Note: Descriptions are shown in the official language in which they were submitted.
METHOD AND APPARATUS FOR PROCESSING PRODUCTION DATA OF
REFRACTURED OIL-GAS WELL
TECHNICAL FIELD
[0001] The present disclosure relates to the technical field of oil-gas
exploration, and in
particular to a method and an apparatus for processing production data of a
refractured oil-gas
well.
BACKGROUND
[0002] Refracturing is an important technic widely adopted to increase
production of an
oil-gas well with low permeability after an initial fracture fails. After
initial fracturing,
expansion of clay minerals and closure of fractures is caused by crushing of
proppant and
leaking-off of a fracturing fluid, which reduces conductivity of the fracture
and even disable
the fracture. Hence, it is important to reform low-production wells through
the refracturing
technique, so as to stabilize and increase production of a tight gas
reservoir. Branch
fractures are formed in the oil-gas wells through the refracturing technique,
increasing the
permeability of an existing fracture, a control degree of fractures over the
reservoir, and a
stimulated reservoir volume. Thereby, exploitation and production of oil-gas
are further
improved.
[0003] A technique of forming new branch fractures in refracturing is
generally applied, in
order to further connect oil-gas resources far away from a fractured area.
That is, various
temporary plugging agents are applied in a refracturing process to form
multiple branch
fractures on the existing fracture, and the branch fractures are used to
connect an area not
controlled by the existing fracture. A reservoir is better controlled by the
fractures after the
branch fractures are formed through refracturing.
[0004] In conventional technology, productivity of a refractured oil-gas well
developed for
tight gas reservoirs is generally calculated based on a field production test,
and few studies on
calculation have been made based on reservoir percolation. The field
production test on an
oil-gas filed is only capable to apply costly transient measurement, and is
not capable to
predict production. Generally, an analytic productivity equation is for
evaluating
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Date Recue/Date Received 2020-05-11
productivity of conventional oil-gas reservoirs, and requires to perform
Laplace transform and
Fourier transform. Such equations are difficult solve, and merely considers
conditions of a
single factor. A nonlinear factor and the refracturing are scarcely considered
in a
comprehensive manner in a model for calculating productivity.
[0005] Specifically, the conventional techniques are at least deficient in
following aspects.
It is difficult to quantize a process of predicting unsteady production of the
refracturing, by
solving a mathematical equation. It is difficult to couple mechanisms of
unsteady
production of the new fractures and the existing fracture, since they product
at different times
after the refracturing. There would be a huge deviation in calculating the
productivity in a
case that permeability of the fractures is set as a fixed value. With a pore
fluid being
exploited, a fracture skeleton filled with proppant deforms due to a change in
effective stress
on the skeleton, resulting in an effect of stress sensitivity that reduces the
permeability of the
fractures. The stress sensitivity increases with a reduced permeability of the
fractures,
according to studies of a percolation mechanism of tight gas reservoirs.
Therefore, it is
necessary to consider the effect of stress sensitivity on the fracture
percolation. It may be
assumed that gases flow uniformly into the fractures along a fracture surface,
and the fractures
are infinite in conductivity. Such assumption is only suitable for fractures
with high
conductivity. The fractures may be represented as an equivalent well diameter
or a skin
factor, and such processing is only suitable for a fracture in a shape of
elongated rectangular
and a well in a stage of radial-flow production. The reservoir percolation and
intra-fracture
flow may be treated as two independent processes, namely, which does not
consider a
practical situation in which a fluid flows non-uniformly into a fracture along
a surface of a
fracture wall. That is, a mode of the intra-fracture flow is not considered,
in which a fluid in
a reservoir flows uniformly into a fracture along a fracture surface, then the
fluid converges at
a tip of the fracture, and then the fluid flows to a wellbore as a regular
radial flow. It may be
assumed that the fracture is a rectangular with a fixed width and the fluid
flows
non-uniformly into the fracture along the fracture surface, and a model for
calculating a
pressure drop of a well with finite-conductivity fractures is established
based on equations
that couple the reservoir percolation and the fracture flow through equal
pressure and
continuous flow. Although the reservoir percolation and the fracture flow are
coupled in
such case, it is not considered that a shape of a hydraulic fracture is
subject to trapezoidal
variations in height and width along a length of the fracture. Such variations
significantly
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Date Recue/Date Received 2020-05-11
affect production of a refractured oil-gas well.
SUMMARY
[0006] In view of the above, a method and an apparatus for processing
production data of a
refractured oil-gas well are provided according to embodiments of the present
disclosure.
Production of a refractured oil-gas well is calculated quickly and accurately,
a reasonable basis is
provided for optimizing parameters of fractures of the refractured oil-gas
well, and an effect of
reforming the refractured oil-gas well is improved.
[0007] In order to address the above issues, following technical solutions are
provided
.. according to embodiments the present disclosure.
[0008] In a first aspect, a method for reforming a refractured oil-gas well is
provided according
to an embodiment of the present disclosure, comprising: discretizing spatially
an existing
fracture in the refractured oil-gas well and a new branch fracture on the
existing fracture, to
obtain a plurality of fracture infinitesimal segments that are same in length;
establishing a model
.. for reservoir percolation for each of the plurality of fracture
infinitesimal segments, based on a
geological characteristic of a reservoir and a basic property of a fluid;
establishing a model of
intra-fracture pressure drop for each of the plurality of fracture
infinitesimal segments, based on
a characteristic of the existing fracture and a characteristic of the new
branch fracture;
determining current production of the refractured oil-gas well, based on a
corresponding
relationship between production and pressure response in the model of
reservoir percolation, a
corresponding relationship between a pressure loss and a fracture width in the
model of
intra-fracture pressure drop, history fracturing data of the refractured oil-
gas well, and a
predetermined rule of intra-fracture fluid flow; optimizing parameters of
fractures of the
refractured oil-gas well, based on the determined current production; and
reforming the
.. refractured oil-gas well based on the optimized parameters.
[0009] In one embodiment, establishing the model for reservoir percolation for
each of the
multiple fracture infinitesimal segments based on the geological
characteristic of the reservoir
and the basic property of the fluid includes: constructing a point-source
function of a box-shaped
gas reservoir with a closed boundary, based on a reservoir boundary effect,
the geological
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Date Recue/Date Received 2021-09-21
characteristic of the reservoir, and the basic property of the fluid;
determining a function of fluid
flow resistance corresponding to each of the multiple fracture infinitesimal
segments, based on
the point-source function; and determining the corresponding relationship
between the
production and the pressure response of the refractured oil-gas well, based on
the function of
fluid flow resistance.
[0010] In one embodiment, constructing the point-source function of the box-
shaped gas
reservoir with the closed boundary includes: determining target reservoir
permeability in the
point-source function, based on a corresponding relationship between a stress
sensitivity
coefficient and reservoir permeability in the geological characteristic of the
reservoir;
constructing a real-gas effect equation based on the basic property of the
fluid; determining a
target stratum pressure in the point-source function; and determining the
point-source function,
based on a Green-function equation of a solution of the point-source function,
a real-gas effect
equation, the target reservoir permeability, and the target stratum pressure.
[0011] In one embodiment, establishing the model of intra-fracture pressure
drop for each of
the multiple fracture infinitesimal segments, based on the characteristic of
the existing fracture
and the characteristic of the new branch fracture includes: obtaining an
equation of intra-fracture
pressure drop, based on a corresponding relationship between preset reservoir
permeability and
production time; and determining the model of intra-fracture pressure drop,
based on the
equation of intra-fracture pressure drop and a corresponding relationship
between the fracture
width and a fracture length in the characteristic of the existing fracture and
the characteristic of
the new branch fracture.
[0012] In one embodiment, determining the current production of the
refractured oil-gas well,
based on the corresponding relationship between the production and the
pressure response in the
model of reservoir percolation, the corresponding relationship between the
pressure loss and the
fracture width in the model of intra-fracture pressure drop, the history
fracturing data of the
refractured oil-gas well, and the predetermined rule of intra-fracture fluid
flow includes:
determining an equation of transient production for the refractured oil-gas
well, based on a preset
flowing bottom-hole pressure, the corresponding relationship between the
production and the
pressure response in the model of reservoir percolation, and the corresponding
relationship
between the pressure loss and the fracture width in the model of intra-
fracture pressure drop;
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Date Recue/Date Received 2021-09-21
discretizing temporally a history refracturing process of the refractured oil-
gas well, to obtain
multiple cycles of stable production; determining a loss due to history
pressure drop, based on
history production corresponding to each of the multiple fracture
infinitesimal segments in each
of the multiple cycles of stable production in the history refracturing
process; determining an
equation of unsteady production in refracturing, for the refractured oil-gas
well, based on the loss
due to history pressure drop corresponding to each of the multiple fracture
infinitesimal
segments, the equation of transient production, and the predetermined rule of
intra-fracture fluid
flow; and obtaining the current production of the refractured oil-gas well,
based on the equation
of unsteady production in refracturing.
[0013] In a second aspect, an apparatus for reforming a refractured oil-gas
well is provided
according to an embodiment of the present disclosure, including: a module for
fracture space
discretization, a module for reservoir percolation model establishment, a
module for
intra-fracture pressure drop model establishment, a module for unsteady
production
determination, a module for parameter optimization, and a module for oil-gas
well reform.
[0014] The module for fracture space discretization is configured to
discretize spatially an
existing fracture in the refractured oil-gas well and a new branch fracture on
the existing fracture,
to obtain a plurality of fracture infinitesimal segments that are same in
length.
[0015] The module for reservoir percolation model establishment is configured
to establish a
model for reservoir percolation for each of the plurality of fracture
infinitesimal segments, based
on a geological characteristic of a reservoir and a basic property of a fluid.
[0016] The module for intra-fracture pressure drop model establishment is
configured to
establish a model of intra-fracture pressure drop for each of the plurality of
fracture infinitesimal
segments, based on a characteristic of the existing fracture and a
characteristic of the new branch
fracture.
.. [0017] The module for unsteady production determination is configured to
determine current
production of the refractured oil-gas well, based on a corresponding
relationship between
production and pressure response in the model of reservoir percolation, a
corresponding
relationship between a pressure loss and a fracture width in the model of
intra-fracture pressure
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drop, history fracturing data of the refractured oil-gas well, and a
predetermined rule of
intra-fracture fluid flow.
[0017a] The module for parameter optimization is configured to optimize
parameters of
fractures of the refractured oil-gas well, based on the determined current
production.
10017b1 The module for oil-gas well reform is configured to reform the
refractured oil-gas well
based on the optimized parameters.
[0018] In one embodiment, the module for reservoir percolation model
establishment includes:
a unit for point-source function construction, a unit for fluid-flow
resistance function
construction, and a unit for reservoir percolation model establishment.
[0019] The unit for point-source function construction is configured to
construct a
20
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Date Recue/Date Received 2021-09-21
point-source function of a box-shaped gas reservoir with a closed boundary,
based on a
reservoir boundary effect, the geological characteristic of the reservoir, and
the basic property
of the fluid.
[0020] The unit for fluid-flow resistance function construction is configured
to determine a
function of fluid flow resistance corresponding to each of the multiple
fracture infinitesimal
segments, based on the point-source function.
[0021] The unit for reservoir percolation model establishment is configured to
determine
the corresponding relationship between the production and the pressure
response of the
refractured oil-gas well, based on the function of fluid flow resistance.
[0022] In one embodiment, the unit for point-source function construction
includes a
subunit for target reservoir permeability determination, a subunit for target
stratum pressure
determination, and a subunit for point-source function construction.
[0023] The subunit for target reservoir permeability determination is
configured to
determine target reservoir permeability in the point-source function, based on
a corresponding
relationship between a stress sensitivity coefficient and reservoir
permeability in the
geological characteristic of the reservoir.
[0024] The subunit for target stratum pressure determination is configured to
construct a
real-gas effect equation based on the basic property of the fluid, and
determine a target
stratum pressure in the point-source function.
[0025] The subunit for point-source function construction is configured to
determine the
point-source function, based on a Green-function equation of a solution of the
point-source
function, a real-gas effect equation, the target reservoir permeability, and
the target stratum
pressure.
[0026] In one embodiment, the module for intra-fracture pressure drop model
establishment
includes a unit for equation of intra-fracture pressure drop determination and
a unit for
intra-fracture pressure drop model establishment.
[0027] The unit for equation of intra-fracture pressure drop determination is
configured to
obtain an equation of intra-fracture pressure drop, based on a corresponding
relationship
between preset reservoir permeability and production time.
[0028] The unit for intra-fracture pressure drop model establishment is
configured to
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Date Recue/Date Received 2020-05-11
determine the model of intra-fracture pressure drop, based on the equation of
intra-fracture
pressure drop and a corresponding relationship between the fracture width and
a fracture
length in the characteristic of the existing fracture and the characteristic
of the new branch
fracture.
[0029] In one embodiment, the module for unsteady production determination
includes a
unit for transient production equation determination, a unit for temporal
discretization, a unit
for history pressure loss determination, and a unit for current production
determination.
[0030] The unit for transient production equation determination is configured
to determine
an equation of transient production for the refractured oil-gas well, based on
a preset flowing
bottom-hole pressure, the corresponding relationship between the production
and the pressure
response in the model of reservoir percolation, and the corresponding
relationship between
the pressure loss and the fracture width in the model of intra-fracture
pressure drop.
[0031] The unit for temporal discretization is configured to discretize
temporally a history
refracturing process of the refractured oil-gas well, to obtain multiple
cycles of stable
production.
[0032] The unit for history pressure loss determination is configured to
determine a loss due
to history pressure drop, based on history production corresponding to each of
the multiple
fracture infinitesimal segments in each of the multiple cycles of stable
production in the
history refracturing process.
[0033] The unit for current production determination is configured to:
determine an
equation of unsteady production in refracturing, for the refractured oil-gas
well, based on the
loss due to history pressure drop corresponding to each of the multiple
fracture infinitesimal
segments, the equation of transient production, and the predetermined rule of
intra-fracture
fluid flow; and obtain the current production of the refractured oil-gas well,
based on the
equation of unsteady production in refracturing.
