A method for predicting the productivity of shale gas fractured horizontal wells considering complex fracture morphology

Abstract

This invention discloses a method for predicting the production capacity of shale gas fractured horizontal wells considering complex fracture morphologies. The method includes: determining the dimensionless bottom-hole flowing pressure in Laplace space based on a production capacity prediction model considering complex fracture morphologies and well reservoir and fracture parameters; determining the dimensionless bottom-hole flowing pressure based on the dimensionless bottom-hole flowing pressure in Laplace space and the expression for the dimensionless bottom-hole flowing pressure considering wellbore reservoir and skin effects; performing a Laplace transform on the dimensionless bottom-hole flowing pressure and obtaining the dimensionless production capacity in Laplace space through the relationship between bottom-hole flowing pressure and production capacity; performing a Stehfest numerical inversion on the dimensionless production capacity in Laplace space to obtain the dimensionless production capacity; and finally converting the dimensionless production capacity into actual production capacity. This invention can predict the production capacity of shale gas fractured horizontal wells with complex fracture morphologies, closely approximating actual production.

Description

Technical Field

[0001] This invention relates to the field of shale gas fracturing technology, specifically to a method for predicting the productivity of shale gas fracturing horizontal wells that takes into account complex fracture morphologies. Background Technology

[0002] With the rapid development of the world economy, the demand for natural gas in human society is increasing daily. Shale gas, with its abundant reserves and huge development potential, has become an important component of unconventional energy and plays an increasingly important role in energy supply. However, the extremely low porosity and permeability of shale reservoir rocks greatly hinder the development process of shale gas. In order to obtain considerable natural gas production, multi-stage fractured horizontal well (MFHW) technology has been widely used in shale gas reservoir development. Therefore, accurately predicting the production of shale gas fractured horizontal wells is crucial. To accurately predict shale gas MFHW production, it is necessary not only to accurately describe the flow law of natural gas through multi-scale pores in the shale matrix and the fracture network formed by hydraulic fracturing, but also to clearly understand the characteristics of shale reservoirs and the distribution characteristics of fractures.

[0003] Describing the pore characteristics of shale is challenging due to the wide range and types of pores. Shale pores are typically classified into two categories: micropores and microfractures. Micropores exist within the shale matrix and act as containers for storing gas through adsorption, with gas diffusion primarily driven by concentration gradients. Microfractures mainly store compressed gas, relying on pressure gradients for transport. In dual-medium reservoirs, fractures are considered crucial channels for natural gas migration. Natural gas flow within microfractures is often viewed as Darcy flow. Besides the complex pore structure, shale reservoirs also include hydraulic fractures formed by hydraulic fracturing. This structure also becomes a major channel for natural gas transport during production. Therefore, to accurately predict shale gas production, multiple migration mechanisms must be considered in the model. Researchers have studied the seepage characteristics and production dynamics of fractured horizontal wells, but have neglected desorption and diffusion processes. Thus, a dual-medium model considering gas diffusion flow has been established. However, this model ignores the impact of shale gas desorption on production. Subsequently, numerous scholars proved that the Langmuir isothermal adsorption equation could accurately describe the desorption process of shale gas. Many scholars began to comprehensively consider the diverse migration processes of shale gas during the modeling process.

[0004] Besides the complex migration mechanism of shale gas, its complex geological conditions and significant differences in physical properties also pose considerable challenges to accurate simulation. In actual strata, when hydraulic fractures extend, they simultaneously open and connect with existing natural fractures, which are then deflected to some extent under the influence of natural fractures and geostress. Furthermore, the natural fractures opened and connected by hydraulic fractures become connected secondary fractures, supplying gas to them. The distribution angle of natural fractures may be uniform or random. When the distribution angle of natural fractures is uniform, the distribution angle of the resulting secondary fractures is also uniform. In existing models, analytical and semi-analytical models only consider the main fracture morphology as a single, regular rectangle, without considering the deflection of the main fracture or the influence of secondary fractures. Most numerical models do not consider the deflection of the main fracture and treat secondary fractures as randomly distributed natural fractures, ignoring the impact of the approach angle and irregular shape of secondary fractures on production capacity. Therefore, establishing a production capacity model requires comprehensive consideration of the influence of multiple factors.

