A shale gas and coalbed methane production quantitative evaluation method based on a gas-water two-phase flow isotope fractionation model

Abstract

The application relates to a shale or coal rock gas evaluation method based on a gas-water two-phase flow isotope fractionation model, which comprises the following steps: 1, collecting data; 2, establishing a gas well model; 3, establishing a control equation set; 4, coupling the influence of real gas effect and effective stress; 5, establishing a gas transmission model and a relative permeability model; 6, establishing a capillary pressure and saturation relationship; 7, considering critical desorption pressure; 8, setting initial conditions and boundary conditions; 9, solving the control equation set; 10, calculating production dynamic parameters and isotope values; 11, performing history matching; 12, verifying the quality of history matching; 13, predicting productivity; 14, calculating gas dynamic output proportion; 15, identifying fractionation inflection points and gas production mechanism conversion; the application realizes the quantitative evaluation of deep reservoir production prediction and output gas dynamic proportion by coupling gas-water two-phase flow, multiple gas transmission mechanisms, stress sensitivity and methane isotope competitive adsorption theory.

Description

Technical Field

[0001] This invention relates to the field of exploration and development technology of unconventional shale oil and gas fields, specifically to a dynamic evaluation method for deep shale gas or coal gas wells based on the gas-water two-phase flow isotope fractionation model (GWF-CIF). Background Technology

[0002] my country is rich in deep shale gas and coal gas resources. As of 2025, the geological resources of deep shale gas reached 21.8 × 10⁻⁶. 12 m 3 The geological resources of deep coal and gas reach 30.05 × 10⁻⁶. 12 m 3 With its enormous resource potential, it is expected to become an important area for stabilizing and increasing natural gas production in my country. As exploration and development technologies and theories continue to improve, the exploration and development of deep shale gas and coal gas in my country is gradually progressing. In 2019, the Daning-Jixian deep coal gas field was established in the Ordos Basin, with recoverable resources reaching 166.41 billion cubic meters. In 2020, the Jiaoye 42-1HF well in the Fuling shale gas field of the Sichuan Basin broke through the bottleneck in deep shale gas development, achieving a daily gas production of 20.1 × 10⁻⁶ cubic meters. 4 m 3 In 2023, the Yangmei 1HF well in the Junggar Basin achieved a major breakthrough, adding 122.6 billion cubic meters of predicted reserves. This series of breakthroughs marks the beginning of a rapid development phase in my country's deep shale / coal gas exploration and development. As the energy structure gradually shifts towards a low-carbon and green model, the accelerated large-scale development of deep shale / coal gas, as a clean energy source, provides crucial support for reducing greenhouse gas emissions.

[0003] Compared to shallow and medium-depth reservoirs, deep shale / coal reservoirs are characterized by "three highs"—high geostress, high fluid pressure, and high formation temperature—and "two lows"—low porosity and low permeability. This leads to significant differences in pore structure, gas occurrence state, and fluid flow mechanism. Deep shale / coal gas reservoirs commonly exhibit two-phase flow (EUR) under gas-water flow conditions during development. The presence of the water phase significantly alters gas migration behavior, affecting gas production by occupying effective pore space and generating mass transfer resistance. Currently, research on EUR evaluation and adsorbed / free gas production mechanisms under two-phase flow conditions in deep shale / coal gas wells is in its early stages. The complex gas occurrence state and unclear water phase influence mechanisms lead to considerable controversy regarding the adsorbed / free gas production ratio and final recoverable reserves during the production process, which to some extent limits accurate understanding and optimized decision-making in deep shale / coal gas development.

