Note: Descriptions are shown in the official language in which they were submitted.
CA 02914348 2015-12-10
METHOD OF MODELLING HYDROCARBON PRODUCTION FROM FRACTURED
UNCONVENTIONAL FORMATIONS
BACKGROUND
[0001] Field of the Invention:
[0002] The invention related to methods of generation of hydrocarbon
production curves from
geological formations, and more specifically provides a method for the
generation of curves of
hydrocarbon production from unconventional reservoirs stimulated by multi-
stage hydraulic
fractures.
[0003] Background:
[0004] There is a long history of technological development and innovation in
the field of
hydrocarbon exploration and extraction. As a capital intensive industry, the
hydrocarbon
extraction industry has much incentive to optimize and maximize production
from particular
hydrocarbon-bearing formations. For example, unconventional reservoirs are
hydrocarbon
reservoirs where permeability is low and stimulation is required for
profitable production.
[0005] In the production of hydrocarbon from unconventional geologic
formations such as
shale, one common extraction optimization technique is to stimulate the
hydrocarbon reservoir
by creating multiple hydraulic fractures along a multi-stage fractured
horizontal well. This
technique is commonly referred to as "fraccing". The resulting hydrocarbon
production in a
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fraccing scenario is a result of flow in matrix, in natural fracture networks
and in the hydraulic
fractures themselves.
[0006] There are a number of problems in trying to model hydrocarbon
production in a
fractured geological formation with high heterogeneity. For example, during
multi-stage
hydraulic fracturing, some pre-existing natural fractures are reactivated.
Hydraulic fractures and
the active natural fractures comprise a hydraulically conductive flow network
for hydrocarbon
production. In other circumstances, unconventional formations along the
horizontal well are
known to be highly heterogenous in petrophysical and geological
characteristics. In this type of
the circumstance, the formation reacts differently at different fracturing
stages and the
generated fracture network along the horizontal well was also highly
heterogenous. A modeling
method can only be reliable by incorporating consideration of the
heterogeneity of these post
fracturing unconventional formations.
[0007] Innovative fracturing techniques are also being developed and used by
many frac
companies, including two representative techniques referred to under the
SIMULFRAC and
ZIPPERFRAC brands. In either the SIMULFRAC or ZIPPERFRAC methods, two or more
Parallel horizontal wells are drilled and then perforated and fractured an
alternate intervals
along the wellbore. This creates a high density network of hydraulic fractures
and accordingly,
the stimulated volume that each hydraulic fracture can control is relatively
reduced. The
stimulated volume beyond hydraulic fracture tips also becomes smaller and its
inside flow may
no longer behave like linear flow. Existing modeling methods are inapplicable,
if they assumed
that the flow beyond the fracture tips is linear.
[0008] Another complication is that fluid flow mechanisms in unconventional
reservoirs are
quite complex when compared with conventional formations. Darcy's law is
always deficient in
such reservoirs. Gas diffusion and desorption appear simultaneously in
production of some
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unconventional gas reservoirs. Moreover, high dependence of reservoir
permeability on stress is
been confirmed by many experiments. Few methods have been developed in any
technical
literature or approach to comprehensively incorporate all of these complex
flow mechanisms
into modeling or evaluating the production of unconventional reservoirs.
[0009] Another one of the issues associated with the modelling or execution of
fracture
treatment in unconventional formations is the difficulty associated with
forecasting or
accurately modelling the likely production from the formation. Although
complex analytical
and numerical methods may be developed to represent the fluid flow towards a
multi-stage
fractured horizontal well, these methods require high computing capacity, long
computing time,
and also show difficulty in iterative applications. One of the main technical
reasons for the
difficulty in these computations is the low matrix permeability.
[0010] Hydrocarbon produced from each fracture stage mainly comes from
stimulated
reservoir volume around the hydraulic fracture(s), which provides
possibilities for decomposing
the reservoir into smaller parts. A fast, simple and reliable method of
considering the
production from an unconventional reservoir, based upon a decomposition of the
unconventional reservoir into smaller parts would it is believed be well
received.
[0011] If it were possible to create a method for the generation of a type
curve of hydrocarbon
production from an unconventional reservoir which is stimulated by multi-stage
hydraulic
fractures this would be desirable in the hydrocarbon production industry.
BRIEF SUMMARY
[0012] The invention comprises a method of modeling hydrocarbon flow from a
fractured
unconventional reservoir which has been subjected to multi-stage fracturing.
The invention
develops type curves of hydrocarbon production from unconventional reservoirs
stimulated by
multi-stage hydraulic fractures. The type curves refer to a series of curves
with time as x-axis
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and production rates q /bottomhole pressure p/bottomhole pressure derivatives
as y-axis under
specified reservoir conditions. Type curves can help predict reservoir
properties, fracture
properties and production trend by matching field production data.
[0013] In some embodiments, a method of modeling hydrocarbon flow from a
fractured
unconventional reservoir may include gathering relative data corresponding to
an
unconventional reservoir which has been subjected to multi-stage hydraulic
fracturing, using
the relative data, modeling the sub-system hydrocarbon flow for each of the
group of flow sub-
systems based upon the at least one set of reservoir properties assigned
thereto and the relative
data corresponding to the flow sub-system, modeling region hydrocarbon flow
for each closed
production region by coupling the calculated sub-system hydrocarbon flows for
each of the
flow sub-systems within the closed production region, and/or modeling
reservoir hydrocarbon
flow for the unconventional reservoir by coupling the calculated region
hydrocarbon flows for
each of the group of closed production regions.
[0014] The method of the present invention comprises in a first step gathering
relative data
corresponding to an unconventional reservoir which has been subjected to multi-
stage hydraulic
fracturing. The relative data will then be used to define a production
reservoir block being the
primary hydrocarbon producing region within the unconventional reservoir,
calculate the
reservoir dimensions of length, width and height of the production reservoir
block; and define
the location and characteristics of each hydraulic fracture within the
production reservoir block.
The production reservoir block is then subdivided into a plurality of closed
production regions,
each closed production region containing at least one hydraulic fracture
therein, and region
dimensions of length, width and height are calculated for each closed
production region. Each
closed production region is then divided into a plurality of flow sub-systems,
and at least one
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set of reservoir properties is assigned to each flow sub-system. Following the
definition of
these key parameters, the modelling can be completed.
[0015] The relative data corresponding to the unconventional reservoir are
selected from the
group of mineral land data, production history, fracture treatment record and
microseismic
activity. The at least one set of reservoir properties assigned to a flow sub-
system is selected
from a group of reservoir properties or a group of fracture properties. The
reservoir properties
selected from include matrix permeability and matrix porosity, and the
fracture properties are
properties of hydraulic fracture and natural fracture. The fracture properties
selected from
include fracture permeability, fracture porosity, fracture thickness/width,
fracture stress-
sensitivity, and hydraulic fracture half-length.
