) 205 and/or storage
device(s)
225.
[0038] In some examples, a client device 250 may connect to or otherwise
communicate
with the device(s) 205 to gain access to the data and/or to instruct or
request that the
device(s) 205 perform some or all of the aspects described herein.
[0039] With reference to Fig. 3, in some embodiments, a well may have
multiple hydraulic
fractures 310, which may be transverse or in any other orientation with
respect to the well.
The wellbore 120 in Fig. 3 is horizontal; however, in other examples,
fractures can be made
relative to a wellbore of any orientation.
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[0040] Fig. 4 shows a top-down view of the horizontal well 120 including
four fractures
310. In some embodiments, a well with multiple fractures can be modelled as
equally-
spaced bi-wing transverse fractures. In some embodiments, the model can assume
that
there is a no flow boundary 315 at a midpoint between each fracture.
[0041] On the right, Fig. 4 shows an example drainage area for a single
fracture 310. In
some embodiments, fracture parameters can include a number of fractures, a
fracture
drainage area half-length Ye, a fracture drainage area half width Xe, a
fracture half-length Xf,
and the like.
[0042] In some examples, the system can be configured to treat each
fracture of a multi-
fracture well as multiple wells with a single fracture each. In some
instances, this may
simplify the models and may reduce the computational load on the system.
[0043] The model can account for spatial differences in geology through
geostatistical
realization. Multiple models are run on a finite and discrete number of areas
with a larger
defined region. Distributions can then be calculated for each area. The model
can
represent one region over a play or can be run on several.
[0044] Fig. 5 shows a flowchart illustrating aspects of an example
method 500 for
modelling hydrocarbon production rates for a subterranean formation. At 510,
one or more
processor(s) 210 and/or other aspects of device(s) 205 may be configured to
receive,
access, compile or otherwise obtain production data for at least one well in
the subterranean
formation 110.
[0045] In some examples, the production data can be obtained from one or
more
memories 215, storage devices 215, 225, and/or sensors or field devices 230,
240. In some
examples, the production data can include periodic (e.g. daily, weekly,
monthly, etc.)
production values, cumulative production values or any other data values from
which
suitable production data can be calculated.
[0046] In some embodiments, the production data for the well(s) should
span at least 6
months of normalized production in order to produce meaningful results.
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[0047] The processor(s) can also obtain drilling data, completion data,
and/or data
associated with geological properties.
[0048] In some examples, data associated with geological properties can
include well
logs such as gamma ray well log(s), bulk density well log(s), neutron density
well log(s),
resistivity well log(s), core and/or well image data, nuclear magnetic
resonance log(s), and/
or any other well log that can be measured in the well.
[0049] In some examples, the processor(s) drilling and/or completion
data can include
fracture heights, fracture half lengths, a number of fractures, a fracture
drainage area half-
lengths, a fracture drainage area half widths, a fracture half-lengths, well
lengths, and the
like.
[0050] In some embodiments, data may be obtained from internal data
sources, or data
collected from drilled wells and fracturing processes.
[0051] In some embodiments, data may be obtained from public sources
such as a data
retrieved from a government or otherwise public fracturing database. This
public data may
include production data for which production values for multiple fractures
and/or wells may
be combined into a single value. In some examples, the public data may not
include all
fracture characteristics or geological data.
[0052] In accordance with some embodiments, the methods, systems and
devices herein
may accommodate for incomplete data sources such as public data or limited
confidential
data from a third party while still providing a production model with a
reasonable degree of
confidence.
[0053] In some embodiments, the processor(s) may combine internal and
external data
sources.
[0054] At 520, the processor(s) identify a range of values for each
parameter in a set of
parameters for the subterranean formation. In some examples, the range of
values for a
parameter can be identified by determining a possible range of values based on
geological
data. In some embodiments, the processors can receive or otherwise obtain
ranges of
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values from one or more input sources which may be based at least in part on
the collected
geological data for the subterranean formation.
