A method for predicting productivity of a segmented fractured horizontal well based on a source function

Abstract

The application relates to a segmented fracturing horizontal well productivity prediction method based on a source function, which comprises the following steps: a segmented fracturing horizontal well physical model considering the distribution characteristics of branch fractures is established, artificial fractures in a formation are equivalent to strip sources under closed boundary conditions, and a main fracture and branch fractures are discretized into multiple equidistant line sink units; a strip source solution under closed boundary conditions is selected, and a corresponding source function is constructed by applying a Newman product method; a formation-fracture-wellbore coupling seepage flow model is established; on the basis of the formation-fracture-wellbore coupling seepage flow model, each line sink unit flow of the segmented fracturing horizontal well is solved step by step in time, corresponding flows at all time steps are obtained; and the corresponding flows at all time steps are used to draw a segmented fracturing horizontal well productivity curve of a tight oil reservoir, so that the productivity of the segmented fracturing horizontal well is predicted. The application has stronger applicability and higher accuracy in complex fracture characterization and productivity prediction.

Description

Technical Field

[0001] This invention relates to the technology of segmented fracturing horizontal well development and production capacity evaluation in tight oil reservoirs, specifically a method for predicting the production capacity of segmented fracturing horizontal wells based on source functions. Background Technology

[0002] Tight oil reservoirs, as an important component of unconventional oil and gas resources, are generally characterized by low porosity, low permeability, strong heterogeneity, and high seepage resistance. Under conventional development conditions, they are prone to problems such as low single-well productivity, difficulty in stabilizing production, and limited development effects (Jia Chengzao, Zou Caineng, Li Jianzhong, Acta Petrolei Sinica, 2012, 33(3): 343-350). Horizontal well staged fracturing technology has become an important technical means in the development of low-permeability tight oil and gas reservoirs because it can effectively increase the reservoir stimulation volume, expand the formation contact area, and improve near-well flow conditions (Zhang Junfeng, Bi Haibin, Xu Hao, Acta Petrolei Sinica, 2015, 36(2): 127-137). As unconventional oil and gas development continues to advance towards lower permeability and more complex reservoir conditions, accurately characterizing the seepage patterns of segmented fractured horizontal wells in complex fracture systems has become a key technical issue in the efficient development and dynamic evaluation of tight oil reservoirs.

[0003] In actual fracturing and production processes, due to factors such as formation anisotropy, effective stress variation, and fracture propagation behavior, the area near the wellbore often does not form a single main fracture, but rather a complex fracture system composed of interconnected main and secondary fractures. Meanwhile, tight reservoirs have complex pore structures, and formation fluids generally exhibit a significant initiation pressure gradient, resulting in low-velocity non-Darcy flow characteristics. As the production pressure drop increases, the permeability of the formation and fractures decreases due to stress sensitivity effects, further exacerbating the nonlinearity and dynamic changes in the seepage process (Li Yongming, Zhou Wenwu, Zhao Jinzhou, Petroleum Reservoir Evaluation and Development, 2018, 8(2): 52-57). Therefore, the combined effects of complex fracture networks, initiation pressure gradients, and stress sensitivity effects make the single-well productivity variation characteristics of segmented fracturing horizontal wells more complex, and traditional analysis methods based on a single main fracture or simplified linear flow assumptions are insufficient to meet the needs of engineering applications.

[0004] For the problem of predicting the productivity of segmented fractured horizontal wells, existing research has developed various technical approaches, including analytical methods, semi-analytical methods, and numerical simulation methods. Extensive studies have been conducted on factors such as the number of main fractures, the half-length of the main fracture, fracture conductivity, initiation pressure gradient, and stress sensitivity effects. However, existing methods are mostly based on a single main fracture or a simplified fracture structure, and do not adequately consider the complex fracture system formed by the interconnection of main fractures and branch fractures. In particular, they lack characterization of the branch fracture angle, branch fracture distribution, and the productivity variation under the combined effects of initiation pressure gradient and stress sensitivity effects. This makes it difficult to meet the needs of productivity prediction and parameter optimization for segmented fractured horizontal wells under complex fracture conditions. Summary of the Invention: The purpose of this invention is to provide a source function-based method for predicting the productivity of segmented fractured horizontal wells. This source function-based method is used to solve the problem that existing methods for predicting the productivity of segmented fractured horizontal wells are unable to accurately characterize the variation law of productivity under complex fracture conditions.

[0005] The technical solution adopted by this invention to solve its technical problem is as follows: This method for predicting the productivity of horizontal wells based on source functions includes the following steps: Step 1: Establish a physical model of a segmented fractured horizontal well that considers the distribution characteristics of the branch fractures: Define the target reservoir as a fully enclosed boundary homogeneous rectangular reservoir and clarify the three-dimensional geometric dimensions of the reservoir; the main fracture penetrates the formation vertically and is located on both sides of the wellbore with the wellbore as the center. The artificial fractures in the formation are equivalent to strip sources under closed boundary conditions. The main fracture and branch fractures are discretized into multiple equidistant line sink units. Step 2: Select the strip source solution under closed boundary conditions, and construct the corresponding source function using the Newman product method. x , y , z The product of three one-dimensional instantaneous source functions in three directions yields a three-dimensional instantaneous source function. This is achieved by analyzing the instantaneous source function over time from 0 to... t Integrating upwards yields the persistent source function, which is the pressure drop at any point within the formation: (5); in, q ( τ () indicates time τ The flow rate of the strip source or line sink unit; Δ p ( x , y , z , t () indicates time t The coordinates within the strata are ( x , y , z The pressure drop generated at the location of ); τ Represents the time integral variable; C t Indicates the overall compression ratio; ϕ Indicates porosity; t Indicates production time; Step 3: Establish a coupled seepage model of formation-fracture-wellbore; Step 4: Based on the formation-fracture-wellbore coupled seepage model, solve the time-step flow rate of each sink unit in the segmented fractured horizontal well, assuming an initial time... t Pressure at the intersection of the fracture and the wellbore when =0 p fw equal to the bottom pressure p wf The coefficient matrix of the coupled formation-fracture-wellbore seepage model is solved by matrix separation. A To obtain the flow rate of all line sinks at the initial time step. q Then solve for the unknown matrix q at the next time step. (n+1) Repeat the solution to obtain the flow rate at each time step; Step 5: Using the flow rates corresponding to all time steps, plot the productivity curves of the segmented fractured horizontal wells in tight oil reservoirs to predict the productivity of the segmented fractured horizontal wells.