[0016] The at least one set of reservoir properties assigned to each flow sub-
system can be
selected from the group of linear flow in reservoir, linear flow from
reservoir to hydraulic
fractures, flow towards fracture tips, and flow inside hydraulic fractures.
The at least one set of
reservoir properties assigned to each flow sub-system within the production
reservoir block can
be the same, or different.
[0017] The next step in the method of the present invention is to, in respect
of at least one
selected point in time:
a. model the sub-system hydrocarbon flow for each of the plurality of flow sub-
systems based upon the at least one set of reservoir properties assigned
thereto
and the relative data corresponding to the flow sub-system;
b. model region hydrocarbon flow for each closed production region by coupling
the
calculated sub-system hydrocarbon flows for each of the flow sub-systems
within
said closed production region; and
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c. model reservoir hydrocarbon flow for the unconventional reservoir by
coupling
the calculated region hydrocarbon flows for each of the plurality of closed
production regions.
[0018] Following the modelling of the sub-system hydrocarbon flow, region
hydrocarbon flow
or reservoir hydrocarbon flow, various type curves can be generated using the
results of these
models at the at least one selected point in time. For example, where the sub-
system
hydrocarbon flow for at least one of the plurality of flow sub-systems is
modeled in respect of a
plurality of selected points in time, the method can further comprise the step
of generating at
least one type curve displaying the modeled sub-system hydrocarbon flow for
the selected flow
sub-system on one axis thereof and the related selected points in time on
another axis thereof.
[0019] Similarly where region hydrocarbon flow for at least one of the
plurality of closed
production regions is modeled in respect of a plurality of selected points in
time, the method
can further comprise the step of generating at least one type curve displaying
the modeled
region hydrocarbon flow for the selected closed production region on one axis
thereof and the
related selected points in time on another axis thereof.
[0020] Where reservoir hydrocarbon flow is modeled in respect of a plurality
of selected
points in time, and further comprising the step of generating at least one
type curve displaying
the modeled reservoir hydrocarbon flow for the production reservoir block on
one axis thereof
and the related selected points in time on another axis thereof.
[0021] In certain embodiments of the invention, the sub-system hydrocarbon
flow for each of
the plurality of flow, sub-systems is modeled by creating a partial
differential sub-system partial
differential flow equation representing the determined hydrocarbon flow for
said flow sub-
system, whereby each sub-system partial differential flow equation can be
coupled to the sub-
system partial differential flow equation for other flow sub-systems within
the corresponding
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closed production region. Region hydrocarbon flow for each closed production
region can be
modeled by coupling the sub-system partial differential flow equations for
each of the plurality
of flow sub-systems within said closed production region to yield a partial
differential region
partial differential flow equation, whereby each region partial differential
flow equation can be
coupled to region partial differential flow equations for other closed
production regions within
the production reservoir block. Alternatively the reservoir hydrocarbon flow
can be modeled
by coupling the region partial differential flow equations for all of the
plurality of closed
production regions within the production reservoir block, to yield a reservoir
flow equation.
The result of the reservoir flow equation is the anticipated hydrocarbon
production from the
production reservoir block adjusted for the unconventional geology and
multiple fractures
therein.
[0022] The closed production regions might each have at least one hydraulic
fracture either
centered or uncentered therein.
[0023] Each sub-system partial differential flow equation can comprises at
least one of a linear
flow equation, a radial flow equation, or a source/sink function.
[0024] The region dimensions of at least one closed production region can be
modified from
the region dimensions initially calculated based on the hydraulic fracture
locations and the
relative data.
[0025] In addition to the method for the generation of type curve data points
for use in the
assessment of hydrocarbon production in a stimulated unconventional reservoir,
the method can
be practiced in a computer software implementation. In this phase, the
invention comprises a
non-transitory computer-readable storage medium for use in a method of
modeling hydrocarbon
flow from a fractured unconventional reservoir, the computer-readable storage
medium
including instructions that when executed by a computer, cause the computer
to:
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a. assemble relative data corresponding to an unconventional reservoir which
has
been subjected to multi-stage hydraulic fracturing;
b. using the relative data:
i. define a production reservoir block being the primary hydrocarbon
producing region within the unconventional reservoir;
ii. calculate reservoir dimensions of length, width and height of the
production reservoir block; and
iii. define the location and characteristics of each hydraulic fracture within
the production reservoir block
iv. subdivide the production reservoir block into a plurality of closed
production regions, each closed production region containing at least one
hydraulic fracture therein;
v. calculate region dimensions of length, width and height for each closed
production region;
vi. subdivide each closed production region into a plurality of flow sub-
systems; and
vii. assign at least one set of reservoir properties to each flow sub-system
[0026] Following generation of these first parameters the next step undertaken
by the software
is to, in respect of least one selected point in time:
a. model the sub-system hydrocarbon flow for each of the plurality of flow sub-
systems based upon the at least one set of reservoir properties assigned
thereto
and the relative data corresponding to the flow sub-system;
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b. model region hydrocarbon flow for each closed production region by coupling
the
calculated sub-system hydrocarbon flows for each of the flow sub-systems
within
said closed production region; and
c. model reservoir hydrocarbon flow for the unconventional reservoir by
coupling
the calculated region hydrocarbon flows for each of the plurality of closed
production regions.
The various paramaters and permutations of the modeling method outlined above
could all be
implemented in the software and all such modifications are contemplated within
the scope of
the present invention.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
[0027] To easily identify the discussion of any particular element or act, the
most significant
digit or digits in a reference number refer to the figure number in which that
element is first
introduced.
