A method for predicting the productivity of shale gas infill wells considering inter-well interference

Abstract

The present invention discloses a method for predicting the productivity of shale gas infill wells considering well interference, which includes obtaining the number of horizontal wells in a well group in a target area, the relative positions of each well, the open well interval time of each well, geological parameters, production life T, and the fracturing parameters of each well; determining the dimensionless bottom-hole flowing pressure in the Laplace space of each well; after performing perturbation inverse transformation and numerical inversion on the dimensionless bottom-hole flowing pressure in the Laplace space of each well, then determining the dimensionless bottom-hole flowing pressure of each well; performing Laplace transformation on the dimensionless bottom-hole flowing pressure to obtain the dimensionless production in the Laplace space; performing Stehfest numerical inversion on the dimensionless production in the Laplace space to obtain the dimensionless production; and finally converting the dimensionless production into the actual production. The productivity model constructed by the present invention makes up for the deficiencies of the existing models, making the prediction results more objective and accurate, and this model can also be applied to optimize the deployment parameters of infill wells, having a wide application prospect.

Description

Technical Field

[0001] The present invention relates to the technical field of shale gas fracturing, and particularly relates to a method for predicting the productivity of shale gas infill wells considering well interference. Background Art

[0002] With the increase in global energy demand and the decline of conventional oil and gas reserves, unconventional resources (such as shale gas) are considered an important and reliable energy replacement force. However, due to the poor permeability of shale reservoirs and low gas production, after the application of multi-stage fractured horizontal well (MFHW) technology, it shows the characteristics of high initial production and rapid decline in later production, and the overall recovery rate of gas reservoirs is low. Therefore, deploying infill wells has become an important measure to improve the degree of reserve utilization and recovery rate in major shale gas production areas. During the deployment of infill wells, determining the deployment location and timing of infill wells is a key factor to ensure the effectiveness of infill wells. However, there are few reports on this in existing research. Therefore, it is necessary to evaluate and analyze the impact of the deployment location and timing of infill wells on shale gas productivity, and then optimize the deployment location and timing of infill wells.

[0003] The migration mechanism of shale gas in the reservoir (adsorption, desorption, and diffusion), reservoir characteristics, and the distribution and relative position of natural fractures and artificial fractures (fractures formed during the fracturing process) will all affect the productivity of infill wells.

[0004] The flow law of natural gas between multi-scale pores, shale reservoir characteristics, and the distribution characteristics of fractures will all affect the accurate prediction of infill well production. Scholars have studied the seepage characteristics and production dynamics of fractured horizontal wells, but ignored the desorption and diffusion processes. Therefore, a dual-medium model considering gas diffusion flow was established. However, this model ignores the impact of shale gas desorption on production. Since then, a large number of scholars have proved that the Langmuir isothermal adsorption equation can be used to accurately describe the desorption process of shale gas. Many scholars have begun to comprehensively consider the diverse migration processes of shale gas during the modeling process. In addition to the complex migration mechanism of shale gas, its complex geological conditions and large physical property differences also bring great difficulties to accurate simulation. In the actual formation, when the hydraulic fracture extends, it deflects under the influence of natural fractures and in-situ stress. In existing models, the analytical model and semi-analytical model only consider the main fracture shape as a single regular rectangle and do not consider the deflection of the main fracture. And most numerical models do not consider the main fracture deflection. Therefore, when establishing the productivity model of infill wells, it is necessary to comprehensively consider the influence of multiple factors.

[0005] Meanwhile, the deployment of infill wells and fracturing stimulation are not single-well issues. At a certain well spacing and fracturing stimulation scale, there is also the problem of interference between wells. Research results of a large number of scholars show that when the well spacing is too small, the fracturing cracks of infill wells will be affected by the "Frac-hit" effect, weakening the fracturing stimulation effect of infill wells and reducing the productivity of old wells at the same time. Therefore, it is crucial to select a reasonable well spacing when deploying infill wells. Since the well spacings of existing infill wells are all too small, under the existing well pattern conditions, when deploying infill wells, it is necessary to consider both the change of physical property conditions during the production process of old wells and the interference effect between infill wells and old wells. Different production times, formation conditions, and the interference effect between old wells and infill wells are dynamically changing. Therefore, it is particularly important to optimize the reasonable fracturing timing of infill wells. Therefore, scholars simulated the change of in-situ stress state during the production process and its influence on the fracture propagation of infill wells, and considered that the best fracturing timing of infill wells is when the in-situ stress between old wells all turns. However, the above model only considered single fractures and did not consider special gas flow conditions such as desorption and diffusion. In addition, some scholars combined the UFM hydraulic fracture propagation model and the finite element mechanics model to systematically study the production changes of infill wells and old wells under different infill timings, and considered that the earlier the fracturing timing of infill wells, the smaller the influence on the productivity of old wells and infill wells. In addition, scholars combined the displacement discontinuity method and the finite volume method to discuss the influence of old well production on the hydraulic fracturing cracks of infill wells. The research results show that the later the infill timing, the worse the development effect. Summary of the Invention

