Method and equipment for calculating productivity curve of fracture-vug type gas reservoir and storable medium

Abstract

The invention provides a method and equipment for calculating a productivity curve of a fractured-vuggy gas reservoir and a storable medium, and belongs to the technical field of gas reservoir development. The method comprises the steps that a well testing model of a well to be analyzed is established, Laplace transformation solving is conducted, and a Laplace space bottom hole pressure solution function is obtained; on the basis of the Laplacian space bottom hole pressure solution function, a numerical inversion technology is used for solving a real space bottom hole pressure solution; substituting the real space bottom hole pressure solution into a bottom hole pressure calculation formula under the four-stage pressure to obtain a fracture-vuggy gas reservoir productivity calculation result, and fitting to obtain a fracture-vuggy gas reservoir productivity curve; the invention further provides corresponding equipment and a storable medium. Compared with the prior art, the method for calculating the productivity curve of the fractured-vuggy gas reservoir provided by the invention is suitable for production analysis, prediction and dynamic data inversion in the actual production process of the fractured-vuggy gas reservoir; practice can be effectively guided, and economic benefits are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of gas reservoir development, and particularly relates to a method, device and storage medium for calculating the productivity curve of a fracture-cavity type gas reservoir. Background Technique

[0002] At present, carbonate oil reservoirs account for more than 50% of the proven oil and gas reservoir reserves globally, and among them, carbonate fracture-cavity type oil reservoirs account for 60%. Fracture-cavity type oil reservoirs have complex pore structures, various fracture-cavity connection forms, and various flow mechanisms. The reservoir has extremely strong heterogeneity and anisotropy. The research on fracture-cavity type oil reservoirs has become the focus of current oil and gas reservoir development.

[0003] The productivity of an oil and gas reservoir is the basis and core of oil and gas field development, and plays an important role in aspects such as development strategy formulation, surface facility engineering, and production system adjustment. Due to differences in geological conditions and development methods, the productivity evaluation and prediction methods for oil and gas reservoirs are different. Due to the extremely complex flow behavior inside fracture-cavity type oil reservoirs, there are still controversies in its flow mechanism at present, and there are fractures and caves of different sizes inside, with various flow forms. Conventional methods are also not applicable to the productivity prediction of fracture-cavity type oil and gas reservoirs. Therefore, the productivity prediction of fracture-cavity type oil and gas reservoirs has always been an unsolved problem and new methods need to be studied.

[0004] CN111485867A discloses a method and device for predicting the productivity of a fracture-cavity type carbonate reservoir. The method includes: obtaining the reservoir thickness, formation lithology, acoustic travel time curve, electrical imaging logging image and productivity of the excavated wells in the target work area; determining the reservoir porosity according to the formation lithology and acoustic travel time curve; processing the electrical imaging logging image to obtain a binary image; determining the first fractal dimension corresponding to the binary image; processing the first fractal dimension using a power function to obtain a second fractal dimension; establishing a productivity prediction model according to the reservoir thickness, reservoir porosity, second fractal dimension and productivity of the excavated wells; and using the productivity prediction model to predict the productivity of the fracture-cavity type carbonate reservoir of the unexcavated wells in the target work area. It uses multi-faceted exploration data including reservoir thickness to predict productivity, but does not disclose the prediction method of the productivity curve, resulting in its expected effect being difficult to fully meet the technical requirements of this field.

[0005] CN114427445A discloses a method and system for calculating the dynamic productivity of an infinite formation in a fracture-cavity reservoir. This method is based on several preset flow rate values in the backpressure well test and uses the superposition principle for calculation to obtain an expression for the ratio of the difference between the bottom-hole flowing pressure and the original pressure corresponding to each flow rate to the respective flow rates. Through the established well test model for the fracture-cavity reservoir, the calculation results related to the karst cave are obtained. Virtual well test data are generated by the numerical method to simulate the well test process in several stages, and the flow rate and pressure data in the backpressure well test are obtained to accurately obtain the productivity curve. It is applicable to production diagnosis and prediction in the actual production process of fracture-cavity reservoirs, as well as dynamic data inversion, filling the defect that static data cannot recognize the fracture-cavity reservoir structure.