[0028] FIG. 1 is a flowchart showing the steps in one embodiment of the method
of modeling
hydrocarbon flow from a fractured unconventional reservoir of the present
invention;
[0029] FIG. 2 is a flowchart of the method of Figure 1, adding the step of the
generation of
type curves from the modeled reservoir production;
[0030] FIG. 3 is a flowchart of the method of Figure 2, adding the step of
modification of the
plurality of closed production regions once initially calculated;
[0031] FIG. 4 is a schematic representation of an unconventional reservoir
stimulated by
multi-stage hydraulic fracturing;
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[0032] FIG. 5 is a plan view of streamlined distribution in the unconventional
reservoir of
Figure 4;
[0033] FIG. 6 demonstrates the subdivision of a closed production region of
Figure 5 into a
plurality of flow sub-systems in accordance with one embodiment of the present
invention
(Region 1 of Figure 5);
[0034] FIG. 7 demonstrates an alternate embodiment of the subdivision of a
closed production
region of Figure 5 into a plurality of flow sub-systems in accordance with the
present invention
(Region 1 of Figure 5);
[0035] FIG. 8 demonstrates another embodiment of the subdivision of a closed
production
region into a plurality of flow sub-systems in accordance with the invention;
[0036] FIG. 9 demonstrates another embodiment of the subdivision of a closed
production
region into a plurality of flow sub-systems in accordance with the invention;
[0037] FIG. 10 demonstrates another embodiment of the subdivision of a closed
production
region into a plurality of flow sub-systems in accordance with the invention;
[0038] FIG. 11 demonstrates another embodiment of the subdivision of a closed
production
region into a plurality of flow sub-systems in accordance with the invention;
[0039] FIG. 12 is a sample of a type curve produced by the method of modeling
hydrocarbon
flow from a fractured unconventional reservoir of the present invention;
[0040] FIG. 13 is a flowchart showing the steps involved in one embodiment of
a
computerized embodiment of the method of modeling hydrocarbon flow from a
fractured
unconventional reservoir herein.
CA 02914348 2015-12-10
DETAILED DESCRIPTION
Description
[0041] The present invention is a method of modeling hydrocarbon flow from a
fractured
unconventional reservoir. The "unconventional reservoir" implies a reservoir
where
permeability is low and stimulation is required for profitable production.
Multi-stage hydraulic
fracturing techniques are often used to maximize oil and gas hydrocarbon
recovery from such a
formation, and the type curve is a useful modeling technique used to assess
reservoir
productivity.
[0042] A type curve is a visual tool used to evaluate hydrocarbon production -
it is a graph
with time as x-axis and production rates q /bottomhole pressure p/bottomhole
pressure
derivatives as y-axis under specified reservoir conditions. Typically multiple
type curves are
generated based on adjustments to formation paramaters. Type curves can help
predict reservoir
properties, fracture properties and production trend by matching field
production data.
[0043] As outlined herein, the invention comprises a method of modeling
hydrocarbon flow
from a fractured unconventional reservoir. Current techniques for hydrocarbon
production
modeling in a fractured unconventional reservoir are time consuming, and less
accurate than
they could be in certain cases. The current method, of effectively
deconstructing the particular
unconventional reservoir into a pplurality of closed production regions and a
plurality of flow
sub-systems therein, each of which accommodates individual hydraulic fracture
locations in the
formation, provides a more accurate outcome with higher efficiency as well as
speed of
rendering the completed type curves in question.
[0044] Method overview:
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[0045] Figure 1 is a flow chart demonstrating the steps of the method of the
present invention,
which we first refer to. As outlined herein, the invention is a method of
modeling hydrocarbon
flow from a fractured unconventional reservoir - type curves of hydrocarbon
production
parameters in an unconventional reservoir are generated based on the modelling
technique
outlined herein.
[0046] The first step in the method of modeling hydrocarbon flow from a
fractured
unconventional reservoir of the present invention is to assemble relative data
corresponding to
the unconventional reservoir, which has been subjected to multi-stage
hydraulic fracturing
either natural or manmade. This is shown at Step 1-1. The relative data which
would be useful
to the present method would include, but not be limited to, mineral land data,
production
history, fracture treatment record and microseismic activity. The relative
data will be used in
the remainder of the method of modeling hydrocarbon flow from a fractured
unconventional
reservoir to render models of the unconventional reservoir, a production
reservoir block, and
the location and characteristics of hydraulic fractures which are used in
determining reservoir
hydrocarbon flow.
[0047] Following the assembly of the relative data, the relative data is used
in the next step of
the method of modeling hydrocarbon flow from a fractured unconventional
reservoir - shown at
Step 1-2. The first element of this next step is to define a production
reservoir block, which is
the primary hydrocarbon producing region within the unconventional reservoir
which it is
desired to model. Using the relative data the production reservoir block can
be selected from
the overall geology of the unconventional reservoir. In addition to selecting
the overall shape
and size of the production reservoir block, the reservoir dimensions being the
length, width and
height of the production reservoir block will also be determined. The
production reservoir block
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volume and other calculations related to the reservoir hydrocarbon flow can be
calculated using
the reservoir dimensions.
[0048] Following the definition of the production reservoir block and
determination of the
reservoir dimensions, the hydraulic fracture locations and fracture properties
of each of the at
least one hydraulic fracture within the production reservoir block will also
be determined and
reflected in the model of the production reservoir block. This is shown at
Step 1-3. Hydraulic
fracture locations are important parameters to the remainder of the modeling
of the method of
modeling hydrocarbon flow from a fractured unconventional reservoir of the
present invention
as the production reservoir block will be divided into a plurality of closed
production regions
based upon the hydraulic fracture locations.
[0049] The production reservoir block is then subdivided into a plurality of
closed production
regions based upon the hydraulic fracture locations therein - shown at 1-4.
Each closed
production region typically will contain at least one complete hydraulic
fracture. Again, based
upon the relative data associated with the particular selected area comprising
each closed
production region, the region dimensions for each closed production region,
being the length,
width and height of each such closed production region will be determined. In
modeling each
closed production region, the at least one hydraulic fracture therein can be
centered in the
closed production region, or can be uncentered therein. Both such approaches
are contemplated
herein.
[0050] Based upon the dimensions, geology and at least one hydraulic fracture
located within
each closed production region will be divided into a plurality of flow sub-
systems. The division
of each of the plurality of closed production regions into a plurality of flow
sub-systems is
shown at Step 1-5. Effectively the division of each closed production region
into a plurality of
flow sub-systems comprises parsing the closed production region into a
granular set of sub-
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units each of which can best be accurately and quickly modeled from a
production perspective,
based upon the granularity of the available relative data and conditions
therein for that purpose.
[0051] Next at 1-6, each flow sub-system will then have at least one set of
reservoir properties
assigned thereto, which are additional parameters in addition to the
dimensions and other
available relative data which can be used to formulaically determine the
likely hydrocarbon
flow in the flow sub-system. A number of different types of reservoir
properties can be relevant
to formation production and to the modeling and creation of type curve related
to
unconventional reservoirs where multi-stage hydraulic fracturing will be or
have been
employed. These include reservoir properties as well as fracture properties.
The reservoir
properties mainly include matrix permeability k and porosity cp. The fracture
properties refer to
properties of natural fracture and hydraulic fracture, which include fracture
permeability kF,
fracture porosity 9F, fracture thickness/width wf, fracture compressibility
cF, and hydraulic
fracture half-length xf.
