CA3080609A1 - Method and apparatus for processing production data of refractured oil-gas well - Google Patents

Abstract

A method and an apparatus for processing production data of a refractured oil- gas well. The method includes: discretizing spatially an existing fracture and a new branch fracture on the existing fracture, to obtain multiple fracture infinitesimal segments; establishing a model for reservoir percolation for each fracture infinitesimal segment, 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 fracture infinitesimal segment, based on a characteristic of the existing fracture and a characteristic of the new branch fracture; and 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.

Description

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 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 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 processing production data of a refractured oil-gas well is provided according to an embodiment of the present disclosure, including: discretizing 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;
establishing a model for reservoir percolation for each of the multiple 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 multiple fracture infinitesimal segments, based on a characteristic of the existing fracture and a characteristic of the new branch fracture; and 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.

[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 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 Date Recue/Date Received 2020-05-11 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; 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 Date Recue/Date Received 2020-05-11 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 processing production data of 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, and a module for unsteady production determination.

[0014] The module 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.

[0015] The module for reservoir percolation model establishment is configured to establish a model for reservoir percolation for each of the multiple 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 multiple 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 drop, history fracturing data of the refractured oil-gas well, and a predetermined rule of intra-fracture fluid flow.

[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 Date Recue/Date Received 2020-05-11 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 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.

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 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;

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.

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.

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 es, 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 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 t1 (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 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 es, 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,y0,zo,t)= Si(x,x0,r)= S2(y, yo, z) = S3(z, zo, z)d (1) OC, Date Recue/Date Received 2020-05-11 where:
- i i -1 erf + erf xf / 2 + (x ¨ xo) xf / 2 ¨ (x ¨ x0) SI (x, xo , 1-)= ¨
2 2V77 / ,1- 2V/7,T
\ \ / _ 1 Yd __ /2+(Y¨)0) Yd __ / 2 ¨ (Y ¨ Yo ) SI (Y, Yo ,r)= ¨ erf + erf (2) 2 2 \177,z- ; 2\111,r x--P"
S, (z, zo , r)= 4 1 1 1+ -2., - exp i 22z-271j \ sin niz- coslrz-z cos ¨bz-z IC n-1 n h2 i h h h [0086] Symbols in equation (2) are described as follows.
[0087] Pi represents a pseudo original stratum pressure. A unit of pi may be MPa2/(Pa.$).
_ [0088] p(x,y,z,t) represents a pseudo instantaneous pressure at a coordinate point (x, y, z) in an infinite plane, after producing ¨
q(xo, y 0, zo,t) with a constant flow and a constant mass at a coordinate point (x0, y0, z0) for (t ¨to) . A unit of p¨ (x,y,z,t) may be MPa2/(Pa= s) _ [0089] q(xo,yo,zo,t) represents a production at the coordinate point (x0, y0,z0) with a _ constant flow. A unit of q(xo,Yozo,t) may be kg/ks.
[0090] 0 represents reservoir matrix porosity, without dimension. Ct.
represents a fluid compression coefficient, of which a unit may be MPa-1. t represents a time of production measured from a start of the production, of which a unit may be ks. v represents a duration of continuous production, of which a unit may be ks. S1(x,x0, z-) , Si(y, y0, z-) , and S3 (z, z0, T) are Green functions in x, y, and z directions, respectively. xf represents a position in x direction along a length of a fracture, of which a unit may be m.
[0091] Iq. represents piezometric conductivity in the x direction, of which a unit may be m2=MPa/(Pa.5), and ii, = K,I OuCt . iy represents piezometric conductivity in the y , , dt i, direction, of which a unit may be m2=MPa/(Pa.$), and 77 = K I OuC.
represents 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. Ky 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).
(3) p P se Ts z 2 1 p C se (p p 2 ) 2pse TZ 1 [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).
2 2qp scZT
p,2 ¨ p = S i(x ,x 0 , r) = S 2(y , y 0, r) =
S3(z,zo,r)dr (4) OCtZscTsc [0096] In equation (4), there is q=q(x0,y0,z0,01 ps, = 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 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.