[0055] The set of parameters can include one or more geological
parameters
representative of geological characteristics of the subterranean formation.
For example,
geological parameters can include one or more of formation height, reservoir
depth, porosity,
permeability, water saturation, and the like. In some examples, the geological
parameters
can include pressure properties, and/or rock and fluid properties including,
for example,
pressure gradient, initial pressure, operating conditions such as early or
late well flowing
pressure, months to well flowing pressure change, temperature gradient,
reservoir
temperature, rock compressibility, water compressibility, API (American
Petroleum Institute)
gravity, gas-to-oil ratio, combined gas gravity, relative gas permeability,
residual gas
saturation, critical gas saturation, gas viscosity, condensate gas ratio and
the like.
[0056] In some examples, the set of parameters can include well
parameters such as
completion parameters and fracture parameters. These parameters can include
fracture
heights, fracture half lengths, a number of fractures, fracture drainage area
half-lengths,
fracture drainage area half widths, fracture half-lengths, well lengths, and
the like.
[0057] In some instances, one or more parameters may be fixed or
constant based on
the parameter itself or the obtained data. These parameter(s) will have a
single value.
However, other parameters may be unknown or may not be pinpointed exactly, so
the
processor(s) generate or receive a range of potential values for the
parameter(s). These
ranges can be based on the obtained geological and/or other obtained data.
[0058] For example, the processor(s) can generate or receive parameter
ranges which
would be reasonable or possible based on log data, geostatistical models
and/or
extrapolated data between wells. In some examples, the processor(s) can
generate or
receive parameter ranges based on correlations with other parameters. For
example,
pressure(s) may be correlation with reservoir depth. In some examples, the
range of values
may be based on correlations with other geological formations having similar
geological
data.
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[0059] In some embodiments, the processor(s) can generate or receive a
granularity or
increment by which the ranges of parameter values can be varied in the system.
[0060] Each combination of values including a selection from each range
for the set of
parameters corresponds to, defines or otherwise represents a potential
subterranean
formation model, and the total set of different combinations of values for the
set of
parameters defines a set of potential subterranean formation models.
[0061] At 530, the processor(s) match the set of potential subterranean
formation models
to the production data for the well(s). The matching is based on an analytical
fracture model.
In some examples, the analytical fracture model can generate a production
model based on
the geological parameters. However, as described herein, the base analytical
model can
include a number of unknowns which cannot be solved directly. In some
embodiments, a
number of these unknowns can be combined into a single stimulated area value.
In some
examples, the stimulated area value can be based on a number of parameters in
the set of
parameters defining or otherwise associated with properties of a subterranean
formation
model.
[0062] In some examples, using a combination of values for the set of
parameters as
inputs to the analytical fracture model, the processor(s) can generate a
production model for
the potential subterranean formation model corresponding to the set of input
values. In some
examples, the processor(s) can determine a stimulated area value for the
generated
production model.
[0063] The processor(s) compare the generated production model with the
production
data from the well(s) to generate an error value between the production of the
generated
model and the physical well production data. In some examples, the error value
may be a
total error over the production period, an average error, a maximum error, or
any other error
metric. In some embodiments, the error value may be based on individual
production values
for each time period.
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[0064] In some embodiments, the error value may be based on one or more
of
cumulative gas production, gas production rate, cumulative oil production, oil
production
rate, and the like.
[0065] In some embodiments, the processor(s) are configured to select
parameter values
for inputting in a subsequent iteration based on a machine learning algorithm
and previous
error values. In some examples, the processor(s) can be configured to use a
genetic
algorithm to select subsequent parameter values for generating subsequent
models.