[0052] With the production reservoir block having been defined and subdivided
into a
plurality of closed production regions each comprising a plurality of flow sub-
systems, the
modeling of the actual production of hydrocarbons from each flow sub-system
can be
commenced (shown at 1-7), for subsequent coupling to yield a completed
calculation of
reservoir hydrocarbon flow. This is done by firstly, with respect to each flow
sub-system,
modeling the sub-system hydrocarbon flow based upon the at least one set of
reservoir
properties assigned in respect of the flow sub-system in question. There are
many ways that the
sub-system hydrocarbon flow will be able to be modeled, as will be understood
to those skilled
in the art, and all such approaches are contemplated within the scope of the
present invention. It
is specifically contemplated that the sub-system hydrocarbon flow could be
modeled by the
creation of a sub-system partial differential flow equation which is a partial
differential
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equation which could be coupled to similar partial differential equations for
adjacent flow sub-
systems in the assembly of a grouped total region hydrocarbon flow etc. The
sub-system partial
differential flow equation could comprise at least one of a linear flow
equation, a radial flow
equation, or a source/sink function.
[0053] In an embodiment where the sub-system hydrocarbon flow is modeled by
the creation
of such a sub-system partial differential flow equation, the sub-system
partial differential flow
equation could use the available and relevant relative data along with the
assigned at least one
set of reservoir properties in respect of the flow sub-system in question. The
same type of a
partial differential equation could be created for the modeling of the sub-
system hydrocarbon
flow for each flow sub-system within the closed production region or within
the production
reservoir block, or different types of sub-system partial differential flow
equations could be
used for different flow sub-systems based upon the avaialbe parameters, and
the geology and
other characteristics of the assigned area comprising the flow sub-system.
[0054] Following the modeling of the production from each flow sub-system, the
next step in
the method of the present invention is the modeling of the anticipated region
hydrocarbon flow
for each of the plurality of closed production regions (Step 1-8) which is
done by aggregating
the anticipated sub-system hydrocarbon flow for all of the flow sub-systems
within the closed
production region. Where the anticipated sub-system hydrocarbon flow for each
flow sub-
system within the closed production region is represented by a sub-system
partial differential
flow equation, the region hydrocarbon flow can be modeled by the coupling of
said sub-system
partial differential flow equations. The precise coupling of such sub-system
partial differential
flow equations to yield a rolled up model of the anticipated region
hydrocarbon flow will be
understood by those skilled in geology and mathematics and all such approaches
again are
contemplated within the present invention. The region hydrocarbon flow might
be represented
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by another region partial differential flow equation, or otherwise, and all
such approaches again
are contemplated herein.
[0055] Finally the reservoir hydrocarbon flow can be modelled (Step 1-9) by
aggregating the
region hydrocarbon flow for each of the plurality of closed production regions
within the
production reservoir block. This again can be done either by coupling region
partial differential
flow equations representing the anticipated aggregated hydrocarbon flow from
each of the flow
sub-systems within each of the plurality of closed production regions, or in
other approaches
and again all are contemplated within the scope hereof.
[0056] Where each sub-system partial differential flow equation is a couplable
partial
differential equation, the solution to each sub-system partial differential
flow equation can
represent production pressure and production volume rate for the corresponding
flow sub-
system. Similarly where the region hydrocarbon flow is represented by a
couplable differential
region partial differential flow equation, the solution to such a region
partial differential flow
equation can represent production pressure and production flow rate for the
corresponding
closed production region. If the reservoir hydrocarbon flow is modeled as a
coupled reservoir
flow equation comprised of the solutions of a plurality of region partial
differential flow
equations, the solution to the reservoir flow equation represents production
pressure and
production flow rate for the unconventional reservoir.
[0057] The method of Figure 1 can be enhanced by the plotting of one or more
type curves
using the modeled reservoir production. Following the modelling of the
anticipated reservoir
hydrocarbon flow from the production reservoir block, being the production
pressure and
production volume rate therefrom, one or more type curves can be created using
said reservoir
hydrocarbon flow in a following step. Type curves could be generated at the
flow sub-system,
closed production region, or production reservoir block level. The flowchart
of Figure 2
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demonstrates an extension of the method of Figure 1 in which the first nine
steps are the same
as the method of Figure 1, with the plotting of one or more type curves shown
at Step 2-10.
[0058] A further modification of the underlying method of modeling hydrocarbon
flow from a
fractured unconventional reservoir of the present invention of Figure 1 or
Figure 2 is shown in
Figure 3. The difference in the steps of the method shown in Figure 3 versus
that of Figure 2 is
the insertion of Step 3-5, following the subdivision of the production
reservoir block into a
plurality of closed production regions, showing the manual or interventionist
modification of at
least one of the plurality of closed production regions following their
initial determination or
assignment. The remainder of the steps shown in Figure 3 are the same as those
of the method
embodiment of Figure 2, subject to the renumbering of the steps sequentially
after the insertion
of Step 3-5 therein.
[0059] Modeling examples:
[0060] Having reviewed the method of modeling hydrocarbon flow from a
fractured
unconventional reservoir in high level concept, we now wish to outline the
efficacy of the
method itself and describe in further detail the development of the production
reservoir block,
the plurality of closed production regions and plurality of flow sub-systems
with respect to a
particular unconventional reservoir.
[0061] Figure 4 shows one embodiment of an unconventional reservoir which has
been
stimulated with multi-stage hydraulic fracturing. A multi-stage fractured
horizontal well is
shown centered therein. In this Figure 4 the production reservoir block refers
to the primary
hydrocarbon producing region within the unconventional reservoir which it is
desired to model.
The reservoir length L in Figure 4 equals the wellbore's horizontal length.
Well spacing is
chosen as the width W. In general, the target formation thickness works as the
height H. For the
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fractured horizontal well, each hydraulic fracture has half length xf and
width wf. The hydraulic
fracture numbers, locations and intervals are determined based on fracturing
treatment records.
According to treatment records, hydraulic fracturing is always completed in
several stages with
several perforation clusters per stage. Some embodiments take one fracture per
stage when
calculating fracture numbers and spacing while some embodiments may consider
one fracture
per perforation cluster. The numbering or grouping of the hydrs could vary and
any approach
thereto is contemplated within the scope of the present invention.
[0062] The hydraulic fractures shown in Figure 4 are assumed to fully
penetrate the target
formation and therefore have same height as the reservoir height H. Fracture
properties in any
two hydraulic fractures can be different as well.
[0063] Although the stimulated reservoir is complex, certain methods can still
lead to fast,
simple and reliable modeling of the inside fluid flow. Figure 5 shows the
streamline distribution
during production for the stimulated production reservoir block in Figure 4.