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 es, 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 APfk+ld (t)=P, Si(x,x0,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-kid 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).
2nsts 2qfk iipseZTit Apfk2 ii(o_p2 _ p ___________________________________________________________________ Si(x,x0,r)=S2(y,yo,r)=S3(z,zo,r)dl-k,m=1 /-1 OCtZsc Tsc (8) N 2ns+2cs =E E gifk+1,/ = Fla (k+1)j(t) 1c41 1-1 [0105] In equation (8), Fiõ,(k+i)il(t) represents an effect of a discrete element at a position of 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 p seZT
F ,(k+i),(t) ____________________ S i(x, xo,r) = S 2(y , y 0,r) = S 3(z , zo,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).
K m(p) = K mo exp[¨ a m(p 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 Date Recue/Date Received 2020-05-11 (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.
[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.
(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. 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=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).

Date Recue/Date Received 2020-05-11 2q1-7c+1 pseZT st APt2k+id(t)=P2 ¨ P2 S1(XX0r)=S2.(y,y0,z-)=S,(z,zo,r)dr (7) 0C,ZseTse [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 Ap 2n,s+2cs 2qa+1ipseZT_pt2kõ, E E
si(x,,,r)= S2 (y,yo,r)=S3(z,zo,r)dr k,m=1 1-1 OCtZseTse (8) N 2nA+2cA
=E E qfk+1,,, = Fki (k+1)j(t) k41 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, Fki,(k+i)i(t) represents a function of fluid flow resistance, which may be expressed as the aforementioned equation (9).
2pseZT
Fki,(k+i);(t) S1(x,x0,r)= S2 (y,y0,2-)=S3(z,zo, z)dr ___________________ (9) 0CtZseTse [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 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.

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 K11 (t) = 81.512C 343 (10) [0127] In equation (10), K+11(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+i, /iv', +1, /
(11) AXk +1, Kfk +1, (t) [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,/ 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.

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 w =w + ______________________________ (w ¨w fk+1, mm,k+1 max,k+1 mm,k+1 ns and for j > ns, w = Hmm,k+1+j ¨ ns ¨1 r vI max,k+1 Hmm,k+1) (13).
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, wm,o+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 Ap,10 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 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, Ap2 P fk +1, j P fk+1,0 v i\ x AXfk+1,1qfk+1,1 lilk+1kt)wfk+1,jhiT se 2flgpseZT
x(Axfk+1,1+ Axfk+1,2) X qfk+1,2 = = =
K fk+1(t)Wfk+1, jh T
2JIg p scZT 2dugpseZT
x(Axfk+1,1+ Axfk+1,2 = = = AXfk+1,j)q fk+1 \
K fk+1(t)W fk+1, jh T 11 v 11c+1 i 1Wfk-pi,j11Ts, (14);
x(Axfk+1,1 + = = = +
2,ugps,ZT
X qfk+1, J+1 +.. = c,\ x(Axfk+11 Axfk+1,2 = = = A X fk+1,j)xKfk+l qfk+1,n,s-Fes kt)wfk+i,fhTs, 2,ugps,ZT n (qfk+i,iL Axfk+1,i) qfk+1,n(L &+1j)fk, Kfk+l(t)w+lIh.Ci=1 i=1 n= j +1 _ i=1 for ns/2 < j < ns, Date Recue/Date Received 2020-05-11 2 2//g pscZT
AP t2-k+1, J-0 = Pt2k+1,j v Ffk+1,0 x Axfk+1,1qfk+1,1 11- fk+1ri ii'vfk+1,jh 2pgps,ZT
______________________________ x(AXfk+1,1 Axfk+1,2 )qfk+1,2 = =
Kfk+1(t)wfk+1, jhisc 2 p g p scZT 2pg pscZT
___________________ x(Axfk+1,1 Axfk+1,2 = ' + AXfk+i, j)qfk+1 Kfk+1(t)wfk+1 T, SC Kfk+1(t)Wfk+1,/hTsc X (AXfk+1,1 Ax1k+1,2 = = = A xfk+1, j) 2 p g p scZT
Xqfk+1,j+1 v _____________________________ T X (AXfk+1,1 Axfk+1,2 = = AXfk+i, ) X qt.k+ims ''fk+1V1Wfk+1,/hi Sc 2/./gpscZT
_________________________ x(AXfk+1,1 Axfk+1,2 = = = Axfk+1,ns12) X q fk+1,ns+1 (15);
Kfk+1(t)wfk+1,j" sc 2 p g p scZT
_________________________ x(Axix+1,1+ Axfk+1,2 = = Ax fk+1,ns 12) x fk+1,ns+2 Kfk+1(t)wfk+1,/hiT sc 2 p g p scZT
___________________________ x(AXfk+1,1 Axfk+1,2 = = AXfk+i,ns ) a /2 fk+1,ns+cs Kfk+1(t)wfk+1,/hisc 2pg p scZT ns (q1I+1,ilt AX fk+1,i) fk+1,n Axfk+1,i) Kfk+1 (t)Wfk+1,jh Tsc i=1 i=1 n= j+1 _ i=1 2 p g p scZT ns+cs x(AXfk+1,1 Axfk+1,2 = = .. Ax fk+1,ns12)I fk,i Kfk+1(t)wfk+1,j" sc ns+1 and if ns < j < ns + CS, 2 2pgp,õ.ZT
APf2k-pid-o Pf2k+1, j Pfk+1,0 ____ " T X AXfk+1,1qfk+1,1 11- fk+1r lwfk+1, jh isc 2pgpscZT
______________________________ x(Axfk+1,1+ Axfk+1,2)qfk+1,2 = =
Kfk+1(t)l'vfk+1,1h' T sc 2pgpscZT 211g pscZT
___________________ x(Axfk+1,1+ Axfk+1,2 AXfk+1,nsI2 )qfk+1,ns12 Kfk+1 i T sc Kfk+1(t)Wfk+1,1h1sc (16).
x(Axfk+1,1+ Axfk+1,2 = = A7Cfk+1,ns/2 ) 2pgpscZT
xa ,fk+1,ns/2+1 = ____ r x(AXfk+1,1 Axfk+1,2 = = Axfk+1,ns12) v qfk+1,ns+as 11-fk+1 V,1wfk+1, jhiT sc 2//gpscZT[ns/2 I ns+cs ns/2 I(qfk+1,1IA7cfk+i,i) q fk+1,n(IA7cflc+1,i) Kfk+1(t)wfk+1,jhTcc i=1 i=1 n=ns12+1 _ i=1 [0133] In equations (14) to (16), symbols are described as follows. APLI,J-0 represents a Date Recue/Date Received 2020-05-11 pressure drop generated by the fluid flowing from M(xfk+i,/, Ya+1,/, za+iil) to Ofk+1,0, of which a unit may be MPa.
,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 = qfk+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. qfk+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).