[0006] The present invention mainly overcomes the disadvantages existing in the prior art, and provides a method for predicting the productivity of shale gas infill wells considering interference between wells.

[0007] To solve the above technical problems, the technical solution provided by the present invention is: a method for predicting the productivity of shale gas infill wells considering interference between wells, comprising the following steps:

[0008] Step 1, obtain the number of horizontal wells in the well group in the target area, the relative positions of each well, the open well interval time of each well, geological parameters, production life T, and the fracturing parameters of each well;

[0009] Step 2, determine the dimensionless bottom-hole flowing pressure in the Laplace space of each well according to the productivity prediction model of shale gas infill wells considering interference between wells, geological parameters, and the fracturing parameters of each well;

[0010] The productivity prediction model of shale gas infill wells considering interference between wells is:

[0011] A·B = C

[0012] In the formula:

[0013]

[0014] C = [0···00···0···0···01 / s11 / s2···1 / s K ′

[0015]

[0016]

[0017] Step 3: After performing perturbation inverse transformation and numerical inversion on the dimensionless bottom-hole flowing pressure in the Laplace space of each well, and then determining the dimensionless bottom-hole flowing pressure of each well according to the dimensionless bottom-hole flowing pressure expression considering wellbore storage effect and skin effect;

[0018] Step 4: Perform Laplace transform on the dimensionless bottom-hole flowing pressure, and then obtain the dimensionless production in the Laplace space through the relationship between bottom-hole flowing pressure and production;

[0019] Step 5: Perform Stehfest numerical inversion on the dimensionless production in the Laplace space to obtain the dimensionless production;

[0020] Step 6: Finally, convert the dimensionless production into the actual production.

[0021] 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, gas viscosity, gas reservoir temperature, Langmuir volume, Langmuir pressure, shale density, and original formation pressure.

[0022] A further technical solution is that the fracturing parameters include number of fractures, fracture spacing, half-length of artificial fracture, hydraulic fracture conductivity, bottom-hole flowing pressure, fixed production rate, and horizontal well length.

[0023] A further technical solution is that in Step 3:

[0024] First, calculate the dimensionless bottom-hole flowing pressure in the Laplace space of Well 1 from 0 to △T2;

[0025] Then, calculate the dimensionless bottom-hole flowing pressure in the Laplace space of Well 1 from △T2 to △T2 + △T3 and the dimensionless bottom-hole flowing pressure in the Laplace space of Well 2 from 0 to △T3;

[0026] Finally, calculate the dimensionless bottom-hole flowing pressure in the Laplace space of Well 1 from △T2 +... + △T k to T, the dimensionless bottom-hole flowing pressure in the Laplace space of Well 2 from △T3 +... + △T k to T - △T2... the dimensionless bottom-hole flowing pressure in the Laplace space of Well K from 0 to T - (△T2 +... + △T k );

[0027] Among them, well 1 is put into production. When the production reaches ΔT2, well 2 is put into production; when the production of well 1 reaches ΔT2 + ΔT3, well 3 is put into production; the operation is repeated until well K is put into production.

[0028] A further technical solution is that the dimensionless bottom-hole flowing pressure expression considering the wellbore storage effect and skin effect is:

[0029]

[0030] In the formula: is the dimensionless bottom-hole flowing pressure; S c is the skin factor; C D is the dimensionless wellbore storage coefficient.

[0031] A further technical solution is that the relationship between the dimensionless production rate in the Laplace space and is:

[0032]

[0033] In the formula: is the dimensionless production rate in the Laplace space.