Streamlines
represent a snapshot of the instantaneous flow field. For simplicity, the
production reservoir
block in Figure 5 is homogeneous and single-porosity. Streamlines show that
each hydraulic
fracture controls a part of the production reservoir block where the fluid
only flows towards this
hydraulic fracture. Corresponding to the six hydraulic fractures in Figure 5,
the production
reservoir block comprises six closed production regions with all-closed outer
boundaries. No
fluid flows across these boundaries. Each closed production region further
comprises four kinds
of fluid flow. Since the flow distribution is symmetrical to the wellbore,
studying half of the
production reservoir block is enough for building reliable models. Referring
for example to
Region 1 of the formation shown in Figure 5, in the upper part of Region 1,
streamlines show
that flow from the production reservoir block in this area converges towards
the hydraulic
fracture tips. On the left and right of Region 1, flows down to the hydraulic
fracture from both
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sides are normal to the fracture plane and in the hydraulic fracture of Region
1, inside flow
moves towards the horizontal wellbore.
[0064] Complex fluid flows in the stimulated production reservoir block can be
reduced to
several kinds of simple flows, which provides the basis for this invention.
The simple flows
within the flow sub-systems and closed production regions then give type
curves for the whole
production reservoir block. For each kind of simple flow in Figure 5,
mathematical solutions
exist in Laplace domain to describe corresponding instantaneous pressure/flow
rates field.
[0065] Region 1 of Figure 5 is divided into four flow sub-systems. Each flow
sub-system
contains one kind of simple fluid flow (arrows show fluid direction), and each
of these flow
sub-systems has independent reservoir properties. Figure 6 and Figure 7 show
two samples of
the flow sub-systems for Region 1 in Figure 5.
[0066] In the flow sub-system shown in Figure 6, the flow towards fracture
tips is shown in
terms of Green's function method. A line sink exists at Point A. The Green's
function for a line
sink in the closed rectangular flow sub-system shown is calculated as follows:
19
CA 02914348 2015-12-10
¨
1 ) 1õ(xv,h,)----2:71,2,..of'S xS re-wa ihD ..... (2.1)
0 =
r ,
1 F, (xõ ¨ x i, + nY- ; kx 1, - i - x An Hy
sx . õ E expi - , j= _________ cxpl ¨ .
21 %Pah(! b - r D) ,,,,,, I 1111.1 e - r0) Ill(' v ¨
r D)
_
................................................. (2.2)
_
I - ( v ¨ v -,- irY 1 ( v = + v - +
¨ ____________ \ ____ 2.., , exp - P - AD . i + exp , . AD ,
- 21.v" ..7-iii(i n ¨ r õ 1 õ....,,,,t ...1,) I
_
................................................. (2.3)
where
pw is the dimensionless pressure in sub-system 1.1
Q13,u
In is the dimensionless time, ktil(Opc,12,.).
1
11 is the dimensionless reservoir diffusivity of sub-system 1.1 ( , ki---
A Pet 1 ) Allet
gip is the dimensionless flow rate into the line sink at Point A in sub-system
1.1, gig).
B is the formation volume factor.
Q, ii, Lr, et and (1) are production rate, viscosity, length, compressibility
and porosity used as
reference values in dimensionless definition, respectively.
When applying radial equations, embodiments here assume a semi-radial
reservoir with Dietz
shape factor is equivalent to sub-system 1.1. Figure 7 shows the hypothetical
radial sub-system 1.1
in dash lines with boundaries /..= and r,. The radial flow equation of sub-
system 1.1 in Laplace
domain is
...¨ \
1 a ( opin s ¨
__I rt., ,,
P1D =I ) * ................ (.I A )
rD ari, ik. cro
with outer boundary condition
en
= to =0
................................................. (1.2)
Or,
)
where
.v is the Laplace variable.
rD is the dimensionless hypothetical radius,i- / 1,,, .
[0067] Detailed descriptions and solutions of the radial flow equations and
Green's function in
Laplace domain are fully described via several references including E.
Stalgorova, L. Mattar
"Analytical Model for Unconventional Multifractured Composite systems" SPE
Reservoir
Evaluation & Engineering, SPE 162516 and S. Yao, F. Zeng, H. Liu, G. Zhao, "A
Semi-
analytical Model for Multi-stage Fractured Horizontal Wells" Journal of
Hydrology 507: 201-
212. In designing the plurality of closed production regions of any
unconventional reservoir,
CA 02914348 2015-12-10
closed boundaries are usually placed at the center of two adjacent hydraulic
fractures. However,
closed boundaries can also lie off the center. The final sizes of each closed
production region
are determined based on best matching results.
[0068] In designing flow sub-systems of any closed production region, yi in
Figure 6 or Figure
7 is usually smaller than xf. When Green's function is applied, location of
Point A is (0, yi+Ay)
and location of Point B is (0, yi). The final values of yi and Ay are
determined based on best
matching results.
[0069] In sub-systems 1.2 and 1.3, linear flow equations can describe the
fluid flow normal to
hydraulic fracture planes C and D. For example, the linear sub-system partial
differential flow
equation of sub-system 1.2 is:
.............................................................. (3.1)
cx-i; 11,
1-'
=0 ........................................................... (3.2)
CAD .TID
[0070] Detailed descriptions and solutions of linear flow equations in Laplace
domain are
fully described via several references including one SPE paper M. Brown, E.
Ozkan, R.
Raghavan, H. Kazemi "Practical Solutions for Pressure-Transient Response of
Fractured
Horizontal Wells in Unconventional Shale Reservoirs" SPE Reservoir Evaluation
& Engineers
SPE 12504.
[0071] In sub-system 1.4, a modified linear flow equation can describe the
fluid flow inside
the hydraulic fracture. Sub-system 1.4 that is connected to wellbore has the
sub-system partial
differential flow equation:
21
CA 02914348 2015-12-10
P,n 2irk1.2 ¨ ¨
2FD 3FD r P rp ¨ 1)- ....... (4.1)
en 1'. k 1 ii
k
= 2,7
= .............................................. 1 D,teonl (4.2)
FIvi) 0 1'
Where
FcD is the dimensionless fracture conductivity, (h-FwF )/(U, ).
cp,Fand Tir are the flow rates into the hydraulic fracture from Planes C and
D.
qi,,,,õ,õ1 is the flow rate out of Region 1 through the intersection of
hydraulic fracture and horizontal
wellbore, Q .
[0072] Detailed description and solutions of this linear equation in Laplace
domain are fully
described via several references including L. Larsen, T. M. Herge, "Pressure
Transient Analysis
of Multifractured Horizontal Wells" SPE 28389. For initial conditions,
pressure is equal to
initial reservoir pressure in all flow sub-systems.
[0073] Following this work with respect to individual flow sub-systems, the
next step in the
method of modeling hydrocarbon flow from a fractured unconventional reservoir
is to couple
the solutions and the sub-system partial differential flow equation for each
of the plurality of
flow sub-systems within each closed production region to derive a solution,
representing a
region partial differential flow equation for each closed production region.