[0005] To more accurately predict shale gas production capacity, this invention proposes a method for predicting shale gas production capacity that comprehensively considers multiple migration mechanisms (adsorption-desorption and gas diffusion) and complex fracture morphology, building upon previous research. The accuracy of this method is verified through field case analysis. Summary of the Invention

[0006] The present invention aims to overcome the shortcomings of the existing technology and provides a method for predicting the production capacity of shale gas fracturing horizontal wells that takes into account complex fracture morphology.

[0007] This invention solves the above-mentioned technical problems and provides the following technical solution: a method for predicting the productivity of shale gas fracturing horizontal wells considering complex fracture morphology, comprising the following steps:

[0008] Step 1: Determine the dimensionless bottom hole flowing pressure in the Laplace space based on the production capacity prediction model considering complex fracture morphology and geological and fracturing parameters;

[0009] The production capacity prediction model that considers complex crack morphology is as follows:

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] Where: h is the reservoir thickness;

[0026] Step 2: Determine the dimensionless bottom hole flowing pressure based on the dimensionless bottom hole flowing pressure in Laplace space and the dimensionless bottom hole flowing pressure expression considering wellbore storage effect and skin effect;

[0027] Step 3: Perform Laplace transform on the dimensionless bottom hole pressure, and then obtain the dimensionless production in the Laplace space through the relationship between bottom hole pressure and production.

[0028] Step 4: Perform Stehfest numerical inversion on the dimensionless products in the Laplace space to obtain the dimensionless products;

[0029] Step 5: Finally, convert the dimensionless output into the actual output.

[0030] A further technical solution is that the geological parameters include natural fracture stress sensitivity coefficient, natural fracture porosity, natural fracture permeability, matrix porosity, gas reservoir thickness, matrix compressibility coefficient, gas viscosity, gas layer temperature, Langmuir volume, pore medium tortuosity, Langmuir pressure, shale density, and original formation pressure.

[0031] A further technical solution is that the fracturing parameters include the number of fractures, fracture spacing, artificial fracture half-length, hydraulic fracture conductivity, bottom hole flowing pressure, fixed production rate, and horizontal wellbore length.

[0032] A further technical solution is that the production capacity prediction model considering complex crack morphology is derived based on Fick's diffusion law, Langmuir's isothermal adsorption equation and dual-medium flow theory, using the point source method, Duhamel's principle and Laplace transform.

[0033] A further technical solution is the dimensionless bottom hole flowing pressure expression considering wellbore storage effect and skin effect:

[0034]

[0035] Where: S is the dimensionless bottom-hole flowing pressure in Laplace space; c C is the epidermal coefficient. D The dimensionless wellbore storage coefficient; The bottom pressure is dimensionless.

[0036] A further technical solution is the relationship between the bottom hole flowing pressure and the production rate:

[0037]

[0038] Where: It represents the dimensionless production in Laplace space.

[0039] The beneficial effects of this invention are: This invention can predict the production of shale gas fractured horizontal wells under complex fracture morphology, and is very close to the actual production. Attached Figure Description

[0040] Figure 1 A simplified diagram of the dual-medium model;

[0041] Figure 2 A schematic diagram of fracture discretization in a multi-stage fracturing horizontal well with limited flow;

[0042] Figure 3 This is a diagram illustrating the seepage effect in a hydraulic fracture.

[0043] Figure 4 The model fitting curve is shown in the example. Detailed Implementation

[0044] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0045] The present invention provides a method for predicting the productivity of shale gas fractured horizontal wells considering complex fracture morphology, comprising the following steps:

[0046] Step 1: Determine the dimensionless bottom-hole flowing pressure in the Laplace space based on the production prediction model considering complex fracture morphology and geological parameters (natural fracture stress sensitivity coefficient, natural fracture porosity, natural fracture permeability, matrix porosity, gas reservoir thickness, matrix compressibility coefficient, gas viscosity, gas layer temperature, Langmuir volume, pore medium tortuosity, Langmuir pressure, shale density, original formation pressure), and fracturing parameters (number of fractures, fracture spacing, artificial fracture half-length, hydraulic fracture conductivity, bottom-hole flowing pressure, fixed production rate, horizontal wellbore length).