[0066] In some embodiments, the genetic algorithm can optimize or
improve the
searching of a large solution space. It can include selecting several sets of
random values
from all parameters and solving for the objective matching function. The
results which
provide the best matching function result can be merged together to find new
sets of values
for testing. This process is iterated with the best matching function results
from each iteration
used in subsequent sets of values for testing. In addition to or alternatively
to previous inputs
sets being combined, in some embodiments, random variations can be introduced
to input
sets. In some instances, this can reduce the chance of solutions converging on
a local
optimal rather than a global optimal.
[0067] In some instances, this may reduce the number of models to be
analyzed, and
may reduce the computation time and resources required to complete the model
matching
process.
[0068] At 540, the processor(s) identify the models from the set of
potential subterranean
formation models which fit the production profile from the production data
within a defined
error threshold. In some examples, this includes identifying the models having
an error value
less than the defined error threshold. In some examples, the error threshold
may be a
statically defined threshold. In other examples, the error threshold may be
based on a
defined percentile of the models.
[0069] In some embodiments, the error at different stages of production
can be weighted
differently. For example, if early production results are more important, the
error for earlier
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stages of production can be weighted more than error for later stages of
production; and vice
versa. These weightings can be applied to objective matching functions.
[0070]
In some embodiments, the determination of the stimulated area values includes
performing two runs to deliver a stable region. On the first run, a consistent
number (e.g.
5000) of trials are performed on each run. On the second run, the model can be
rerun with
the last good solution as a starting point to ensure tight clustering of
values. Again a
consistent number of runs should be used. In some embodiments, three criteria
are then
used to define an acceptable solution space. First, a minimum absolute error
of at least 20%
should be achieved for a run to be considered valid. All runs should be
completed with
similar weighting to ensure the results are comparable. Second, the mean error
can be
examined as it progresses through the solution space. Cases that are within a
best fit mean
error will be retained. Only trials with a deviation of less than 1% will be
used. Third, the
maximum error of 2x the minimum error should be used to bound the cases.
The
corresponding total error for this stable region of running average stimulated
area value can
be used to pick a minimum and maximum stimulated area value . In other
embodiments,
different mechanisms for determining the stimulated area values may be used.
[0071]
At 550, the processor(s) select a range of stimulated area values from the
identified models which fit the production profile from the production data
within the defined
error threshold. In some examples, the selected range is based on the models
having the
lowest error values. In some examples, the selected range is based on a
concentration of
stimulated area values which correspond to models having a low error value.
[0072]
At 560, the processor(s) create a forecast production model for the
subterranean
resource having inputs based on the geological data, and stimulated value
input(s) based on
the selected range. The process for forecasting production model is described
in the
following sections.
Analytical Model
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[0073] As described above, in some embodiments, the matching process at
530 is based
on an analytical fracture model. In some examples, the analytical fracture
model can involve
a gas model, an oil model or both.
[0074] Fig. 6 shows an example flowchart 600 outlining aspects of an
example gas
model. As described herein or otherwise, the processor(s) generate or receive
physical input
values or ranges of physical input values based on obtained geological data.
In some
examples, such geological data can be derived from petrophysical
interpretation of well logs
from adjacent or nearby wells. In some embodiments, the geological data can
include time
steps, pressure differences (initial, early, late), net pay, gas permeability,
porosity, drainage
area half width, fracture spacing half distance, condensate gas ratio, and the
like.
PARAMETER Units Min Max Increments
Skin Shape Function 0.5 3 0.1
Krg 0.1 0.5 0.02
Formation Net Thickness m 53.24 70.69 0.25
Frac Height % 60% 100% 2%
Frac half length m 20 85 2
Well Length m 1200 1391 5
Number of Fracs Count 9 12 1
Reservoir Depth m 3236 3328 0
Pressure Gradient psi/ft 0.759927 0.834638
0.01
Early Pwf psig 2000 7500.0 100
Late Pwf psig 200 2000.0 20
Pwf Change Time Months 0 6.0 1
Temperature Gradient F/ft 0.02 0.03 0.001
Rock Compressibility 1/psi 1.0E-07 6.0E-06 2.0E-07
Porosity % 5% 6% 0.1%
Permeability (log scale) mD -4 -2.52 0.01
Water Saturation % 10% 18% 0.25%
CGR Bbl/Mmcf 50.00 89.00 5.00
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[0075] From the physical inputs, the processor(s) may calculate other
inputs which may
be dependent or otherwise correlated with the physical inputs or other
calculated inputs.