Referring to the
examples shown for Region 1. Two cases exist in coupling sub-systems 1.1 and
1.4. If Green's
functions are applied, the pressure at Point B(xB, yB) in 1.1 is assumed to
equal that on the
fracture tip in 1.4. Also the sink rate at Point A in 1.1 equals to that
through fracture tip. The
coupling conditions become:
22
CA 02914348 2015-12-10
and rho --==-= -F.CDfrPFD (5)
P ib(-T RD- Y Bo Fp ku. YID)
ey I)
If radial flow equations are applied in 1.1, both the pressure and flow rates
out of inner boundary
in 1.1 are equal to those through the fracture tip in 1.4. The coupling
conditions are
_ ¨ k 1 r , p1D'Cl)1:
1) 11)(rewD)=-= P FDI ........................... and " (6)
k CrD 2 D
rõõ
[0074] Pressure values in 1.2 and 1.4 at interface Plane C are the same.
Similar condition also
applies to interface Plane D. Flow rates into Plane C in 1.2 are equal to
these out of Plane C in
1.4. Similarly, flow rates into Plane D in 1.3 are equal to these out of Plane
D in 1.4. The
coupling conditions are:
k, P 'D
P 2D '1' ¨PFD FD
271-1, r (1-';XD
P- a 3D
P3D ______ = P EDI riD 3FD = _____________________________ (7)
i= ' D
[0075] There is no interaction among sub-systems 1.1, 1.2 and 1.3. At Plane E,
flow rates out
of the hydraulic fracture are assumed to equal gregionl. Then the linear flow
equation for sub-
system 1.4 can be solved in Laplace domain under all above boundary and
coupling conditions.
The derived mathematical solution can give the instantaneous pressure at Plane
E. Solutions for
other regions can be derived in the same way.
[0076] Following the coupling of the sub-system partial differential flow
equations into region
partial differential flow equations for each closed production region, the
next step in the method
of modeling hydrocarbon flow from a fractured unconventional reservoir is to
couple the region
partial differential flow equations for the plurality of closed production
regions to obtain a
solution for the whole production reservoir block. After coupling the sub-
system partial
differential flow equations into region partial differential flow equations,
the only unknown
23
CA 02914348 2015-12-10
parameter in each region partial differential flow equation or solution is the
flow rate out of a
hydraulic fracture gregioni n is the number of hydraulic fractures). Since
hydraulic
fractures are connected by horizontal wellbore, the pressure at the end of
hydraulic fractures are
equal to each other. Furthermore, in mathematical modeling the horizontal well
often operates
at constant pressure or constant rate. By applying this additional condition,
the method here
develops a system of n linear equations and solves it analytically in Laplace
domain. For
instance, the system of linear equations under constant-rate production is
like
_
-411 z412 0 0 = = = D.iegionl
0 Aõ A,3 0 0 = == 0
qD4egionl
0 0 A. A. 0 = == 0 0
D,leolon3
................................................................ (8)
=
0 0 0 === 0 AA,, ,
C D,rerrion n-I
1 1 1 1 1 1 1
,ie,Ion 77 _Al
C D
¨ s_
[0077] The solution of Eq. 8 gives the instantaneous bottomhole pressure and
flow rates
distribution along the horizontal wellbore in Laplace domain. Stehfest
algorithm can convert
values from Laplace domain to real-time domain. In Stehfest algorithm,
pressure changes into
real-time domain as
1112 , ¨I A
P D(t D)= ........................................... LT P VS (9)
D j=1
[0078] The Stehfest algorithm is fully described in H. Stehfest, "Numerical
Inversion of
Laplace Transforms" Communications of the ACM 13 (1):47-49. This invention
select a series
of time points tp, find corresponding Laplace time points s, calculate
solutions at different time
points s and convert results to real time space according to Eq. 9. The final
real-time solution is
24
CA 02914348 2015-12-10
a series of bottomhole pressure/flow rates at different time points. Type
curves are generated
based on the data of pressure/flow rates vs. time.
[0079] A real stimulated hydrocarbon reservoir might be more complex in
geology and
behaviour than that shown in Figure 6 and Figure 7 - reservoir properties may
change as the
distance from hydraulic fractures increases. Figure 8 through Figure 11 show
several additional
complex combinations plurality of flow sub-systems within a closed production
region.
[0080] Referring first to Figure 8, seven flow sub-systems exist within a
closed production
region. The flow sub-systems shown in this Figure can simulate an
unconventional reservoir
with gradual changes in reservoir properties throughout the production
reservoir block. Each
flow sub-system contains one kind of a simple flow and has independent
reservoir properties.
Radial flow moves through flow sub-system 1.2 towards flow sub-system 1.1. In
flow sub-
system 1.1, radial flow converges towards the inner boundary rw. Flow sub-
system 1.3 contains
linear flow. Flow sub-system 1.4 receives flow from flow sub-system 1.3 and
induces linear
flow to the hydraulic fracture. Similarly, linear flows occur in flow sub-
systems 1.5 and 1.6,
and flow sub-system 1.7 has linear flow inside the hydraulic fracture.
Governing equations of
these flow sub-systems are already listed.
[0081] The coupling conditions for the sub-system partial differential flow
equations based on
the embodiment of Figure 8 are different from those outlined above. The
coupling approach
shown in this context centers around coupling of the sub-system partial
differential flow
equation for flow sub-system 1.1 to the sub-system partial differential flow
equation for flow
sub-system 1.2 by equalizing pressure and flow rates across interface Plane A.
The sub-system
partial differential flow equations for flow sub-systems 1.3 and 1.4 are
coupled under same
pressure and flow rates across interface Plane B. he sub-system partial
differential flow
equations for flow sub-systems 1.5 and 1.6 are coupled with equal pressure and
flow rates
CA 02914348 2015-12-10
across interface Plane C. The sub-system partial differential flow equation
for flow sub-system
1.7 is coupled with the sub-system partial differential flow equations for
flow sub-systems 1.1,
1.4 and 1.6 by flow rates continuity across fracture tip and Planes D and E,
respectively. The
solution scheme, or the region partial differential flow equation, when
completed is similar to
the embodiments of Figure 6 and Figure 7. The resulting type curves can also
match and predict
reservoir production.
[0082] Figure 9 shows another different combination of flow sub-systems within
a closed
production region. The closed production region of Figure 9 is divided into
eight flow sub-
systems. Each og the flow sub-system in this Figure has one simple fluid flow.