[0034] The beneficial effects of the present invention: The productivity model constructed by the present invention makes up for the deficiencies of the existing models, making the prediction results more objective and accurate. Moreover, this model can also be applied to optimize the deployment parameters of infill wells, and has a broad application prospect. Description of the Drawings

[0035] Figure 1 is the simplified dual-porosity model diagram;

[0036] Figure 2 is the schematic diagram of the horizontal well group layout;

[0037] Figure 3 is the schematic diagram of the fracture discretization of a finite conductivity multi-stage fractured horizontal well;

[0038] Figure 4 is the numerical calculation process;

[0039] Figure 5 is the relative position diagram of three wells;

[0040] Figure 6 is the hydraulic fracture distribution diagram of three wells;

[0041] Figure 7 is the distribution diagram of the conductivity in the hydraulic fracture;

[0042] Figure 8 is the fitting diagram of the production data of well 1;

[0043] Figure 9It is the fitting graph of the production data of Well 2;

[0044] Figure 10 It is the fitting graph of the production data of Well 3. Specific implementation manner

[0045] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0046] A method for predicting the productivity of shale gas infill wells considering well interference in the present invention includes the following steps:

[0047] Step 1: Obtain the number of horizontal wells in the well group in the target area, the relative positions of each well, the opening interval time of each well, geological parameters, production life T, and the fracturing parameters of each well;

[0048] Step 2: Determine the dimensionless bottom-hole flowing pressure in the Laplace space of each well according to the productivity prediction model of shale gas infill wells considering well interference, geological parameters, and the fracturing parameters of each well;

[0049] First, calculate the dimensionless bottom-hole flowing pressure in the Laplace space of Well 1 from 0 to △T2;

[0050] Then, calculate the dimensionless bottom-hole flowing pressure in the Laplace space of Well 1 from △T2 to △T2 + △T3 and the dimensionless bottom-hole flowing pressure in the Laplace space of Well 2 from 0 to △T3;

[0051] Finally, calculate the dimensionless bottom-hole flowing pressure in the Laplace space of Well 1 from △T2 +... + △T k to T, the dimensionless bottom-hole flowing pressure in the Laplace space of Well 2 from △T3 +... + △T k to T - △T2, the dimensionless bottom-hole flowing pressure in the Laplace space of Well K from 0 to T - (△T2 +... + △T k );

[0052] Among them, Well 1 is put into production. When it is produced to △T2, Well 2 is put into production; when Well 1 is produced to △T2 + △T3, Well 3 is put into production; the operation is repeated until Well K is put into production;

[0053] Step 3: After performing perturbation inverse transformation and numerical inversion on the dimensionless bottom-hole flowing pressure in the Laplace space of each well, determine the dimensionless bottom-hole flowing pressure of each well according to the dimensionless bottom-hole flowing pressure expression considering wellbore storage effect and skin effect;

[0054] Step 4: Perform Laplace transform on the dimensionless bottom-hole flowing pressure, and then obtain the dimensionless production rate in Laplace space through the relationship between the bottom-hole flowing pressure and the production rate;

[0055]

[0056] In the formula: is the dimensionless bottom-hole flowing pressure; S c is the skin factor; C D is the dimensionless wellbore storage coefficient;

[0057] Step 5: Perform Stehfest numerical inversion on the dimensionless production rate in Laplace space to obtain the dimensionless production rate;

[0058]

[0059] In the formula: is the dimensionless production rate in Laplace space;

[0060] Step 6: Finally, convert the dimensionless production rate into the actual production rate.

[0061] The establishment process of the productivity prediction model for shale gas infill wells considering well interference in the present invention is specifically as follows:

[0062] 1. Physical model and basic assumptions

[0063] (1) The shale gas reservoir has dual-porosity medium characteristics, including natural fractures and shale matrix containing nano-micro pores, with closed upper and lower boundaries and an infinite outer boundary;

[0064] (2) The natural fracture system contains free gas, and its flow law follows Darcy's law, considering the stress sensitivity effect of natural fractures;

[0065] (3) The shale matrix blocks are spherical, and shale gas mainly exists in adsorbed and free states in the matrix system;

[0066] (4) Due to the extremely low permeability of the shale matrix, the seepage of shale gas in the matrix system due to pressure difference is not considered, and the shale gas in the matrix pores migrates to the natural fracture system in a diffusive manner after desorption;

[0067] (5) The desorption of adsorbed shale gas in the matrix pores follows the Langmuir isothermal adsorption equation;

[0068] (6) The shale gas reservoir is a single-phase gas isothermal seepage, ignoring the effects of gravity and capillary force;

[0069] (7) The gas flow process in the gas reservoir is matrix - natural fracture - artificial fracture - horizontal wellbore.