These calculated inputs or correlations may include gas z factor calculations,
critical
temperatures and pressures for miscellaneous gasses, gas viscosity
correlations, gas
compressibility correlations, gas pseudopressure miscellaneous gasses,
temperature, skin, k
slippage and the like. These calculations may be performed with any currently
known or
future techniques.
[0076] The table above illustrates example physical and calculated
inputs which may be
used to create models for the subterranean formation.
[0077] Based on Darcy's Law, in its simplest form, radial flow q is based
on both an
effective permeability, and a fracture area:
[0078] q = kA* LAp
[0079] Assuming all other factors are constant, if permeability
increases, the fracture area
must be lower to achieve the same flow rate. Since these parameters are both
unknown, the
relationship between these parameters can be determined to select appropriate
forecast
models which will produce accurate results. These unknowns can be combined
into a
stimulated area value which may be solved based on the known production data.
[0080] In a simplified linear flow equation:
[0081] = mA5 + b'
[0082] Oil and gas flow equations are different:
31.3B Tu 1
[0083] Oil:
m oct * Pi-Pwf
315.4T 1 1
m = __________________________
[0084] Gas: *
toggct pi-pwf xfvk
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[0085] As highlighted these linear flow equations share the unknowns of
pay thickness h,
the fracture half-width xf, and the square root of the permeability k. In some
embodiments,
processor(s) can be configured to combine these into a single stimulated area
value. This
stimulated area value can, in some embodiments, be the stimulated area A (h*
xr) times the
root of the effective permeability k.
[0086] In some embodiments, the analytical model for gas may be based on
an
equivalent gas flow rate equation:
(skin)(# of fracs)(4)(h)(Kgas)
[0087] (1)
qg = (Gas Constant)(460+T)(Pwd Gas)
Frtc
[0088] Where
skin = permeability adjustment factor due to liquid drop out
Lp = difference in pressure across wellface
h = pay thickness
Kg as= gas permeability
T = reservoir temperature in degrees Farenheit
Pwa Gas =dimensionless pressure
Frac
[0089] The dimensionless pressure can be based on a Gringarten (Gringarten,
A.C.,
Ramey, H.J., "Unsteady-State Pressure Distributions created by a well with a
single Infinite-
Conductivity Vertical Fracture", Stanford University, Aug. 1974) approach
using
dimensionless time:
0.00633*Kgas*Green Function Time
Tda Gas =
(2)
I1g*O*ctGas*4*xe*Ye
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[0090] Where
pig = gas viscosity
0 = porosity
Ct Gas= gas compressability
Xe = drainage area half width, and
Ye = drainage area half-length or half distance between fracs
[0091] With equation (2), the processor(s) can generate a log of
dimensionless time
values. In some examples, this model may assume and treat each fracture as a
single
vertical well with a single horizontal fracture. In some embodiments, the
processor(s) handle
each fracture in a well with multiple fractures as individual identical single
fracture wells with
a well length based on the original well length divided by the number of
fractures.
[0092] Based on the above and using Green Equations, the processor(s)
can generate
an analytical model including a log of dimensionless time and pressure
estimates. From
these logs and equation (1), a single phase gas forecast estimate can be
provided for each
time step. These cumulative gas volumes are at surface conditions prior to
liquids being
removed.
[0093] The relationship of pressure drop over time p/z can be used to
calculate pressure
steps as the gas is produced. In some embodiments, the processor(s) generate
the p/z
relationship based on initial pressure, and final pressure from the measured
or calculated
data. For example, an initial pressure can be a known measured data point, or
it can be
calculated based on depth and gradient data. In some examples, the gradient
may be a
varied parameter during the matching process.