[0034] In a third aspect, an electronic device is provided according to an
embodiment of the
present disclosure, including: a memory, a processor, and a computer program
stored on the
memory and executable on the processor. The computer program when executed by
the
processor implements the method for processing production data of the
refractured oil-gas
well.
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Date Recue/Date Received 2020-05-11
[0035] In a fourth aspect, a computer-readable storage medium storing a
computer program
is provided according to an embodiment of the present disclosure. The computer
program
when executed by a processor implements the method for processing production
data of the
refractured oil-gas well.
[0036] The method and the apparatus for processing production data of the
refractured
oil-gas well are provided. The existing fracture in the refractured oil-gas
well and the new
branch fracture on the existing fracture are spatially discretized to obtain
the multiple fracture
infinitesimal segments that are same in length. The model for reservoir
percolation is
established for each of the multiple fracture infinitesimal segments, based on
the geological
.. characteristic of the reservoir and the basic property of the fluid, so as
to accurately obtain the
corresponding relationship between the production and the pressure response.
The model of
intra-fracture pressure drop is established for each of the multiple fracture
infinitesimal
segments, based on the characteristic of the existing fracture and the
characteristic of the new
branch fracture, so as to accurately obtain the pressure loss corresponding to
different fracture
widths. Afterwards, the history fracturing data of the refractured oil-gas
well and the
predetermined rule of intra-fracture fluid flow are combined in a temporal
dimension, and
thereby the accurate current production of the refractured oil-gas well is
obtained. The
reasonable basis is provided for optimizing parameters of fractures of the
refractured oil-gas
well, and the effect of reforming the refractured oil-gas well is improved.
BRIEF DESCRIPTION OF THE DRAWINGS
[0037] For clearer illustration of the technical solutions according to
embodiments of the
present disclosure or conventional techniques, hereinafter are briefly
described the drawings
to be applied in embodiments of the present disclosure or conventional
techniques.
Apparently, the drawings in the following descriptions are only some
embodiments of the
present disclosure, and other drawings may be obtained by those skilled in the
art based on
the provided drawings without creative efforts.
[0038] Figure 1 is a flow chart of a method for processing production data of
a refractured
oil-gas well according to an embodiment of the present disclosure;
.. [0039] Figure 2 is a flow chart of a method for processing production data
of a refractured
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Date Recue/Date Received 2020-05-11
oil-gas well according to another embodiment of the present disclosure;
[0040] Figure 3 is a flow chart of a method for processing production data of
a refractured
oil-gas well according to another embodiment of the present disclosure;
[0041] Figure 4 is a flow chart of a method for processing production data of
a refractured
oil-gas well according to another embodiment of the present disclosure;
[0042] Figure 5 is a flow chart of a method for processing production data of
a refractured
oil-gas well according to another embodiment of the present disclosure;
[0043] Figure 6 is a structural diagram of an apparatus for processing
production data of a
refractured oil-gas well according to an embodiment of the present disclosure;
[0044] Figure 7 is another structural diagram of an apparatus for processing
production data
of a refractured oil-gas well according to an embodiment of the present
disclosure;
[0045] Figure 8 is another structural diagram of an apparatus for processing
production data
of a refractured oil-gas well according to an embodiment of the present
disclosure;
[0046] Figure 9 is another structural diagram of an apparatus for processing
production data
of a refractured oil-gas well according to an embodiment of the present
disclosure;
[0047] Figure 10 is another structural diagram of an apparatus for processing
production
data of a refractured oil-gas well according to an embodiment of the present
disclosure;
[0048] Figure 11 is a schematic structural diagram of an existing fracture and
new branch
fractures on the existing fracture in a refractured oil-gas well according to
an embodiment of
the present disclosure;
[0049] Figure 12 is a schematic diagram of variables on an existing fracture
and a new
branch fracture in a refractured oil-gas well according to an embodiment of
the present
disclosure;
[0050] Figure 13 is a graph of reservoir permeability with respect to
production time of a
refractured oil-gas well according to an embodiment of the present disclosure;
[0051] Figure 14 is a schematic diagram of a fluid in a new branch fracture
flowing into an
existing fracture in a refractured oil-gas well according to an embodiment of
the present
disclosure;
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Date Recue/Date Received 2020-05-11
[0052] Figure 15 is a graph of daily production of a refractured oil-gas well
with respect to
time according to an embodiment of the present disclosure;
[0053] Figure 16 is a graph of cumulative gas production of a refractured oil-
gas well under
different fracture conductivities according to an embodiment of the present
disclosure;
[0054] Figure 17 is a graph of comparison in daily gas production between a
refractured
oil-gas well with a new branch fracture and an un-refractured oil-gas well
according to an
embodiment of the present disclosure;
[0055] Figure 18 is a graph of comparison in cumulative gas production between
a
refractured oil-gas well with a new branch fracture and an un-refractured oil-
gas well
according to an embodiment of the present disclosure;
[0056] Figure 19 is a graph of comparison in daily gas production between an
existing
fracture and a new branch fracture in a refractured oil-gas well according to
an embodiment of
the present disclosure;
[0057] Figure 20 is a graph of daily gas production of a refractured oil-gas
well under
different fracture conductivities according to an embodiment of the present
disclosure;
[0058] Figure 21 is a graph of daily gas production of a refractured oil-gas
well under
different time of refracturing according to an embodiment of the present
disclosure;
[0059] Figure 22 is a graph of comparison in growth rates of cumulative
production
between a refractured oil-gas well and an un-refractured oil-gas well
according to an
embodiment of the present disclosure; and
[0060] Figure 23 is a schematic structural diagram of an electronic device
according to an
embodiment of the present disclosure.
DETAILED DESCRIPTION OF THE EMBODIMENTS
[0061] To make the object, technical solutions and advantages of the present
application
clearer, hereinafter technical solutions in embodiments of the present
disclosure are described
clearly and completely in conjunction with the drawings in embodiments of the
present
closure. Apparently, the described embodiments are only some rather than all
of the
embodiments of the present disclosure. Any other embodiments obtained based on
the
-11) -
Date Recue/Date Received 2020-05-11
embodiments of the present disclosure by those skilled in the art without any
creative effort
fall within the scope of protection of the present disclosure.
[0062] In conventional technology, productivity of a refractured oil-gas well
developed for
tight gas reservoirs is generally calculated based on a field production test,
and few studies on
calculation have been made based on reservoir percolation. The field
production test on an
oil-gas filed is only capable to apply costly transient measurement, and is
not capable to
predict production. Generally, an analytic productivity equation is for
evaluating
productivity of conventional oil-gas reservoirs, and requires to perform
Laplace transform and
Fourier transform. Such equations are difficult solve, and merely considers
conditions of a
single factor. A nonlinear factor and the refracturing are scarcely considered
in a
comprehensive manner in a model for calculating productivity. In order to
address the above
technical issues, a method and an apparatus for processing production data of
the refractured
oil-gas well are provided according to embodiments of the present disclosure.
An existing
fracture in a refractured oil-gas well and a new branch fracture on the
existing fracture are
spatially discretized to obtain multiple fracture infinitesimal segments that
are same in length.
A model for reservoir percolation is established for each of the multiple
fracture infinitesimal
segments, based on a geological characteristic of a reservoir and a basic
property of the fluid,
so as to accurately obtain a corresponding relationship between production and
pressure
response. A model of intra-fracture pressure drop is established for each of
the multiple
fracture infinitesimal segments, based on a characteristic of the existing
fracture and a
characteristic of the new branch fracture, so as to accurately obtain a
pressure loss
corresponding to different fracture widths. Afterwards, history fracturing
data of the
refractured oil-gas well and a predetermined rule of intra-fracture fluid flow
are combined in a
temporal dimension, and thereby an accurate current production of the
refractured oil-gas well
are obtained. A reasonable basis is provided for optimizing parameters of
fractures of the
refractured oil-gas well, and an effect of reforming the refractured oil-gas
well is improved.
[0063] A method for processing production data of a refractured oil-gas well
is provided
according to an embodiment of the present disclosure, in order to calculate
production of a
refractured oil-gas well quickly and accurately, provide a reasonable basis
for optimizing
.. parameters of fractures the refractured oil-gas well, and improve an effect
of reforming the
refractured oil-gas well. Referring to Figure 1, a method for processing
production data of a
refractured oil-gas well includes following steps S101 to S104.
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Date Recue/Date Received 2020-05-11
[0064] In step S101, an existing fracture in a refractured oil-gas well and a
new branch
fracture on the existing fracture are spatially discretized to obtain multiple
fracture
infinitesimal segments that are same in length.
[0065] Reference is made to Figure 11. In conventional technology, a technique
of
forming new branch fractures in refracturing is generally applied, in order to
further connect
oil-gas resources far away from a fractured area. That is, various temporary
plugging agents
are applied in a refracturing process to form multiple branch fractures on the
existing fracture,
and the branch fractures are used to connect an area not controlled by the
existing fracture.
A reservoir is better controlled by the fractures after the branch fractures
are formed through
refracturing.
[0066] In one embodiment, the existing fracture (such as an existing single-
wing fracture)
in the refractured oil-gas well and the new branch fracture on the existing
fracture are divided
through spatial discretization, into line-congruences (that is, the fracture
infinitesimal
segments) of a quantity of ns and cs, respectively. The line-congruences are
same in length.
Accuracy and reliability of calculation can be improved by analyzing each line-
congruence in
subsequent processes.
[0067] In step S102, a model for reservoir percolation is established for each
of the multiple
fracture infinitesimal segments, based on a geological characteristic of a
reservoir and a basic
property of a fluid.
[0068] In one embodiment, the geological characteristic of the reservoir
includes, but is not
limited to: a length of a gas reservoir length, a width of a gas reservoir, a
thickness of a gas
reservoir, a length of the existing fracture, a width of the existing
fracture, a location of a new
branch fracture, a length of a new branch fracture, a width of a new branch
fracture, a
stress-sensitivity coefficient of a gas reservoir, a relation of fracture
conductivity, irreducible
water saturation of a gas reservoir, reservoir temperature, reservoir
permeability, reservoir
porosity, and an original stratum pressure.
[0069] In one embodiment, the basic property of the fluid includes, but is not
limited to:
critical temperature of a natural gas, a critical pressure of a natural gas,
reduced temperature
of a natural gas, a compression coefficient of a natural gas, a relative
density of a natural gas,
a density of a natural gas, and a viscosity of a natural gas.
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Date Recue/Date Received 2020-05-11
[0070] In one embodiment, the model of reservoir percolation may be
established further
based on a parameter of a shaft. The parameter of the shaft may include, but
is not limited to,
a radius of the shaft radius and a flowing bottom-hole pressure.
[0071] In one embodiment, the existing single-wing fracture in the refractured
oil-gas well
and the new branch fracture on the existing single-wing fracture are
sequentially numbered.
The existing single-wing fracture and the new branch fracture have been
divided through
spatial discretization into line-congruences of the quantity of ns and cs, and
each
line-congruence same in length. For each line-congruence, a reservoir boundary
effect, a
real-gas effect, and a stress sensitive effect are considered, and a model of
reservoir
percolation is established through the Green function. Such process
characterizes a
corresponding relationship between oil-gas production and pressure response of
the existing
single-wing fracture and the new branch fracture in the refractured oil-gas
well.
[0072] In step S103, a model of intra-fracture pressure drop is established
for each of the
multiple fracture infinitesimal segments, based on a characteristic of the
existing fracture and
a characteristic of the new branch fracture.
[0073] In one embodiment, the characteristic of the existing fracture
includes, but is not
limited to, the length of the existing fracture and permeability of the
existing fracture.
[0074] In one embodiment, the characteristic of the new branch fracture
includes, but is not
limited to, a quantity of the new branch fracture, the location of the new
branch fracture, the
length of the new branch fracture, and permeability of the new branch
fracture.
[0075] In one embodiment, the model of intra-fracture pressure drop is
established for a
fluid in fractures, based on an effect that the fluid flows non-uniformly into
the existing
fracture and the new branch fracture along irregular fracture surfaces and
then flows into the
existing fracture from the new branch fracture, a distribution of intra-
fracture heterogeneous
conductivity, and an intra-fracture Darcy flow. The model of intra-fracture
pressure drop is
configured to determine accurately a corresponding relationship between a
pressure loss and a
fracture width in the existing fracture and the new branch fracture in the
refractured oil-gas
well.
[0076] In step S104, current production of the refractured oil-gas well is
determined based
on the corresponding relationship between the production and the pressure
response in the
- 13 -
Date Recue/Date Received 2020-05-11
model of reservoir percolation, the corresponding relationship between the
pressure loss and
the fracture width in the model of intra-fracture pressure drop, history
fracturing data of the
refractured oil-gas well, and a predetermined rule of intra-fracture fluid
flow.
[0077] In one embodiment, a current time period is discretized into n parts,
based on the
history fracturing data of the refractured oil-gas well. A temporal length of
each of the n
parts is At, such as one day. Production within any At may be considered as a
fixed
value. Therefore, a process with a varying production in reality may be
simplified as
processes with fixed production in multiple time periods.
[0078] Reference is made to Figure 15. In one embodiment, the rule of intra-
fracture fluid
flow may be defined as follows based on a principle of mirror image. Before a
moment to,
the infinitesimal segments of the new fracture product with a constant
intensity and are
injected with a constant intensity, and the infinitesimal segments of the
existing fracture keeps
products until a moment tl (ti < to). After the moment to, the infinitesimal
segments of the
new fracture are not injected and product with a constant intensity for a
period of (t2 - to), and
the infinitesimal segments of the existing fracture keeps until a moment t2
(t2> to). The rule
of intra-fracture fluid flow is equivalent to an actual refracturing
production. Accordingly, a
mode for rapid calculation of unsteady production of the refractured oil-gas
well may be
established, in which fluids in a reservoir matrix and in the new branch
fracture are coupled,
so as to determine the current production of the refractured oil-gas well
accurately.