[0070] 2. Seepage model of the natural fracture system

[0071] The mathematical model of the natural fracture system can be obtained by combining the law of conservation of mass, the gas state equation, and the equation of motion:

[0072] (1) Converting the mass conservation equation to radial coordinates gives:

[0073]

[0074] Where: ρ f is the gas density in the natural fracture system, kg / m 3 ; is the natural fracture porosity; q ex is the cross-flow rate from the matrix system to the natural fracture system, kg / (m 3 ·h); v is the seepage velocity of the gas in the r direction in the natural fracture system, m / s; V is the gas adsorption amount in the matrix system, m 3 / t.

[0075] (2) Equation of motion

[0076]

[0077] Where: μ is the gas viscosity in the fracture system at the average temperature and pressure, mPa·s; k is the permeability at the formation pore pressure of p f , m 2 .

[0078] Considering the stress-sensitive effect of the natural fracture system:

[0079]

[0080] Where: k i is the permeability at the original formation pressure p fi , m 2 ;

[0081] γ is the stress-sensitive factor, Pa -1 .

[0082] (5) Differential equation

[0083] Substituting the gas state equation and the cross-flow equation into (1) gives:

[0084]

[0085] At higher pressures, p / μZ can be approximated as a constant. Therefore, the relationship between the pseudo-pressure and the pressure is:

[0086]

[0087] Where: is the pseudo-pressure of the natural fracture system, MPa 2 / (mPa·s); is the pseudo-pressure of the matrix system, MPa 2 / (mPa·s);

[0088] Substitute Equation (5) into Equation (4), and take the values under the initial conditions of the gas reservoir for linearization to obtain the seepage model:

[0089]

[0090] In the formula: φ m is the matrix porosity; μ i is the bulk viscosity in the natural fracture system under the initial conditions, mPa·s; C fgi is the comprehensive compressibility of the natural fracture system under the initial conditions, MPa -1 ;

[0091] Define the dimensionless variables as follows:

[0092]

[0093] In the formula: h is the reservoir thickness, m; T sc is the gas reservoir temperature under standard conditions, K; p sc is the formation pressure under standard conditions, MPa; q sc is the reference total flow rate of the fractured horizontal well, assumed to be constant, m 3 / s; ω is the elastic storage ratio, dimensionless; λ is the crossflow coefficient, dimensionless; V i is the gas adsorption amount in the matrix system under the initial conditions, m 3 / t; γ D is the dimensionless stress sensitivity factor, dimensionless.

[0094] Use the defined dimensionless variables to dimensionlessize Equation (6) into:

[0095]

[0096] Use the perturbation method to linearize (7), and after its Laplace transform, we can get:

[0097]

[0098] 3. Gas flow model of shale matrix

[0099] The pore size of the shale matrix is in the nanometer range. The migration of gas in such porous media does not conform to the molecular continuum flow hypothesis and cannot be described by Darcy's law. It is found that there is only diffusion and no viscous flow in the migration of gas in the shale reservoir. Use Fick's diffusion law to describe the migration of shale gas in the matrix pores.

[0100] Pseudo-steady state diffusion refers to the distribution of gas concentration in the matrix not changing with time t, which can be described by Fick's first law. Then, the diffusion flux passing through a unit volume of spherical matrix block per unit time is as follows:

[0101]

[0102] Define the dimensionless variable: V ED = V i - V E

[0103] Using the defined dimensionless variables, perform dimensionless transformation on Equation (9) to obtain:

[0104]

[0105] The desorption of shale gas follows the Langmuir isothermal adsorption equation and is expressed in the form of pseudo-pressure as:

[0106]

[0107] In the formula: V E is the gas adsorption amount at adsorption equilibrium, m 3 / t; V L is the Langmuir adsorption volume, m 3 / t; P L is the Langmuir pressure, MPa.