[0006] Step two in the above scheme is specifically as follows: Treating artificial fractures in the formation as thick plate sources within a closed space, strip source solutions under closed boundary conditions are selected, and the Newman product method is applied to construct the corresponding source functions. x direction, y direction and z If the source functions of the directions are all strip sources in strip-shaped strata, then: (1); (2); (3); in, x , y , z These represent the pressure response points within the formation. x , y , z Coordinates in the direction; x e , y e , h These represent the length, width, and thickness of the strata, respectively. w f Indicates the width of the main crack; x f Indicates half the length of the main crack;n s This represents the number of line unit segments divided into each main crack half-wing, dimensionless; x w , y w , z w These respectively represent the strip source or line sink unit in x , y , z Coordinates in the direction; t Indicates production time; ν represents the order of the Fourier series, and is a positive integer; η x , η y , η z They represent the strata in x , y , z The pressure conductivity coefficient in the direction; μ Indicates the dynamic viscosity of formation fluids; k Indicates formation permeability; By applying the Newman product method, a three-dimensional instantaneous source function is obtained by multiplying the one-dimensional instantaneous source functions in three directions: (4); in, S ( x , t ), S ( y , t ), S ( z , t ) respectively represent x , y , z A one-dimensional instantaneous source function in the direction, dimensionless; S ( x , y , z , t () represents a three-dimensional instantaneous source function, dimensionless; By analyzing the instantaneous source function from time 0 to... t Integrating upwards yields a persistent source function.

[0007] Step three in the above plan specifically refers to: (1) No. f The first main crack d One and a half wings j The inflow rate of each line unit is q xh（f）d,j Then all line sink units in the reservoir are related to this line sink (x (f)d，j , y (f)d，j , z (f)d，j ) t The voltage drop generated at time t is: (6); in, x (f)d,j , y (f)d,j , z (f)d,j They represent the first f The main crack d One and a half wings j The center of each target line unit is at x , y , z Coordinates in direction; Δ p (f)d,i Indicates the first f The main crack d The first half of the wing i Pressure drop exerted by the source bus unit on the target bus unit; subscript xh Indicates a line unit; (2) During the production process, an additional pressure drop term is introduced based on the starting pressure gradient. Each sink element in the formation affects the target sink ( x (f)d，j , y (f)d，j , z (f)d，j The additional pressure drop generated at point ) is expressed as: (7); (3) Considering the stress-sensitive effect in tight oil reservoirs, the stress-sensitive equation is: (8); (4) Assuming the fluid flow in the main fracture and branch fractures conforms to Darcy's law, the pressure drop from any line sink unit of the main fracture to the wellbore location is: (9); (5) The pressure drop from any line confluence unit of the branch crack to the location where it intersects with the main crack is: (10); (6) Assuming the fluid first flows from the branch fracture into the main fracture, and then from the main fracture into the wellbore, the pressure drop at any point from the branch fracture manifold to the wellbore location is: (11); in, x zfIndicates half the length of the crack; K zf Indicates the permeability of the support crack; K f Indicates the permeability of the main fracture; w zf Indicates the width of the support crack; p xh(f)d,l,j,m Indicates the first f The main crack d On the wing half, and the first j The first main crack confluence unit is connected to the first l The first branch crack m The pressure on each line unit; Indicates the position of all line assembly units up to the first f The first crack j The average distance of each line unit; G Indicates the initiation pressure gradient; α Indicates the stress sensitivity coefficient; N Indicates the total number of main cracks; M This indicates the number of branch cracks on each main crack half-wing; n n This indicates the number of line unit segments divided for each branch crack; Δ p ( x (f)d,j , y (f)d,j , z (f)d,j , t () indicates time t Pressure drop at the location of the target main crack confluence element; p This indicates the formation pressure at the current calculation location and the current production time. p 0 represents the initial formation pressure; p xh(f)d,j Indicates the first f The main crack d One and a half wings j The pressure on each line unit; p xh(f)d,l,j,m Indicates the first f The main crack d On the wing half, and the first j The first main crack unit connected to the first l The first branch crack m The pressure on each line unit; p f(f)d,j Indicates the first l Span crack and the first j Pressure at the intersection of the main fracture elements; q xh(f)d,i Indicates the flow of strata into the first i The flow rate of each line unit;Q (f)d,i Indicates the main crack number 1 i The flow rate within the section flowing towards the wellbore; Q (f)d,l,i Indicates the first l The first branch crack i The flow rate within the segment flowing towards the main fracture; S (f)d,i Indicates the first i The three-dimensional instantaneous source function corresponding to each source line sink unit; p G(f)d,j This indicates the additional pressure drop caused by the starting pressure gradient; (f)d,j Indicates all line assembly units up to the first one. f The main crack d One and a half wings j The average distance of each target line unit; k 0 represents the original formation pressure. p Initial permeability under 0 conditions; f =1,2,…, N Indicates the main crack number; d =1,2 represents the two fins of the main crack; l =1,2,…, M Indicates the branch crack number on the same main crack half-wing; j =1,2,…, n s This indicates the main crack line unit number and also the connection position between the branch crack and the main crack; m =1,2,…, n n Indicates the branch crack line junction unit number; i Indicates the source line sink cell number in the summation term; (7) When the wellbore is an infinitely conductive well, the pressure inside the wellbore is equal everywhere, and the pressure at the intersection of the main fracture and the wellbore is equal to the bottom hole pressure; p fw =p wf (12); in, p fw This indicates the pressure at the junction of the main fracture and the wellbore; p wf Indicates the bottom hole flowing pressure; (8) By solving the pressure drop coupling and discrete time step, the flow rates of all line sinks at each time step are determined. Equations (6), (7), (9), (11), and (12) are combined to obtain the formation-fracture-wellbore coupled seepage model: (13); (14); in, n Indicates the current time step number; Δ t Indicates the time step; n Δ t = indicates the current calculation time; g Indicates the historical time step number. g =1,2,…, n -1.