[0079] In one embodiment, after the step S104, a fracture parameter of the
refractured
oil-gas well are optimized under a predetermined reservoir condition and a
predetermined
flowing bottom-hole pressure and aiming, with an objective of maximizing an
increase in
cumulative production of the refractured oil-gas well. Accordingly, the
reasonable basis is
provided for optimizing the fracture parameter of the refractured oil-gas
well, and an effect of
reforming the refractured oil-gas well is improved.
[0080] Describe above is the method for processing production data of the
refractured
oil-gas well according to an embodiment of the present disclosure. The
existing fracture in
the refractured oil-gas well and the new branch fracture on the existing
fracture are spatially
discretized to obtain the multiple fracture infinitesimal segments that are
same in length.
The model for reservoir percolation is established for each of the multiple
fracture
- 14 -
Date Recue/Date Received 2020-05-11
infinitesimal segments, based on the geological characteristic of the
reservoir and the basic
property of the fluid, so as to accurately obtain the corresponding
relationship between the
production and the pressure response. The model of intra-fracture pressure
drop is
established for each of the multiple fracture infinitesimal segments, based on
the characteristic
of the existing fracture and the characteristic of the new branch fracture, so
as to accurately
obtain the pressure loss corresponding to different fracture widths.
Afterwards, the history
fracturing data of the refractured oil-gas well and the predetermined rule of
intra-fracture fluid
flow are combined in a temporal dimension, and thereby the accurate current
production of
the refractured oil-gas well are obtained. The reasonable basis is provided
for optimizing
.. parameters of fractures of the refractured oil-gas well, and the effect of
reforming the
refractured oil-gas well is improved.
[0081] Reference is made to Figure 2. The step 102may include following steps
S201 to
S203 according to an embodiment of the present disclosure, so as to obtain the
corresponding
relationship between the oil-gas production and the pressure response of the
existing fracture
and the new branch fracture in the refractured oil-gas well.
[0082] In step S201, a point-source function of a box-shaped gas reservoir
with a closed
boundary is constructed based on a reservoir boundary effect, the geological
characteristic of
the reservoir, and the basic property of the fluid.
[0083] In step S202, a function of fluid flow resistance corresponding to each
of the
.. multiple fracture infinitesimal segments is established based on the point-
source function.
[0084] In step S203, the corresponding relationship between the production and
the
pressure response of the refractured oil-gas well is determined based on the
function of fluid
flow resistance.
[0085] In one embodiment, after the existing single-wing fracture in the
refractured oil-gas
well and the new branch fracture on the existing single-wing fracture are
divided equally into
line-congruences of a quantity of ns and cs, respectively, a Green function of
a solution of the
point-source function is constructed for each line-congruence, as shown in
equations (1) and
(2).
1 ¨
p,¨ p(x,y,z,t)=f
¨ q(x0,yozo,t)=Si(x,x0,z-)= S2(y, yo,r)=S,(z,z0,2-
)dr (1)
OC,
- 15 -
Date Recue/Date Received 2020-05-11
where:
1 erf +erf
/ 2 + - xo) /2-(x-x0)
(x, i-)= -
2 2V77,1- 2V/7,T
\ 1 Yd __ 2-F(Y Yo) Yd __ 2- (Y -Y0)
SI(Y,Yo, r) - erf + erf (2)
2
2 .\177,z- 2.\111,z-
_
x-,+"
S, (z, zo , z-)=1+ - exp 12 27-2 \
4 1 niz- i= cos¨bz-z
h2 sin cos
[0086] Symbols in equation (2) are described as follows.
[0087] Pi represents a pseudo original stratum pressure. A unit of pi may be
MP a2/(P a. s).
[0088] p(x,y,z,t) represents a pseudo instantaneous pressure at a coordinate
point (x, y, z)
in an infinite plane, after producing -
q(xo,yo,zo,t) with a constant flow and a constant mass
at a coordinate point (x0, y0, z0) for (t -to). A unit of (x,y,z,t) may be
MPa2/(Pa= s)
[0089] q(xo,yo,zo,t) represents a production at the coordinate point
(x0,y0,z0) with a
constant flow. A unit of q(x0,y0,z0,t) may be kg/ks.
[0090] 0 represents reservoir matrix porosity, without dimension. Ct.
represents a fluid
compression coefficient, of which a unit may be MPa-1. t represents a time of
production
measured from a start of the production, of which a unit may be ks. v
represents a duration
of continuous production, of which a unit may be ks. S1(x,x0, , S1(y,y0, z-) ,
and
S3 (Z, Z0 T) are Green functions in x, y, and z directions, respectively. xf
represents a
position in x direction along a length of a fracture, of which a unit may be
m.
[0091] /7, represents piezometric conductivity in the x direction, of which a
unit may be
m2=MPa/(Pa.$), and r,i = K, 1 011C, . iy represents piezometric conductivity
in the y
direction, of which a unit may be m2=MPa/(Pa.$), and 77, = K, I OpC, . II,
represents
- 16 -
Date Recue/Date Received 2020-05-11
piezometric conductivity in the z direction, of which a unit may be
m2=MPa/(Pa.$), and
= Kz I OfiCt .
[0092] K.,. represents original permeability of the reservoir in the x
direction, of which a unit
may be D. K3, represents original permeability of the reservoir in the y
direction, of which a
unit may be D. Kz represents original permeability of the reservoir in the z
direction, of
which a unit may be D.
[0093] ,u represents fluid viscosity, of which a unit may be Pas. Two
boundaries in the x
direction are located at x = 0 and x = xf, and two boundaries in the y
direction are located at y
= 0 and y = yd, for an area of the box-shaped gas reservoir with the closed
boundary. n
represents a counting unit without dimension. h represents a thickness of the
reservoir, of
which a unit may be m.
[0094] In addition, production under a ground-standard condition is calculated
based on a
real-gas effect equation, as shown in equation (3).
Pse SceZsc 2
Pi P = (Pi ¨ P2) (3)
2 p 5c TZ
[0095] The point-source function of the box-shaped gas reservoir with the
closed boundary
is obtained by combining equation (1) and equation (3), as shown in equation
(4).
2qp,,ZT
p,2 - p 2 = Si(x,x0,r) = S 2(y , y 0,r) = S3(z,zo,r)dr
(4)
0CtZ
[0096] In equation (4), there is q= q(x0 , y 0 ,z0 ,t)I pse = p, represents an
original stratum
pressure, of which a unit may be MPa. p represents a current stratum pressure,
of which a
unit may be MPa. q represents a volume flow under the ground-standard
condition, of
which a unit may be m3/ks. p, represents a pressure of a standard condition,
of which a unit
of MPa. p, represents a gas density of the standard condition, of which a unit
may be kg/m3.
T, represents temperature of the standard condition, of which a unit may be K.
T represents
temperature of the reservoir, of which a unit may be K. Z represents a
deviation factor of a
- 17 -
Date Recue/Date Received 2020-05-11
natural gas under a current reservoir pressure, without dimension. Z,
represents a deviation
factor of the natural gas under the standard condition, without dimension.
[0097] Considering the reservoir matrix being stress-sensitive, a decrease in
a pressure of
the reservoir results in a decrease in permeability during the production of
the refractured
oil-gas well. Therefore, the reservoir permeability is a function of a stratum
pressure at any
time. The reservoir permeability under an effect of stress sensitivity may be
expressed as
equation (5).
Km(p)=Km0 exp [¨am(pi ¨ p)] (5)
[0098] In equation (5), symbols are described as follows. Km(p) represents a
current
reservoir permeability, of which a unit may be mD. Kmo represents a matrix
permeability
(mD) under a stratum pressure of põ of which a unit may be mD. am represents a
stress
sensitivity coefficient of the reservoir, of which a unit may be MPa-1. p,
represents an
original stratum pressure, of which a unit may be MPa. p represents a current
stratum
pressure, of which a unit may be MPa.
[0099] Since the gas reservoir is box-shaped and with a closed boundary, the
current
stratum pressure p may be calculated based on a material balance equation for
a box-shaped
gas reservoir with a closed boundary and a fixed volume, as expressed in
equation (6).
(6)
z zi
[0100] In equation (6), symbols are described as follows. z represents a gas
deviation
factor under the current stratum pressure, without dimension. z, represents a
gas deviation
factor under the original stratum pressure, without dimension. Gp represents
cumulative
production of the refractured oil-gas well, of which a unit may be m3. G
represents an
original geological reserve, of which a unit may be m3, and G= xf = yd=
h=(1¨sw)IBg . h
represents a height of the box-shaped gas reservoir with the closed boundary,
of which a unit
may be m. sw represents water saturation, of which a unit may be %. Bg
represents a gas
volume factor, without dimension.
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Date Recue/Date Received 2020-05-11
[0101] A model of reservoir matrix percolation is established for the
refractured oil-gas well,
based on a real-gas effect, stress sensitivity, and a reservoir boundary
effect in the refractured
oil-gas well.
[0102] In one embodiment, each single-wing existing fracture and each new
branch fracture
are spatially discretized into line-congruences of the quantity of ns and cs,
respectively. The
pressure response of each source of the line-congruences during production may
be obtained
by superimposing the pressure response of each line-congruence during
production. At any
position of the fractures, the pressure response generated at a line-
congruence M with
production of qfk+id may be expressed as equation (7).
=2qfk+idpseZT st
2 2 2
APfk+ld (t)=P, Si(x, xo,z-) = S2(y, yo, r)= S3(z, zo, r)d r ____________ (7)
0CtZseTse
[0103] In equation (7), symbols are described as follows. pfk+id represents a
pressure at
the middle of a j-th infinitesimal section (line-congruence) of a (k+l)th
fracture, of which a
unit may be MPa. qfk-kii represents a volume flow of the j-th infinitesimal
section
(line-congruence) on of the (k+l)th fracture under a ground standard
condition, of which a
unit may be m3/ks. j represents a sequential number of an element in a
discretized fracture,
without dimension.
[0104] It is assumed that a total quantity of fractures is N. Each fracture
includes the
existing single-wing fracture discretized into ns line-congruences, and the
new branch
single-wing fracture discretized into cs line-congruences. The pressure
response generated
by Nx(ns+cs) discrete elements at a location 0 in a stratum at a moment t
during production
may be expressed as equation (8). Namely, the point-source function of the box-
shaped gas
reservoir with the closed boundary may be expressed as equation (8).
N Ap 211s 2cs 2qfk i pseZT fk2 +1,,(0_r- ,õ2 _ r)2 E
E .
si(x,xo, r)= S2 (y,yo,r)= S3(z,zo,r)dz-
,
k,m=1 1-1 OCtZsc Tsc
(8)
N 2ms +2.
=E E gifk+1,/ = Fld (k+1)j(t)
Ic=1) i=1
[0105] In equation (8), F/õ.(/c of(t) represents an effect of a discrete
element at a position of
- 19 -
Date Recue/Date Received 2020-05-11
an i-th infinitesimal section of a k-th fracture on a discrete element at a
position of a j-th
infinitesimal section of a (k+l)th fracture. That is, Fki,(k+i)il(t)
represents a function of fluid
flow resistance, which may be expressed as equation (9).
2 pseZT
Fki,(k+1)j(t) ___________________ Si(X, x 0 , r) = S2(y , yo, r) = S3(z , z
0, r)d r (9)
0C,Z seTse
[0106] In equation (8), symbols are described as follows. N represents a total
quantity of
the existing fractures. ns represents the quantity of discrete elements in
each existing
single-wing fracture. cs represents the quantity of discrete elements in each
new branch
single-wing fracture. k represents a sequential number of the fracture
(including the exiting
fracture and the new branch fracture), and 1 < k < N. i represents a
sequential number of a
discrete element in a fracture, and 1 < i < (ns+cs). j represents another
sequential number of
a discrete element in a fracture, and 1 <j < (ns+cs).
[0107] Reference is made to to Figure 3. The step S201 may further include
following
steps S301 to S303 according to an embodiment of the present disclosure, in
order to fully
consider influences of the real-gas effect and the stress sensitivity in
determining the
.. corresponding relationship between the oil-gas production and the pressure
response.
[0108] In step S301, target reservoir permeability in the point-source
function is determined
based on a corresponding relationship between a stress sensitivity coefficient
and reservoir
permeability in the geological characteristic of the reservoir.
[0109] In one embodiment, the stress sensitivity of the reservoir matrix is
considered. A
decrease in the reservoir pressure results in a decrease in the permeability
during production
of the refractured oil-gas well. Therefore, the reservoir permeability is a
function of the
stratum pressure at any time. The
reservoir permeability, i.e. the target reservoir
permeability, under the effect of stress sensitivity is as shown in the
aforementioned equation
(5).
Km(p)= Kino exp[¨ain(pi ¨ p)] (5)
[0110] In equation (5), symbols are described as follows. Km(p) represents a
current
reservoir permeability, of which a unit may be mD. Kmo represents a matrix
permeability
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Date Recue/Date Received 2020-05-11
(mD) under a stratum pressure of põ of which a unit may be mD. an, represents
a stress
sensitivity coefficient of the reservoir, of which a unit may be MPa-1. pi
represents an
original stratum pressure, of which a unit may be MPa. p represents a current
stratum
pressure, of which a unit may be MPa.
[0111] In step S302, a real-gas effect equation is constructed based on the
basic property of
the fluid, and a target stratum pressure in the point-source function is
determined.
[0112] In one embodiment, the gas reservoir is box-shaped and with the closed
boundary.
The current stratum pressure p (that is, the target stratum pressure) may be
calculated based
on the aforementioned material balance equation (6) of a box-shaped gas
reservoir with a
closed boundary and a fixed volume.
P P
(6)
z zi
[0113] In equation (6), symbols are described as follows. z represents a gas
deviation
factor under the current stratum pressure, without dimension. zi represents a
gas deviation
factor under the original stratum pressure, without dimension. Gp represents
cumulative
production of the refractured oil-gas well, of which a unit may be m3. G
represents an
original geological reserve, of which a unit may be m3, and G=x, =
yd=h=(1¨sw)IBg. h
represents a height of the box-shaped gas reservoir with the closed boundary,
of which a unit
may be m. sw represents water saturation, of which a unit may be %. Bg
represents a gas
volume factor, without dimension.