[0108] Then the dimensionless gas equilibrium concentration is:

[0109]

[0110] According to the defined dimensionless pseudo-pressure, there is:

[0111]

[0112] Among them, σ is the desorption coefficient

[20] , indicating the strength of the desorption effect, dimensionless, and the specific definition is as follows:

[0113]

[0114] Substitute Equation (13) into (10) and perform Laplace transform to obtain:

[0115]

[0116] Then simplify to obtain the solution of the seepage model of the matrix system in the Laplace space under pseudo-steady state diffusion:

[0117]

[0118] 4. Coupled Seepage Model of Natural Fractures and Shale Matrix

[0119] Substituting Equation (15) into (8) and simplifying, we get:

[0120]

[0121] When solving Equation (16), the general solution form of the Bessel equation with imaginary argument is used

[57] Combined with the boundary conditions, we get:

[0122]

[0123] 5. Hydraulic Fracture Seepage Model

[0124] The establishment of the hydraulic fracture model for a fractured horizontal well group in a shale gas reservoir needs to comprehensively consider factors such as the number of hydraulic fractures in each horizontal well, the hydraulic fracture conductivity, the fracture morphology, and the interference between fractures. By discretizing the hydraulic fractures and using the superposition principle method, the pressure response of the fractured horizontal well group is obtained.

[0125] 5.1 Establishment of Hydraulic Fracture Discrete Model and Determination of Microelement Coordinates

[0126] (1) Establishment of Discrete Fracture Model

[0127] a. Along the x - direction, a total of K horizontal wells are vertically arranged. The distance between the k - th (k = 1, 2,..., K) horizontal well and the first horizontal well is d 1,k ;

[0128] b. The y - axis is along the direction of the first horizontal wellbore. The k - th horizontal well is fractured to generate M k hydraulic fractures, and each fracture is discretized into 2N elements;

[0129] c. For the i - th hydraulic fracture on the k - th well, the total lengths of the two wings of the fracture are x k,fli and x k,fri respectively. The length of each discrete element of the two wings is x k,fli / N and x k,fri / N;

[0130] d. For the upper - wing of the i - th hydraulic fracture on the k - th well: along the negative x - axis direction, the angle between each discrete element and the y - axis is α k,iξ (ξ = 1, 2,..., N);

[0131] e. For the lower - wing of the i - th hydraulic fracture on the k - th well: along the positive x - axis direction, the angle between each discrete element and the y - axis is α k,iξ (ξ = N + 1, N + 2,..., 2N);

[0132] (2) Determination of Discrete Fracture Microelement Coordinates

[0133] The hydraulic fractures on the k-th well are numbered from 1 to M in sequence from the leftmost end to the rightmost end of the horizontal well. k , and after each hydraulic fracture is discretized, the micro-elements are numbered from 1 to 2N in sequence from the left-wing tip to the right-wing tip. There are a total of 2×N×M k fracture elements.

[0134] The central coordinates of the fracture micro-elements (1≤j≤N):

[0135]

[0136] Among them,

[0137] The central coordinates of the fracture micro-elements (N+1≤j≤2N):

[0138]

[0139] Among them,

[0140] 5.2. Derivation of Pressure Response

[0141] Define dimensionless variables: x D = x / L y D = y / L (15)

[0142] According to the point source function theory

[13] and the coordinate transformation relationship, through integration, the line source solution of any micro-element (x wD , y wD ) on the hydraulic fracture to any point (x D , y D ) in the formation can be obtained as:

[0143]

[0144] In the formula: is the dimensionless flow rate on the reference length of the discrete segment; x wDi is the dimensionless abscissa of any micro-element on the i-th fracture; y wDi is the dimensionless ordinate of any micro-element on the i-th fracture;

[0145] 1≤j≤N: g = N-j+1, N+1≤j≤2N: g = j;

[0146] s k is the complex Laplace space variable corresponding to the k-th well and is related to the opening time of this well;

[0147]

[0148] Therefore, M1+M2+…+M K The pressure drop caused by the hydraulic fractures on the tip of the mth hydraulic fracture in the kth well is:

[0149]

[0150] Where:

[0151]

[0152] Considering the limited conductivity of hydraulic fractures, according to the principle of equal area, the seepage of hydraulic fractures is regarded as plane radial flow, and the seepage equations of each section of the mth hydraulic fracture on the kth well are obtained as follows:

[0153]

[0154] Where: p fkmn is the pressure at the end of the nth (n=1, 2, ...N)th fracture in the mth hydraulic fracture on the kth well, MPa; p wk is the bottom hole pressure of the kth well, MPa; q fkm is the flow rate of the mth hydraulic fracture on the kth well, m 3 / s;