[0008] Step four in the above scheme is specifically as follows: (1) Assume there is near the wellbore N There are main cracks, and each half of the main crack has M Under the condition of a single-strand crack, construct about 2 N ×( n s +2 M × n n A system of equations for the flow rates of unknown linear sinks; by separating the positional quantities from the coefficient matrix, the equations for the next time step are obtained. n Δ t The following system of linear equations is A· q (n) = B (n) ; coefficient matrix A for: (15); (2) Coefficient matrix A In the calculation of the main crack line sink element, the general formula is: A f,d,m The general formula for calculating the branch crack line sink element is: A (f)l,d,m , d =1 or 2, and its general formula for calculation is expanded as follows: (16); (17); in: , , , ; (3) Time step n Δ t The unknown matrix q (n) for: (18); (4) Constant term matrixB for: (19); in: (20); (twenty one); (twenty two); (twenty three); (5) Solve for the initial time step Δ t Corresponding traffic q The matrix form of its linear equation system is: (twenty four); in, A Represents the coefficient matrix of a system of linear equations; A f,d,j This represents the rows of the coefficient matrix corresponding to the target line sink element of the main crack; A (f)l,d,m Indicates the first f The main crack d On the wing l The first branch crack m Rows of the coefficient matrix corresponding to each target line unit; q This represents a column vector consisting of all unknown line sink flows at the current time step, m. 3 / s; B Pa represents the column vector of constant terms in a system of linear equations. E This represents a column vector representing the cumulative pressure response caused by the flow rate at historical time steps. Λ This represents the pressure response coefficient of the formation source function; D This represents the flow resistance coefficient within the main fracture; D ′ represents the flow resistance coefficient within the support crack; β This represents the time integral value of the source function at the current time step; β ′ represents the time integral value of the source function within the historical time step interval; ξ This represents the cumulative pressure drop generated by the flow rate at historical time steps; the superscript T indicates the transpose of a matrix or vector; Δ p eff,r Indicates the first r The effective production pressure difference of the target line unit corresponding to the main crack after deducting the additional pressure drop due to the starting pressure gradient; The linear equation system is solved using numerical integration, assuming an initial time... t Pressure at the intersection of the fracture and the wellbore when =0 p fw equal to the bottom pressure p wfThe coefficient matrix can be solved by matrix separation of the coupled flow equations. A To obtain the flow rate of all line sinks at the initial time step. q Then solve the constant term matrix in the system of linear equations. B Then, by solving the system of linear equations, the unknown matrix q for the next time step is obtained. (n+1) Repeat this step to obtain the corresponding flow rate for all time steps.

[0009] Beneficial effects: (1) The present invention takes the main fracture and the branch fracture together as the components of the segmented fracturing horizontal well production capacity model, which can characterize the complex fracture system formed by the interconnection of the main fracture and the branch fracture, avoid the problem of insufficient characterization of the actual fracturing fracture structure when only a single main fracture is considered, and improve the applicability of the production capacity prediction model under complex fracture conditions.

[0010] (2) Based on the source function method, pressure drop superposition principle and Newman product method, this invention establishes a segmented fractured horizontal well production capacity model under closed boundary conditions, and discretizes the main fracture and branch fracture into multiple line sink units for coupled solution, which can better describe the flow relationship between formation, fracture and wellbore, and provides an implementable technical means for calculating the production capacity of segmented fractured horizontal wells.

[0011] (3) The present invention considers both the starting pressure gradient and stress sensitivity effect in the production capacity model, which can reflect the influence of low-speed non-Darcy flow and production pressure drop changes on the formation and fracture seepage capacity of tight oil reservoirs. It overcomes the problem that the traditional model does not adequately consider the starting pressure gradient and stress sensitivity effect, and is conducive to improving the reliability of production capacity evaluation of segmented fractured horizontal wells in tight oil reservoirs.

[0012] (4) The present invention can quantitatively evaluate fracturing parameters such as main fracture half length, number of main fractures, main fracture conductivity, number of branch fractures, branch fracture angle and branch fracture distribution in a unified formation-fracture-wellbore coupled production capacity model, clarify the response differences of horizontal well daily production under different fracture configuration conditions, and improve the pertinence and reliability of fracturing parameter optimization of horizontal wells in tight oil reservoirs.

[0013] (5) This invention addresses the complex fracture structure formed by the interconnection of the main fracture and the branch fractures at different angles after segmented fracturing. It establishes a physical model suitable for segmented fracturing horizontal wells in tight oil reservoirs to describe the spatial and connectivity relationships between the main fracture, branch fractures and wellbore, thus solving the problem of insufficient characterization of the distribution characteristics of branch fractures and complex fracture systems in existing methods.

[0014] (6) Based on source-sink functions, pressure drop superposition principle and Newman product method, this invention establishes a semi-analytical model of the production capacity of segmented fractured horizontal wells in tight oil reservoirs that considers the coupling flow between formation and fracture in the formation and stress sensitivity effect, thus solving the problem that the production capacity variation law of segmented fractured horizontal wells under complex fracture conditions is difficult to accurately characterize.

[0015] (7) This invention solves and verifies the established model, and further analyzes the influence of main fracture parameters, secondary fracture properties, starting pressure gradient and stress sensitivity effect on the production capacity of horizontal wells, thereby providing a theoretical basis for the prediction, evaluation and optimization design of production capacity of horizontal wells in tight oil reservoirs through staged fracturing.

[0016] (8) This invention comprehensively considers the main fracture, the secondary fracture, the starting pressure gradient and the stress sensitivity effect, and establishes a semi-analytical model of horizontal well production capacity considering the mutual coupling between the formation and the fracture, so as to realize the calculation of horizontal well production capacity and parameter optimization under complex fracture conditions.

[0017] (9) This invention overcomes the limitations of traditional production prediction methods that only consider a single main fracture or a simplified fracture structure. It incorporates the main fracture along with secondary fractures of different angles and distribution patterns into the model, enabling a more accurate characterization of the connectivity of complex fracture systems after fracturing. Furthermore, based on the source function method and the pressure drop superposition principle, this invention achieves coupled solutions between the formation, fractures, and wellbore, and further considers the initiation pressure gradient and stress sensitivity effects, reflecting the impact of low-velocity non-Darcy flow and pressure changes on production capacity in tight oil reservoirs. Compared to existing methods, this invention has greater applicability and higher accuracy in characterizing complex fractures and predicting production capacity.

[0018] Instruction manual illustrations: Figure 1 This is the physical model of crack distribution on the wellbore according to the present invention; Figure 2 This is a schematic diagram of the crack space discretization of the present invention; Figure 3 Productivity curves for horizontal wells fractured in tight oil reservoirs; Figure 4 This is the daily production curve for different main crack half-lengths according to the present invention; Figure 5 This is a daily production curve for different numbers of main cracks according to the present invention; Figure 6 The daily production curves under different main fracture conductivity are shown in this invention. Figure 7 The daily production curves under different stress sensitivity coefficients are shown in this invention. Figure 8 The daily production curves under different start-up pressure gradients of the present invention are shown below. Figure 9This is the daily production curve for different numbers of branch cracks according to the present invention; Figure 10 This is the daily production curve for different support crack angles according to the present invention; Figure 11 This is a schematic diagram illustrating different distribution types of branch cracks according to the present invention; Figure 12 The daily production curves for different branch crack distribution patterns under the four branch cracks of the present invention are shown. Figure 13 Schematic diagram of a horizontal well with segmented fracturing in a tight oil reservoir; Figure 14 This is a curve comparing the daily oil production of the present invention with the actual production data and historical fitting results. Detailed implementation method: The present invention will be further described below with reference to the accompanying drawings: The method for predicting the productivity of horizontally fractured wells based on source functions is as follows: Step 1: Establish a physical model of a segmented fractured horizontal well that takes into account the distribution characteristics of the fractures. This invention establishes a physical model for segmented fractured horizontal wells that considers the distribution characteristics of fractures, providing a physical basis and constraint boundaries for subsequent seepage mathematical model construction and productivity calculation. The specific construction process is as follows: (1) Define the reservoir and wellbore foundation model The target reservoir is defined as a fully enclosed, homogeneous rectangular reservoir, and its three-dimensional geometric dimensions are clearly defined; the reservoir is located along the horizontal well. y The fractures are arranged in a central parallel manner, with the main fracturing fractures penetrating the formation vertically and symmetrically distributed on both sides of the wellbore with the wellbore as the center.