Date Recue/Date Received 2020-05-11 , Pfk+1'1 + V fk +11 P fk+1'4 Vfk+1'4 hfk +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. hfic+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).

qa+1,3 2v1qfk+1,3A gVfk+1,3 COS co 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 V1qfk+1,3P
Pfk+1,1 Pfk+1,4 hfk+1,1,4Pg _L (20) [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.

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+1,/, R+1/, z+11).

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 O+ between between the fracture and the shaft, and may be expressed as in equation (21) po=pwf (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 2pgps,ZT {x¨,-/ 1 K i Pi Pwf ¨ ______ L., _____ kg fk+1,11, Axfk+u) L q11+1,n (1, AX11+1,i) + õ(t)hTsõ 1=1 wfk+Li 1=1 n=J+I W11+1,/ _ 1=1 (22);
=\ 2 pg p,s,zT N 2ris+2 õ, es Ei (X11,i X11+1, j)2 (Y Yf k+1, j ) (Zad¨ Zfk+,J )2 ________________________________________________________________ }
______________ L L q jx 22-Km (p)hTs, k=1 1=1 4qt for ns/2 <j < ns, _ 2 2 ,õ x_,,i 1 ns 1 1 Pi Pwf ¨ 2pgpZT 1 __ (qfk-d,ilt AXfk-d,i) + L qfk-d,n(L A7Cfk-d,i)1 +
Kfk_d(t)hTsc Li_, wfk+1,/ i=1 n= j-dWfk+1j ¨ i=1 2pgpZT ns+c 1 _______________ x(Axtt-d,i + AXfk+1,2 = = + AXfk+1,ns/2) L q fk,i +
(23);
Kfk+,(t)hTsc i=ns-dWfk+1,ns+1 ¨ i N2 i \ 2 i _ R-pgpscZT N 2n s+2 Ei x q cs Vfk ,i ¨ Xfk+i ), j + Vfk,i ¨ yf", j ) +
Vfk,i ¨ Zf", i )2 _____________ L L
2Km(p)hT õ,i sc k_1 i_1 4qt and for ns <j < ns + cs, Date Recue/Date Received 2020-05-11 2it, põZT
Ar,2 = ,,, P,2 _ 2 _______ =
fk+1, j Pfk+1,0 X Ax a fk+1,1 = fk+1,1 K (Ow .hT
fk+1 fk+1, i sc 2pgpõZT
, x(Axfk+t,t a+1,2 )qa+1,2 Kfk+1 (t)Wfk+1, ini,, 1,T sc 2,L1gpõZT 2,ugpscZT
x(Axa+1,1+ Axfk+1,2 ... AXfk+1,ns/ 2 )qfk+1 In I 2 ________ Ka+,(t)wa_õ,/hTõ ' ' Kfk, (t)Wa+,, ihTsc X(AXfk+1,1 AXfk+1,2 ... AX fk+1,ns12) 2idgpscZT
Xqf7c+1,ns/2+1 ... x(Axa+1,1+ Axfk+1,2 ...
AXfk+1,ns/2 ) X q fk+1,ns-cs (24) jig põ ,+ q xEi _____________________________ ZT ' v n2 s+2cs (Xfo - x_11)2 ( ,,V fk,i )2 f k+1,I ) +
(Z fk,i- Z f "1,1 _______________ E E ,,i 2R-K,õ(p)hT, k=1 I, I-1 41g - _ 2,u,p,ZT {'72 1 i ns+cs 1 ns/ 2 1}+
Ka+,(t)hTõ 1=1 Wa+1,1 1=1 j=ns12+1Wfk+1,1 ' 1=1 pgp Ei sc x q ZT ' v n2 s+2cs ()Lai- xfk 1,i) +(yfk,1 Yf k+1, j ) (Zgo - Zf "1,1 _____________ E E ,,,i " _____________________________ 2R-K,õ(p)hTõ 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.

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, ,qn) of all days before to to the current moment and a pressure drop due to production increments (or negative increments) q, ¨ q,_i 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,¨ t1) with the production increments (or negative increments) q1-1), a production well products (t, ¨ 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,,,, (At) F (At)+ q,1,2 (At) Fi2,õ (At) + q,1,3 (At) F,3,õ (At) +
L + q2ç (At)F,2,,õ (At) p ,2 ¨p (At) = q ,, (At) F, In (At) + q,12 (At) F12,12 (At) + qf13 (At) F13,12 (At) +
L + (At)F, (At) p ,2 ¨p3 (At) = q 1,1 (At) F 1,13 (At) + qf12 (At) F12,13 (At) + q,13 (At) F13,13 (At) + (25) L + qt. (At) F,õõs,,, (At) p ,2 ¨ p,2õ, (At) = q ,, (At) F, (At) + q,12 (At)F12,N2ns (At)+ q,13 (At) F13,N2ns (At) +
L qf/V ,Des ( At )FN2ns,N2ns (At) [0159] In case of t = 2At, the equation of unsteady production in refracturing may be expressed as equation (26).