[0004] Current methods for quantitatively evaluating the energy loss (EUR) of deep shale / coal gas wells and the dynamic production ratio of adsorbed / free gas during the production process mainly include empirical decline curve methods, mass balance methods, numerical simulation methods, and nuclear magnetic resonance methods. Among these, empirical decline curve methods such as the Arps decline curve method, SEPD method, and Duong method establish decline behavior based on fitting historical production data, assuming relatively stable reservoir properties. However, they do not consider the dynamic impact of physical processes such as effective stress changes and the evolution of relative permeability between the gas and water phases on reservoir properties, leading to significant uncertainty in long-term predictions. The mass balance method, based on the assumption of a constant-volume gas reservoir, calculates the adsorbed / free gas ratio at different times by fitting measured pressure and cumulative gas production data. However, this method can only evaluate the adsorbed / free gas volume within existing production periods and cannot predict future gas production ratios and EUR. Furthermore, under gas-water two-phase flow conditions, changes in the water phase volume affect the accuracy of the effective gas volume calculation. Numerical simulation methods predict EUR (Earning Equivalent Tolerance) by constructing a mass transfer model that couples gas diffusion, adsorption / desorption, and seepage processes. However, traditional models mainly target single-phase gas flow, failing to adequately consider the influence of water relative to gas transport, and contain too many unknown parameters, leading to different results from different optimization algorithms. Nuclear magnetic resonance (NMR) methods obtain T2 relaxation time spectra at different times by online monitoring of hydrogen nuclear relaxation signals of gas in reservoir pores, and calculate adsorbed / free gas volume by setting a T2 cutoff value. However, this method requires long monitoring times and cannot monitor the entire process in real time; the T2 cutoff value setting lacks specific industry standards and is subject to subjective influence. Based on field analysis and indoor simulation experiments, it is shown that gas mass transfer in low-permeability rocks exhibits multi-stage isotopic fractionation, and the isotopic fractionation characteristics at each stage are related to the adsorbed / free gas production ratio in the production process. Isotopic fractionation provides a new approach for evaluating the adsorption / free gas ratio in deep coal seams (coal-rock). By constructing an isotopic fractionation model and fitting isotopic values ​​using indoor simulation experiments, the adsorbed / free gas ratio in the production process can be determined. Current indoor simulation experiments do not apply confining pressure to the core samples, resulting in inconsistencies with the isotope fractionation phenomena observed in real-world deep coal seam (coal-rock) gas wells. Furthermore, isotope fractionation models are only applicable to homogeneous and structurally simple conditions; their applicability to deep coal-rock reservoirs with both cleavage / fracture and matrix pores remains to be verified. Therefore, a new technical method is urgently needed to evaluate the dynamic production ratio of adsorbed / free gas during deep coal seam (coal-rock) gas production.

[0005] Based on field monitoring and indoor simulation experiments, the mass transfer process of gas in low-permeability rocks exhibits a multi-stage methane carbon isotope fractionation phenomenon, displaying a three-stage evolution characteristic of "early stability (I) - mid-term decrease (II) - late-term increase (III)". The isotope fractionation characteristics of each stage are closely related to the ratio of adsorbed / free gas produced during the production process: in the early stage, fracture gas is produced rapidly, and the isotopic composition is relatively stable; in the mid-term stage, fracture gas and matrix free gas are produced together, with free gas dominating, and δ¹⁴C⁻¹… 13 The C1 value gradually decreases; in the later stage, after a large amount of matrix free gas is extracted, desorbed gas becomes the main source, δ 13 The C1 value gradually increases. The isotope fractionation inflection point can serve as a key indicator for identifying changes in gas production mechanisms, providing a scientific basis for selecting the timing of production enhancement measures. However, most current indoor simulation experiments do not consider gas-water two-phase flow conditions, leading to inconsistencies with the isotope fractionation phenomena observed in real deep shale / coal-rock gas wells. Existing isotope fractionation models are mainly applicable to single-phase gas flow; a systematic theoretical model has not yet been established for the isotope fractionation mechanism under gas-water two-phase flow conditions and the influence of water on isotope fractionation.