[0006] Due to the extremely complex flow behavior inside the fracture-cavity gas reservoir, there is still controversy about its flow mechanism at present. Moreover, there are fractures and karst caves of different sizes inside, and there are various flow forms. At the same time, compared with the oil reservoir, the gas reservoir has stronger compressibility and faster fluid flow velocity. The flow equation of the oil reservoir cannot fully describe the flow behavior of the gas reservoir. Therefore, the existing productivity calculation methods for fracture-cavity oil reservoirs are not applicable to the productivity prediction of fracture-cavity gas reservoirs. Therefore, the productivity prediction of fracture-cavity gas reservoirs is a problem that those skilled in the art have been eager to solve, and new methods need to be studied. Summary of the Invention

[0007] Aiming at the lack of a productivity prediction method applicable to fracture-cavity gas reservoirs in the existing technology, the present invention provides a method for calculating the productivity curve of a fracture-cavity gas reservoir based on pressure build-up well test data. To address the deficiencies of the conventional systematic well test analysis method, a numerical method is proposed to generate virtual systematic well test data. This method combines the pressure build-up well test interpretation model and results with the superposition principle, simulates the systematic well test process, obtains the flow rate and pressure data in the backpressure well test, and then conducts a systematic well test to more accurately calculate the productivity curve of the fracture-cavity gas reservoir.

[0008] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0009] The present invention involves multiple formulas. Except for the specially noted content, the same parameter meanings are the same. The meanings and units of some parameters in the formulas are shown in Table 1 and Table 2.

[0010] Table 1 Meanings and Units of Parameters

[0011]

[0012]

[0013] Table 2 Meanings of Subscripts

[0014] Subscript Meaning c Cavern i Initial state f Fracture m Matrix w Gas well D Dimensionless sc Standard state (ψ)j Pseudo (pressure)

[0015] A method for calculating the productivity curve of a fracture-vuggy gas reservoir, comprising the following steps:

[0016] S1. Establish a well test model for the well to be analyzed;

[0017] S2. Solve the well test model established in step S1 by Laplace transform to obtain the bottom-hole pressure solution function in Laplace space;

[0018] S3. Based on the bottom-hole pressure solution function in Laplace space obtained in step S2, use numerical inversion technology to obtain the bottom-hole pressure solution in real space;

[0019] S4. Substitute the bottom-hole pressure solution in real space obtained in step S3 into the bottom-hole pressure calculation formula under four-level pressure to obtain the productivity calculation result of the fracture-vuggy gas reservoir, and fit to obtain the productivity curve of the fracture-vuggy gas reservoir.

[0020] Preferably, the well test model in step S1 is:

[0021]

[0022] More preferably, in the well test model, the parameters and their definitions are as follows:

[0023] Dimensionless radius:

[0024] Dimensionless pseudo-pressure:

[0025] Dimensionless time:

[0026] Dimensionless height:

[0027] Storage ratio:

[0028] Inter-porosity flow coefficient:

[0029] Dimensionless wellbore storage coefficient:

[0030] Dimensionless vug storage coefficient:

[0031] Pressure propagation coefficient:

[0032] Vug coefficient:

[0033] q sc is the flow rate under standard conditions, m 3 / s;.

[0034] Preferably, the condition for solving the Laplace transform in step S2 is: an infinite formation boundary.

[0035] Preferably, the bottom-hole pressure solution function in the Laplace space in step S2 is:

[0036]

[0037] More preferably, in the bottom-hole pressure solution function in the Laplace space:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] s is the Laplace variable; K0, K1, I0, and I1 are Bessel functions; e is the wall thickness, S w is the wellbore skin, r eD is the outer boundary radius.

[0051] Preferably, the numerical inversion technique in step S3 is the Stehfest numerical inversion technique.