[0047] Step 2: After performing perturbation inverse transformation and numerical inversion on the dimensionless bottom hole pressure in Laplace space, determine the dimensionless bottom hole pressure based on the dimensionless bottom hole pressure expression that considers wellbore storage effect and skin effect.

[0048]

[0049] Where: S is the dimensionless bottom-hole flowing pressure in Laplace space; c C is the epidermal coefficient. D The dimensionless wellbore storage coefficient; The dimensionless bottom hole flowing pressure;

[0050] Step 3: Perform Laplace transform on the dimensionless bottom hole pressure, and then obtain the dimensionless production in the Laplace space through the relationship between bottom hole pressure and production.

[0051]

[0052] Where: For dimensionless production in Laplace space;

[0053] Step 4: Perform Stehfest numerical inversion on the dimensionless products in the Laplace space to obtain the dimensionless products;

[0054] Step 5: Finally, the dimensionless output is converted into the actual output by converting the dimensionless output into the dimensionless output.

[0055] The specific process for establishing the energy production equation set considering the long-term conductivity of fractures in this invention is as follows:

[0056] 1. Physical model and basic assumptions;

[0057] (1) Shale gas reservoirs have dual-pore media characteristics, including natural fractures and shale matrix containing nano-micro pores, with closed upper and lower boundaries and infinitely large outer boundaries;

[0058] (2) The natural fracture system contains free gas, and the flow law follows Darcy's law. The stress sensitivity effect of natural fractures should be considered.

[0059] (3) The shale matrix blocks are spherical, and shale gas exists mainly in the adsorbed and free states in the matrix system;

[0060] (4) Due to the extremely low permeability of the shale matrix, without considering the seepage of shale gas in the matrix system due to pressure difference, the shale gas in the matrix pores is desorbed and migrates to the natural fracture system by diffusion.

[0061] (5) The desorption of adsorbed shale gas in the matrix pores follows the Langmuir isotherm adsorption equation;

[0062] (6) Shale gas reservoirs are single-phase gas isothermal seepage, and the effects of gravity and capillary force are ignored.

[0063] (7) The flow process of gas in the gas reservoir is matrix-natural fracture-artificial fracture-horizontal wellbore.

[0064] 2. Seepage model of natural fracture system;

[0065] The mathematical model of a natural fracture system can be obtained by combining the law of conservation of mass, the equation of state for gases, and the equation of motion:

[0066] (1) Transforming the mass conservation equation into radial coordinates yields:

[0067]

[0068] In the formula: ρ f The gas density in a natural fracture system is kg / m³. 3 ; Porosity of natural cracks; q ex The flux from the matrix system to the natural fracture system, kg / (m³) 3 •h); v is the gas seepage velocity in the r direction in the natural fracture system, m / s; V is the gas adsorption capacity of the matrix system, m 3 / t.

[0069] (2) Equations of motion

[0070] Considering the stress sensitivity effect of natural fracture systems

[52] Equations of motion during time

[51] :

[0071]

[0072] In the formula: k i The original formation pressure p fi The permeability under the following m 2 γ is the stress-sensitive factor, Pa -1 μ is the gas viscosity in the fracture system at average temperature and pressure, in mPa·s.

[0073] (5) Differential equations

[0074] Gas state equation and crossflow equation

[53] Substituting into (1), we get:

[0075]

[0076] At higher pressures, p / μZ can be approximated as a constant. Therefore, the relationship between pseudo-pressure and pressure is:

[0077]

[0078] Where: The pseudo-pressure of the natural fracture system, MPa 2 / (mPa·s); The pseudo-pressure of the matrix system, MPa 2 / (mPa·s);

[0079] Substituting equation (5) into equation (4), and linearizing the values ​​under the initial conditions of the gas reservoir, we obtain the seepage model:

[0080]

[0081]

[0082] Where: φ m For matrix porosity; μ i C represents the gas viscosity in a natural fracture system under initial conditions, in mPa·s; fgi The comprehensive compressibility coefficient of the natural fracture system under initial conditions is given in MPa. -1 ;