[0006] Therefore, there is an urgent need to establish a new technical method that comprehensively considers gas-water two-phase flow, effective stress evolution, multi-mechanism gas transport, and kinetic isotope fractionation effects, and applies it to the accurate evaluation of the dynamic production ratio of adsorbed / free gas in deep shale / coal gas wells during the production process. Summary of the Invention

[0007] Because the carbon isotopes of methane in deep shale / coal gas contain rich geochemical information, during gas-water two-phase flow, due to... 12 CH4 and 13 The difference in adsorption potential during the adsorption / desorption of CH4 leads to 13 CH4 relative 12 CH4 is preferentially adsorbed, causing isotope fractionation; during the diffusion process... 12 CH4 has a high diffusion coefficient and a faster diffusion rate, which can also cause isotope fractionation. Furthermore, the presence of the aqueous phase significantly affects isotope fractionation behavior by occupying pore space, altering the relative permeability of the gas phase, and generating mass transfer resistance. Therefore, the purpose of this invention is to propose a quantitative evaluation method for the dynamic production of EUR and free gas in deep shale or coalbed methane wells based on a gas-water two-phase flow isotope fractionation model. Based on production data from deep shale / coalbed methane wells and methane carbon isotope values ​​of wellhead gas, a reservoir-scale isotope fractionation model is established, considering the coupling of multiple gas transport regions (HF zone, SRV zone, and USRV zone), multiple mechanisms (viscous flow, Knudsen diffusion, and surface diffusion), and multiphase flow (gas-water two-phase flow). This model systematically considers... 12 CH4 and 13The differences in diffusion and adsorption / desorption behavior of CH4 are coupled with real gas effects and effective stress. By simultaneously performing historical fitting on data such as cumulative gas production, cumulative water production, and methane carbon isotope values, model parameters are determined. Then, forward modeling is used to calculate the dynamic production ratio of adsorbed gas / free gas during the production process and the 20-year EUR, ultimately achieving production prediction and quantitative evaluation of the gas production ratio in deep shale / coal gas wells.

[0008] The technical solution provided by this invention is: a quantitative evaluation method for shale gas and coal-fired gas production based on a gas-water two-phase flow isotopic fractionation model, comprising the following steps:

[0009] (1) Collect basic data of gas wells: Collect basic geological and engineering data of target deep shale or coal gas wells, including reservoir basic parameters, fracturing parameters, production dynamic data and wellhead gas isotope data;

[0010] (2) Establish a multi-zone geometric model for gas wells: establish a segmented fracture network geometric model for horizontal wells and a multi-zone composite geometric model for vertical wells; based on the fracturing and reservoir heterogeneity, divide shale or coal reservoirs into three flow zones: the hydraulic fracturing high-permeability zone (HF zone), the reservoir stimulation volume zone (SRV zone), and the unstimulated reservoir zone (USRV zone);

[0011] (3) Establish the governing equations for carbon isotope fractionation in gas-water two-phase flow, i.e., the GWF-CIF model: Based on mass conservation, momentum conservation, and the equation of state, establish the governing equations considering... 12 CH4 and 13 The governing equations for the carbon isotope fractionation of CH4-differential gas-liquid two-phase flow;

[0012] (4) Coupled with real gas effects: Considering the effects of temperature and pressure on the compressibility factor Z of methane gas g Density ρ g and viscosity μ g The impact;

[0013] (5) The effect of coupled effective stress evolution on reservoir properties: As gas wells produce, the pore pressure decreases, leading to an increase in effective stress, which in turn causes a decrease in porosity and permeability. An effective stress model is established.

[0014] (6) Establish a multi-mechanism gas transport model;

[0015] (7) Establish a relative permeability model of air and water;

[0016] (8) Establish the relationship between capillary pressure and saturation;

[0017] (9) Considering the critical desorption pressure: The desorption of adsorbed gas is controlled by the reservoir pressure; when the reservoir pressure is higher than the critical desorption pressure, the adsorbed gas remains stable and desorption will not occur. Desorption will only begin when the reservoir pressure drops below the critical desorption pressure.