[0052] Preferably, the calculation formula for the bottom-hole pressure under the four-level pressure in step S4 is:

[0053]

[0054]

[0055]

[0056]

[0057] Among them, q1, q2, q3, and q4 are preset values of flow rate, and t p is the open - well time.

[0058] The present invention also provides an electronic device, including: at least one processor, and at least one memory;

[0059] Among them, the memory stores at least one instruction executable by the processor. When the instruction is executed by the at least one processor, the productivity curve of the fractured - vuggy gas reservoir is calculated according to the above - mentioned method for calculating the productivity curve of the fractured - vuggy gas reservoir based on pressure buildup test data.

[0060] The present invention also provides a readable storage medium, storing at least one instruction executable by the processor. When the instruction is executed by the at least one processor, the productivity curve of the fractured - vuggy gas reservoir is calculated according to the above - mentioned method for calculating the productivity curve of the fractured - vuggy gas reservoir based on pressure buildup test data.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] The present invention conducts a series of rigorous calculations, derivations, and fittings for the actual production situation of the fractured - vuggy gas reservoir. The method for calculating the productivity curve of the fractured - vuggy gas reservoir based on pressure buildup test data provided by the present invention solves the problem that the existing system well test cannot obtain the productivity curve of the fractured - vuggy gas reservoir, and obtains an accurate expression of the productivity relationship of the fractured - vuggy gas reservoir. The method for calculating the productivity curve of the fractured - vuggy gas reservoir provided by the present invention is applicable to production analysis, prediction, and dynamic data inversion in the actual production process of the fractured - vuggy gas reservoir, and can effectively guide practice and improve economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 It is the double - logarithm fitting graph of the example well;

[0064] Figure 2 The binomial productivity analysis graph obtained from the well test design of the example well;

[0065] Figure 3 The IPR curve graph obtained from the well test design of the example well. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0066] Embodiment A method for calculating the productivity curve of a fractured - vuggy gas reservoir based on pressure buildup test data

[0067] S1. Establish a well test model of the well to be analyzed;

[0068] The well test model is as follows:

[0069]

[0070] Dimensionless radius:

[0071] Dimensionless pseudo - pressure:

[0072] Dimensionless time:

[0073] Dimensionless height:

[0074] Storage ratio:

[0075] Inter - wellbore flow coefficient:

[0076] Dimensionless wellbore storage coefficient:

[0077] Dimensionless solution cavity storage coefficient:

[0078] Pressure propagation coefficient:

[0079] Solution cavity coefficient:

[0080] S2. Perform Laplace transform on the well - test model established in step S1 to obtain the bottom - hole pressure solution function in Laplace space;

[0081] After performing Laplace transform on the well - test model, the bottom - hole pressure solution function in Laplace space under the infinite - formation boundary condition is solved as:

[0082]

[0083] Where:

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] s is the Laplace variable; K0, K1, I0, and I1 are Bessel functions, e is the wall thickness, S w is the wellbore skin, r eD is the outer boundary radius.

[0097] The derivation process is as follows:

[0098] First, study the internal model. When natural gas enters the wellbore from the karst cave and then flows in the wellbore, the continuity equation and momentum equation need to be satisfied. In this process, the present invention only considers the flow in the vertical direction and regards the karst cave as an equipotential body. A large amount of natural gas is stored in the karst cave and the wellbore, forming a high-pressure fluid storage space. When the well is opened, due to the compressibility of the fluid and the pipe wall, a fluctuating pressure will be caused.

[0099]

[0100]

[0101] In the above formula, t is the time, s; ρ is the gas density, kg / m 3 ; v is the gas velocity, m / s; r w is the wellbore radius, m; f is the friction coefficient, dimensionless.

[0102] For the fluid microelement, equation (5) can be written through the law of conservation of mass:

[0103]

[0104] where N is the cross-sectional area of the fluid microelement.