[0019] (2) Characterizing the distribution pattern of branch cracks To address the complex fracture network formed by the main fracture and accompanying branch fractures after staged fracturing, an adjustable angle range between the branch fractures and the main fracture is defined, and three typical distribution patterns are identified: uniform distribution along the main fracture, proximal distribution near the wellbore, and distal distribution far from the wellbore.

[0020] (3) Model coupling and solution foundation construction Based on the Green's function method and the source function method, artificial fractures in the formation are equivalent to strip sources under closed boundary conditions, and the corresponding source functions are constructed by combining the Newman product method. At the same time, the main fracture and the secondary fracture are discretized into multiple equidistant line sink elements, and the fracture is treated as a superposition of multiple source functions by applying the superposition principle, so as to obtain the corresponding solution.

[0021] Step 2: Solution of the source function under closed boundary conditions;

[0022] Artificial fractures in the formation are considered as stripe sources under closed boundary conditions, i.e., thick plate sources within a closed space. The stripe source solution under closed boundary conditions is selected, and the Newman product method is applied to construct the corresponding source function. Based on the proposed assumptions, this model... x direction, y direction and z If the source functions of the directions are all strip sources in strip-shaped strata, then: (1); (2); (3); in, x , y , z These represent the pressure response points within the formation. x , y , z The coordinates in the direction, in meters; x e , y e , h These represent the length, width, and thickness of the strata, respectively, in meters (m). w f Indicates the width of the main crack, in meters (m). x f Indicates the half-length of the main crack, in meters (m). n s This represents the number of line unit segments divided into each main crack half-wing, dimensionless; x w , y w , z w These respectively represent the strip source or line sink unit in x , y , z The coordinates in the direction, in meters; t Indicates production time, in seconds; τ Let s represent the time integral variable. ν represents the order of the Fourier series, and is a positive integer; η x , η y , η z They represent the strata in x , y , z The compressive conductivity in the direction, m 2 / s; ϕ Porosity is a dimensionless quantity. C t The overall compression coefficient is expressed in Pa.-1 ; μ The dynamic viscosity of formation fluids is expressed in Pa·s. k Represents formation permeability, m 2 .

[0023] By applying the Newman product method, a three-dimensional instantaneous source function can be obtained by multiplying the one-dimensional instantaneous source functions in three directions: (4); in, S ( x , t ), S ( y , t ), S ( z , t ) respectively represent x , y , z A one-dimensional instantaneous source function in the direction, dimensionless; S ( x , y , z , t ) represents a three-dimensional instantaneous source function, which is dimensionless.

[0024] By analyzing the instantaneous source function from time 0 to... t Integrating upwards yields the persistent source function, which is the pressure drop at any point within the formation: (5); in, q ( τ () indicates time τ The flow rate of a strip source or line sink unit, m 3 / s;Δ p ( x , y , z , t () indicates time t The coordinates within the strata are ( x , y , z The pressure drop at the location of ) is Pa.

[0025] Step 3: Establish a coupled seepage model of formation-fracture-wellbore; Based on the above physical model and source function solution, and taking into account the flow relationship between the formation, fractures and wellbore, as well as the effects of the initiation pressure gradient and stress sensitivity on the seepage process, a coupled seepage model of formation-fracture-wellbore in a segmented fractured horizontal well in a tight oil reservoir is established, thus providing a basis for solving the subsequent production capacity model.

[0026] (1) No. f The first main crack d One and a half wings j The inflow rate of each line unit is q xh（f）d,j Then all line sink units in the reservoir are related to this line sink ( x (f)d，j , y (f)d，j , z (f)d，j ) t The voltage drop generated at time t is: (6); in, x (f)d,j , y (f)d,j , z (f)d,j They represent the first f The main crack d One and a half wings j The center of each target line unit is at x , y , z Coordinates in direction, m; Δ p (f)d,i Indicates the first f The main crack d The first half of the wing i Pressure drop (Pa) generated by the source bus unit on the target bus unit; subscript xh This indicates a line unit.

[0027] (2) Considering the influence of the starting pressure gradient on the fluid seepage process in tight oil reservoirs, the formation fluid flow exhibits nonlinear seepage characteristics. During the production process, an additional pressure drop term is introduced due to the starting pressure gradient. Therefore, each sink unit in the formation affects the target sink ( x (f)d，j , y (f)d，j , z (f)d，j The additional pressure drop generated at point ) is expressed as: (7); (3) Considering the stress-sensitive effect in tight oil reservoirs, the stress-sensitive equation is: (8); (4) Assuming the fluid flow in the main fracture and branch fractures conforms to Darcy's law, the pressure drop from any line sink unit of the main fracture to the wellbore location is: (9); (5) The pressure drop from any line confluence unit of the branch crack to the location where it intersects with the main crack is: (10); (6) Assuming the fluid first flows from the branch fracture into the main fracture, and then from the main fracture into the wellbore, the pressure drop at any point from the branch fracture manifold to the wellbore location is: (11); in, x zf Indicates the half-length of the support crack, in meters (m). K zf The permeability of the fracture is expressed in m. 2 ; K f The permeability of the main fracture is expressed in m². w zf Indicates the width of the support crack, in meters (m). p xh(f)d,l,j,m Indicates the first f The main crack d On the wing half, and the first j The first main crack confluence unit is connected to the first l The first branch crack m Pressure of each line unit, Pa; Indicates the position of all line assembly units up to the first f The first crack j The average distance between each line unit, in meters; G Indicates the starting pressure gradient, Pa / m; α This represents the stress sensitivity coefficient, Pa⁻¹; N Indicates the total number of main cracks; M This indicates the number of branch cracks on each main crack half-wing; n n This indicates the number of line unit segments divided for each branch crack; Δ p ( x (f)d,j , y (f)d,j , z (f)d,j , t () indicates time t Pressure drop at the location of the target main fracture confluence element, Pa; p The formation pressure, in Pa, represents the current calculation location and current production time. p 0 represents the initial formation pressure, in Pa; p xh(f)d,j Indicates the first f The main crack d One and a half wings j Pressure of each line unit, Pa; p xh(f)d,l,j,m Indicates the first f The main crackd On the wing half, and the first j The first main crack unit connected to the first l The first branch crack m Pressure of each line unit, Pa; p f(f)d,j Indicates the first l Span crack and the first j Pressure at the intersection of the main fracture elements, Pa; q xh(f)d,i Indicates the flow of strata into the first i The flow rate of each line unit, m 3 / s; Q (f)d,i Indicates the main crack number 1 i The flow rate (m) within the section towards the wellbore. 3 / s; Q (f)d,l,i Indicates the first l The first branch crack i The flow rate (m) within the segment flowing towards the main fracture. 3 / s; S (f)d,i Indicates the first i The three-dimensional instantaneous source function corresponding to each source line sink unit; p G(f)d,j This represents the additional pressure drop caused by the starting pressure gradient, in Pa; (f)d,j Indicates all line assembly units up to the first one. f The main crack d One and a half wings j The average distance between each target line unit, in meters; k 0 represents the original formation pressure. p Initial permeability under 0 condition, m 2 ; f =1,2,…, N Indicates the main crack number; d =1,2 represents the two fins of the main crack; l =1,2,…, M Indicates the branch crack number on the same main crack half-wing; j =1,2,…, n s This indicates the main crack line unit number and also the connection position between the branch crack and the main crack; m =1,2,…, n n Indicates the branch crack line junction unit number; i This indicates the source line sink cell number in the summation term.