[0018] (10) Set the initial conditions for the model;

[0019] (11) Set the boundary conditions for the model;

[0020] (12) Numerical solution of the governing equations; import the geometric model, governing equations, variables, initial conditions and boundary conditions established above into numerical simulation software for solution;

[0021] (13) Calculate production dynamic parameters and isotope values: Based on the pressure field obtained by the solution, calculate the production dynamic parameters by volume integration and mass conservation;

[0022] (14) Construct the objective function for historical fitting: The cumulative gas production calculated by the model in step (13) is used to perform historical fitting. Cumulative water production , and carbon isotope values ​​of methane By comparing the data with the field measurement data, a multi-objective optimization function is constructed;

[0023] (15) Verify the quality of historical fitting: Substitute the optimized parameters into the model and plot the fitting curve and the actual data comparison graph;

[0024] (16) Predicting the full life cycle production capacity and EUR of gas wells: Based on the optimal parameters determined by historical fitting, the model calculation time is extended to the economic limit of gas wells to predict the production dynamics of the entire life cycle.

[0025] (17) Calculate the dynamic production ratio of adsorbed gas and free gas;

[0026] (18) Identify the relationship between the isotope fractionation inflection point and the gas production mechanism conversion.

[0027] In step (2) above:

[0028] A. Establishing a geometric model of the fracture network in a horizontal well segment: For the complex fracture network formed by segmented horizontal well modification, a branch fracture model in a rectangular coordinate system is established. The wellbore in the model is parallel to the y-direction. The HF region mainly consists of two parts: the main fracture and secondary fractures. The main fracture extends perpendicularly to the wellbore along the x-direction, with a length of... Width is Several secondary cracks flank the main crack, simulating a complex fishbone or dendritic network of cracks. These secondary cracks are symmetrical about the main crack and have a length of [missing information]. Width is An SRV region was formed around the HF region, and the length of the SRV region in the x-direction is [missing information]. The length in the y direction is A USRV region is formed around the SRV region, consisting of three regions: the upper, lower, and left sides of the SRV region. The length of the upper and lower USRV regions in the x-direction is... The length in the y direction is The length of the USRV region to the left of the SRV region in the x-direction is... The length in the y direction is .

[0029] B. Establish a multi-zone composite geometric model for vertical wells: Establish a two-dimensional planar geometric model based on a rectangular coordinate system. With the wellbore as the center, divide the formation into three elliptical or rhomboid composite zones with different seepage characteristics: HF zone: The innermost rhomboid zone of the model, representing the range of the artificial main fracture with high conductivity; its half-length in the x-direction is x1, and its half-width in the y-direction is y1; SRV zone: The elliptical zone surrounding the HF zone, representing the secondary fracture network zone formed by fracturing; its half-length in the x-direction is x2, and its half-width in the y-direction is y2; USRV zone: The outermost elliptical zone of the model, representing the original formation unaffected by fracturing; its half-length in the x-direction is x3, and its half-width in the y-direction is y3.

[0030] In step (3) above:

[0031] This set of equations applies to the matrix regions of both the SRV and USRV regions:

[0032] (1);

[0033] For the partial derivative with respect to time;

[0034] Equation coefficients in equation (1) , , , , , and Defined as:

[0035] (2)

[0036] (3)

[0037] (4)

[0038] In equations (1) to (4), and They are respectively 12 CH4 and13 Partial pressure of CH4 in the gas phase, Pa; The pressure in the aqueous phase is Pa; and These are the saturation levels of the gas phase and the aqueous phase, respectively. ; For matrix porosity; and They are respectively 12 CH4 and 13 The effective diffusion coefficient of CH4, m 2 / s; and The relative permeability of the aqueous phase and the gas phase; m represents absolute penetration rate. 2 ; and The viscosity of the aqueous phase and the gas phase are respectively, in Pa·s; The density of the aqueous phase is kg / m³. 3 ; The density of the aqueous phase at the reference pressure is taken as 1000 kg / m³. 3 ; Let be the compressibility coefficient of water, taken as 3.84 × 10⁻⁶. -10 1 / MPa; Capillary inlet pressure, Pa; For aperture distribution parameters; and These are the residual water saturation and residual gas saturation, respectively. and They are respectively 12 CH4 and 13 The Langmuir adsorption constant of CH4, 1 / Pa, is related to the following: ,in , ; Density of rock, kg / m³ 3 ; Let m be the volume of Langmuir. 3 / t; Let K be the reservoir temperature. The volume occupied by a unit amount of gas under standard conditions is 22.4 L / mol.