Date Recue/Date Received 2020-05-11 p - p11 (2At) = q f (2At) + [qf (2At) - qf ,,(At)]F, (At) +
qf 1,2 (A0F12,11 (2At) + [qf 1,2 (2At) qf 1,2 (At)]P12,11 (AO +L +
qw,2õ(AOFN211 (2A() + [gfAT,2 (2At) (AOWN(2õs),11 (At) - pf21,2 (2At) = qf (At)Ft 1,12 (2At) + [qf1,1 (2At) - qf (At)]Ft 1,12 (At) +
qf (At)Ff ,2,12 (2At) +[qf12(2At) - qf (At)]F,2,12 (At) +L +
(26) gm, (At) F N 12 (2At) + [q (2At) - q õAc2n, (At)]FN2ns,12 (At) - p fv2 ,2ns (2At = qf (At)Ft 1,N2nS (2At) + [qf11 (2At) - qf,,, (MY; 1õV2,,, (At) qf (At)Ff,2,N2.(2At) +[qf12(2At) - qf (At)]F,2,,2õ (At) +L +
(At)FN2ns,N2ns (2At) + [gfAT,2. (2At) qfN,2ns (AWN2ns,N2. (At) [0160] Similarly, in case of t = 3At, the equation of unsteady production in refracturing may be expressed as equation (27).
( 2 2 P, Pf1,1(3At)= qn,1(A0Fi1,11(3At)+Eqn,1(2At)-qn,1(At)1F11,11(2A0+
Egfij (At) + qf1,2 (At)F12,11(3At) +
[qn,2(2At) - qn,2 (At)]F12,11(2At) + [qf1,2(3At) - qn,2(2At)] X
2,1 I (At) +L + qThi,2õs (At)FN2õs ji(3At) + [q2õs (2At) - qThi,2õs (At)] X
FN2nsji(2At) + [qfN,2 (3At) qfN,2iis (2At)]FN2flS I (At) P,2 p12(3At) = qn (At)F11,12(3A() + (2At) (At)iFi 1,12(2At) +
[qn,1(3At) qt1,1(2At)iFi1,12(At) + qf1,2 (At)F12,12(3At) +
[qn,2(2At) - qn,2 (At)]F12,12(2At) + [qn,2(3At) - qf 1,2(2At)] x Fi2,12(At) +L + qThi,2ns (At)FN2iis Ji(3At) + [qfN,2 (2At) - qfN,2ns (At)] x (27) FN2iis ji(2At) + [qfN,2ns (3At) qfN,2iis (2At)]FN2 I (At) pi2 p2 (3At) = qn,i(At)Fil,N2ns (3At) [gf1,1 (2 At) - qti,i (At)iFi 1,N2ns (2At) +
, (At )P2 [gf1,1(3At) qn,1 (2AtAF11,N2ns (At) af12 (AtlF12 N2ris . (3 A t) [qn,2(2At) - qn,2 (At)]F12,N2ns (2At) + [qn,2(3At) - qn,2(2At)] x F 2,N2ns (At) +L + qThi,2ns (At)FN2.x2,is (3At) + [q2ns (2At) - i qfN,2ns (At)] x FN2 (2At) +
[qfN,2ns (3At) qfN,2ns (2At)]FN2õ,,,,N2,,s (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).

Date Recue/Date Received 2020-05-11 N 2n, ¨