[0028] (7) When the wellbore is an infinitely conductive well, the pressure inside the wellbore is the same everywhere. Therefore, the pressure at the junction of the main fracture and the wellbore is equal to the bottom hole pressure.

[0029] p fw =p wf (12) in, p fw This represents the pressure at the junction of the main fracture and the wellbore, in Pa. p wf This represents the bottom hole flowing pressure, in Pa.

[0030] (8) By solving the pressure drop coupling and discrete time step, the flow rates of all line sinks at each time step can be determined. Therefore, by combining equations (6), (7), (9), (11), and (12), the coupled flow equation considering the formation and fracture can be obtained: (13); (14); in, n Indicates the current time step number; Δ t Indicates the time step, in seconds; n Δ t = indicates the current calculation time, in seconds; g Indicates the historical time step number. g =1,2,…, n -1.

[0031] Step 4: Coupled solution method for the production capacity model of segmented fracturing horizontal wells; Based on the above model, in order to solve the flow rate of each sink unit in a segmented fractured horizontal well stepwise, a combination of pressure drop coupling and discrete time step advancement is adopted to solve the flow relationship between the main fracture, the branch fracture and the wellbore simultaneously, thereby establishing a coupled solution method for the production capacity model of a segmented fractured horizontal well.

[0032] (1) Assume there is near the wellbore N There are main cracks, and each half of the main crack has M Under the condition of a single-strand crack, construct about 2 N ×( n s +2 M × n n A system of equations for the flow rates of unknown linear sinks; by separating the positional quantities from the coefficient matrix, the equations for the next time step are obtained. n Δ t The following system of linear equations is A· q (n) = B(n) .

[0033] coefficient matrix A for: (15); (2) Coefficient matrix A In the calculation of the main crack line sink element, the general formula is: A f,d,m The general formula for calculating the branch crack line sink element is: A (f)l,d,m , d =1 or 2, and its general formula for calculation is expanded as follows: (16); (17); in: , , ; ; (3) Time step n Δ t The unknown matrix q (n) for: (18); (4) Constant term matrix B for: (19); in: (20); (twenty one); (twenty two); (twenty three); (5) Therefore, when solving for the initial time step Δ t Corresponding traffic q When the linear system of equations is in matrix form, it is as follows: (twenty four); in, A Represents the coefficient matrix of a system of linear equations; A f,d,j This represents the rows of the coefficient matrix corresponding to the target line sink element of the main crack; A (f)l,d,m Indicates the first f The main crack d On the wing l The first branch crack mRows of the coefficient matrix corresponding to each target line unit; q This represents a column vector consisting of all unknown line sink flows at the current time step, m. 3 / s; B Pa represents the column vector of constant terms in a system of linear equations. E This represents a column vector of cumulative pressure response caused by flow rates at historical time steps, in Pa. Λ Represents the pressure response coefficient of the formation source function, in Pa / m 3 ; D This represents the flow resistance coefficient within the main fracture, expressed in Pa·s / m. 3 ; D ′ represents the flow resistance coefficient within the fracture, Pa·s / m 3 ; β This represents the time integral value of the source function within the current time step, in seconds. β ′ represents the time integral value of the source function within the historical time step interval, in seconds; ξ The cumulative pressure drop (Pa) represents the flow rate at a historical time step; the superscript T indicates the transpose of a matrix or vector; Δ p eff,r Indicates the first r The effective production pressure difference (Pa) of the target line unit corresponding to the main crack after deducting the additional pressure drop due to the starting pressure gradient.

[0034] Linear equation systems can be solved using numerical integration methods, assuming an initial time... t Pressure at the intersection of the fracture and the wellbore when =0 p fw equal to the bottom pressure p wf The coefficient matrix can be solved by matrix separation of the coupled flow equations. A Therefore, the flow rate of all line sinks at the initial time step can be obtained. q Then solve the constant term matrix in the system of linear equations. B Then, by solving the system of linear equations, the unknown matrix q for the next time step is obtained. (n+1) Repeat the above steps to obtain the traffic corresponding to all time steps.

[0035] Step 5: Based on the mathematical model obtained above, the productivity curve of the segmented fractured horizontal well in the tight oil reservoir can be plotted to predict the productivity of the segmented fractured horizontal well.

[0036] The first step of this invention is to establish a physical model of complex fractures in a segmented fractured horizontal well, clarifying the spatial and connectivity relationships between the reservoir, horizontal wellbore, main fracture, and secondary fractures. The second step is to establish a source function solution for closed boundary conditions, equating artificial fractures to strip sources under closed boundary conditions to describe the formation pressure response. The third step is to establish a coupled seepage model of the formation-fracture-wellbore, discretizing the main fracture and secondary fractures into multiple line sink units, and considering the initiation pressure gradient and stress sensitivity effects. The fourth step is to establish a coupled solution method for the production capacity model, solving for the flow rate of each fracture unit step-by-step by constructing a system of linear equations. The fifth step is to predict the production capacity of the segmented fractured horizontal well, analyzing the impact of fracture parameters, initiation pressure gradient, and stress sensitivity effects on the horizontal well's production capacity.