[0105] Expand equation (5):

[0106]

[0107] Equation (6) can be simplified to:

[0108]

[0109] Since the pressure change is large, the wellbore will also deform. Its deformation is determined by the wall thickness, wellbore radius, and elastic modulus of the tubing material. When the pressure changes, the relationship between its radial deformation and pressure is:

[0110]

[0111] In the above formula, r w is the wellbore radius, m; e is the pipe wall thickness, m; E w is the elastic modulus of the tubing, MPa.

[0112] From the tubing area formula, we can get:

[0113]

[0114] Combining equations (8) and (9), we can obtain the equation:

[0115]

[0116] By converting the density term into a function of pressure and combining equations (7) and (10), we can get the equation:

[0117]

[0118] At this time, a variable needs to be defined:

[0119]

[0120] In the above formula, χ is the velocity of pressure wave propagation, m / s; E f is the bulk modulus of elasticity of the gas, MPa.

[0121] Combining equation (11) and equation (12), we can get:

[0122]

[0123] Combining the continuity equation, the momentum equation and equation (13), we can obtain the equation:

[0124]

[0125] When the gas flows in the karst cave, the velocity is very slow. According to the actual data, it is approximately on the order of 1×10 -4 m / s to 1×10 - 3 m / s. The friction term is related to the square of the velocity. Therefore, the friction term is very small and can be ignored here.

[0126] The relationship between the karst cave storage coefficient and the velocity is:

[0127]

[0128] Therefore, equation (14) can be rewritten as:

[0129]

[0130] The solution of equation (16) is as follows:

[0131]

[0132] v0 is the initial gas velocity, in m / s.

[0133] The velocity at the connection between the karst cave and the wellbore is:

[0134]

[0135] The cross-sectional area of the karst cave is much larger than that of the wellbore, and the connection between the two is like a contraction tube. When the gas enters the wellbore from the karst cave, the velocity will increase rapidly, and at the same time, the gas pressure will decrease. At this time, some gas will form vortices near the pipe wall, and these vortices will consume energy. The energy equation from the karst cave to the wellbore is equation (19):

[0136]

[0137] In the above formula, p c is the karst cave pressure, in MPa; p w is the bottom hole pressure, in MPa; h j is the local loss, in m.

[0138] The empirical formula for the local loss of the contraction tube is:

[0139]

[0140] In the above formula, A w is the cross-sectional area of the wellbore, in m 2 ; A c is the cross-sectional area of the karst cave, in m 2 .

[0141] Combining equations (18), (19), and (20), equation (21) can be obtained:

[0142]

[0143] For the external model, this paper uses the double-porosity medium model to describe the gas flow. At the same time, the pseudo-pressure is introduced to replace the pressure.

[0144]

[0145] The equations are as follows:

[0146]

[0147]

[0148] When the gas approaches the wellbore, an inertia-turbulence effect will occur, resulting in an additional pressure drop. In well testing, the total skin factor is introduced to describe this pressure drop.

[0149] S w = s w + D′q sc (25)

[0150] In the above formula, S w is the total skin factor, dimensionless; s w is the true skin factor, dimensionless; q sc is the production rate at the wellhead, m 3 / s, D′ is the turbulence coefficient, s / m 3 .

[0151] The bottom-hole pressure can be expressed as:

[0152]

[0153] The gas production rate under formation conditions is:

[0154]

[0155] In the above formula, q is the production rate under formation conditions, m 3 / s; B g is the formation volume factor, dimensionless; p sc is the pressure under standard conditions, 0.101 MPa; T sc is the temperature under standard conditions, 288.16 K.

[0156] The gas state equation is:

[0157]

[0158] The total production consists of four parts: (1) wellbore storage; (2) cavern storage; (3) gas flowing from the fracture into the wellbore. (4) gas flowing from the fracture into the cavern.

[0159]

[0160] To sum up, the Laplace space bottom-hole pressure solution function can be obtained.