(28) 1:)= qt,(At)F,õ,,,q(nAt)+1{q,(mAt)¨qt[(m-1)Ati}F(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).

Date Recue/Date Received 2020-05-11 p,2 ¨ p f21,1(n,At + At) = q f ,,, (At) F,,,õ (n,At + At) + [q f (2At) ¨ qf (At)] x F(n,At) +L + [q f ,,,(n,At)¨ q f,,, (n,At - (2 At) +
f 1,1(00 ¨ q f,,,[(n, ¨1)At] }F,,,õ (2At) +
f,,, [(n, +1)At]¨ qf ,,,(niAt)} Fii,õ (At) +
qf ,,2 (At) F,2,õ (n,At + At) +[q f1 2 (20 ¨ qf ,,2 (At)]x F, 2,11 (n,At)+L + [q f12 (n,At) ¨ q f ,,2 (n,At ¨ At)]F12,11 (2 At) +
f 1,2(00 ¨ q f ,,2[(n, ¨1)At] } F,2,11 (2At) +
Iqf 1,2[(n, +1)At]¨ qf ,,2(n,At)1F,2,õ (At) +
L + q + 1) AtWN, ,õ (At) +L + q õ + 1) At]F
,,,,(2,2s+2cs),11 (At) p2 p2l,2nt ( At + At) = qf ,,2 (At) F (n,At + At) + [q f ,,2 (2At) ¨
qf ,,2 (At)] x f F11,12 (n,At)+L + [qf,,2 (n,At)¨ q f ,,2 (n,At ¨ At)]F,1,12 (2 At) +
f ,,,(n,At) ¨ qf ¨ 1) At]l F,1,12 (2At) + Iqf12 [(n, + 1)At] ¨
q f ,,2(n,At)1F,,,,2 (At) + qf (At) F,2,,2 (n,At + At) +
[qf,,2 (2At) ¨ qf (At)]F,2,12 (n,At) +L + [qf1,2 (n,At)¨ q f ,,2 (n,At ¨ At)]
x F, 2,12 (20+ Iqf1,2 (niAt) ¨ q f,,2[(n, ¨1) At] } F,2,12 (2At) + (29) Iqf1,2 [(n, + 1)At] ¨ qf1,2 (n1At)1F,2,12 (At) +
L q2,s+1[(n1 + 1) At]F,,,2 (At) +
L fAr,2ns+2cs[(n1 + 1) At]F,,õ (2ns+2cs),12 (At) pi2 ¨ (n,At + At) = q f ,,, (At) F,,,,, (2 2,) (n,At + At) + [q f,,,(2At) ¨ qf (At)] x FII,N(2ns+2es) (n,At)+L +[q 11,1(00¨ q (n,At ¨ At)W,I,N(2,2s+2cs) (2At) Iqf 1,1(00 ¨ q f,,,[(n, ¨ 1)At] }Ft 1õV(2ns+2cs) (2At) [(n, + 1)At] ¨ q f 1,N(2ns+2cs) (At) ( At )F1 1,N(2ns+2,) (n,At + At) +[qf12(2At) ¨qf12 (At)], 1,N(2,2s+2cs) (ntAt) L [q f12 (n,At) ¨ qf12 (n,At ¨ At),1Ft2,N(2ns+2es)(2 Iqn,2 (n,At) ¨ qf1,2 [(n, ¨1)At]
,2,N(2ns+2a) (2At) +
Iqn,2 [(n, + 1)At] ¨ qf (niAt)IF,2,,(2.+2,) (At) +
L q 2,[(n, + 1) At]F N1,Ar (2ns+2cs) (At) +
L + + 1) At]F N (2ns+2cs),N(2ns+2cs)(At) [0165] In case oft = niAt + 2At, the equation of unsteady production in refracturing may be expressed as equation (30).