[0094] Based on iterations of:
Pw f ¨ Pi
P/Z slope -
Qg
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the pressures at each interval can be generated.
[0095] In some embodiments, each time interval can be divided into two
or more
subintervals. The processor(s) can be configured to determine the pressure,
P/Z slope and
Q for each subinterval. The average pressure across these subintervals is then
used as the
pressure for the whole interval. In some examples, this can potentially
provide a more
accurate estimation of the changing pressure as the well ages.
[0096] In some embodiments, the processor(s) can be configured to
account for changes
to the gas/liquid composition changes with pressure. Based on the condensate
gas ratio
parameter, the processor(s) can generate or access a database of PVT (pressure-
volume-
temperature) tables at different yield bands.
[0097] In addition to the analytical model for gas production, in some
embodiments, the
processor(s) can generate an analytical model which alternatively or
additional accounts for
oil production. Fig. 7 shows an example flowchart 700 outlining aspects of an
example oil
model. As described herein or otherwise, the processor(s) generate or receive
physical input
values or ranges of physical input values based on obtained geological data.
In some
examples, such geological data can be derived from petrophysical
interpretation of well logs
from adjacent or nearby wells. In some embodiments, the physical inputs can
include time
steps, pressure differences, net pay, effective permeability, porosity,
drainage area half
width, fracture spacing half distance, condensate gas ratio or gas oil ratio,
initial water
saturation and the like.
[0098] From the physical inputs, the processor(s) may calculate other
inputs which may
be dependent or otherwise correlated with the physical inputs or other
calculated inputs.
These calculated inputs or correlations may include oil viscosity, gas
viscosity, oil expansion
factor, gas expansion factor, bubble point pressure, oil compressibility,
formation volume
factors, solution gas-oil ratio, formation volume factor, oil expansion
factor, and the like. In
some examples, these calculated inputs may be calculated relative to a bubble
point
pressure. These calculations may be performed with any currently known or
future
techniques.
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[0099] As described above, the processor(s) can generate the oil
analytical model by
determining a stimulated area value (e.g. A root K) similar to the gas model.
However, the
dimensionless time value function for oil can be based on:
0.00633*Koll*Green Function Time
[00100] Tda = and
o*O*Ct*4*((Xe*Ye)/(0.3048)2)
[00101] a, ¨ (# of fracs)(4)(h)(keff)(kro)
(141.2)(120)(Pwd)(Bti)
[00102] Where
[00103] Tda= dimensionless time
[00104] Ap = difference in pressure across wellface
[00105] h = pay thickness or layer thickness * frac height
[00106] Keff= absolute effective permeability
[00107] K01 = relative permeability to oil
[00108] Pwd =dimensionless pressure
[00109] pto = gas viscosity
[00110] Ct= gas compressability
[00111] Xe = drainage area half width
[00112] Ye = drainage area half-length or half distance between fracs
[00113] # of fracs = number of fractures in the horizontal well
[00114] Bti = Total expansion factor
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[00115] Based on the above and using Green Equations, the processor(s) can
generate
an analytical oil model including a log of dimensionless time and pressure
estimates. From
these logs and equations, an oil forecast estimate can be provided for each
time step. These
cumulative gas volumes are at surface conditions prior to liquids being
removed.
[00116] In some embodiments, the processor(s) can apply material balance
equations to
adjust the oil production model to account for different gas-oil ratios at
different pressures.
[00117] Absolute permeability is the measure of the ability of a single phase
fluid to move
through a porous medium. When multiple phases (ie. Gas and oil, or oil and
water) are
present at the same time inefficiencies are created resulting in a
permeability that is a
fraction of the absolute permeability. This is referred to as relative
permeability. Relative
permeability changes as a function of the saturation of one phase as a
percentage of pore
volume. Relative permeability curves describe this relationship. The curves
can be
determined through special core analysis or assumed based on an analog. In the
oil
production model, relative perm can be used to account for changes in
productivity as the
reservoir is depleted and gas is introduced out of solution. The relative
permeability
adjustment causes an appropriate reduction in productivity.