[0039] For the artificial fracture region in the HF region, since the pore size is much larger than the molecular size, adsorption / desorption effects are not considered, let ,and 12 CH4 and 13 The diffusion coefficient of CH4 is the same. The governing equations simplify to:

[0040] (5)

[0041] Where the subscript F represents the HF region parameter, such as Porosity in the HF region.

[0042] In step (4) above:

[0043] (1) The gas compressibility factor was calculated using a polynomial fitting formula at different temperatures and pressures. :

[0044] (6)

[0045] In the formula, A function of temperature T:

[0046] (7)

[0047] (2) Gas density:

[0048] (8)

[0049] In the formula The molar mass of methane is 0.016 kg / mol. The gas constant is 8.314 J / mol·K;

[0050] (3) Gas viscosity is expressed using Lee's empirical formula:

[0051] (9)

[0052] In the formula, , and These are the parameters related to temperature and the molar mass of methane in the viscosity calculation formula. In step (5) above:

[0053] (1) Calculation of effective stress:

[0054] (10)

[0055] (11)

[0056] In the formula The effective stress is Pa; The overlying formation pressure is expressed in Pa. The rock correction factor is set to 1. Pore ​​pressure, Pa;

[0057] (2) Porosity evolution:

[0058] The matrix porosity under effective stress is expressed as:

[0059] (12)

[0060] middle To take into account the stress-sensitive matrix porosity; K' represents the initial matrix porosity; K' represents the rock bulk modulus, in Pa. This is the initial time. For any time;

[0061] The matrix porosity under the combined influence of the adsorption layer and effective stress is expressed as:

[0062] (13)

[0063] in The average pore radius of the matrix is ​​given in meters (m). Let be the average pore radius under the influence of the adsorption layer, in meters (m). The diameter of a methane molecule is 0.38 nm. and They are respectively 12 CH4 and 13 CH4 coverage.

[0064] In step (6) above:

[0065] (1) Establishment of a multi-mechanism gas transport model: In the matrix pores, methane transport involves multiple mechanisms such as viscous flow, Knudsen diffusion, and surface diffusion, which are determined by the Knudsen number Kn.

[0066] (14)

[0067] In the formula, Kn is the Knudsen number;

[0068] Combining the three transmission mechanisms with effective stress, 12 The apparent permeability of CH4 is:

[0069] (15)

[0070] In the formula, c is the mass balance constant, Pa; Langmuir pressure, MPa; m is the inherent permeability of the rock. 2 ;

[0071] In the formula, the first term inside the curly braces is the viscous flow contribution, the second term is the Knudsen diffusion contribution, and the third term is the surface diffusion contribution. The surface diffusion coefficient is related to the gas coverage. The relationship is:

[0072] (16)

[0073] in The surface diffusion coefficient at zero coverage For blocking parameters; 13 CH4 and 12 The ratio of the apparent diffusion coefficient of CH4 The range is 0.97 to 0.999;

[0074] In step (7) above:

[0075] (1) Establishment of the gas-water relative permeability model: The empirical formula for gas-water relative permeability applicable to coal / shale is adopted:

[0076] (17)

[0077] middle and These are the maximum relative permeability of the gas phase and the aqueous phase, respectively. , ; and The fitting index is set to 2; For effective water saturation, .

[0078] In step (8):

[0079] Capillary pressure The relationship with water saturation is as follows:

[0080] (18)

[0081] In the formula For the capillary inlet pressure, The aperture distribution parameter is taken as 0.5~2; Residual gas saturation; This represents the residual water saturation.