Date Recue/Date Received 2020-05-11 pi2 - pLi (niAt + 2.6,0= c i., (At) f111 (niAt +2At)+[qf11 (2At)- chu (At)] x F (niAt+ At) +L +{ c hi.i(niAt) - c .,[(ni -1)At]}Fi1.11 (3 At) +
lq fitir(ni+1) At] - q (niAti)} F (2 At) +
+ 2)At]qf11[(n1+1)At1}Fi1.11 (At)+
chi.2 (At)Fi2.11 (niAt +2At)+[qti1.2 (2At)- chi.2 (At)] x (niAt+ At) +L + {Ch1.2 (niAt) - qn.2[(n1 -1)At]IF,2.11 (3A0+
chi.2 [(n,+1)At] -q=2 (niAti)} Fi2.õ (2 At) +
{c hi.2[(ni + 2)At]-qf12[(n1+1) At (At) +L +q,,.2j(n, +1)At] x F,(2õs+0.11 (2At) + {qfN .2 + 2)At] -q,.2H[(n1 +1)Adi xF(2~1)11001_, fq,,.(2.õ,)[(ni + 2)Ad-q,.(22c)Rn1 +1)Ad} FA,(2õ.,+20).11 (At) - pL2(niAt + 2At) = qf11 (At)Fi 1.12 (niAt + 2At)+[ch11 (2At) - I (At)] x Fi1.12 (n, At+At)+L +{qfll(niAt) - qf11 -1)At], VII .12 (3 At)+
r(ni+1)At]-qf11(n1At)1F11.12 (2At) +
+ 2)At]qffl[(n1+1) At1} Fi1.12 (At) +
chi.2 (At)2.2 (niAt + 2At) +[ch1.2 (2At)- ch1.2 (At)] x 2.12 (niAt+At)+L + {Ch1.2(n1At)-ch1.2[(n1 Fun (3A0+
(30) {Ch1.2 [(n,+1)At] - qn.2 (n1At)V12.12 (2At) +
chi.2[(ni + 2)At] qf.2 [(ni+1)At1}Fi2.12 (At)+L +
+1)At]F,(2õs+i).,2 (2At) + {qf 21 . + 2)At] -q,.2õõ[(ni +1)At]i} x (At)L + fq ,(2+2c)Rni + 2)At] -qt(2õs+2c,)[(n1 +1)Ad} F
,V(2ns+2a),12 (At) - .,) (niAt + 2At) = qf11 (At) Fii.õ(2õ+,õ) (niAt + 2At)+[c hi., (2At) - qf11 (At)]x At) +L + tqm (n1 At) - -1)At]} Fii.,(2õõ2c.v) (3 At) +
{gm [(n+1) qf. (niAt)} Fi1.,(2õ.,2c.) (2At) +
tchi[( + 2)At]qf11[(n1 +i) At] Fi 1.õ(2,,.,2) (At) +
chi.2 (At)Fi2.,;(2õ,õc) (niAt + 2At) + [c .2 (2At)-ch1.2 (At)] x F12.W(2ris+2cs) (niAt+ At) +L + lc/n.2 (niAt) - c .2[(ni -1)A1]} (3At) chi.2 [(n1+1) chi.2 (niAt)} Fi2N(2.+2cs) (2At) {gni [(ni + 2)At] qf.2 [(11+1) At]} Fi 2.õ(2.+2cs) (At) +L +
qw,2õ,][011 1)At]Tv(2ns+1),AT(2ns+2.) (2At) qfV.2.+1 [(11 2)At]
grN,2,s+1[(11+ 1)Ad} x (At)L + q(2.+2)[(n1 +2)At] -4Thr,(2õs+2coRni eAd} FN(2ns+2.),N(Ms+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).