[0161] S3. Based on the Laplace space bottom-hole pressure solution function obtained in step S2, use the numerical inversion technique to obtain the real-space bottom-hole pressure solution;

[0162] Using the Stehfest numerical inversion technique, from the Laplace space bottom-hole pressure solution function, obtain the real-space bottom-hole pressure solution.

[0163] S4. Substitute the true bottom-hole pressure solution obtained in step S3 into the bottom-hole pressure calculation formula under the fourth-stage pressure to obtain the productivity calculation result of the fracture-vuggy gas reservoir, and fit to obtain the productivity curve of the fracture-vuggy gas reservoir:

[0164] According to the superposition principle, the expression of ψ wD (t D ) under the fourth-stage flow rate can be given

[0165]

[0166]

[0167]

[0168]

[0169] Among them, q1, q2, q3, and q4 are preset values of the flow rate.

[0170] Substitute the bottom-hole pseudo-pressure solution ψ wD (t D ) obtained from the well test model of the fracture-vuggy gas reservoir into the above equations (30)-(33), and the value of Δψ / Q at different flow rates and production times can be obtained. Then, plot the values of Δψ / Q at different flow rates Q in a rectangular coordinate system to obtain the binomial productivity analysis diagram. Through linear regression, the linear relationship between Δψ / Q and the flow rate Q can be obtained, which is the binomial analysis equation:

[0171]

[0172] Where a and b are the slope and intercept of the straight line respectively, and further the productivity equation can be obtained:

[0173] ψ w =ψ i -aQ 2 -bQ (35)

[0174] Subsequently, the curve between the pseudo-pressure ψ and the flow rate Q can be plotted, which is the productivity curve.

[0175] This embodiment analyzes the pressure buildup data of a well test in a certain area of Xinjiang, obtains the productivity curve of this well, and compares it with the actual productivity, specifically including the following steps:

[0176] (1) For the pressure buildup data of this well, then use the well test model of the fracture-vuggy reservoir proposed in the present invention for fitting. The fitting results are as Figure 1 shown. The basic constants of this well are shown in Table 3, and the interpretation results are shown in Table 4.

[0177] Table 3 Basic parameters of the example well

[0178] Parameter Value Unit Gas well radius 0.1073 m Porosity 0.1036 Rock compressibility 0.0065 <![CDATA[MPa -1 > Initial pressure 86.5699 MPa Formation height 10.5 m Gas reservoir temperature 433.27 K

[0179] Table 4 Interpretation results of the example wells

[0180] Interpretation parameter Value Unit Time fitting value 30.1027 1 / Hour Pressure fitting value 13.4188 <![CDATA[MPa -1 > Wellbore storage constant 1.1549 <![CDATA[m 3 / MPa]]> Total skin factor 0.1019 Pressure propagation coefficient 0.4430 Cavern coefficient 0.6968

[0181] (2) According to the obtained interpretation results, substitute the parameters into the equation, and then use the parameters in Table 5 to calculate the bottom-hole pressure at different flow rates. The calculation results are shown in Table 6.

[0182] Table 5 Production time and flow rate input for the well test design of the example wells

[0183]

[0184]

[0185] Table 6 Calculation results of the example wells

[0186] Serial number <![CDATA[Flow rate Q (m 3 / d)]]> <![CDATA[Pseudo-pressure at the bottom of the well Ψ wf (MPa)]]> 1 60 85.472829 2 120 84.064873 3 180 82.589123 4 240 81.047975

[0187] (3) Calculate the value of Δy / Q at different flow rates Q and plot it in a rectangular coordinate system, then the corresponding binomial productivity analysis diagram can be obtained, as Figure 2 shown. Then, a fitted straight line can be obtained through linear regression, as shown by the straight line in Figure 2 . The expression of this straight line is:

[0188]

[0189] Correspondingly, the productivity equation is:

[0190] ψ w = ψ i - 3.0352Q 2 - 0.0159Q (35)

[0191] where y i is 86.5699. Plotting Equation 35 in a rectangular coordinate system gives the productivity curve of this well, as Figure 3 shown.