[0083] The following variable is defined without this limitation:

[0084] V D =V i -V

[0085] In the formula: h is the reservoir thickness, in meters; T sc The reservoir temperature is given in Kelvin (p) under standard conditions. sc q represents the formation pressure under standard conditions, in MPa; sc The reference total flow rate for a fractured horizontal well is assumed to be constant, m 3 / s; ω is the elastic storage capacity ratio, dimensionless; λ is the crossflow coefficient, dimensionless; V i m represents the amount of gas adsorbed by the matrix system under initial conditions. 3 / t;γ D It is a dimensionless stress-sensitive factor, which is dimensionless.

[0086] Using the defined dimensionless variables, equation (6) can be dimensionless as follows:

[0087]

[0088] Linearizing (7) using the perturbation method and then performing its Laplace transform yields:

[0089]

[0090] 3. Gas flow model of shale matrix;

[0091] The pore size of the shale matrix is ​​on the nanometer scale. Gas migration in such porous media is not suitable for the molecular continuous flow hypothesis and cannot be described by Darcy's law. Studies have found that gas migration in shale reservoirs involves only diffusion and not viscous flow. Fick's diffusion law is used to describe the migration of shale gas in the matrix pores.

[0092] Quasi-steady-state diffusion occurs when the gas concentration distribution in the matrix does not change with time t, and can be described using Fick's first law. Therefore, the diffusion flux through a unit volume of spherical matrix block per unit time is:

[0093]

[0094] Define a dimensionless variable: V ED =V i -V E

[0095] Using the defined dimensionless variables, we can perform a dimensionless transformation on equation (9) to obtain:

[0096]

[0097] Shale gas desorption follows the Langmuir isotherm adsorption equation, and is expressed in pseudo-pressure form as follows:

[0098]

[0099] In the formula: V E m represents the amount of gas adsorbed at adsorption equilibrium. 3 / t;V L Let m be the Langmuir adsorption volume. 3 / t;P L Langmuir pressure, MPa.

[0100] The dimensionless gas equilibrium concentration is:

[0101]

[0102] According to the definition of dimensionless pseudo-pressure, we have:

[0103]

[0104] Where σ is the desorption coefficient, representing the strength of the desorption effect. It is dimensionless and is defined as follows:

[0105]

[0106] Substituting equation (13) into (10) and performing a Laplace transform, we get:

[0107]

[0108] Further simplification yields the solution for the matrix system seepage model in Laplace space under quasi-steady-state diffusion:

[0109]

[0110] 4. Coupled seepage model of natural fractures and shale matrix;

[0111] Substituting equation (15) into equation (8) and simplifying, we get:

[0112]

[0113] In the formula:

[0114] When solving equation (16), the general solution form of the imaginary argument Bessel equation, combined with the boundary conditions, can be obtained as follows:

[0115]

[0116] 5. Hydraulic fracture seepage model;

[0117] The establishment of a hydraulic fracture model for shale gas reservoirs requires comprehensive consideration of factors such as fracture conductivity, fracture azimuth, and secondary fracture morphology. The seepage from secondary fractures is incorporated into the model using the principles of flow distribution, mass balance, and isobaric equations. The pressure response of the fractured horizontal well is obtained by discretizing the hydraulic fractures and employing the superposition principle.

[0118] 5.1 Establishment of Discrete Model of Hydraulic Fracture and Determination of Coordinates of Micro-elements

[0119] (1) Establishment of discrete crack model;

[0120] The a and y axes are along the direction of the horizontal wellbore, and fracturing produces M hydraulic fractures;

[0121] b. Each crack is discretized into 2N elements. At the center node of each element, two secondary hydraulic cracks extend from the left and right sides of the hydraulic crack. Each hydraulic crack generates a total of 4N secondary cracks.