[0037] (I) Constructing a complex fracture physical model for a segmented fracturing horizontal well using this invention. The following assumptions are made: ① The horizontal well is located in a homogeneous rectangular oil reservoir with closed boundary conditions; the reservoir volume is... x e × y e × h ② The main fracture penetrates vertically through the formation and is located on both sides of the wellbore, with the wellbore as the center. The main fracture intersects with several branch fractures of the same shape, which are symmetrically distributed on the main fracture. ③ Fluid flow in the fracture follows Darcy's law, and the fluid is weakly compressible. ④ Fluid flows into the wellbore from the main fracture; consider the pressure drop loss in the horizontal wellbore. Figure 1 As shown, a seepage channel is formed where formation fluid first flows into the secondary fracture and then from the secondary fracture into the main fracture. Figure 2 As shown, all cracks are divided into multiple equidistant rectangular segments, i.e. line sink units, so that the cracks become a seepage process of multiple line sink units. The superposition principle is applied to process the cracks into a superposition of multiple source functions, thereby obtaining the corresponding solution.

[0038] (II) This invention establishes a production prediction model for segmented fractured horizontal wells that considers the coupled flow relationships between the formation, main fractures, branch fractures, and wellbore. Based on the source function solution under closed boundary conditions, and combining the Newman product method and the pressure superposition principle, the pressure response generated in the formation by each main fracture and branch fracture confluence unit is calculated. Simultaneously, considering the formation fluid initiation pressure gradient, reservoir stress sensitivity effect, and pressure loss generated by fluid flow within the main and branch fractures, a coupling equation between pressure and flow rate of each confluence unit is established. By discretizing and matrixing the control equations of each confluence unit, the flow rate of each main fracture and branch fracture confluence unit is solved step-by-step, and the flow rates of all confluence units are superimposed to obtain the daily and cumulative production of the segmented fractured horizontal well at different production times. Figure 3As shown, the established production capacity prediction model can be used to obtain the production capacity curve of a segmented fractured horizontal well in a tight oil reservoir. The curve can reflect the dynamic change characteristics of the horizontal well, which is high in the early stage of production, gradually decreases, and tends to flatten in the later stage of production. This provides a calculation basis for further analysis of the impact of different fracture parameters and formation parameters on the production capacity of the horizontal well.

[0039] (III) Using this invention to determine the impact of main fracture parameters on horizontal well productivity. For example... Figure 4 As shown, as the half-length of the main fracture increased from 80m to 160m, the initial daily production of the horizontal well increased from 20m³ / h. 3 / d rises to 40m 3 During production, daily output gradually decreases, and the curve flattens out in the later stages, but fractures with larger half-lengths consistently maintain high output. When the formation control area remains constant, increasing the main fracture length increases the seepage area, leading to a gradual decrease in the cumulative output growth rate, thus affecting the productivity of horizontal wells. The half-length of the main fracture is a crucial parameter in fracturing production; therefore, the length of the main fracture should be optimized appropriately during actual fracturing operations. Figure 5 As shown, with the increase of the number of main fractures, the daily production of the horizontal well increases almost proportionally, but the rate of decline in daily production is rapid. This is due to fracture interference; the fracture spacing decreases with the increase of the number of main fractures, resulting in greater interference between fractures, which is more severe in the later stages of production, thus affecting the production of each fracture. Figure 6 As shown, in the early stages of production, the daily production of horizontal wells increases with the increase of the conductivity of the main fracture, and the higher the conductivity, the faster the daily production of horizontal wells decreases. Due to the decrease in formation pressure in the later stages of production, when the conductivity of the main fracture increases to a certain extent, the fluid supply from the formation to the fracture reaches its maximum, resulting in insufficient formation fluid supply and a slower rate of increase in the cumulative production of horizontal wells. Fracture conductivity reflects the relative capacity of fluid to flow into the wellbore through the fracture and the capacity of formation to seep into the fracture. Therefore, in the fracturing design process, the fracture conductivity should be rationally optimized to improve the recovery rate of tight oil reservoirs.

[0040] (iv) Using this invention to determine the impact of start-up pressure gradient and stress sensitivity effects on horizontal well productivity. For example... Figure 7 As shown, as the stress sensitivity coefficient decreases from 0 MPa -1 Increased to 0.2 MPa -1 The daily production of horizontally fractured wells gradually decreased, with each curve showing a rapid decline in the early stage followed by a slow decline. This indicates that the stress sensitivity effect has a more significant impact on early-stage production. Because the stress sensitivity effect causes formation and fracture permeability to decrease with decreasing formation pressure during development, a higher stress sensitivity coefficient results in a faster decrease in formation pressure, leading to reduced permeability of the formation and fracture systems. This increases the flow resistance of fluids within the fractures, thereby reducing the production capacity of the horizontal well. Figure 8 As the starting pressure gradient increases from 0 MPa / m to 0.004 MPa / m, the daily production of the staged fractured horizontal well gradually decreases, with each curve showing a rapid decrease in the early stage followed by a slow decrease in the later stage. This indicates that the starting pressure gradient has a more significant impact on the initial production capacity. The increase in the starting pressure gradient leads to a decrease in the formation's permeability, increasing the flow resistance of formation fluids, thus consuming more formation energy and causing greater pressure loss, thereby reducing the production capacity of the horizontal well.

[0041] (v) Using this invention to determine the impact of fracture parameters and distribution patterns on horizontal well productivity. For example... Figure 9 As shown, when the number of fractured sections increases from none to eight, the daily production gradually increases, with a more significant increase in the early stages. The increase in the number of fractured sections enhances formation connectivity and the controlled area of ​​the fractured reservoir, thereby increasing the production capacity of horizontal wells. However, the degree of interference between fractures increases with the number of fractured sections, leading to a gradual decrease in the cumulative production growth rate. Figure 10 As shown, when the angle between the main fracture and the branch fracture increases from 15° to 90°, the daily production of the segmented fractured horizontal well gradually increases, with the difference being more pronounced in the early stages. This is because increasing the angle between the main fracture and the branch fracture simultaneously increases the affected area, leading to greater production capacity in the horizontal well. Therefore, the horizontal well achieves the best production capacity when the branch fracture is perpendicular to the main fracture. Figure 11 As shown, the distribution of the secondary fractures on the main fractures is considered to be close to the wellbore. Figure 11 a) Distant from wellbore distribution ( Figure 11 b) Uniform distribution ( Figure 11 c) Three cases; three types of branch crack distribution were obtained through calculation ( Figure 11 The production change curves for (a), (b), and (c) are shown below. Figure 12 As shown, horizontal well productivity is highest when the fractures are evenly distributed within the main fracture. When the fractures are close to the wellbore, the productivity is higher than when they are far from the wellbore. Comparing the cumulative productivity of the three fracture distribution types at different production times, the order is: even distribution > near-end distribution > far-end distribution. Because the spacing between fractures increases under even distribution, the degree of interference between fractures decreases, and the fracture control area increases, leading to increased horizontal well productivity in the early stages of production. However, in the later stages of production, due to rapid energy consumption and insufficient formation fluid supply, the rate of increase in cumulative productivity gradually decreases.