Date Recue/Date Received 2020-05-11 2ns+2cs p ¨ J(nAt)=L q õ(At)F (nAt)+Liq õ(m At) ¨ q1 [(m ¨1) Atl} F,õ,õ,j(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 = I I qfk+1,/ (32) [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 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.

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 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 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 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 m 2000 Gas critical pressure MPa 4.5 Gas reservoir m 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 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 mm 3.5 irreducible water % 10 existing fracture saturation Heel width of mm 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 mm 2 refractured new mm 2 branch fracture branch fracture 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 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.

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 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 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 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 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 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 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 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.

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 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.

Date Recue/Date Received 2020-05-11

Claims (12)

1. A method for processing production data of a refractured oil-gas well, 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; and 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.

2. The method according to claim 1, wherein establishing the model for reservoir percolation for each of the plurality of fracture infinitesimal segments based on the geological characteristic of the reservoir and the basic property of the fluid comprises:
constructing 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;
determining a function of fluid flow resistance corresponding to each of the plurality of 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.

3. The method according to claim 2, wherein the constructing the point-source function of the box-shaped gas reservoir with the closed boundary comprises:
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.

4. The method according to claim 1, wherein the establishing the model of intra-fracture pressure drop for each of the plurality of fracture infinitesimal segments, based on the characteristic of the existing fracture and the characteristic of the new branch fracture comprises:
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.

5. The method according to claim 1, wherein 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, comprises:
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;
discretizing temporally a history refracturing process of the refractured oil-gas well, to obtain a plurality of cycles of stable production;
determining a loss due to history pressure drop, based on history production corresponding to each of the plurality of fracture infinitesimal segments in each of the plurality of 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 plurality of 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.

6. An apparatus for processing production data of a refractured oil-gas well, comprising:
a module for fracture space discretization, 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;
a module for reservoir percolation model establishment, 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;
a module for intra-fracture pressure drop model establishment, 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; and an module for unsteady production determination, 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.

7. The apparatus according to claim 6, wherein the module for reservoir percolation model establishment comprises:
a unit for point-source function construction, 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;
a unit for fluid-flow resistance function construction, configured to determine a function of fluid flow resistance corresponding to each of the plurality of fracture infinitesimal segments, based on the point-source function; and a unit for reservoir percolation model establishment, 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.

8. The apparatus according to claim 7, wherein the unit for point-source function construction comprises:
a subunit for target reservoir permeability determination, 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;
a subunit for target stratum pressure determination, 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; and a subunit for point-source function construction, 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.

9. The apparatus according to claim 6, wherein a module for intra-fracture pressure drop model establishment comprises:
a unit for equation of intra-fracture pressure drop determination, configured to obtain an equation of intra-fracture pressure drop, based on a corresponding relationship between preset reservoir permeability and production time; and a unit for intra-fracture pressure drop model establishment, 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 length in the characteristic of the existing fracture and the characteristic of the new branch fracture.

10. The apparatus according to claim 6, wherein the module for unsteady production determination comprises:
a unit for transient production equation determination, 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;
a unit for temporal discretization, configured to discretize temporally a history refracturing process of the refractured oil-gas well, to obtain a plurality of cycles of stable production;
a unit for history pressure loss determination, configured to determine a loss due to history pressure drop, based on history production corresponding to each of the plurality of fracture infinitesimal segments in each of the plurality of cycles of stable production in the history refracturing process; and a unit for current production determination, 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 plurality of 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.

11. An electronic device, comprising:
a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the computer program when executed by the processor implements the method according to any one of claims 1 to 5.

12. A computer-readable storage medium, storing a computer program, wherein the computer program when executed by a processor implements the method according to any one of claims 1 to 5.