[0122] c. The total lengths of the two flanks of the i-th hydraulic fracture are x. fli and x fri The slit length of each discrete unit on both wings is x. fli / N and x fri / N;

[0123] d. The upper wing of the i-th hydraulic fracture along the y-axis: along the negative half of the x-axis, the angle between each discrete element and the y-axis is α. ik (k = 1, 2, ..., N);

[0124] e. The lower wing of the i-th hydraulic fracture along the y-axis: along the positive x-axis, the angle between each discrete element and the y-axis is α. ik (k = N+1, N+2, ..., 2N);

[0125] f. A complete secondary fracture is divided into two parts by the main fracture. The left and right parts are considered as two independent secondary fractures, and the total length of each independent secondary hydraulic fracture is x. fic (c = 1, 2, 3, ..., 4N), all are discrete n elements, along the direction connecting the hydraulic fractures, and the angle between each discrete element and the y-axis is α. icv (v = 1, 2, ..., n);

[0126] g. The hydraulic fractures are symmetrically distributed on both sides with the horizontal well as the centerline. The flow splitting coefficients at the central nodes of each unit are also symmetrically distributed. The flow splitting coefficient at the central node of the j-th unit of the i-th hydraulic fracture is k. ij0 The flow splitting coefficients of the two corresponding secondary hydraulic fractures are k. i(2j-1) and k i(2j) .

[0127] (2) Determination of the coordinates of discrete principal crack elements;

[0128] The hydraulic fractures are numbered from 1 to M from the leftmost to the rightmost end of the horizontal well. Each hydraulic fracture is discretized into infinitesimal elements, which are numbered from 1 to 2N from the left wing tip to the right wing tip, resulting in a total of 2×N×M fracture elements.

[0129] Coordinates of the center of the crack element (1≤j≤N):

[0130]

[0131] in,

[0132]

[0133] Coordinates of the center of the crack element (N+1≤j≤2N):

[0134]

[0135] in,

[0136]

[0137] (3) Determination of the coordinates of discrete secondary crack micro-elements;

[0138] For any secondary fracture on a hydraulic fracture, they are numbered sequentially from 1 to 4N from left to right and from top to bottom. The discrete micro-elements of each secondary fracture are numbered sequentially from 1 to n from the end connected to the formation to the end connected to the main hydraulic fracture, resulting in a total of 4×n×N×M secondary fracture elements.

[0139] The coordinates of the center of the secondary crack micro-element (1≤j≤N, 1≤c≤2N, 1≤v≤n):

[0140]

[0141] in, (When c is odd, c = 2j - 1; when c is even, c = 2j).

[0142] The coordinates of the center of the secondary crack micro-element (N≤j≤2N, 2N≤c≤4N, 1≤v≤n):

[0143]

[0144] in, (When c is odd, c = 2j - 1; when c is even, c = 2j).

[0145] 5.2 Derivation of pressure response;

[0146] Define a dimensionless variable: x D =x / L y D =y / L(18)

[0147] According to the point source function theory

[58] And the coordinate transformation relationship, through integration, can be obtained for any infinitesimal element (x) on the hydraulic fracture. wD y wD For any point (x) in the strata D y D The source solution of ) is:

[0148]

[0149] In the formula: To represent the dimensionless flow rate over the reference length of the discrete segment; x wDi Let y be the dimensionless x-coordinate of any infinitesimal element on the i-th crack; wDi Let be the dimensionless ordinate of any infinitesimal element on the i-th crack;

[0150] 1≤j≤N: g=N-j+1, N+1≤j≤2N: g=j;

[0151]

[0152] Therefore, the pressure drop exerted by the M hydraulic fractures on the tip of the m-th hydraulic fracture is:

[0153]

[0154] Where:

[0155]

[0156] Similarly, the pressure drop exerted by the M hydraulic fractures on the tip of the c-th secondary hydraulic fracture on the m-th hydraulic fracture is:

[0157]

[0158] Where:

[0159] When 1≤c≤2N:

[0160]

[0161] When 2N≤c≤4N:

[0162]

[0163] Similarly, the pressure drop exerted by the 4N secondary hydraulic fractures on the tip of the m-th hydraulic fracture on the M-th hydraulic fracture is:

[0164]

[0165] In the formula: k ic x is the flow splitting coefficient of the c-th (c = 1, 2, ..., 4N) secondary hydraulic fracture on the i-th fracture; fic Let be the total length of the c-th (c = 1, 2, ..., 4N) secondary hydraulic fractures on the i-th fracture;