[0114] In step S303, the point-source function is determined based on a Green-
function
equation of a solution of the point-source function, a real-gas effect
equation, the target
reservoir permeability, and the target stratum pressure.
[0115] In one embodiment, the existing fracture and each new branch single-
wing fracture
are spatially discretized into line-congruences of the quantity of ns and cs,
respectively. The
pressure response of each source of the line-congruences during production may
be obtained
by superimposing the pressure response of each line-congruence during
production. At any
position of the fractures, the pressure response generated at a line-
congruence M with
production of qfk+id may be expressed as in the aforementioned equation (7).
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Date Recue/Date Received 2020-05-11
2qfk+ldpseZT rt
= S1 (x, xo,
z-) = S2(y, yo, z-) = S3(z,zo, i-)d (7)
0 , C Z se Te i
[0116] In equation (7), symbols are described as follows. pfk+id represents a
pressure at
the middle of a j-th infinitesimal section (line-congruence) of a (k+l)th
fracture, of which a
unit may be MPa. qfk-kii represents a volume flow of the j-th infinitesimal
section
(line-congruence) on of the (k+l)th fracture under a ground standard
condition, of which a
unit may be m3/ks. j represents a sequential number of an element in a
discretized fracture,
without dimension.
[0117] It is assumed that a total quantity of fractures is N. Each fracture
includes the
existing fracture discretized into ns line-congruences, and the new branch
fracture discretized
into cs line-congruences. The pressure response generated by Nx(ns+cs)
discrete elements
at a location 0 in a stratum at a moment t during production may be expressed
as the
aforementioned equation (8). Namely, the point-source function of the box-
shaped gas
reservoir with the closed boundary may be expressed as the equation (8).
N 2ns+2cs 2qt,c+ii pseZT
=
Si(x,x0,r)= S2(y, yo, z-)= S3(z,zo,z-)dr
k,m=1 1-1 C tZseTse
(8)
N 2ns+2cs
=1 E qfk+1,,, = Fki (k+1)j(t)
k4 i=1
[0118] In equation (8), Fid(k+i)i(t) represents an effect of a discrete
element at a position of
an i-th infinitesimal section of a k-th fracture on a discrete element at a
position of a j-th
infinitesimal section of a (k+l)th fracture. That is, Fti,(t+i)i(t) represents
a function of fluid
flow resistance, which may be expressed as the aforementioned equation (9).
2 pseZT
Fk1,(k+1)j(t) S1(X,X0, r) = S2(y, yo, z-) = S3(z,zo, z-)d ______________ (9)
0CtZ seTse
[0119] In equation (8), symbols are described as follows. N represents a total
quantity of
the existing fractures. ns represents the quantity of discrete elements in
each existing
single-wing fracture. cs represents the quantity of discrete elements in each
new branch
single-wing fracture. k represents a sequential number of a fracture
(including the existing
fracture and the new branch fracture), and 1 < k < N. i represents a
sequential number of a
discrete element in a fracture, and 1 < i < (ns+cs). j represents another
sequential number of
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Date Recue/Date Received 2020-05-11
a discrete element in a fracture, and 1 <j < (ns+cs).
[0120] Reference is made to Figure 4. The step S103 may further include
following steps
S401 and S402 according to an embodiment of the present disclosure, in order
to determine
accurately the corresponding relationship between the pressure loss and the
fracture width of
the existing fracture and the new branch fracture in the refractured oil-gas
well.
[0121] In step S401, an equation of intra-fracture pressure drop is obtained
based on a
corresponding relationship between preset reservoir permeability and
production time.
[0122] In step S402, the model of intra-fracture pressure drop is determined,
based on the
equation of intra-fracture pressure drop and a corresponding relationship
between the fracture
width and a fracture length in the characteristic of the existing fracture and
the characteristic
of the new branch fracture.
[0123] In one embodiment, the effect of stress sensitivity of the fractures is
considered first.
[0124] During production of the refractured oil-gas well, an artificial
fracture filled with
proppant may be treated as a rock matrix with high permeability. A stress
state of the
fracture in stratum is same as that of the rock matrix in the stratum. Grains
in the fracture is
larger in size and more uniform in shape than those in the rock matrix. Thus,
the fracture
has a much higher permeability than the rock matrix. Therefore, the decreased
permeability
of the fracture due to an increase in skeleton stress is similar to the stress
sensitivity of the
rock in the stratum, as a pressure of a stratum fluid decreases over time. A
temporal change
in the fracture permeability is obtained through experimental fitting.
[0125] In one embodiment, experiment data of fracture permeability are
obtained at
different times under a closure stress of 40MPa and a fracture width of 2.5mm,
as shown in
Table 1.
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Date Recue/Date Received 2020-05-11
Table 1 Experimental data on the change of fracture permeability with time
Time, d Fracture permeability (D) Time, d Fracture
permeability (D)
0.04 240 22 28.06
0.4 120.0 25 26.9
0.8 80.0 28 26.1
1.3 72.0 29 25.7
1.7 68.0 30 25.4
2 67.2 33 24.7
3 54.1 35 24.0
46.0 38 23.5
9 39.1 39 23.2
36.9 44 22.3
13 33.4 48 21.6
18 30.3 50 21.4
[0126] Reference is to Figure 13. The fracture permeability under the effect
of stress
sensitivity may be expressed as equation (10).
5 K (t) =81.512t 343 (10)
[0127] In equation (10), K11(t) represents a permeability of a j-th
infinitesimal section of
a (k+l)th fracture at a moment t during production, of which a unit may be D;
and t represents
production time, of which a unit may be day.
[0128] The equation of intra-fracture pressure drop for an un-uniform
diversion fracture is
10 established based on the effect of stress sensitivity, which may be
expressed as equation (11).
APt+1 if vk +1, /
(11)
Axk+1,1 K fk +1. 1(0
[0129] In equation (11), symbols are expressed as follows. pk-kid represents a
pressure of
an intra-fracture fluid at the middle of a j-th discrete element of a (k+l)th
fracture, of which a
unit may be Pa. Vk+1 1 represents a velocity of the intra-fracture fluid at
the middle of the j-th
discrete element of the (k+l)th fracture, of which a unit may be m/s. and
K+11(t) a
permeability of a j-th discrete element of a (k+l)th fracture at a moment t
during production,
of which a unit may be D.
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Date Recue/Date Received 2020-05-11
[0130] In equation (11), a total pressure gradient APk+1,//Axk+1,, is
determined by the right
term representing an intra-fracture pressure drop. Each fracture infinitesimal
is processed
into isosceles trapezoids in spatial discretization, based on a fact that a
width of the
single-wing fracture (both the existing fracture and the new branch fracture)
in refracturing
gradually narrows from a heel to a toe. That is, each fracture including the
existing
single-wing fracture and the new branch single-wing fracture includes ns + cs
isosceles
trapezoids, so as to achieve such a trapezoid-like variation of a fracture
width along the
fracture length. A fracture width wrk+id at the middle of the j-th discrete
element of the
(k+l)th fracture may be expressed as equations (12) and (13).
For j < ns,
j ¨1
W11 =w + ___ (w ¨w
a+1, mm,k+1 max,k+1 mm,k+1
ns
and for j > ns,
j ¨ns ¨1 r
w = Hmm,k+1
(13).
a+1, max,k+1 iimm,k+1)
CS
[0131] In equations (12) and (13), wfk+iil represents a width of the middle of
the j-th discrete
element of the (k+l)th fracture, Wmm,k+1 represents a width at the toe of the
existing fracture in
the (k+l)th fracture, Wmax,k+1 represents a width at the heel of the existing
fracture in the
(k+l)th fracture, Hmm,k+1 represents a width at the toe of the new branch
fracture in the (k+l)th
fracture, and Hm
ax,k+1 represents a width at the heel of the new branch fracture on the
(k+l)th
fracture, of which units may be mm.
[0132] In one embodiment, the fluid flows non-uniformly into the existing
fracture and the
new branch fracture along a fracture surface, and then a linear flow is
generated. It is
assumed that a conjunction point is at a middle infinitesimal section (with a
sequential
number of ns/2) of the existing fracture. There is a total pressure loss of
APLI,o generated
by the fluid flowing from M(xrk+i,/, Yrk+i,/, zrk+iil) to an intersection
point Ofk+1,0 between a
horizontal shaft and the existing fracture. The total pressure loss when
converted to a
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Date Recue/Date Received 2020-05-11
pressure drop under a ground standard condition may be expressed as equations
(14) to (16).
For 1 <j < ns/2,
2 2 2/-igpscZT
APf2k-pij-o Pfk+1,j Pfk+1,0 v x AXfk+1,1qfk+1,1
kt Wfk-pi,jh 'se
2flgpseZT
____________________________ x(Axfk+i,i Axfk+1,2) X qfk+1,2 = = =
K fk+1(t)Wfk+1,1h Ls,
2pgps,ZT 2dugpseZT
________________ 7, v x(Axfk+1,1+ Axfk+1,2 = =
= AXfk+1,j)qfk+1 \
K fk+1(t)Wfk+1,j11 11-fk+1 i1Wfk-pi 1hT (14);
x(AXfk+1,1 + Axfk+1,2 = = = Axfk+1,j)
2,ugps,ZT
X qfk+1, j+1+ = = = 1,\ 7, X(AXfk+1,1 AXfk+1,2 = = = &fk+1j)x
qfk+1,11,s-hes
ii-fk+lktlWfk+1, jh se
2,ugps,ZT
______________________ L(qfk+1,iLA0cfk+1,i) qfk+1,n(L
&+1j)Kfk+1(t)wfk+1,j1IT, i=1 i=1 n=f +1 _ i=1
for ns/2 < j < ns,
- 26 -
Date Recue/Date Received 2020-05-11
2 2/igpscZT
AP f2x+i, Pf2x n-pi,i v x Axfk+1,1qfk+1,1
11- fk+1 ii'vfk+Lih
2 p gp scZT
x(AXix+1,1+ AXfk+1,2 )qfk+1,2 = =
Kfk+1(t)Wfk+1, jhisc
2//gpscZT 2 p g p scZT
x(Axix+1,1+ AXfk+1,2 = = = AXfk+i, j)qfk+1,i
Kfk+1(t)Wfk+1, jhT SC Kfk+1(t)Wfk+1,jhTsc
X (AXfk+1,1 AXfk+1,2 = = = AXR+1,i )
2 p g p scZT
x a
fk+1,j+1 v T X (A=Xfk +1,1 Axfk+1,2
= = = Axfk+1,j )x fk+1,ns
''fk+1V1Wfk+1,jhjsc
2/ig p,,cZT
________________________ X (AXfk+1,1 AXfk+1,2 = = ' AXfk+i
(15);
ns/2) X q fk+1,ns+1
Kfk+1(t)Wfk+1, /hi sc
2 p g p scZT
________________________ x(Axfk+1,1+ AXfk+1,2 = = AXfk+i
,ns12) X q fk+1,ns+2
Kfk+1(t)Wfk+1,jhjT sc
2 p g p scZT
+ __________________________ x(Axfk+1,1+ AXfk+1,2 = = ' AXfk+i,ns12 )
X q fk+1,ns+cs
v
11-1I+1k.1" 11/Vfk+1,jh sc
2pg p scZT ns
(q1I+1,1I Ax fk+1,i) q fk+1
Axfk+lj )
Kfk+1(t)Wfk+1,jhTsc i=1 i=1 n=j+1 _ i=1
2 p g p scZT ns+cs
__________________________ X(AXfk+1,1 AXfk+1,2 = = ' AXfk+i,ns12)
qfk,i
Kfk+1(t)Wfk+1,jhjsc ns+1
and if ns < j < ns + cs,
A 2 2 2 2pgp,5.ZT
Pfk+1,j-0 Pfk+1,j Pfk+1,0 v " T X AXfk+1,1qfk+1,1
11- fk+1 V1Wfk+1, j"isc
2pgpscZT
X(AXfk+1,1 AXfk+1,2)qfk+1,2 = = =
Kfk+1 (t)Wfk+1, j÷ T
2pgpscZT 211g pscZT
X(A)Cfk+1,1 A7Cfk+1,2 A7Cfk+1,ns12)qfk+1,ns12+
Kfk+1 Wfk+1, j"L j T sc Kft,
1(t)Wfk+1,1h Tsc (16).
x(Axfk+1,1+ AXfk+1,2 = = = AXfk+1,ns/2 )
2pgpscZT
xa
,fk+1,ns/2+1 x(x(&11AXfk+1,2= = = AXfk+1,ns12) X
v qfk+1,ns+as
''fk+1 /Wfk+1, j'"T sc
2pgpscZT nsI2I ns+cs ns/2
T AXfk+1,/ qfk+1,n(I Ax)
Kfk+1(t)wfk+1,jhtsc i=1 i=1 n=ns12+1 _ i=1
[0133] In equations (14) to (16), symbols are described as follows. APLI,J_,
represents a
- 27 -
Date Recue/Date Received 2020-05-11
pressure drop generated by the fluid flowing from M(xfk+i,/, Y(+1,/, za+iil)
to Ofk+1,0, of which a
unit may be MPa.
r fk+1,0 represents a pressure at an intersection point of each fracture and
the shaft, namely, pwf, of which a unit may be MPa. K+1(t) represents a
permeability of a
(k+l)th fracture at a moment t during production, of which a unit may be mD.
wfk+1,/
.. represents a width of a j-th infinitesimal segment of the (k+l)th fracture,
of which a unit may
be m.
[0134] In one embodiment, a pressure drop in the existing fracture is further
calculated
based on equations (14) to (16), for a position other than the intersection
point between the
exiting fracture and the new branch fracture. A pressure drop of convergence
and a pressure
drop of acceleration are generated at the intersection between the existing
fracture and the
new branch fracture, besides the Darcy pressure drop.