[0082] In step (9) mentioned above:

[0083] 12 CH4 and 13 The coverage of CH4 is as follows:

[0084] (19)

[0085] In the formula The critical desorption pressure is given in MPa.

[0086] In step (10) above:

[0087] (1) Setting initial conditions for the model: The specific initial conditions for each region are as follows:

[0088] (20)

[0089] in , middle These are the gas phases in the initial SRV region, USRV region, and HF region reservoirs, respectively. 12 Partial pressure of CH4, Pa; , middle These are the gas phases in the initial SRV region, USRV region, and HF region reservoirs, respectively. 13 Partial pressure of CH4, Pa; , middle These are the water phase pressures in the initial SRV, USRV, and HF reservoirs, respectively, in Pa; It is the initial reservoir pressure ( ), Pa; yes 13 CH4 and 12 The initial molar ratio of CH4; and These are the initial capillary pressures in the HF and matrix regions, respectively, in Pa; , and The value can be calculated based on the initial methane carbon isotope composition and the initial water saturation:

[0090] ;(twenty one)

[0091] in This is the initial carbon isotope value of methane; The carbon isotope value of the standard sample; Capillary inlet pressure, Pa; and These are the effective water saturation levels in the HF and matrix regions, respectively. and These are the initial water saturation levels in the HF and matrix regions, respectively. and These are the residual water saturation and residual gas saturation in the HF region, respectively. and These are the residual water saturation and residual gas saturation in the matrix region, respectively.

[0092] In step (11) above:

[0093] (1) Set the model boundary conditions. On the wellbore wall... or noodles Set production boundaries at this point:

[0094] ;(twenty two)

[0095] In the formula The radius of the horizontal or vertical well, in meters (m). It is an exponential function obtained by fitting measured bottom flow pressure data, Pa; It is the fitting coefficient of the exponential function; It is the pressure corresponding to constant pressure production in the production well, in Pa.

[0096] In step (13) above:

[0097] The cumulative gas production of the HF region, SRV region, USRV region, and all regions is given by the following formula:

[0098] (twenty three) ;

[0099] In the formula , and Porosity in the HF region, SRV region, and USRV region, respectively; and These represent the free HF region. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; and These represent free SRV regions. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; and These represent the free areas of the USRV region. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; and These represent the adsorption of SRV regions. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; and These represent the adsorption of USRV regions. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; For the total cumulative gas production across all regions, m 3 ; is the derivative within the corresponding region; h is the reservoir thickness, in meters;

[0100] The cumulative water production of the HF region, SRV region, USRV region, and all regions is calculated as follows:

[0101] (twenty four) ;

[0102] In the formula , , and The cumulative water production in m³ represents the total cumulative water production in the HF region, SRV region, USRV region, and all regions. 3 ; The density of water phase at atmospheric pressure is kg / m³. 3 ; The density of the aqueous phase is kg / m³. 3 ;

[0103] The carbon isotope value of methane in gas produced from deep shale / coal gas wells is given by the following formula:

[0104] (25).

[0105] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0106] (1) A novel isotope fractionation model applicable to gas-water two-phase flow is established: Existing isotope fractionation models mainly target single-phase gas flow and do not consider the influence of water phase on gas transport and isotope fractionation. This invention innovatively couples gas-water two-phase flow theory with isotope fractionation theory, systematically considering the influence of water phase occupying pore space and generating mass transfer resistance on... 12 CH4 and 13 The influence of differential CH4 migration is more consistent with the actual production conditions of deep gas wells.

[0107] (2) Comprehensive coupling of multi-physics fields and multi-scale processes: The GWF-CIF model established in this invention comprehensively considers complex physical processes such as effective stress evolution, real gas effects, multi-mechanism gas transport (viscous flow, Knudsen diffusion, surface diffusion), the occupation of pore space by adsorption layer, relative gas-water permeability and capillary pressure. It has a complete theoretical framework, clear physical mechanisms and high prediction accuracy.