[0166]

[0167] Similarly, the pressure drop exerted by the 4N secondary hydraulic fractures on the tip of the c-th secondary hydraulic fracture on the m-th hydraulic fracture is:

[0168]

[0169] Where:

[0170] When 1≤c≤2N:

[0171]

[0172] When 2N≤c≤4N:

[0173]

[0174] In summary, the pressure drop exerted by the M hydraulic fractures and the 4N secondary hydraulic fractures on the tip of the m-th hydraulic fracture is:

[0175]

[0176] The pressure drop exerted by the M hydraulic fractures and the 4N secondary hydraulic fractures on the M hydraulic fractures on the tip of the c-th secondary hydraulic fracture of the m-th hydraulic fracture is:

[0177]

[0178] 5.3. Secondary fracture seepage equation;

[0179] Considering the limited conductivity of hydraulic fractures, and based on the principle of equal area, the seepage of hydraulic fractures and secondary hydraulic fractures can be regarded as radial flow in a plane. Therefore, the seepage equations for each segment of the c-th secondary hydraulic fracture on the m-th fracture, from the end connecting to the formation to the end connecting to the main hydraulic fracture, can be obtained as follows:

[0180]

[0181] In the formula: p fmcn p is the pressure at the end of the nth segment of the c-th (c = 1, 2, ..., 4N) secondary fracture in the m-th hydraulic fracture, in MPa. fmj Let q be the pressure at the end of the j-th segment of the hydraulic fracture that connects to the c-th secondary fracture (j = (c+1) / 2 when c is odd; j = c / 2 when c is even), in MPa; fm Let m be the flow rate of the m-th hydraulic fracture. 3 / s;k Fcn w Fcn Let D·m;r' be the conductivity of the nth segment of the c-th secondary fracture within the m-th hydraulic fracture. ecn Let r be the equivalent seepage radius at the initiation point of the (n-1)th segment of the c-th secondary fracture within the m-th hydraulic fracture, in meters. ecn Let r be the equivalent seepage radius at the end of the nth segment of the cth secondary fracture within the mth hydraulic fracture, in meters. ec0 Let r be the equivalent seepage radius at the junction of the c-th secondary fracture and the hydraulic fracture in the m-th hydraulic fracture, in meters. ec0 =|x ij | / sin(α icn )

[0182] Combining the equations in equation (26), we can obtain the final seepage equation for the m-th hydraulic fracture and the c-th secondary fracture:

[0183]

[0184] In the formula: r ecv Let r' be the outer diameter of the equivalent radial flow radius in the plane of the v segment (v = 1, 2, ..., n) of the c-th secondary fracture within the m-th hydraulic fracture, in meters. ec(v+1) Let be the inner diameter length (m) of the equivalent radial flow radius in the plane of the v segment (v = 1, 2, ..., n) of the c-th secondary fracture in the m-th hydraulic fracture.

[0185] Based on the principle of equal area, we can conclude that:

[0186] πr' ec(v+1) 2 =x fmcv h (28)

[0187] In the formula: x fmcv The length from the initiation point of the c-th secondary fracture in the m-th hydraulic fracture to the main hydraulic fracture along the direction of the secondary hydraulic fracture;

[0188] Substituting equation (28) into equation (27) and simplifying, we get:

[0189]

[0190] Where:

[0191]

[0192] 5.4. The seepage equation of the main fracture;

[0193] The seepage flow on both sides of the hydraulic fracture is considered as a whole, that is, a planar radial flow composed of N segments, such as... Figure 3 As shown, each major hydraulic fracture segment is diverted by four secondary fractures. Specifically, for the radial flow in the planar segment j (j = 1, 2, ... N) of the m-th hydraulic fracture, the flow is diverted by the (2j+2N-1), (2j+2N), (2N-2j+2), and (2N-2j+1) secondary hydraulic fractures. The relationship between the diversion coefficients of the hydraulic fractures and the secondary fractures is as follows:

[0194] k m(2j+2N) +k m(2j+2N-1) +k m(2N-2j+2) +k m(2N-2j+1) +k m(j+N)0 =k m(j+N-1)0 (30)