[0135] Reference is made to Figure 14. In one embodiment, considered is a
control body
AT generated when a gas introduced from the new branch fracture is blended
with a gas in the
existing fracture. It is assumed that a flow path of the gas before changing a
velocity
direction is a, and a flow path of the introduced gas is c, and a flow at a
position where the
two gases are blended is simplified as a slowly varying flow. A pressure loss
due to the
convergency of fluids is determined based on a continuity equation and an
energy
conservation equation.
[0136] For mixing loss, the continuity equation may be expressed as equation
(17).
qa+1,1 qa+1,3 = qa+1,4
(17)
[0137] In equations (17), symbols are described as follows. qfk+1,1 represents
a flow at an
entrance along the existing fracture in a (k+l)th fracture, of which a unit
may be m3/s. q(k+1,3
represents a flow introduced from the new branch fracture in the (k+l)th
fracture, of which a
unit may be m3/s. qfk+1,4 represents a sum of a flow after the convergence of
the existing
fracture and the new branch fracture in the (k+l)th fracture, of which a unit
may be m3/s.
[0138] An energy conservation equation at a position of convergence may be
expressed as
equation (18).
- 28 -
Date Recue/Date Received 2020-05-11
2 2
, Pfk+1'1 + V fk +11 P fk +1'4 Vfk+1'4 fk+1,1,4
(18)
Pg 2g Pg 2g
[0139] In equations (18), symbols are described as follows. pfk+1,1 and
pfk+1,4 represents
pressures at an entrance and an exit, respectively, along the existing
fracture in a (k+l)th
fracture, of which units may be MPa. va+1,1 and vfk+1,4 represent gas flow
rates at the
entrance and an exit, respectively, along the existing fracture in the (k+l)th
fracture, of which
units may be M/S. ha+1,1,4 represents an energy loss due to the convergence in
the (k+l)th
fracture, of which a unit may be m. p represents density, of which a unit may
be kg/m3. g
represents acceleration of gravity, of which a unit may be m/s2.
[0140] The energy loss due to convergence may be expressed as equation (19).
2
qa+1,3 2v1qfk+1,3A gVfk+1,3 COS c0
hfk+1,1,4
(19)
2gA2 gA
[0141] In equations (19), symbols are described as follows. qfk+1,3 represents
a flow
introduced from the new branch fracture in a (k+l)th fracture, of which a unit
may be m3/s.
A represents a cross-sectional area of the existing fracture, of which a unit
may be m2.
vfk+1,3 represents a gas flow rate in the new branch fracture, of which a unit
may be m/s. co
represents an angle between the existing fracture and the new branch fracture,
of which a unit
may be degree.
[0142] Based on equations (18) and (19), a pressure difference between the
entrance and the
exit along the existing fracture due to a pressure drop of acceleration and a
pressure drop of
fraction may be obtained, as expressed in equation (20).
Pqfk+1 3 V1 qa+1,3 P
Pfk-1,1 Pfk+1,4 hfk+1,1,4Pg _L +
(20)
2A 2 A
[0143] The pressure drops of acceleration and fraction calculated through
equation (20) and
the pressure drop calculated through equation (17) are combined, thereby
obtaining a pressure
drop equation for the existing fracture which considers the pressure loss due
to convergence
concerning the new branch fracture.
- 29 -
Date Recue/Date Received 2020-05-11
[0144] A pressure drop of a fluid in the existing fracture follows the
equation (17), after the
fluid flows from the new branch fracture into the existing fracture.
[0145] Reference is made to Figure 5, the step S104 may include following
steps S501 to
S504 according to an embodiment of the present disclosure, in order to
determine accurately
the current production of the refractured oil-gas well.
[0146] In step S501, an equation of transient production for the refractured
oil-gas well is
determined based on a preset flowing bottom-hole pressure, the corresponding
relationship
between the production and the pressure response in the model of reservoir
percolation, and
the corresponding relationship between the pressure loss and the fracture
width in the model
of intra-fracture pressure drop.
[0147] In step S502, a history refracturing process of the refractured oil-gas
well is
temporally discretized, to obtain multiple cycles of stable production.
[0148] In step S503, a loss due to history pressure drop is determined, based
on history
production corresponding to each fracture infinitesimal segments in each cycle
of stable
production in the history refracturing process.
[0149] In step S504, an equation of unsteady production in refracturing is
determined for
the refractured oil-gas well, based on the loss due to history pressure drop
corresponding to
each fracture infinitesimal segment, the equation of transient production, and
the
predetermined rule of intra-fracture fluid flow, and the current production of
the refractured
oil-gas well is obtained based on the equation of unsteady production in
refracturing.
[0150] In one embodiment, a model of reservoir-matrix coupled flow is
established for the
refractured oil-gas well. Fluid percolation from the reservoir to the shaft is
divided into
reservoir percolation and an intra-fracture flow, and a gas flows non-
uniformly into the
fracture from the reservoir along a fracture surface. Thereby, a continuity
equation of
pressures is constructed based on equations (8) and (14) to (16), according to
a rule that a
pressure at a surface of a fracture wall is continuous and equal. Namely, a
pressure is
continuous at an observation point M(xfk-k1,/, R+1/, za+1,/).
- 30 -
Date Recue/Date Received 2020-05-11
[0151] Production is assumed to be under a constant flowing bottom-hole
pressure. The
flowing bottom-hole pressure is a pressure at the intersection Ofk-ki ,0
between the fracture and
the shaft, and may be expressed as in equation (21)
PO = Af
(21)
[0152] In equations (21), po represents a pressure at the intersection between
the existing
fracture and the shaft, and pwf represents a flowing bottom-hole pressure, of
which units may
be Mpa.
[0153] A model of transient percolation is established for a matrix-fracture
coupled flow of
the refractured oil-gas well. In one embodiment, the equations (8), (14) to
(16), and (21) are
combined to acquire an equation of transient percolation for the matrix-
fracture coupled flow
at a -th discrete infinitesimal segment of a (k+l)th fracture at a moment t.
For 1 <j <ns/2,
2 2 2p p s,ZT {x-,-/ 1 i i }
i
Pi Pwf ¨ _______ L., kg fk+li L Axfk+u) L (1 fk+1,n (1, A X
fk+1,i) +
K f k+i(t)hTsõ 1=1 wf k+L . 1=1 n=j+1 W11+1./ -
1=1
(22);
pg p,s,zT N 2n s+2 õ,j x es
Ei (x11,1¨ xfk+1, j)2 (Y11,i Yf k+1,j)2
(Zad¨Zfk+,J )2
________________________________________________________________ }
______________ L L q
22-Km (p)hTs, k=1 1=1 4qt
for ns/2 < j <ns,
_
P2 2 2pgp,õZT x_,,i 1 1 ns 1 1
i Pwf ¨ (qfk+1,ilt Axfk+1,i)+ L qfk+1,n(L AXfk+1,id
Kfk_d(t)hTsc Li_i wfõ,i i=1 n= j+1 Wfk+1, j - i=1
2pgpZT ns+c 1
_______________ x(Ax(k-d,i + Axfk+1,2 = = = + Axfk+los/2 ) L q fk,i +
(23);
Kfk_d(t)hT, i=ns--1 Wf1+1,ns+1
pgpscZT 2n csq xEi N s+2
(X fk ,i Xfk+1, j ) +(y fic,i Yf k+1, j ) +( Z fk ,i Z f k+1,j)2 -
}
. L
2R-Km(p)hTsc k t.õ1,i_1 i_1 477t
and for ns < j <ns + cs,
- 31 -
Date Recue/Date Received 2020-05-11
2itgArZT
A ,2 ,2 2
Pfk+1, j _ l' ,a = +1,0 AXfk+1,1qfk+1,1
Kfk, (t)wa+,,fhTscx
2p gp,ZT
x(Axfk+1,1+ a+1,2 )qa+1,2 ' ' '
Kfk+1 (t)Wfk+1, j"'LT sc
2,t1gpscZT 2,ugpscZT
xWcfk+1,1+ Axfk+1,2 ' ' ' AXfk+1,n,s/2 )qfk+1 ns12+
Ka+1(t)wa+,,i127'sc ' Kfk, (t)wa+1,1127'sc
x(Axa+1,1+ AXfk+1,2 ' ' ' AXfk+1,ns12)
2pgpscZT
Xqf7c+1,ns/2+1 ... x(Axa+1,1+ Axfk+1,2 ' ' ' AXfk+1,n,s/2 ) x q
fk+1,ns¨cs
(24)
A2
jigp Ei sc x q
R- ZT ' 2V ns+2cs (Xfo ¨ xfk 1,1 )2 +( V
,, fk,i )2 f k+1, 1 ) + (Z a ,1 ¨ Z f k+t, f )2
______________ E E i
2Km(p)hT fk+1,
sc k=1 1,1=1 41g
¨ _
ZugpscZT nsI2 1
{ i
ns+cs 1r / 2
________________________________________________ qa+, i(EAxa+,,i)11
+
Ka,(t)hTsc 1=1 wa+,,i 1-1 j=ns12+1 Wfk+1, j ' 1=1
¨ , 2 A2
fig p Ei sc x q
ZT ' 2V ns+2cs ( Xfk i ¨ xfk 1,i) +(yfk,1 Yfk+1,/ ) (z1 ¨ Zfk+t, i
)2
_____________ E E a,,i " ______________________________
2R-Km(p)hTsc k=1 1=1 + 4r7t
¨ ¨
[0154] The model for transient production is established for the refractured
oil-gas well in
equations (22) to (24).
[0155] An oil-gas reservoir is closed at an upper top and a lower bottom.
During
production under a constant flowing bottom-hole pressure, production of the
refractured
oil-gas well decreases as a stratum pressure decreases before to, and
increases abruptly at to
due to the new fracture that increases a drainage area and control on the
reservoir.
Afterwards, the production of refractured oil-gas well decreases as the
stratum pressure
decreases. The whole period up to a current moment is discretized into n equal
parts, and
each part is referred to At. The production is treated as constant within each
At, namely, that
the production is stable within each At. Thus, a practical production with a
variable rate is
simplified.
[0156] Reference is made to Figure 15. First, a period up to a current moment
t is
temporally discretized into n parts, and each part At represents one day. That
is, the
production is considered as stable within each At. A solution process is for
stable
productivity in such tiny period. Then, a existing single-wing fracture with
or without new
branch single-wing fracture is spatially discretized into ns or ns+cs equal
fracture
infinitesimal segments. Each fracture infinitesimal segment is equivalent to a
straight well.
- 32 -
Date Recue/Date Received 2020-05-11
[0157] In one embodiment, production of the new and existing fractures before
to is solved
first. Only initial fracturing is performed before to, and the new and
existing fractures are
both discretized into fracture infinitesimal segments based on a principle
mirror reflection and
a method for discretizing fractures. An algebraic sum of, a pressure drop due
to extending
productions (qi, q2, ,q) of all days before to to the current moment and a
pressure drop due
to production increments (or negative increments) qi ¨ at
each moment is a pressure drop
produced by all fracture infinitesimals at the moment t. It expresses a
physical process in
which an injecting well injects (t,¨ t,) with the production increments (or
negative increments)
(qi ¨ a production well products (ti ¨ t1_1) with i =
1, 2, ..., n, and the fracture
infinitesimal segments of the new fracture perform both injection and
production with a
constant level. The physical process is equivalent to a practical production
in refracturing.
Then, n sets of linear equations from the first day to a current are solved in
a chronological
order, so as to obtain production of all fracture infinitesimal segments at
each moment before
to. The
obtained production is brought into a process of solving production at each
moment
after refracturing.
[0158] In case of t = At, the equation of unsteady production in refracturing
may be
expressed as equation (25).
p ,2 ¨p (At) = q f 1,1 (At) F (At) + q f 1,2 (At) F12,õ (At) + qf 1,3 (At)
F13,õ (At) +
L + (At)FN211 (At)
p,2 ¨p12 (At) = qf11 (At) F112 (At) + f1,2 (At) F12,12 (At) + qf13 (At) F13,12
(At) +
L qt1V,2n, (AOFN2ns,12 (At)
p ,2 ¨ 14.1,3 (At) = qflo (At) F11,13 (At)-- qf 1,2 (At) F12,13 (At) + q f 1,3
(At) F13,13 (At) + (25)
L + qõ (At) F,õns,i3 (At)
P,2 pf2N,2n, (At) = qf1,1 (At)FII,N2ns (At) + q",2 (At)F12,N2ns (AO+
qto (At)F13,N2n, (AO+
L + (At)F,2õ.s,
N2ns ,At
[0159] In case of t = 2At, the equation of unsteady production in refracturing
may be
expressed as equation (26).
- 33 -
Date Recue/Date Received 2020-05-11
p,2 - p f21,1(2 At) = qf,,,(At)F,,,õ (2At) + [qf (2At) - qf ,,,(At)]F,,,õ(At)+
qf1,2 (A0F12,11(2At) + [gfl,2 (2At) qf1,2 (At)]f12,11 (At) +L +
qw (At)FN211 (2At) + [gfAT,2 (2At) (AOWN(2õ,),õ (At)
- pf21,2 (2At) = qf (At)Ft 1,12 (2At) + [qf 1,1 (2At) - qf (At)]Ft 1,12 (At) +
qf (At)Ff12,12 (2At)
+[qf12(2At) - qf (At)]F,2,12 (At) +L +
(26)
qw.2.(At)FN2ns,12 (2At) + [q,,,2ns (2At) - qm, (At)]FN2õs,12 (At)
- pt,2 (2At) = qf (At)Ft 1,N2W (2At) + [qf 1,1 (2At) - qf,,,(At)iFt
1õv2,7, (At) +
qf1,2 (At)Ff,2,N2.(2At) +[qf12(2At) - qf1,2 (At)]P,2,N2õ (At) +L +
qify,2ns (AI)PN2ns,N2ns (2At) + [qtN,2ns (2At) qfN,2ns(At)]FN2ns,N2n,(At)
[0160] Similarly, in case of t = 3At, the equation of unsteady production in
refracturing may
be expressed as equation (27).