[0192] It can be seen that by using the productivity curve calculation method for fractured-vuggy gas reservoirs based on pressure buildup test data provided by the present invention, a well-fitted productivity curve can be obtained to guide production and increase the production rate.

[0193] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, rather than to limit the protection scope of the present invention. Any simple modification or equivalent replacement of the technical solution of the present invention by those of ordinary skill in the art shall not depart from the essence and scope of the technical solution of the present invention.

Claims

1. A method for calculating the productivity curve of a fractured-vuggy gas reservoir, characterized in that, It includes the following steps: S1. Establish a well test model for the well to be analyzed, which includes dimensionless pseudo - pressure; S2. Solve the well test model established in step S1 by Laplace transform to obtain the bottom - hole pressure solution function in Laplace space; S3. Based on the bottom - hole pressure solution function in Laplace space obtained in step S2, use numerical inversion technology to obtain the bottom - hole pressure solution in real space; S4. Substitute the bottom - hole pressure solution in real space obtained in step S3 into the bottom - hole pressure calculation formula under four - stage pressure to obtain the productivity calculation result of the fracture - cave gas reservoir, and fit to obtain the productivity curve of the fracture - cave gas reservoir.

2. The method according to claim 1, characterized in that It includes the following steps: The well test model described in step S1 is: where r D is the dimensionless radius, ψ jD is the dimensionless pseudo - pressure, ψ fD is the dimensionless fracture pseudo - pressure, λ is the inter - wellbore flow coefficient, ψ mD is the dimensionless matrix pseudo - pressure, t D is the dimensionless time, ω is the storage ratio, S w is the wellbore skin, C wD is the dimensionless wellbore storage coefficient, C cD is the dimensionless solution cavity storage coefficient, ψ cD is the dimensionless solution cavity pseudo - pressure, h D is the dimensionless height, r cD is the dimensionless solution cavity radius, ψ wD is the dimensionless wellbore pseudo - pressure, ξ is the solution cavity coefficient, η is the pressure propagation coefficient.

3. According to the method described in claim 2, it is characterized in that: The expression of the dimensionless radius is: where r is the radius, m; r w is the wellbore radius, m; The expression of the dimensionless pseudo - pressure is: Among them, k f is the fracture permeability, m 2 ; h1 is the wellbore depth, h2 is the karst cave depth, T sc is the standard state temperature, 288.15 K; q sc is the production at the wellhead, m 3 / s; T is the temperature, K; p sc is the standard state pressure, MPa; ψ i is the pseudo-pressure in the initial state, MPa; ψ j is the pseudo-pressure.

4. According to the method described in claim 2, it is characterized in that: The expression of the dimensionless time is: where k f is the fracture permeability, m 2 ; Φ m is the matrix porosity, dimensionless; c m is the matrix compressibility, MPa -1 ; Φ f is the fracture porosity, dimensionless; c f is the fracture compressibility, MPa -1 ; μ i is the dynamic viscosity at the initial state, m 2 / s; rw is the wellbore radius; The expression of the dimensionless height is: Where, h1 is the wellbore depth, in m; h2 is the karst cave depth, in m.

5. According to the method described in claim 2, it is characterized in that: The expression of the storage - capacity ratio is: Among them, Φf is the fracture porosity, dimensionless; c f is the fracture compressibility, MPa -1 ; Φ m is the matrix porosity, dimensionless; c m is the matrix compressibility, MPa -1 ; The expression of the inter - wellbore flow coefficient is: where α is the shape factor; km is the matrix permeability, m 2 ; k f is the fracture permeability, m 2 ; r w is the wellbore radius, m.