[0195] From equation (26), we can obtain:

[0196]

[0197]

[0198]

[0199]

[0200] In the formula, p fm(j+N) =p fm(N-j+1) =p fmj

[0201] Simplifying the above equation, we get:

[0202]

[0203]

[0204] The seepage equations for each section of the hydraulic fracture are as follows:

[0205]

[0206] In the formula: p fmn p is the pressure at the end of the nth (n = 1, 2, ..., k, ... N)th segment of the mth hydraulic fracture, in MPa. w q is the bottom hole flowing pressure, MPa; fm Let m be the flow rate of the m-th hydraulic fracture. 3 / s;r ek Let r be the outer diameter of the equivalent radial flow radius in the plane of the k-th (k = 1, 2, ..., n) segment of the m-th hydraulic fracture, in meters. ek,(k-1) Let be the inner diameter length (m) of the equivalent radial flow radius in the plane of the k-th (k = 1, 2, ..., n) segment of the m-th hydraulic fracture.

[0207] Combining the equations in equation (33), we can obtain the final seepage equation for the m-th hydraulic fracture:

[0208]

[0209] Based on the principle of equal area, we can conclude that:

[0210] πr ek 2 =(x frmk +x flmk )h (35)

[0211] In the formula: x frmk x flmkLet be the length from the end of the kth segment of the hydraulic fracture on both wings of the mth hydraulic fracture to the horizontal wellbore along the direction of the hydraulic fracture.

[0212] Substituting equations (30), (32), and (35) into (34) and then performing dimensionless transformation, Laplace transformation, and perturbation transformation, we obtain:

[0213]

[0214] Where:

[0215]

[0216] (c = 2N + 2k or 2N - 2k + 2 (k = 1, 2, ..., N))

[0217] The dimensionless fracture conductivity of the k-th segment of the m-th hydraulic fracture:

[0218]

[0219] 5.5. Wellbore pressure analysis and gas well production of MFHW;

[0220] Combining equations (24) and (25), the pressure expression at the m-th hydraulic fracture wellbore can be obtained as follows:

[0221]

[0222] Where:

[0223]

[0224]

[0225]

[0226]

[0227]

[0228]

[0229]

[0230]

[0231]

[0232]

[0233]

[0234]

[0235] Assuming that the flow pressure in each fracture is the same in the horizontal wellbore, that is:

[0236]

[0237] The flow normalization conditions are as follows:

[0238]

[0239] Combining equations (34) and (35), we obtain a set of linear equations for determining the pressure in a horizontal wellbore:

[0240]

[0241] Where:

[0242]

[0243]

[0244]

[0245]

[0246]

[0247]

[0248]

[0249]

[0250]

[0251]

[0252]

[0253]

[0254]

[0255]

[0256] Example

[0257] Table 1 Relevant Parameters

[0258]

[0259]

[0260] Based on actual field data from well X-2HF in the Fuling shale gas demonstration area (see Table 1), the production capacity after fracturing of this well was predicted using the model established in this patent, and the prediction results were compared with the actual production data. Figure 4 As shown in the figure, the production decline curve derived from the model established in this patent generally matches the real-time production decline trend reflected in the production data well. The average daily gas production over 542 days in the production data and the simulation data of this patent are 20.591 × 10⁻⁶. 4 m 3 / d and 19.084×10 4 m 3 / d, the difference between the two is 7.9%, which demonstrates the accuracy of the model established in this patent in predicting the production of fractured horizontal gas wells.