Well Matchinq
[00118] As discussed above, the processor(s) match the set of potential
subterranean
formation models to the production data for the well(s) based on an analytical
fracture
model. In some embodiments, the processor(s) can match the potential
subterranean
formation models based on both an oil analytical fracture model and a gas
analytical fracture
model. In some embodiments, each model can produce its own production models
and
associated stimulated area values. In some examples, the processor(s) can use
the results
of the two different models (gas or oil) to determine a probability that a
portion or all of a
subterranean formation will use one model over the other.
[00119] After matching the models, the processor(s) can store and/or compile
all the
production models and their corresponding error values and stimulated area
values. Fig. 8
shows a plot 800 of stimulated area vs. error with each data point
representing a matched
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production model. In some examples, the processor(s) can be configured to
generate such a
plot and output it on an output device such as a display, printer, or
communication device.
[00120] The processor(s) can be configured to identify a subset 810 of the
production
models (see Figs. 8 and 9) which have an error value below a defined threshold
or which
otherwise fit the production profile from the production data within a defined
error threshold.
Forecasting Model
[00121] At 560, the processors generate a forecast production model. In some
embodiments, the forecast production model is defined by a number of input
parameters
representative of geological characteristics of the subterranean formation.
The forecast
production model is based on the stimulated area values identified by the
analytical model
and well matching.
[00122] By applying distributions of reservoir input parameters for the area
of interest, the
forecast production model can generate production forecasts over time for the
area of
interest. In some embodiments, ranges and/or distributions of input parameters
for the area
of interest can be used as inputs to generate an average production forecast
for the area.
[00123] In some embodiments, the forecasting model can be run
deterministically using
single values for each parameter or Monte Carlo or similar techniques can be
used to deliver
a distribution of production forecasts. Forecasts can be created for both
hydrocarbon liquids
and gas.
[00124] In some embodiments, the forecast models can provide an indication of
predicted
average production rates over time. In other embodiments, the forecast models
can provide
probabilistic production rates based on the possible distributions for input
parameters
including the geological characteristics and the stimulated area value. As
illustrated in Fig.
11, in some embodiments, graphs are generated to illustrated different
probabilistic
production rates over time.
[00125] In some embodiments, by applying input parameters representative of
geological
characteristics of a particular area or localized region, the system can, in
some instance,
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model production rates which account for physical and potentially subtle
geological
variations across an area.
[00126] As illustrated in Fig. 10, in some embodiments, forecast models can be
used to
generate a visual map illustrating different production forecasts across a
prospective area. In
some instances, the forecast models can be used to generate a probabilistic
financial
viabilities of different potions of an area.
[00127] As described herein, in some embodiments, these forecast models can in
some
instances account for various unknowns in the available production data and/or
variations in
geological characteristics across a play.
[00128] Although the embodiments have been described in detail, it should be
understood
that various changes, substitutions and alterations can be made herein without
departing
from the scope as defined by the appended claims.
[00129] Moreover, the scope of the present application is not intended to be
limited to the
particular embodiments of the process, machine, manufacture, composition of
matter,
means, methods and steps described in the specification. As one of ordinary
skill in the art
will readily appreciate from the disclosure of the present invention,
processes, machines,
manufacture, compositions of matter, means, methods, or steps, presently
existing or later to
be developed, that perform substantially the same function or achieve
substantially the same
result as the corresponding embodiments described herein may be utilized.
Accordingly, the
appended claims are intended to include within their scope such processes,
machines,
manufacture, compositions of matter, means, methods, or steps
[00130] As can be understood, the examples described above and illustrated are
intended
to be exemplary only. The scope is indicated by the appended claims.
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