[0042] Example: like Figure 13As shown, this segmented fractured horizontal well consists of a horizontal wellbore, eight main fractures, and branch fractures distributed on both sides of the main fractures. The main fractures are arranged at intervals along the horizontal well section, and each branch fracture is interconnected with the main fractures, forming a complex seepage channel for formation fluids to flow from the matrix into the branch fractures, and then through the main fractures into the horizontal wellbore. This embodiment uses a segmented fractured horizontal well in the tight oil reservoir of Block X in the Daqing Oilfield to perform productivity fitting. The fitting curve is shown in the figure. Figure 14 As shown. The matrix permeability of this block is 0.01 mD. Eight main fractures are set in the horizontal well section, with a main fracture permeability of 1 D and a half-length of 120 m. Based on the results of the field fracture initiation test, eight branch fractures are set in each main fracture, and the daily oil production of the well is calculated using the method described in this invention.

[0043] Depend on Figure 14 It is evident that the daily oil production at the site decreases rapidly in the initial stage of production, gradually leveling off later. The calculation curve of this invention can reflect this production change characteristic, and most of the field-measured data points are distributed near the calculation curve, resulting in a generally good fit. Therefore, the method described in this invention can be used to predict the production capacity of segmented fractured horizontal wells in actual tight oil reservoirs and provide a basis for optimizing horizontal well fracturing parameters.

[0044] This invention effectively addresses the challenges of complex post-fracturing fracture morphology, difficulty in characterizing the connectivity between main and secondary fractures, and significant influences from initiation pressure gradients and stress sensitivity effects in staged fracturing horizontal wells in tight oil reservoirs. It establishes a production capacity calculation method based on source functions. This method equates artificial fractures to strip sources under closed boundary conditions, constructs a three-dimensional source function using the Newman product method, and discretizes the main and secondary fractures into multiple line sink units. The coupling solution between the formation, main fractures, secondary fractures, and wellbore is achieved through pressure drop superposition. Furthermore, this invention introduces an additional pressure drop term based on the initiation pressure gradient and a stress-sensitive permeability correction relationship, reflecting the impact of low-velocity non-Darcy flow and changes in production pressure drop on production capacity in tight oil reservoirs. Therefore, this invention can obtain daily and cumulative production changes in staged fracturing horizontal wells under different fracture parameters and flow conditions, providing a reliable technical basis for production capacity prediction, fracture parameter optimization, and development scheme adjustment in staged fracturing horizontal wells in tight oil reservoirs.

Claims

1. A method for predicting the productivity of segmented fractured horizontal wells based on source functions, characterized in that... Includes the following steps: Step 1: Establish a physical model of a segmented fractured horizontal well that considers the distribution characteristics of the branch fractures: Define the target reservoir as a fully enclosed boundary homogeneous rectangular reservoir and clarify the three-dimensional geometric dimensions of the reservoir; the main fracture penetrates the formation vertically and is located on both sides of the wellbore with the wellbore as the center. The artificial fractures in the formation are equivalent to strip sources under closed boundary conditions. The main fracture and branch fractures are discretized into multiple equidistant line sink units. Step 2: Select the strip source solution under closed boundary conditions, and construct the corresponding source function using the Newman product method. x , y , z The product of three one-dimensional instantaneous source functions in three directions yields a three-dimensional instantaneous source function. This is achieved by analyzing the instantaneous source function over time from 0 to... t Integrating upwards yields the persistent source function, which is the pressure drop at any point within the formation: （5）； in, q ( τ () indicates time τ The flow rate of the strip source or line sink unit; Δ p ( x , y , z , t () indicates time t The coordinates within the strata are ( x , y , z The pressure drop generated at the location of ) τ Represents the time integral variable; C t Indicates the overall compression ratio; ϕ Indicates porosity; t Indicates production time; Step 3: Establish a coupled seepage model of formation-fracture-wellbore; Step 4: Based on the formation-fracture-wellbore coupled seepage model, solve the time-step flow rate of each sink unit in the segmented fractured horizontal well, assuming an initial time... t Pressure at the intersection of the fracture and the wellbore when =0 p fw equal to the bottom pressure p wf The coefficient matrix of the coupled formation-fracture-wellbore seepage model is solved by matrix separation. A To obtain the flow rate of all line sinks at the initial time step. q Then solve for the unknown matrix q at the next time step. (n+1) Repeat the solution to obtain the flow rate at each time step; Step 5: Using the flow rates corresponding to all time steps, plot the productivity curves of the segmented fractured horizontal wells in tight oil reservoirs to predict the productivity of the segmented fractured horizontal wells.

2. The method for predicting the productivity of segmented fractured horizontal wells based on source functions according to claim 1, characterized in that: Step two specifically involves: Treating artificial fractures in the formation as thick plate sources within a closed space, strip source solutions under closed boundary conditions are selected, and the Newman product method is applied to construct the corresponding source functions. x direction, y direction and z If the source functions of the directions are all strip sources in strip-shaped strata, then: （1）； （2）； （3）； in, x , y , z These represent the pressure response points within the formation. x , y , z Coordinates in the direction; x e , y e , h These represent the length, width, and thickness of the strata, respectively. w f Indicates the width of the main crack; x f Indicates half the length of the main crack; n s This represents the number of line unit segments divided into each main crack half-wing, dimensionless; x w , y w , z w These respectively represent the strip source or line sink unit in x , y , z Coordinates in the direction; t Indicates production time; ν represents the order of the Fourier series, and is a positive integer; η x , η y , η z They represent the strata in x , y , z The pressure conductivity coefficient in the direction; μ Indicates the dynamic viscosity of formation fluids; k Indicates formation permeability; By applying the Newman product method, a three-dimensional instantaneous source function is obtained by multiplying the one-dimensional instantaneous source functions in three directions: （4）； in, S ( x , t ), S ( y , t ), S ( z , t ) respectively represent x , y , z A one-dimensional instantaneous source function in the direction, dimensionless; S ( x , y , z , t () represents a three-dimensional instantaneous source function, dimensionless; By analyzing the instantaneous source function from time 0 to... t Integrating upwards yields a persistent source function.