[0155] Combining the equations in formula (18) we can get the final seepage equation of the mth hydraulic fracture on the kth well:

[0156]

[0157] Where: r ek’ is the outer diameter length of the equivalent radius of the k'th (k'=1, 2, ...n)th fracture plane radial flow in the mth hydraulic fracture on the kth well, m;

[0158] r ek’,(k’-1) is the inner diameter length of the equivalent radius of the k'th (k'=1, 2, ...n)th fracture plane radial flow in the mth hydraulic fracture on the kth well, m;

[0159] According to the principle of equal area, we can get:

[0160] πr ek' 2 =(x k,frmk' +x k,flmk' )h (20)

[0161] Where: x k,frmk’ , x k,flmk’ is the length from the end of the k'th segment of the mth hydraulic fracture on both wings of the kth well to the horizontal wellbore along the direction of the hydraulic fracture;

[0162] Substituting Equation (20) into (19), and after non-dimensionalization, Laplace transform, and perturbation transform, we can obtain:

[0163]

[0164] In the formula, the non-dimensional fracture conductivity of the k'-th section of the m-th hydraulic fracture in the k-th well:

[0165]

[0166] 5.3, Wellbore Pressure Solution and Gas Well Production of MFHW

[0167] Combining Equations (17) and (21), the pressure expression at the wellbore of the m-th hydraulic fracture in the k-th well can be obtained as:

[0168]

[0169] Assume that the flowing pressures of each fracture at the horizontal wellbore in the k-th (k = 1, 2,..., K) well are the same, that is:

[0170]

[0171] The flow rate normalization condition for the k-th well is as follows:

[0172]

[0173] By simultaneously solving (22) and (23), a linear equation system for obtaining the horizontal wellbore pressure can be obtained:

[0174] A·B = C (25)

[0175] In the formula:

[0176]

[0177] C = [0 ··· 0 0 ··· 0 ··· 0 ··· 0 1 / s1 1 / s2 ··· 1 / s K ′

[0178]

[0179] Example

[0180] Table 1 Basic Reservoir Parameter Table

[0181]

[0182] Table 2 Fracturing Parameter Table of Production Wells

[0183]

[0184] Based on the actual field data in the Changning shale gas area of Sichuan (see Table 1), the post-fracture productivity of 3 fractured horizontal wells simultaneously put into production in the same reservoir in this block was predicted using the model established in this patent. The basic fracturing parameters of the three fractured horizontal wells are shown in Table 2. The positional relationship of the three wells is as Figure 5 shown. The spacing between the three wells is: d 1,2 = 350 m, d 1,3 = 400 m.

[0185] According to the idea of establishing and solving the well group model, a program was compiled for solving, and the specific calculation process is as follows Figure 4 shown;

[0186] (1) Determine the number K of horizontal wells in the well group in this area, their relative positions, and the shut-in interval time △T of each well k (k = 1, 2...K, △T1 = 0);

[0187] (2) Input the geological parameters and fracturing parameters of each horizontal well;

[0188] (3) Determine and input the production life T of the horizontal well group;

[0189] (4) Put Well 1 into production. When it has produced for △T2, put Well 2 into production. When Well 1 has produced for △T2 + △T3, put Well 3 into production. Repeat the operation until Well K is put into production. After that, let the K wells produce until the Tth year.

[0190] (5) After performing perturbation inverse transformation and numerical inversion on the dimensionless bottom-hole flowing pressure in the Laplace space of each well calculated, the dimensionless bottom-hole flowing pressure of each well can be obtained;

[0191] (6) Perform Laplace transformation on the dimensionless bottom-hole flowing pressure of each well obtained, and then obtain the dimensionless production in the Laplace space through the relationship between the bottom-hole flowing pressure and the production;

[0192] (7) Finally, perform constant numerical inversion and dimensionalization on the dimensionless production of each well output, and the actual production of each well can be output.

[0193] Compare the prediction results with the actual production data, as Figures 8 - 10 shown. It can be seen that the production decline curve obtained by the model established in this patent has a good overall match with the real-time production decline trend reflected in the production data. For Well 1, the cumulative gas production after 350 days of production is 1.979×10 7 m 3 , and the cumulative gas production simulated by the model proposed in this patent is 1.887×10 7 m 3 , with a difference of 4.65% between the two. For Well 2, the cumulative gas production after 350 days of production is 1.986×10 7 m3 , the cumulative gas production obtained by simulating with the model in this paper is 1.982×10 7 m 3 , with a difference of 0.2% between them. For Well 3, the cumulative gas production after 350 days of production is 2.363×10 7 m 3 , and the cumulative gas production obtained by simulating with the model in this paper is 2.239×10 7 m 3 , with a difference of 5.25% between them. The errors between the actual production and the simulated production of these three wells are all within a reasonable range, thus demonstrating the accuracy of the model established in this patent when predicting the production of horizontal wells.