In flow sub-
system 2.1, a line sink exists on the hydraulic fracture tip and Green's
function method
describes the pressure field. Linear flow goes through flow sub-system 2.2
towards flow sub-
system 2.4. Likewise, linear flow in flow sub-system 2.3 enters flow sub-
system 2.6. Flow sub-
systems 2.4 and 2.5 obtain flow from adjacent flow sub-systems and develop
inside linear flow.
Flow sub-systems 2.6 and 2.7 also have linear flow. For flow sub-system 2.8,
the hydraulic
fracture receives flow from surrounding flow sub-systems and leads linear flow
into horizontal
wellbore. Governing equations of fluid flows in the eight flow sub-systems can
be found from
those in Figures 4 and 5.
[0083] Coupling conditions are different for the different combinations of
flow sub-systems
shown in Figure 9. The flow into flow sub-system 2.4 is equal to that
perpendicular to interface
Plane A of flow sub-system 2.2. The flow into flow sub-system 2.6 is equal to
that
perpendicular to interface Plane B in flow sub-system 2.3. Flow sub-systems
2.4 and 2.5 are
coupled under flow rates continuity across Plane C. Flow sub-systems 2.6 and
2.7 are also
coupled based on flow rates continuity across Plane D. Flow sub-system 2.8 is
coupled with
flow sub-systems 2.1, 2.5 and 2.7 with flow continuity across fracture tip,
Plane E and Plane F
26
CA 02914348 2015-12-10
respectively. The solution scheme is similar to that of Figures 4 and 5. The
resulting type
curves can match and predict reservoir production. The selection of
appropriate coupling
conditions and other elements of the differential equations in question will
be understood to
those skilled in the art and the selection of appropriate conditions and
equation elements are all
contemplated within the scope of the present invention.
[0084] Modeling of another complex unconventional reservoir is shown with
reference to
Figure 10. As the unconventional reservoir becomes more complex in fractures
and flow, the
method of modeling hydrocarbon flow from a fractured unconventional reservoir
herein would
simply divide the reservoir into a larger number of flow sub-systems within
closed production
regions. Referring to Figure 10, seven flow sub-systems contain linear flow
inside the
unconventional reservoir and three flow sub-systems have radial flow towards
the hydraulic
fracture tip. In the embodiment of Figure 11, eleven flow sub-systems have
linear flow inside
the reservoir and one flow sub-system has a line sink on the fracture tip.
This implies that flow
sub-systems in a closed production region are not fixed. Plenty of
combinations of flow sub-
systems exist according to this method. Although the present invention has
been described with
preferred embodiments, it is to be understood that modifications and
variations may be utilized
without departing from the spirit and scope of this invention, as those
skilled in the art will
readily understand. Such modifications and variations are considered to be
within the purview
and scope of the appended claims.
[0085] One advantage of this invention is to easily model heterogeneous
reservoirs.
Heterogeneity is quite common for unconventional reservoirs. The reservoir
properties around a
horizontal wellbore can change significantly. To address heterogeneity, this
invention can
assign different reservoir properties to different flow sub-systems. Any two
flow sub-systems
can have different reservoir properties no matter the two sub-systems are in
same region or not.
27
CA 02914348 2015-12-10
For example, flow sub-systems 1.5 and 1.6 in Figure 8 may have different
reservoir properties
although they are the same side of the hydraulic fracture. Also any two flow
sub-systems can
have different fracture properties. For example, fracture permeability in
Region 1 of Figure 5
can be different from that in Region 5.
[0086] One more advantage of this invention is to model dual-porosity
reservoirs. Hydraulic
fracturing may reactivate dead natural fractures and part of the reservoir may
behave like dual-
porosity. Dual-porosity reservoirs are composed of two mediums: reservoir
matrix and natural
fractures. Furthermore, such dual-porosity characteristics may change along
the horizontal
wellbore. In this invention, any flow sub-system can be easily modified to a
dual-porosity flow
sub-system. This modification introduces two new parameters, storability ratio
co and flow
capacity ratio k, to characterize natural fractures. Solutions of single-
porosity flow sub-systems
apply to dual-porosity flow sub-systems with modified Laplace variable u as
tr --= sf (s) , .............................................. (1 0.1 )
_________________________ for pseudosteady dual - porosity reservoir
1 + VA@/(3s) tarili(V3ms/2 )for transient dual - porosity reservoir
.............................................................. (10.2)
[0087] A detailed description of this modification is given in J. E. Warren,
P. J. Root, "The
Behavior of Naturally Fractured Reservoirs", SPE Journal SPE 426 and 0. A. de
Swaan
"Analytical Solutions for Determining Naturally Fractured reservoir properties
by Well
Testing" SPE Journal SPE 5346. Likewise, any two flow sub-systems can have
different dual-
porosity parameters no matter if the two flow sub-systems are in same closed
production region
or not - the usual way is to make flow sub-systems dual porosity when they are
closer to
hydraulic fractures.
28
CA 02914348 2015-12-10
[0088] Another advantage of this invention is to easily consider complex flow
mechanisms in
shale gas reservoirs. Due to gas slippage, Knudsen diffusion and stress-
sensitivity, reservoir
matrix permeability becomes a function of reservoir pressure and gas
properties besides
intrinsic reservoir characteristics: F. Javadpour "Nanopores and Apparent
Permeability of Gas
Flow in Mudrocks (shale and siltstone)" Journal of Canadian Petroleum
Technology 48 (8): 16-
21 and A. R. Bhandari, P. B. Flemings, P. J. Polito, M. B. Cronin, S. L.
Bryant, "Anisotropy
and Stress Dependence of Permeability in the Barnett Shale", Transport in
Porous Media108
(2):393-41. Moreover, natural and hydraulic fractures may become stress-
sensitive during
production:
k r) ........................................ (11)
[0089] The semi-analytical method in this invention can model the impact of
above flow
mechanisms on hydrocarbon production. At initial time point, embodiments
herein initialize
properties of reservoir matrix and fractures in all flow sub-systems. Then
pressure/flow rates
field are calculated for all flow sub-systems. Reservoir matrix and fracture
properties are
updated based on the pressure/flow rates field. Then the updated properties
are used for next
time step calculation. This iterative process can continue until last time
step. Overall, in this
invention reservoir matrix and fracture properties can change with time
smoothly in every flow
sub-system and any two flow sub-systems can have different properties. Figure
13 provides a
flow chart that summarizes the modeling scheme. This scheme applies to basic
and complex
combinations of flow sub-systems.
[0090] By applying this semi-analytical method, reservoir heterogeneity, dual
porosity and
complex flow mechanisms can occur simultaneously in one closed production
region. Take
Region 1 in Figure 6 for example. Flow sub-system 1.1 can be single-porosity.