6. According to the method described in claim 2, it is characterized in that: The expression of the dimensionless wellbore storage coefficient is: Among them, C w is the gas well storage coefficient, m 4 s 2 / kg; Φ m is the matrix porosity, dimensionless; c m is the matrix compressibility, MPa -1 ; Φf is the fracture porosity, dimensionless; c f is the fracture compressibility, MPa -1 ; h1 is the wellbore depth, m; h2 is the karst cave depth, m; r w is the wellbore radius, m; The expression of the dimensionless karst cave storage coefficient is: Among them, C c is the karst cave storage coefficient, m 4 s 2 / kg; Φ m is the matrix porosity, dimensionless; c m is the matrix compressibility, MPa -1 ; Φf is the fracture porosity, dimensionless; c f is the fracture compressibility, MPa -1 ; h1 is the wellbore depth, m; h2 is the karst cave depth, m; r w is the wellbore radius, m.

7. According to the method described in claim 2, it is characterized in that: The expression of the pressure propagation coefficient is: where d c is the diameter of the karst cave; r w is the radius of the wellbore, m; Φ m is the matrix porosity, dimensionless; c m is the matrix compressibility, MPa -1 ; Φf is the fracture porosity, dimensionless; c f is the fracture compressibility, MPa -1 ; μ i is the initial dynamic viscosity, m 2 / s; z i is the initial gas compressibility, dimensionless; R is the universal gas constant, m 2 / (s 2 *mol*K); p i is the initial pressure, MPa; χ is the wave velocity, m / s; M is the gas molecular weight, kg / mol; C c is the karst cave storage coefficient, m 4 s 2 / kg; k f is the fracture permeability, m 2 ; The expression of the karst cave coefficient is: where d c is the diameter of the karst cave; v0 is the initial gas velocity, m / s; k f is the fracture permeability, m 2 ; h1 is the wellbore depth, m; h2 is the karst cave depth, m; T sc is the standard state temperature, 288.15K; p i is the initial pressure, MPa; M is the gas molecular weight, kg / mol; r w is the wellbore radius, m; P sc is the standard state pressure, 0.101 MPa; q sc is the flow rate under standard conditions, m 3 / s; T is the temperature, K; R is the universal gas constant, m 2 / (s 2 *mol*K); z i is the initial gas compressibility factor, dimensionless; μ i is the initial dynamic viscosity, m 2 / s.

8. The method according to claim 1, wherein The conditions for the Laplace transform solution in step S2 are: Infinite - formation boundary.

9. The method according to claim 1, wherein The bottom - hole pressure solution function in Laplace space in step S2 is: s is the Laplace variable; ξ is the solution cavity coefficient; η is the pressure propagation coefficient; λ is the crossflow coefficient; C cD is the dimensionless solution cavity storage coefficient; C wD is the dimensionless wellbore storage coefficient; r cD is the dimensionless solution cavity radius; K0, K1, I0, and I1 are Bessel functions; e is the pipe wall thickness, S w is the wellbore skin, r eD is the boundary radius.

10. The method according to claim 1, wherein The numerical inversion technology in step S3 is the Stehfest numerical inversion technology.

11. The method according to claim 1, wherein The bottom - hole calculation formula under four - stage pressure in step S4 is: q1, q2, q3 and q4 are preset values of flow rate; t p is the open well time, s; t pD is the dimensionless open - hole time; ψ i is the pseudo - pressure in the initial state, MPa; ψ wf is the pseudo - pressure of the gas - well fracture, MPa; B is the volume coefficient, dimensionless; μ is the dynamic viscosity, m 2 / s; k is the permeability, m 2 ; h is the height, m; ψ wD is the dimensionless pseudo-pressure of the gas well; ψ wD (t D ) is the solution of the bottom-hole pseudo-pressure.

12. An electronic device, characterized in that, It includes: At least one processor, and at least one memory; Wherein, the memory stores at least one instruction executable by the processor, and when the instruction is executed by the at least one processor, the productivity curve of the fracture - cave gas reservoir is calculated according to the method described in any one of claims 1 - 11.

13. A readable storage medium, characterized in that, Stores at least one instruction executable by the processor, and when the instruction is executed by the at least one processor, the productivity curve of the fracture - cave gas reservoir is calculated according to the method described in any one of claims 1 - 11.

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