[0261] The above description is not intended to limit the present invention in any way. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for predicting the productivity of shale gas fracturing horizontal wells considering complex fracture morphology, characterized in that, Includes the following steps: Step 1: Determine the dimensionless bottom hole flowing pressure in the Laplace space based on the production capacity prediction model considering complex fracture morphology and geological and fracturing parameters; The production capacity prediction model that considers complex crack morphology is as follows: Where: h is the reservoir thickness; x is the dimensionless bottom-hole flowing pressure in Laplace space; frmk x flmk x is the length from the end of the k-th segment of the m-th hydraulic fracture along the direction of the hydraulic fracture to the horizontal wellbore; fic k is the total length of the c-th secondary hydraulic fracture on the i-th fracture; ic k is the flow splitting coefficient of the c-th secondary hydraulic fracture on the i-th fracture; ij0 x is the flow splitting coefficient at the center node of the j-th element of the i-th hydraulic fracture; fli and x fri denoted as the total lengths of the two flanks of the i-th hydraulic fracture; μ is the gas viscosity in the fracture system at the average temperature and pressure, in mPa·s; r wD Where L is the dimensionless equivalent radius; C is the crack half-length; fdk Let α be the conductivity of the dimensionless fracture in the k-th segment; ig For the i-th hydraulic fracture below the y-axis: along the positive x-axis direction, discretize the angle between the n-element and the y-axis: K0 is the permeability of the natural fracture; x wDi,j x is the dimensionless x-coordinate of any infinitesimal element on the j-th element of the i-th crack; wDi,c,v Let α be the dimensionless abscissa of any infinitesimal element at the initiation point of the i-th crack, the c-th secondary crack, and the v-th crack segment; icv For a uniformly discrete n-element array, along the direction connecting the hydraulic fractures, the angle between each discrete element and the y-axis; x frmD x flmD These are the dimensionless abscissas of the ends of the k-th segment of the two wings of the i-th hydraulic fracture; α mk Let be the angle between the c-th secondary hydraulic fracture on the m-th hydraulic fracture and the y-axis; f(s) is a function; R D (*) represents the source solution; Re m(*)D k is the dimensionless Reynolds number of the m-th hydraulic fracture; m(*) Let be the flow splitting coefficient of the m-th hydraulic fracture; Step 2: After performing perturbation inverse transformation and numerical inversion on the dimensionless bottom hole flowing pressure in the Laplace space, determine the dimensionless bottom hole flowing pressure based on the dimensionless bottom hole flowing pressure expression that takes into account the wellbore storage effect and skin effect. Step 3: Perform Laplace transform on the dimensionless bottom hole pressure, and then obtain the dimensionless production in the Laplace space through the relationship between bottom hole pressure and production. Step 4: Perform Stehfest numerical inversion on the dimensionless products in the Laplace space to obtain the dimensionless products; Step 5: Finally, convert the dimensionless output into the actual output.

2. The method for predicting the productivity of shale gas fracturing horizontal wells considering complex fracture morphology as described in claim 1, characterized in that, The geological parameters include natural fracture stress sensitivity coefficient, natural fracture porosity, natural fracture permeability, matrix porosity, gas reservoir thickness, matrix compressibility coefficient, gas viscosity, gas layer temperature, Langmuir volume, pore medium tortuosity, Langmuir pressure, shale density, and original formation pressure.

3. The method for predicting the productivity of shale gas fracturing horizontal wells considering complex fracture morphology as described in claim 1, characterized in that, The fracturing parameters include the number of fractures, fracture spacing, artificial fracture half-length, hydraulic fracture conductivity, bottom hole flowing pressure, fixed production rate, and horizontal wellbore length.

4. The method for predicting the productivity of shale gas fractured horizontal wells considering complex fracture morphology as described in claim 1, characterized in that, The production capacity prediction model considering complex crack morphology is derived based on Fick's diffusion law, Langmuir isothermal adsorption equation, and dual-medium flow theory, using the point source method, Duhamel's principle, and Laplace transform.

5. The method for predicting the productivity of shale gas fractured horizontal wells considering complex fracture morphology as described in claim 1, characterized in that, The dimensionless bottom hole flowing pressure expression considering wellbore storage effect and skin effect is as follows: In the formula: S is the dimensionless bottom-hole flowing pressure in Laplace space; c C is the epidermal coefficient. D The dimensionless wellbore storage coefficient; is the dimensionless bottom hole pressure; s is the complex parameter variable in the Laplace transform.

6. The method for predicting the productivity of shale gas fractured horizontal wells considering complex fracture morphology as described in claim 1, characterized in that, The relationship between bottom hole flowing pressure and production rate is as follows: In the formula: For dimensionless production in Laplace space; The dimensionless bottom-hole flowing pressure in Laplace space after perturbation inverse transformation; s is a complex parameter variable in the Laplace transform.

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