Flow sub-
systems 1.2 and 1.3 are dual-porosity and the inside natural fractures are
stress-sensitive. But
29
CA 02914348 2015-12-10
reservoir matrix and fracture properties can be different in flow sub-system
1.2 and 1.3. For
flow sub-system 1.4, hydraulic fractures are stress-sensitive. Gas slippage
and Knudsen
diffusion play a role in flow sub-systems 1.1, 1.2 and 1.3. It summarizes that
a closed
production region can have plenty of flow sub-system combinations while each
flow sub-
system can have plenty of property combinations. Although the present
invention has been
described with preferred embodiments, it is to be understood that
modifications and variations
may be utilized without departing from the spirit and scope of this invention.
[0091] The above solutions are based on liquid hydrocarbon production. To use
the solutions
and type curves for gas flow, the dimensionless pressure should be expressed
in terms of real
gas pseudopressure. The definition of pseudopressure can be found via the
reference Al-
Hussainy, R., Ramey Jr., H.J., Crawford, P.B "The Flow of Real Gases Through
Porous Media"
Journal of Petroleum Technology18(5):624-636.
[0092] Type curves can be used to match and predict production of the
stimulated
unconventional reservoir. Type curves are grouped under given reservoir and
fracture properties
of each flow sub-system in the model. Based on known information, one can at
first select
groups of type curves that conform to the information. Put type curves above
filed production
data under exactly same coordinate system. If one type curve can best fit
field data, conditions
behind the type curve represent the unknown reservoir and hydraulic
fracturefracture properties.
The trend of such type curve also implies the possible future production
behavior. One can
collect as much information as possible to reduce time spent in matching and
predicting.
Generation of the type curves as outlined herein provides different models and
scnearios for
consideration in reviewing or understanding the potential reservoir production
from the present
method.
CA 02914348 2015-12-10
[0093] Reservoir properties:
[0094] The types of reservoir properties which could be assigned to individual
flow sub-
systems for the purpose of modeling the production therefrom include various
types of reservoir
properties. The reservoir properties could be selected from a group of
reservoir properties or a
group of fracture properties.
[0095] The reservoir properties selected from include matrix permeability and
matrix porosity.
The at least one set of reservoir properties assigned to each flow sub-system
could also be
selected from the group of linear flow from reservoir to hydraulic fractures,
flow towards
fracture tips, and flow inside hydraulic fractures. Where fracture properties
are used as
reservoir properties assigned to a particular flow sub-system, these could
include properties of
natural fracture or hydraulic fracture, including fracture permeability,
fracture porosity, fracture
thickness/width, fracture stress-sensitivity, and hydraulic fracture half-
length.
[0096] The same reservoir properties could be assigned to one or more flow sub-
systems.
[0097] Considering type curves yielded:
[0098] Figure 12 selects two type curves created based on the geometry of
Figure 5. In Figure
12, the dash line shows the type curve generated based on the method of
reference S. Yao, F.
Zeng, H. Liu, G. Zhao, "A Semi-analytical Model for Multi-stage Fractured
Horizontal Wells"
Journal of Hydrology 507: 201-212. The solid line shows the type curve based
on this
invention. For simplicity, the whole production reservoir block is assumed
homogeneous here.
Figure 12 shows that the two methods give almost the same results. However,
the time of
generating type curves in this invention is dramatically shorter than that
used by the reference's
method. The differences regarding calculation time become wider when more
hydraulic
31
CA 02914348 2015-12-10
fractures are included. The following are the times to compute the type curves
shown in Figure
12 , which demonstrates the significant time benefit:
Calculation time
Calculation time of reference
of this invention method
3 Hydraulic Fractures 3 seconds 19 minutes
6 Hydraulic Fractures 5 seconds 51 minutes
12 Hydraulic Fractures 8 seconds 140 minutes
[00991 Calculation time is also dependent on computers' processing power.
Better computers
will further narrow down the calculation time. In general, this invention
provides a fast and
reliable method of generating type curves for stimulated unconventional
reservoirs.
[00100] Computer software:
[00101] The method of the present invention could also be reduced to practice
in a computer
software program - in fact beyond the mathematical method outlined herein, the
creation of a
computer software approach to the rendering of type curves in accordance with
the present
invention is contemplated to be the most likely commercial embodiment hereof.
The
development of computer software embodying the method of the present invention
will all be
contemplated and understood within the scope of the present invention.
[00102] The software of the present invention, being a non-transitory computer-
readable
storage medium for use in a method of modeling hydrocarbon flow from a
fractured
32
CA 02914348 2015-12-10
unconventional reservoir, the computer-readable storage medium including
instructions that
when executed by a computer, cause the computer to:
assemble relative data corresponding to an unconventional reservoir which has
been subjected to multi-stage hydraulic fracturing;
using the relative data:
define a production reservoir block being the primary hydrocarbon
producing region within the unconventional reservoir and calculate reservoir
dimensions of
length, width and height of the production reservoir block; and
defining the location and characteristics of each hydraulic fracture within
the production reservoir block;
subdivide the production reservoir block into a plurality of closed
production regions, each closed production region containing at least one
hydraulic fracture
therein and calculate region dimensions of length, width and height for each
closed production
region;
subdivide each closed production region into a plurality of flow sub-
systems; and
assign at least one set of reservoir properties to each flow sub-system
model the sub-system hydrocarbon flow for each of the plurality of flow sub-
systems based upon the at least one set of reservoir properties assigned
thereto and the relative
data corresponding to the flow sub-system;
33
CA 02914348 2015-12-10
model region hydrocarbon flow for each closed production region by coupling
the
calculated sub-system hydrocarbon flows for each of the flow sub-systems
within said closed
production region; and
model reservoir hydrocarbon flow for the unconventional reservoir by coupling
the calculated region hydrocarbon flows for each of the plurality of closed
production regions.
[00103] Effectively the software of the present invention could at its highest
level allow for the
computer-assisted execution of the method of modeling hydrocarbon flow from a
fractured
unconventional reservoir shown in Figure 1 through Figure 3. In addition to
the basic modeling
of the reservoir hydrocarbon flow, type curves could be plotted for use based
on the results
thereof.
[00104] The parameter assignments and calculations performed by the software
would be as
outlined above with respect to the method of modeling hydrocarbon flow from a
fractured
unconventional reservoir.
[00105] The computer software of the present invention would be capable of the
development
of couplable differential equations, for execution of embodiments of the
method comprised the
rendering of sub-system partial differential flow equations and region partial
differential flow
equations which were couplable to yield a solution representing the reservoir
hydrocarbon flow
in a reservoir flow equation.
[00106] Figure 13 demonstrates one embodiment of the method of the present
invention carried
out in computer software.
Drawings
34