( P f2 1,1(3 At) = qn,1(A0Fi1,11(3At)+Eqn,1(2At)-qn,1(At)1Fi1,11(2A0+
Eqn,1(3At) qf1,1(2At)]F11,11 (At) qf1,2 (At)F12,11(3At) +
[qn,2(2At) - qn,2 (At)]F12,11(2At) + [qf1,2(3At) - qf 1,2(2At)] X
2,1 I (At) +L + qThi,2õs (At)FN2õ01(3At) + [q2õs (2At) - qThi,2õs (At)] X
FN2noi(2At) + [qfN,2ns (3At) qfN,2ns (2At)]FN2flS I (At)
P,2 p12(3At) = qf (At)Fii,12(3At) [q1-1,1 (2M gr1,1(MiFi1,12(2At) +
[qf 1,1 (3M qn,i (2MiFi 1,12 (At) qf1,2 (At)F12,12(3At) +
[qn,2(2At) - qn,2 (At)]112,12(2At) + [qn,2(3At) - qn,2(2At)] x
Fi2,12(At) +L + qThi,2õs (At)FN2ns,ii(3At) + [qfN,2ns (2At) - qfN,2õs (At)] X
(27)
FN2noi(2At) + [qfN,2ns (3At) qfN,2ns (2At)]FN2ns, j I (At)
p2 (3At) = (MF1 1,N2,õ (3At) WI-1,1(2M qn,i (MiFi 1,N2n, (2At) +
,\-- , \-- -t
[gf1,1(3M qn,1 (2AtAF11,N2ns (At) af12 (At)P2 N2ns (3A . '1
[qn,2(2At) - qn,2 (At)]F12,N2ns (2At) + [qn,2(3At) - qn,2(2At)] x
Fi2,1y2õs (At) +L + qfN,2 (At)FN2ns,N2,is (3At) + [q2õs (2At) -
qfN,2õs (At)] x FN2ns,N2õs (2At) +
[qfN,2ns (3At) qfN,2ns(2At)]FN2.,N2ns (At)
[0161] Analogously, a pressure drop produced by all the fracture infinitesimal
segments on
a j-th target element at the current moment can be obtained, which may be
expressed as in
equation (28).
- 34 -
Date Recue/Date Received 2020-05-11
N 2 N -
(28)
P t2k+1, 1 (n t)= (nA t)+1{ (m At) ¨ [(m ¨1) Atl} Fmqg (n ¨
m+1) At
[0162] Equation (28) shows the pressure drop produced by the infinitesimal
segments of the
N existing fractures on the j-th target element at the current moment. Based
on equation (28),
combined equations (of which a quantity is Nx2ns) for pressure drops produced
by all
infinitesimal segments on all targeted elements can be obtained. The combined
equations
include Nx2ns unknowns (that is, production of all fracture infinitesimal
segments of all
fractures at the current moments). Therefore, the equations are closed, and
the mathematical
model has a unique solution. The solved production of all the infinitesimal
segments of all
the fractures at each moment is used to solve the production after to (after
the refracturing).
[0163] Afterwards, co-production of the new and existing fractures after to is
solved. Due
to a decrease in conductivity of the existing fracture after to, two new
branch fractures are
refractured on each existing fracture (a total quantity of the elements in the
branch fractures
are Nx2cs), so as to increase a flow area of the fracture and improve the
conductivity of the
existing fracture. The new and existing fractures are discretized both
temporally and
spatially into multiple fracture infinitesimal segments in a period from
beginning to t. An
influence of a pressure drop before to on production of each fracture
infinitesimal segment of
the current N fractures is considered. The pressure drop is due to the
production of each
fracture infinitesimal segment of the N existing-and-new fractures in each At
before to, that the
fracture infinitesimal segments of the new fractures both products and injects
with a constant
level before to, and that the new fractures still produce in the current N
fractures. At t after
to, an algebraic sum of two pressure drops is considered. One is due to
extending the
production of each fracture infinitesimal segment of each new and existing
fractures to each
fracture infinitesimal segment of the N existing-and-new fractures at the
current moment t,
where the fracture infinitesimal segments of the new fractures both product
and inject with a
constant level to, and only product but not inject after to. The other is due
to each fracture
infinitesimal segment of the N existing-and-new fractures at the current
moment t.
[0164] In case oft = niAt + At, the equation of unsteady production in
refracturing may be
expressed as equation (29).
-35 -
Date Recue/Date Received 2020-05-11
- p + At) = qf11 (At) F (rtiAt + At) + [q f11 (2At) - q f (At)]x
F111 (TOO +L + [qf11 (TOO - q fu(rtiAt - At)]F (2At) +
f 1,1(10,0 - qf11 (2At) +
+1)At] - (At) +
f1,2 (At) F,2,õ (niAt + At) +[q f1,2 (2At) - f1,2 (At)] x
F, 2,11 (niAt)+L +[q f12 (niAt) - q f (niAt - At)]F12,11 (2 At) +
f 1,2(00 - q f -1)Atfl F,2,11 (2At) +
Iqf1,2 +1)At] - q fi,2(rtiAt)} F,2,11 (At) +
L + q õ ,2,s+1[(n, +1)At]Fm,õ (At) +L + q õ [(n1 + 1) At]F N(2. 2c.,),õ
(At)
p - p f2 (rtiAt + At) = qf12 (At) F, 1,12 (111AI + At) + [q ,2 (2At) - q f
(At)] X
F11,12 (niAt)+L +[qf12(TOO - qf (niAt - At)]F,1,12 (2 At) +
{q f (01) - qf ,,2[(11 - 1)At] }1 (2At) { q f 1,2[(1, + 1)At] -
q fi,2(niAt)} (At) + qn,2 (At)
Fi2j2(niAt + At) +
[qf (2At) - q f (At)]F,2 (00 +L + [qf1,2 (TOO - q f (niAt -
At)] x
F, 2,12 (2At) f ,,2(rtiAt) - qf, ,2[(n, -1) At] } F,2,12 (2At) + (29)
f1,2 + 1)At] - qf1,2 (n1At)1F,2,12 (At) +
L [(n, + 1) At]F,,,,2 (At) +
L qfN,2ns+2cs[(rt1 + 1) At]FN (2ns +2cs),I2 (At)
Pi2 PfN2 ,(2ns+2cs) (niAt + At) = q f ,,, (At) F,,,N (2 2,) (rtiAt + At) +
[qf11 (2At) - q f (At)] x
FII,N(2ns+2cs) (niAt)+L +[q f (niAt) - q 11,1(niAt - At)]F, 1,N(2ns+2cs) (2At
f1,1(niAt) - qf11 -1)At]I 1 i1,A,(2.+2cõ) (2At)
+ 1)At] - q f,,,(11,At)IF,,,N(2+2) (At)
qf1,2 (At)E11,AT(2ns+2es) (I/At + At) + [q (2At) - q f (At)]E,I,N(2,2s+2cs)
(niAt) +
L [q f12 (niAt) - q f12
(rtiAt - At)]F12,N(2ns+2cs)(2
(niAt) - qf1,2 [(rt, -1)At]I
^ ,2,N(2ns+2a) (2At) +
Iqf,,2 [('11 + 1)At] - qf (niAt)IF
^ ,2,3/(2ns+2cs) (AO+
L q + DAVAT,,A,(2ns+2cs) (AO+
L + [(n, + 1)AtWN(2,2cs),N(2.+2cs) (At)
[0165] In case oft = niAt + 2At, the equation of unsteady production in
refracturing may be
expressed as equation (30).
- 36 -
Date Recue/Date Received 2020-05-11
2 2
p; ¨i. (niAt 2.6,0= qf11 (At) f111 (n1 At +2At)+[qf11 (2At)¨qf11(At)] x
Fi 1.11 (niAt+ At) +L +{qfll(niAt)¨ c .,[(n, F, 1.11 (3 AO+
lq fiLir(ni+1) At] ¨qf. (niAti)} õ (2At)+
lc[(n + 2)At] ¨ c hi.,[(ni+1)A1-1} Fii.õ (At) +
c (At) ]2 (niAt 2Ati) [c hi .2 (2At)¨ch1.2 (At)] X
(niAt+ At) +L + lc/n.2 (niAt) ¨ch1.2[(n1 ¨1)At]}Fi2.11 (3At)
chi.2 [(ni+1) At] ¨q.2 (niAti)} Fi2.õ (2 At) +
(c .2[(ni + 2) At] ¨ c hi.2[(ni+1) F12.11 (At) +L +
+1)At] x
(2At) + {q21 [(ni + 2)At] +1)At],} x F,(2.+0.11 (At)L +
{q Thr .(2.+2,$)[(n, + 2)At] a
.N.(2rts+2cs)[(1/1 +1)Ad} FN(22c).11 (At)
¨ pL2(niAt 2At) = qf11 (At)F11.12 (I/At+ 2At)+[qa1 (2At)¨ chi (At)] x
Fi1.12 (n,At+At)+L + {c .,(niAt) ¨ c .,[(n, ¨1)Adi Fi1.12 (3 AO+
fc r(ni+1)Ati ¨gm (00} (2At)+
+2)At]qf11[(n1+1)At1}F,1.12 (At) +
chi.2 (At)F,2.,2 (niAt 2Ati) [qt.1.2 (2At)¨ ch1.2 (At)]
'2 .12 (ni At + At) +L {c hi.2(niAt) ¨ ch,12[(n1 ¨1)At]} Fun (30+
(30)
Ch1.2 [(n, +1)Atl ¨qt,1=2 (00} Fun (2At)+
chi.2[(n, +2)At] ¨qa2 [(n, +1)Atl}F,2.,2 (At)+L +
+1)At]F,(2,,),,2 (2At) + itqfw.2," + 2)At] +1)Adif x
(At)L + fq fiv + 2)At] +1)At],} FA,(2õ.,2s),12
(At)
¨ i(2.+2c.v) (niAt 2At) = qf11 (At) Fi (niAt 2At) [qf11 (2At) ¨ qf11
(At)]x
Fi 1 ., (2.+2,) (niAt+ At)+L + {an., (n1 At) ¨ c õReit, ¨ 1)At].} I', 1
ig(2+2õ) (3 At) +
tan., [(n, +1) At] ¨qf. (00} Fi1õ(2,2cs) (2At) +
tan= ,[(n, + 2)At]qf11[(n1+1) Atl} Fi1.,(2õ,2c) (AO+
q1.12 (At)F,2. ,(2,2 (niAt 2At) [q .2 (2At) ¨ q1.1.2 (At)] x
(ni At+ At)+L + lc/n.2 (niAt) ¨ q fi.2[(ni ¨1)Ad} Fi2i,v(2+2c.) (3 AO+
chi.2 [(111+1) At] ¨ ch,L2 (n1 At)} 2.(2+2) (2At) +
{chi.2[(n, + 2)At] ¨qa2 [(n1+1) At]} Fi 2.(2õ,2..) (At) +L +
qw,21 [(n, + 1)At]F (2At)+{q2õsõ [(n1 + 2)At] ¨ gv,2,s1[(12,
+1)Ad} X
(A01-, + 2) At] ¨
q,(2õs+2e,)[(n1 F
7,1(2ns+2.) (At)
[0166] Analogously, a pressure drop produced by all the fracture infinitesimal
segments on
the j-th target element at the current time can be obtained, which may be
expressed as
equation (31).
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Date Recue/Date Received 2020-05-11
2ns+2cs
p ¨
qõ(mAt)¨ q1 [(m ¨1) Atl} F, (n ¨ m+1) At (31)
[0167] Equation (31) shows the pressure drop produced by the infinitesimal
segments of the
N existing fractures on the j-th target element at the current moment. Based
on equation (31),
combined equations (of which a quantity is Nx2ns) for pressure drops produced
by all
infinitesimal segments on all targeted elements can be obtained. The combined
equations
include Nx2ns unknowns (that is, production of all fracture infinitesimal
segments of all
fractures at the current moments). Therefore, the equations are closed, and
the mathematical
model has a unique solution. The solved production of all the infinitesimal
segments of all
the fractures at each moment is used to solve the production after to (after
the refracturing).
N 2ns+2cs
Q = E I ifk +1,1 (32)
k=0 1=1
[0168] The right term of equation (32) is an algebraic sum of production of
all fracture
elements in the N existing fractures and all new branch fractures.
That is, it is production
of all the fracture elements of all the existing-and-new fractures, after two
new branch
fractures are refractured on each existing fracture.
[0169] In one embodiment, a fracture parameter of the refractured oil-gas well
is refined
and optimized with cumulative production of the refractured oil-gas well as a
target, under a
condition that a length of the refractured fracture is fixed.
[0170] In one embodiment, the fracture parameter of the refractured oil-gas
well is
optimized under different conductivity, based on the rapid calculation model
of unsteady
production established for the matrix-fracture coupled fluid in the
refractured oil-gas well
having. Reference is made to Figure 16, which shows cumulative gas production
of the
refractured oil-gas well under different fracture conductivity (80D= cm,
60D=cm, and 40D = cm),
calculated by using the parameters Table 1. As an example, the fracture
parameter of the
refractured oil-gas well is optimized based on Table 1.
[0171] As shown in Figure 16, all the cumulative production gradually
increases with time
after refracturing on the 720th day, in case of other parameters are same.
Cumulative
production of the oil-gas well before refracturing increases slightly with an
increase of
conductivity. After the refracturing on the 720th day, production of the
refractured oil-gas
- 38 -
Date Recue/Date Received 2020-05-11
well increases significantly due to an interference effect of more refractured
fracture elements
and an improvement of permeability of the existing fracture. Taking the
cumulative
production of the refractured oil-gas well as an objective, the cumulative
production is largest
and the increase in the production after refracturing is largest under a
fracture conductivity of
80D=cm. Therefore, the fracture parameter corresponding to the fracture
conductivity of
80D=cm is best for refracturing.