3. The method for predicting the productivity of segmented fractured horizontal wells based on source functions according to claim 2, characterized in that: Step three specifically involves: (1) No. f The first main crack d One and a half wings j The inflow rate of each line unit is q xh（f）d,j Then all line sink units in the reservoir are related to this line sink ( x (f)d，j , y (f)d，j , z (f)d，j ) t The voltage drop generated at time t is: （6）； in, x (f)d,j , y (f)d,j , z (f)d,j They represent the first f The main crack d One and a half wings j The center of each target line unit is at x , y , z Coordinates in direction; Δ p (f)d,i Indicates the first f The main crack d The first half of the wing i Pressure drop exerted by the source bus unit on the target bus unit; subscript xh Indicates a line unit; (2) During the production process, an additional pressure drop term is introduced based on the starting pressure gradient. Each sink element in the formation affects the target sink ( x (f)d，j , y (f)d，j , z (f)d，j The additional pressure drop generated at point ) is expressed as: （7）； (3) Considering the stress-sensitive effect in tight oil reservoirs, the stress-sensitive equation is: （8）； (4) Assuming the fluid flow in the main fracture and branch fractures conforms to Darcy's law, the pressure drop from any line sink unit of the main fracture to the wellbore location is: （9）； (5) The pressure drop from any line confluence unit of the branch crack to the location where it intersects with the main crack is: （10）； (6) Assuming the fluid first flows from the branch fracture into the main fracture, and then from the main fracture into the wellbore, the pressure drop at any point from the branch fracture manifold to the wellbore location is: （11）； in, x zf Indicates half the length of the crack; K zf Indicates the permeability of the support crack; K f Indicates the permeability of the main fracture; w zf Indicates the width of the support crack; p xh(f)d,l,j,m Indicates the first f The main crack d On the wing half, and the first j The first main crack confluence unit is connected to the first l The first branch crack m The pressure on each line unit; Indicates the position of all line assembly units up to the first f The first crack j The average distance of each line unit; G Indicates the initiation pressure gradient; α Indicates the stress sensitivity coefficient; N Indicates the total number of main cracks; M This indicates the number of branch cracks on each main crack half-wing; n n This indicates the number of line unit segments divided for each branch crack; Δ p ( x (f)d,j , y (f)d,j , z (f)d,j , t () indicates time t Pressure drop at the location of the target main crack confluence element; p This indicates the formation pressure at the current calculation location and the current production time. p 0 represents the initial formation pressure; p xh(f)d,j Indicates the first f The main crack d One and a half wings j The pressure on each line unit; p xh(f)d,l,j,m Indicates the first f The main crack d On the wing half, and the first j The first main crack unit connected to the first l The first branch crack m The pressure on each line unit; p f(f)d,j Indicates the first l Span crack and the first j Pressure at the intersection of the main fracture elements; q xh(f)d,i Indicates the flow of strata into the first i The flow rate of each line unit; Q (f)d,i Indicates the main crack number 1 i The flow rate within the section flowing towards the wellbore; Q (f)d,l,i Indicates the first l The first branch crack i The flow rate within the segment towards the main fracture; S (f)d,i Indicates the first i The three-dimensional instantaneous source function corresponding to each source line sink unit; p G(f)d,j This indicates the additional pressure drop caused by the starting pressure gradient; (f)d,j Indicates all line assembly units up to the first one. f The main crack d One and a half wings j The average distance of each target line unit; k 0 represents the original formation pressure. p Initial permeability under 0 conditions; f =1,2,…, N Indicates the main crack number; d =1,2 represents the two fins of the main crack; l =1,2,…, M Indicates the branch crack number on the same main crack half-wing; j =1,2,…, n s This indicates the main crack line unit number and also the connection position between the branch crack and the main crack; m =1,2,…, n n Indicates the branch crack line junction unit number; i Indicates the source line sink cell number in the summation term; (7) When the wellbore is an infinitely conductive well, the pressure inside the wellbore is equal everywhere, and the pressure at the intersection of the main fracture and the wellbore is equal to the bottom hole pressure; p fw =p wf （12）； in, p fw This indicates the pressure at the junction of the main fracture and the wellbore; p wf Indicates the bottom hole flowing pressure; (8) By solving the pressure drop coupling and discrete time step, the flow rates of all line sinks at each time step are determined. Equations (6), (7), (9), (11), and (12) are combined to obtain the formation-fracture-wellbore coupled seepage model: （13）； （14）； in, n Indicates the current time step number; Δ t Indicates the time step; n Δ t = indicates the current calculation time; g Indicates the historical time step number. g =1,2,…, n -1.

4. The method for predicting the productivity of segmented fractured horizontal wells based on source functions according to claim 3, characterized in that: Step four specifically involves: (1) Assume there is near the wellbore N There are main cracks, and each half of the main crack has M Under the condition of a single-strand crack, construct about 2 N ×( n s +2 M × n n A system of equations for the flow rates of unknown linear sinks; by separating the positional quantities from the coefficient matrix, the equations for the next time step are obtained. n Δ t The following system of linear equations is A· q (n) = B (n) ; coefficient matrix A for: （15）； (2) Coefficient matrix A In the calculation of the main crack line sink element, the general formula is: A f,d,m The general formula for calculating the branch crack line sink element is: A (f)l,d,m , d =1 or 2, and its general formula for calculation is expanded as follows: （16）； （17）； in: ， ， ， ； (3) Time step n Δ t The unknown matrix q (n) for: （18）； (4) Constant term matrix B for: （19）； in: （20）； （21）； （22）； （23）； (5) Solve for the initial time step Δ t Corresponding traffic q The matrix form of its linear equation system is: （24）； in, A Represents the coefficient matrix of a system of linear equations; A f,d,j This represents the rows of the coefficient matrix corresponding to the target line sink element of the main crack; A (f)l,d,m Indicates the first f The main crack d On the wing l The first branch crack m Rows of the coefficient matrix corresponding to each target line unit; q This represents a column vector consisting of all unknown line sink flows at the current time step, m. 3 / s; B Pa represents the column vector of constant terms in a system of linear equations. E This represents a column vector representing the cumulative pressure response caused by the flow rate at historical time steps. Λ This represents the pressure response coefficient of the formation source function; D This represents the flow resistance coefficient within the main fracture; D ′ represents the flow resistance coefficient within the support crack; β This represents the time integral value of the source function at the current time step; β ′ represents the time integral value of the source function within the historical time step interval; ξ This represents the cumulative pressure drop generated by the flow rate at historical time steps; the superscript T indicates the transpose of a matrix or vector; Δ p eff,r Indicates the first r The effective production pressure difference of the target line unit corresponding to the main crack after deducting the additional pressure drop due to the starting pressure gradient; The linear equation system is solved using numerical integration, assuming an initial time... t Pressure at the intersection of the fracture and the wellbore when =0 p fw equal to the bottom pressure p wf The coefficient matrix can be solved by matrix separation of the coupled flow equations. A To obtain the flow rate of all line sinks at the initial time step. q Then solve the constant term matrix in the system of linear equations. B Then, by solving the system of linear equations, the unknown matrix q for the next time step is obtained. (n+1) Repeat step (5) to obtain the corresponding flow rate for all time steps.

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