[0194] As mentioned above, it is not any form of limitation to the present invention. Although the present invention has been disclosed by 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 equivalent embodiments of equivalent changes by using the disclosed technical content within the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for predicting the productivity of shale gas infill wells considering well - to - well interference, characterized in that, The following steps are included: Step 1: Obtain the number of horizontal wells in the target area well group, the relative positions of each well, the open well interval time of each well, geological parameters, production life T, and the fracturing parameters of each well; Step 2: Determine the dimensionless bottom hole flowing pressure in the Laplace space of each well according to the shale gas infill well productivity prediction model considering well interference, geological parameters, and the fracturing parameters of each well; The shale gas infill well productivity prediction model considering well interference is: A·B = C In the formula: C = [0 ··· 0 0 ··· 0 ··· 0 ··· 0 1 / s1 1 / s2 ··· 1 / s K ' where: C fdkk' is the dimensionless fracture conductivity of the m-th hydraulic fracture in the k-th well at the k'-th stage; is the dimensionless bottom-hole flowing pressure; Step 3: After performing perturbation inverse transformation and numerical inversion on the dimensionless bottom hole flowing pressure in the Laplace space of each well, determine the dimensionless bottom hole flowing pressure of each well according to the dimensionless bottom hole flowing pressure expression considering wellbore storage effect and skin effect; Step 4: Perform Laplace transform on the dimensionless bottom hole flowing pressure, and then obtain the dimensionless production in the Laplace space through the relationship between bottom hole flowing pressure and production; Step 5: Perform Stehfest numerical inversion on the dimensionless production in the Laplace space to obtain the dimensionless production; Step 6: Finally, convert the dimensionless production into the actual production.

2. The shale gas infill well productivity prediction method considering well interference according to claim 1, wherein The geological parameters include natural fracture stress sensitivity coefficient, natural fracture porosity, natural fracture permeability, matrix porosity, gas reservoir thickness, matrix compressibility, gas viscosity, gas layer temperature, Langmuir volume, Langmuir pressure, shale density, and original formation pressure.

3. The shale gas infill well productivity prediction method considering well interference according to claim 1, wherein 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 well length.

4. A method for predicting the productivity of shale gas infill wells considering well interference according to claim 1, characterized in that, In the said Step 3: First, calculate the dimensionless bottom hole flowing pressure in the Laplace space of Well 1 from 0 to △T2; Then, calculate the dimensionless bottom hole flowing pressure in the Laplace space of Well 1 from △T2 to △T2 + △T3 and the dimensionless bottom hole flowing pressure in the Laplace space of Well 2 from 0 to △T3; Finally, calculate the dimensionless bottom-hole flowing pressure of Well 1 in the Laplace space from △T2 +... + △T k to T, the dimensionless bottom-hole flowing pressure of Well 2 in the Laplace space from △T3 +... + △T k to T - △T2... the dimensionless bottom-hole flowing pressure of Well K in the Laplace space from 0 to T - (△T2 +... + △T k ); Among them, Well 1 is put into production. When it has been produced to △T2, Well 2 is put into production; when Well 1 is produced to △T2 + △T3, Well 3 is put into production; repeat the operation until Well K is put into production.

5. A method for predicting the productivity of shale gas infill wells considering inter-well interference according to claim 1, characterized in that The dimensionless bottom hole flowing pressure expression considering wellbore storage effect and skin effect is: In the formula: is the dimensionless bottom-hole flowing pressure; S c is the skin factor; C D is the dimensionless wellbore storage coefficient; s k is the Laplace space complex parameter variable corresponding to the k-th well.

6. A method for predicting the productivity of shale gas infill wells considering well - to - well interference according to claim 1, characterized in that, The dimensionless production rate in the Laplace space and The relational expression is: In the formula: is the dimensionless production in the Laplace space; s k is the complex Laplace space variable corresponding to the k-th well.

Images