[0172] An apparatus for processing production data of a refractured oil-gas
well is provided
according to an embodiment of the present disclosure, in order to calculate
production of a
refractured oil-gas well quickly and accurately, provide a reasonable basis
for optimizing
.. parameters of fractures the refractured oil-gas well, and improve an effect
of reforming the
refractured oil-gas well. Referring to Figure 6, an apparatus for processing
production data
of a refractured oil-gas well includes: a module 10 for fracture space
discretization, a module
for reservoir percolation model establishment, a module 30 for intra-fracture
pressure drop
model establishment, and a module 40 for unsteady production determination.
15 [0173] The module 10 for fracture space discretization is configured to
discretize spatially
an existing fracture in a refractured oil-gas well and a new branch fracture
on the existing
fracture, to obtain multiple fracture infinitesimal segments that are same in
length.
[0174] The module 20 for reservoir percolation model establishment is
configured to
establish a model for reservoir percolation for each of the multiple fracture
infinitesimal
20 segments, based on a geological characteristic of a reservoir and a
basic property of a fluid.
[0175] A module 30 for intra-fracture pressure drop model establishment is
configured to
establish a model of intra-fracture pressure drop for each of the multiple
fracture infinitesimal
segments, based on a characteristic of the existing fracture and a
characteristic of the new
branch fracture.
[0176] The module 40 for unsteady production determination is configured to
determine
current production of the refractured oil-gas well, based on a corresponding
relationship
between production and pressure response in the model of reservoir
percolation, a
corresponding relationship between a pressure loss and a fracture width in the
model of
intra-fracture pressure drop, history fracturing data of the refractured oil-
gas well, and a
predetermined rule of intra-fracture fluid flow.
- 39 -
Date Recue/Date Received 2020-05-11
[0177] Described above is the apparatus for processing production data of the
refractured
oil-gas well according to an embodiment of the present disclosure. The
existing fracture in
the refractured oil-gas well and the new branch fracture on the existing
fracture are spatially
discretized to obtain the multiple fracture infinitesimal segments that are
same in length.
The model for reservoir percolation is established for each of the multiple
fracture
infinitesimal segments, based on the geological characteristic of the
reservoir and the basic
property of the fluid, so as to accurately obtain the corresponding
relationship between the
production and the pressure response. The model of intra-fracture pressure
drop is
established for each of the multiple fracture infinitesimal segments, based on
the characteristic
of the existing fracture and the characteristic of the new branch fracture, so
as to accurately
obtain the pressure loss corresponding to different fracture widths.
Afterwards, the history
fracturing data of the refractured oil-gas well and the predetermined rule of
intra-fracture fluid
flow are combined in a temporal dimension, and thereby the accurate current
production of
the refractured oil-gas well are obtained. The reasonable basis is provided
for optimizing
parameters of fractures of the refractured oil-gas well, and the effect of
reforming the
refractured oil-gas well is improved.
[0178] Reference is made to Figure 7. The module 20 for reservoir percolation
model
establishment includes a unit 21 for point-source function construction, a
unit 22 for
fluid-flow resistance function construction, and a unit 23 for reservoir
percolation model
establishment according to an embodiment of the present disclosure, in order
to obtain the
corresponding relationship between the oil-gas production and the pressure
response of the
existing fracture and the new branch fracture in the refractured oil-gas well.
[0179] The unit 21 for point-source function construction is configured to
construct a
point-source function of a box-shaped gas reservoir with a closed boundary,
based on a
.. reservoir boundary effect, the geological characteristic of the reservoir,
and the basic property
of the fluid.
[0180] The unit 22 for fluid-flow resistance function construction is
configured to
determine a function of fluid flow resistance corresponding to each of the
multiple fracture
infinitesimal segments, based on the point-source function.
[0181] The unit 23 for reservoir percolation model establishment is configured
to determine
the corresponding relationship between the production and the pressure
response of the
- 40 -
Date Recue/Date Received 2020-05-11
refractured oil-gas well, based on the function of fluid flow resistance.
[0182] Reference is made to Figure 8. The unit 21 for point-source function
construction
includes a subunit 211 for target reservoir permeability determination, a
subunit 212 for target
stratum pressure determination, and a subunit 213 for point-source function
construction
according to an embodiment of the present disclosure, in order to consider
fully influences of
the real-gas effect and the stress sensitivity in determining the
corresponding relationship
between the oil-gas production and the pressure response.
[0183] The subunit 211 for target reservoir permeability determination is
configured to
determine target reservoir permeability in the point-source function, based on
a corresponding
relationship between a stress sensitivity coefficient and reservoir
permeability in the
geological characteristic of the reservoir.
[0184] The subunit 212 for target stratum pressure determination is configured
to construct
a real-gas effect equation based on the basic property of the fluid, and
determine a target
stratum pressure in the point-source function.
[0185] The subunit 213 for point-source function construction is configured to
determine
the point-source function, based on a Green-function equation of a solution of
the
point-source function, a real-gas effect equation, the target reservoir
permeability, and the
target stratum pressure.
[0186] Referring is made to Figure 9. The module 30 for intra-fracture
pressure drop
model establishment includes a unit 31 for equation of intra-fracture pressure
drop
determination and a unit 32 for intra-fracture pressure drop model
establishment according to
an embodiment of the present disclosure, in order to determine accurately the
corresponding
relationship between the pressure loss and fracture width of the existing
fracture and the new
branch fracture in the refractured oil-gas well,.
[0187] The unit 31 for equation of intra-fracture pressure drop determination
is configured
to obtain an equation of intra-fracture pressure drop, based on a
corresponding relationship
between preset reservoir permeability and production time.
[0188] The unit 32 for intra-fracture pressure drop model establishment is
configured to
determine the model of intra-fracture pressure drop, based on the equation of
intra-fracture
pressure drop and a corresponding relationship between the fracture width and
a fracture
-41 -
Date Recue/Date Received 2020-05-11
length in the characteristic of the existing fracture and the characteristic
of the new branch
fracture.
[0189] Reference is made to Figure 10. The module 40 for unsteady production
determination includes a unit 41 for transient production equation
determination, a unit 42 for
temporal discretization, a unit 43 for history pressure loss determination,
and a unit 44 for
current production determination according to an embodiment of the present
disclosure, in
order to determine accurately the current production of the refractured oil-
gas well.
[0190] The unit 41 for transient production equation determination is
configured to
determine an equation of transient production for the refractured oil-gas
well, based on a
preset flowing bottom-hole pressure, the corresponding relationship between
the production
and the pressure response in the model of reservoir percolation, and the
corresponding
relationship between the pressure loss and the fracture width in the model of
intra-fracture
pressure drop.
[0191] The unit 42 for temporal discretization is configured to discretize
temporally a
history refracturing process of the refractured oil-gas well, to obtain
multiple cycles of stable
production.
[0192] The unit 43 for history pressure loss determination is configured to
determine a loss
due to history pressure drop, based on history production corresponding to
each of the
multiple fracture infinitesimal segments in each of the multiple cycles of
stable production in
the history refracturing process.
[0193] The unit 44 for current production determination is configured to:
determine an
equation of unsteady production in refracturing, for the refractured oil-gas
well, based on the
loss due to history pressure drop corresponding to each of the multiple
fracture infinitesimal
segments, the equation of transient production, and the predetermined rule of
intra-fracture
fluid flow; and obtain the current production of the refractured oil-gas well,
based on the
equation of unsteady production in refracturing.
[0194] A specific application of the apparatus for processing production data
of the
refractured oil-gas well is provided according to an embodiment of the present
disclosure, so
as to implement the method for processing production data of a refractured oil-
gas well. The
application includes: (1) designing different fracture parameter
configurations for the
- 42 -
Date Recue/Date Received 2020-05-11
refractured oil-gas well; and (2) calculating daily production and cumulative
production from
refracturing at the 720th day to the 1440th day, of the refractured oil-gas
well under the
different parameter configurations. The parameters are as shown in Table 2.
Table 2 Basic parameters of a gas reservoir and a refractured fracture
Variable Unit Value Parameter Unit Value
Gas reservoir length m 2000 Gas deviation factor 0.89
Gas reservoir width 111 2000 Gas critical pressure MPa
4.5
Gas reservoir
111 20 Gas relative density 0.6
thickness
Reservoir
K 341 Gas viscosity mP a = s 0.009
temperature
Reservoir original
permeability in x, y, mD 0.45 Gas constant J/(mol=K) 8.314
and z directions
Reservoir porosity 0.14 Gas density kg/m3 0.655
Original stratum Relative molecular
MPa 40 29
pressure mass of air
Flowing
bottom-hole Matrix stress
MPa 20 0.087
pressure under a sensitivity factor
pressure
Quantity of existing Gas critical
1 K 190
fractures temperature
Existing fracture
D 240 Gas critical pressure MPa 4.5
permeability
Existing fracture Acceleration of
m 90 m/s2 9.8
length gravitaty
Gas reservoir
Toe width of
111111 3.5 irreducible water % 10
existing fracture
saturation
Heel width of
111111 1.5 Shaft radius m 0.107
existing fracture
Quantity of discrete
Comprehensive -1
elements of existing 10 MPa 0.035
fracture compression factor
Quantity of discrete
Refractured new
elements of
branch fracture m 45 5
refractured new
width
branch fracture
Toe width of Heel end width of
refractured new 111111 2 refractured new 111111 2
branch fracture branch fracture
- 43 -
Date Recue/Date Received 2020-05-11
[0195] A length of each existing fracture is 90m, and a length of each new
branch fracture
is 45m. Two new branch fractures are refractured on each existing fracture. A
distance
from a position of the new branch fracture on the existing fracture to the
shaft is 45m.
Production of a refractured oil-gas well and an un-refractured oil-gas well
are compared.
[0196] (1) Total daily production and total cumulative production
[0197] Figure 12 is a schematic diagram of a distribution of an existing
fracture and a new
branch fracture in a refractured oil-gas well. Figures 17 and 18 are schematic
diagrams of
comparisons of daily and cumulative gas production of an existing fracture and
anew branch
fracture between a refractured oil-gas well and an un-refractured oil-gas
well. It can be seen
that the daily gas production shows a typical characteristic of gas reservoir
production
characteristics when other parameters are same. The typical characteristic is
a "L" type
production, which indicates a rapid decline in production in an early stage
and a slow decline
in production (stable production) in a later stage. Daily and cumulative
production of
refractured and un-refractured models are same in the early stage before
refracturing (before
the 720th day), thus directly indicating a good match and a good accuracy when
the model
degrades into a conventional fracturing model or an un-refractured model. On
the 720th day,
discrete elements of the refractured new branch fractures connect more
drainage areas, and
permeability of the existing fracture is improved by refracturing.
Accordingly, the daily and
the cumulative gas production increase sharply in the case with refracturing,
and a difference
between the production with and without refracturing gradually decreases over
time.
Thereby, the cumulative gas production can be increased through refracturing.
[0198] (2) Daily production of the existing fracture and new branch fracture
[0200] A schematic diagram of comparison of daily gas production between the
existing
fracture and the new branch fracture after refracturing is obtained based on
the physical model
corresponding to Figure 12, so as to compare an influence of the new fracture
on gas
production of the existing fracture.
[0201] Figure 19 shows the daily gas production of an existing fracture and a
new branch
fracture. It can be seen from that the daily production of the refractured new
branch fracture
is zero in an early stage after refracturing, when other parameters are same.
It proves
accuracy of assuming that the discrete elements of the new branch fracture
both products and
injects with a same level before refracturing. After the refracturing on the
720th day, the gas
- 44 -
Date Recue/Date Received 2020-05-11
production of the existing fracture and the new branch fracture after
refracturing both increase
sharply and then decrease rapidly to a stable production, with a decrease of a
stratum pressure.
The reason is as follows. In the early stage after refracturing, an effect of
the new branch
fracture improving the permeability of the existing fracture is much stronger
than the effect of
the new branch fracture interfering the existing fracture. Thereby, the
production of the
existing fracture goes higher. In the later stage after refracturing, the
effect of the new
branch fracture interfering the existing fracture dominates, thus the
production of the existing
fracture goes lower. There are two reasons why the production of the new
branch fracture is
lower than that of the existing fracture. One is that the conductivity of the
existing fracture
is greater than the conductivity of the new branch fracture. The other is that
a drainage area
connected to the existing fracture is larger than a drainage area connected to
the new branch
fracture.
[0202] (3) Fracture conductivity
[0203] An influence of different fracture conductivity on the daily gas
production of the
refractured oil-gas well is analyzed based on the physical model corresponding
to Figure 12.
Three cases of fracture conductivity of 80 D=cm, 60D=cm, and 40 D=cm are taken
as
examples.
[0204] Figure 20 is a schematic diagram of daily gas production under
different
conductivity (80D= cm, 60D= cm, and 40 D= cm). It can be seen that the
production increases
sharply and then decrease rapidly to a stable production, with a decreasing in
a stratum
pressure after the refracturing on the 720th day, when other parameters are
same. The
production of the refractured oil-gas wells increases by a small magnitude
with an increase of
the conductivity before refracturing. After the refracturing on the 720th day,
the production
of the refractured oil-gas wells increases significantly with an increase of
the conductivity,
due to an influence of more refractured fracture elements and an improvement
in permeability
of the existing fracture.
[0205] (4) Timing of refracturing
[0206] An influence of timing of refracturing on the production of the
refractured oil-gas
well is studied based on the physical model corresponding to Figure 12.
Refracturing is
performed on 720th, 900th, and 1080th days, respectively, to generate new
branch fractures.
- 45 -
Date Recue/Date Received 2020-05-11
[0207] Reference is made to Figure 21, which shows daily gas production at
different
timing of refracturing. An overall trend of the production is consistent with
the above
descriptions for the refractured new branch fracture. It can be seen that the
production of the
new branch fracture increases and then gradually decreases in all cases of the
720th day, the
900th day, and the 1080th day. The production of the new branch fracture
decreases faster in
the early stage than in the later stage. The daily gas production is higher
when the
refracturing is earlier. Therefore, it is better to generate new branch
fractures as soon as
possible for increasing production of the refractured oil-gas well on a gas
reservoir.
[0208] Reference is made to Figure 22, which shows growth rates in cumulative
production
at different timing of refracturing. The growth rate of cumulative production
is zero before
refracturing, when other parameters are same. After the refracturing, the
cumulative
production growth rate increases gradually due to an increased connected
drainage area and
an improved fracture permeability. Amplitude of increase in production varies
at different
timing of refracturing timing. The growth rate of cumulative production is
higher when
refracturing at the 720th day than at 900th day, and is higher than when
refracturing at the
900th day than at the 1080th day. Increases in production over original
production after two
years of refracturing are 10.62%, 8.53%, and 6.27%, for refracturing at the
720th day, the
900th day, and the 1080th day, respectively. Therefore, it is better to
generate new branch
fractures as soon as possible for increasing production of the refractured oil-
gas well on a gas
reservoir.
[0209] An electronic device for implementing all or part of the method for
processing
production data of the refractured oil-gas well is provided in hardware,
according to an
embodiment of the present disclosure, in order to calculate production of a
refractured oil-gas
well quickly and accurately, provide a reasonable basis for optimizing
parameters of fractures
the refractured oil-gas well, and improve an effect of reforming the
refractured oil-gas well.
The electronic device includes: a processor, a memory, a communication
interface, and a bus.
[0210] The processor, the memory, and the communication interface communicate
with
each other via the bus. The communication interface is configured to implement
information
transmission among the apparatus for processing production data of the
refractured oil-gas
well, a core business system, a user terminal, a database, and other related
devices. A logic
controller may be a desktop computer, a tablet computer, a mobile terminal,
and the like, and
- 46 -
Date Recue/Date Received 2020-05-11
this embodiment is not limited thereto. In one embodiment, the logic
controller may be
implemented by referring to embodiments of the method and the apparatus for
processing
production data of the refractured oil-gas well, which is not repeated herein.
[0211] The user terminal may include a smart phone, a tablet electronic
device, a network
set-top box, a portable computer, a desktop computer, a personal digital
assistant (PDA), a
vehicle-mounted device, a smart wearable device, and the like. The smart
wearable device
may include smart glasses, a smart watch, a smart bracelet, and the like.
[0212] In practice, a part of the method for processing production data of the
refractured
oil-gas well may be performed by the electronic device described above, or all
parts of the
method may be implemented in a client device. Such selection may depend on a
processing
capability of the client device and a limitation of an application scenario,
which is not limited
herein. In a case that all parts of the method are implemented in the client
device, the client
device may further include a processor.
[0213] The client device may include a communication module (that is, a
communication
unit) for communicating with a remote server, to achieve data transmission
with the server.
The server may include a server on a side of a task scheduling center. In
another
implementation scenario, the server may include a server on an intermediate
platform, such as
a server on a third-party server platform with a communication link with the
server on the side
of the task scheduling center. The server may include a single computer
device, a server
cluster formed by multiple servers, or a server structure of distributed
devices.
[0214] Figure 23 is a schematic structural diagram of an electronic device
9600 according
to an embodiment of the present disclosure. As shown in Figure 23, the
electronic device
9600 may include a central processor 9100 and a memory 9140. The memory 9140
is
coupled to the central processor 9100. The structure in Figure 23 is
exemplary, and other
types of structures may be used to supplement or replace the structure, in
order to implement
telecommunication functions or other functions.
[0215] In one embodiment, the method for processing production data of the
refractured
oil-gas well may be integrated into the central processor 9100. The central
processor 9100
may be configured to control based on steps S101 to S104.
[0216] In step S101, an existing fracture in a refractured oil-gas well and a
new branch
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Date Recue/Date Received 2020-05-11
fracture on the existing fracture are spatially discretized to obtain multiple
fracture
infinitesimal segments that are same in length.
[0217] In step S102, a model for reservoir percolation is established for each
of the multiple
fracture infinitesimal segments, based on a geological characteristic of a
reservoir and a basic
property of a fluid.
[0218] In step S103, a model of intra-fracture pressure drop is established
for each of the
multiple fracture infinitesimal segments, based on a characteristic of the
existing fracture and
a characteristic of the new branch fracture.
[0219] In step S104, current production of the refractured oil-gas well is
determined based
on the corresponding relationship between the production and the pressure
response in the
model of reservoir percolation, the corresponding relationship between the
pressure loss and
the fracture width in the model of intra-fracture pressure drop, history
fracturing data of the
refractured oil-gas well, and a predetermined rule of intra-fracture fluid
flow.
[0220] Describe above is the electronic device according to an embodiment of
the present
.. disclosure. The existing fracture in the refractured oil-gas well and the
new branch fracture
on the existing fracture are spatially discretized to obtain the multiple
fracture infinitesimal
segments that are same in length. The model for reservoir percolation is
established for each
of the multiple fracture infinitesimal segments, based on the geological
characteristic of the
reservoir and the basic property of the fluid, so as to accurately obtain the
corresponding
relationship between the production and the pressure response. The model of
intra-fracture
pressure drop is established for each of the multiple fracture infinitesimal
segments, based on
the characteristic of the existing fracture and the characteristic of the new
branch fracture, so
as to accurately obtain the pressure loss corresponding to different fracture
widths.
Afterwards, the history fracturing data of the refractured oil-gas well and
the predetermined
rule of intra-fracture fluid flow are combined in a temporal dimension, and
thereby the
accurate current production of the refractured oil-gas well are obtained. The
reasonable
basis is provided for optimizing parameters of fractures of the refractured
oil-gas well, and the
effect of reforming the refractured oil-gas well is improved.
[0221] In another embodiment, the apparatus for processing production data of
the
refractured oil-gas well may be arranged separately from the central processor
9100. For
example, the apparatus for processing production data of the refractured oil-
gas well may be
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Date Recue/Date Received 2020-05-11
configured as a chip connected to the central processor 9100, and the
apparatus is controlled
by the central processor to implement the method for processing production
data of a
refractured oil-gas well.
[0222] As shown in Figure 23, the electronic device 9600 may further include:
a
communication module 9110, an input unit 9120, an audio processor 9130, a
display 9160,
and a power source 9170. It is unnecessary for the electronic device 9600 to
include all the
components as shown in Figure 23. The electronic device 9600 may further
include
components not shown in Figure 23. Reference may be made the conventional
technology.
[0223] The central processor 9100 as shown in Figure 23 is sometimes embodied
as a
controller or an operation control component, and may include a
microprocessor, another
processing apparatus, and/or a logic apparatus. The central processor 9100
receives input
and controls operation of each component of the electronic device 9600.
[0224] As an example, the memory 9140 may be one or more of: a buffer, a flash
memory,
a hard drive, a removable medium, a volatile memory, a nonvolatile memory, or
other
appropriate devices. The memory 9140 may store aforementioned relevant
information, and
may store a program for executing some information. The central processor 9100
may
execute the program stored in the memory 9140 to implement information storage
or
processing.
[0225] The input unit 9120 provides an input to the central processor 9100.
The input unit
9120 may be, for example, an input device with buttons or a touch device. The
power
source 9170 is configured to supply power to the electronic device 9600. The
display 9160
is configured to display objects such as images and characters. The display
may be, for
example, an LCD display, but is not limited thereto.
[0226] The memory 9140 may be a solid-state memory, such as a read-only memory
(ROM), a random-access memory (RAM), and a SIM card. The memory 9140 may be a
memory which can retain information even after being powered off, and may be
selectively
erased and provided with more data. For example, the memory may be called an
EPROM,
or the like. The memory 9140 may be some other types of device. The memory
9140
includes a buffer memory 9141 (sometimes referred to as a buffer). The memory
9140 may
include an application/function storage portion 9142, which is configured to
store an
application program or a function program, or configured to operate the
electronic device
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Date Recue/Date Received 2020-05-11
9600 via the central processor 9100.
[0227] The memory 9140 may further include a data storing portion 9143, which
is
configured to store data such as contacts, digital data, pictures, sounds
and/or any other data
used by the electronic device. A driver storing portion 9144 of the memory
9140 may
include various types of drivers for the electronic device, which are
configured to implement a
communication function and/or other functions (such as a message-transmission
application
or an address-book application) of the electronic device.
[0228] The communication module 9110 is a transmitter (or a receiver) 9110
transmitting
(or receiving) signals via an antenna 9111. The communication module (the
transmitter or
the receiver) 9110 is coupled to the central processing unit 9100 to provide
input signals (or
receive output signals). Such case is similar to operation of a conventional
mobile phone.
[0229] Multiple communication modules 9110 may be provided in the same
electronic
device based on various communication technologies. For example, the
communication
modules 9110 may include a cellular network module, a Bluetooth module, and/or
a WLAN
module. The communication module (the transmitter or the receiver) 9110 is
also coupled to
a loudspeaker 9131 and a microphone 9132 via an audio processor 9130, to
provide an audio
output via the loudspeaker 9131 and receive an audio input from the microphone
9132.
Thereby, common telecommunication functions are achieved. The audio processor
9130
may include any appropriate buffer, decoder, amplifier, and the like. The
audio processor
9130 is further coupled to the central processing unit 9100, thereby enabling
recording a voice
in the electronic device via the microphone 9132 and playing a voice stored in
the electronic
device via the loudspeaker 9131.
[0230] A computer-readable storage medium for implementing the method for
processing
production data of the refractured oil-gas well via an execution subject of a
server or a client
in the aforementioned embodiments is further provided according to an
embodiment of the
present disclosure. The computer-readable storage medium stores a computer
program.
The method for processing production data of the refractured oil-gas well is
implemented via
the execution subject of the server or the client in the aforementioned
embodiments, when the
computer program is executed by a processor. For example, following steps S101
to S104
are implemented when the processor executes the computer program.
[0231] In step S101, an existing fracture in a refractured oil-gas well and a
new branch
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Date Recue/Date Received 2020-05-11
fracture on the existing fracture are spatially discretized to obtain multiple
fracture
infinitesimal segments that are same in length.
[0232] In step S102, a model for reservoir percolation is established for each
of the multiple
fracture infinitesimal segments, based on a geological characteristic of a
reservoir and a basic
property of a fluid.
[0233] In step S103, a model of intra-fracture pressure drop is established
for each of the
multiple fracture infinitesimal segments, based on a characteristic of the
existing fracture and
a characteristic of the new branch fracture.
[0234] In step S104, current production of the refractured oil-gas well is
determined based
on the corresponding relationship between the production and the pressure
response in the
model of reservoir percolation, the corresponding relationship between the
pressure loss and
the fracture width in the model of intra-fracture pressure drop, history
fracturing data of the
refractured oil-gas well, and a predetermined rule of intra-fracture fluid
flow.
[0235] Describe above is the computer-readable storage medium according to an
embodiment of the present disclosure. The existing fracture in the refractured
oil-gas well
and the new branch fracture on the existing fracture are spatially discretized
to obtain the
multiple fracture infinitesimal segments that are same in length. The model
for reservoir
percolation is established for each of the multiple fracture infinitesimal
segments, based on
the geological characteristic of the reservoir and the basic property of the
fluid, so as to
accurately obtain the corresponding relationship between the production and
the pressure
response. The model of intra-fracture pressure drop is established for each of
the multiple
fracture infinitesimal segments, based on the characteristic of the existing
fracture and the
characteristic of the new branch fracture, so as to accurately obtain the
pressure loss
corresponding to different fracture widths. Afterwards, the history fracturing
data of the
refractured oil-gas well and the predetermined rule of intra-fracture fluid
flow are combined
in a temporal dimension, and thereby the accurate current production of the
refractured oil-gas
well are obtained. The reasonable basis is provided for optimizing parameters
of fractures of
the refractured oil-gas well, and the effect of reforming the refractured oil-
gas well is
improved.
[0236] Those skilled in the art should understand that the embodiments of the
present
disclosure may be provided as a method, an apparatus, or a computer program
product.
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Date Recue/Date Received 2020-05-11
Therefore, embodiments of the present disclosure may be implemented completely
in
hardware, completely in software, or in a combination of software and
hardware. Moreover,
the present disclosure may be embodied as a computer program product carried
in one or
multiple computer-usable storage media (including but not limited to, disk
storage, a
CD-ROM, or optical storage) that contain computer-usable program codes.
[0237] The present disclosure is described with reference to flowcharts and/or
block
diagrams of methods, devices (apparatuses), and computer program products
according to
embodiments of the present disclosure. Each flow or a combination of flows in
the
flowcharts, and/or each block or a combination of blocks in the block diagrams
can be
implemented via computer program instructions. The computer program
instructions may
be provided to a processor of a general-purpose computer, a special-purpose
computer, an
embedded processor, or other programmable data processing devices, so as to
produce a
machine. Thereby, the instructions when executed by the processor of the
computer or other
programmable data processing devices are configured to generate a device for
implementing a
function designated by one or more flows in a flow chart and/or one or more
blocks in a block
diagram.
[0238] The computer program instructions may also be stored in a computer-
readable
memory, which is capable of directing a computer or other programmable data
processing
devices to operate in a particular manner.
Thereby, the instructions stored in the
computer-readable memory produce a manufactured article which includes an
instruction
apparatus. The instruction apparatus is configured to implement a function
designated by
one or more flows in a flow chart and/or one or more blocks in a block
diagram.
[0239] These computer program instructions may be loaded on a computer or
other
programmable data processing devices. Thereby, a series of operation steps is
performed on
the computer or other programmable devices, to generate a process to be
achieved by
computers. Hence, the instructions executed by the computer or other
programmable
devices provide steps for implementing a function designated by one or more
flows in a flow
chart and/or one or more blocks in a block diagram.
[0240] Specific embodiments are used herein to illustrate principles and
implementations of
the present disclosure, which only intends to help understand a method and a
concept of the
present disclosure. Variation may be made to a specific implementation and an
application
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Date Recue/Date Received 2020-05-11
scope by those skilled in the art according to the spirit of the present
disclosure. Therefore,
content in the specification should not be construed as a limit to the present
disclosure.
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Date Recue/Date Received 2020-05-11