[0108] (3) Only data that is easily obtained on-site is required, without the need for complex experiments: Traditional methods require conducting full life cycle simulation experiments or complex tests such as mercury intrusion porosimetry and nuclear magnetic resonance. This invention only requires collecting dynamic production data (gas production, water production, bottom hole flowing pressure) and periodically collecting wellhead gas samples to test isotopes. Data acquisition is simple and inexpensive, making it suitable for large-scale on-site applications.

[0109] (4) Simultaneously achieve EUR prediction and quantitative evaluation of adsorbed / free gas: Through a unified model, it is possible to predict the EUR of the gas well throughout its entire life cycle and to quantitatively evaluate the dynamic production ratio of adsorbed gas and free gas, providing a dual basis for reserve assessment and development scheme optimization.

[0110] (5) Using isotope signals to guide the timing of production enhancement measures: The correspondence between the turning point of methane carbon isotope fractionation and the transformation of gas production mechanism has been innovatively established. By monitoring the changing trend of wellhead gas c, the current production stage can be judged in real time, and the best time to implement production enhancement measures such as CO2 injection, casing pressure reduction, and secondary fracturing can be scientifically determined to avoid blind operation.

[0111] (6) Wide range of applications and strong promotion: This method is applicable to all kinds of deep shale gas wells and coal gas wells. Whether it is a vertical well or a horizontal well, a fractured well or an unfractured well, as long as there is basic production data and isotope monitoring data, this method can be used to evaluate EUR and adsorbed / free gas. It has strong practicality and promotion value. Attached Figure Description

[0112] Figure 1 This is a schematic diagram of the multi-region geometric model of the horizontal well of the present invention.

[0113] Figure 2 This is a schematic diagram of the geometric model of a vertical well with multiple regions according to the present invention.

[0114] Figure 3 It is a comparison chart of the fitted curves and measured data of gas production, water production, and methane carbon isotope values.

[0115] Figure 4 This is a graph showing the EUR prediction results for gas wells.

[0116] Figure 5 This is a graph showing the changes in daily gas production and daily water production over time.

[0117] Figure 6 This is a EUR sensitivity analysis chart for gas wells.

[0118] Figure 7 yes and Evolution curves of the production ratio of the two gases. Detailed Implementation

[0119] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0120] Example:

[0121] Step 1: Collect basic gas well data. Collect basic geological and engineering data for the target deep shale / coal gas well, as shown in Tables 1 and 2, including:

[0122] (1) Basic reservoir parameters: Target layer burial depth (m), initial reservoir pressure (MPa), formation temperature T (°C), coal seam / shale thickness h (m), overlying formation pressure (MPa), rock density (kg / m 3 ), rock bulk modulus (GPa).

[0123] (2) Fracturing parameters: For horizontal wells, the collection wellbore radius (m), horizontal section length (m), number of fracturing sections, and number of clusters per section; determine the half-fracture length of the hydraulic fracturing zone based on microseismic monitoring or post-fracturing pressure drop analysis. For vertical wells, collect parameters such as the half-fracture length and fracture height.

[0124] (3) Production dynamic data: Continuously monitor and record production time t (day) and cumulative gas production. (m 3 ), cumulative water production (m 3 Bottom hole flowing pressure (MPa) or pressure (MPa). It is recommended that the monitoring period cover at least 6 months after commissioning, with data collection frequency of daily or weekly.

[0125] (4) Wellhead gas isotope data: Stainless steel or glass sampling bottles were used to periodically collect wellhead gas samples, and the carbon isotope values ​​of methane were determined by gas chromatography-isotope ratio mass spectrometry (GC-IRMS). (‰, relative to PDB standard). The recommended sampling frequency is: once a week in the initial production phase (first 3 months), once every 2 weeks in the middle phase (3-12 months), and once a month in the later phase. Each sampling should record the corresponding production time, gas production, and bottom hole flowing pressure.

[0126] Table 1 Basic Data of Gas Wells

[0127]

[0128] Table 2 Basic Data of Gas Wells

[0129]

[0130] Step 2: Establish a multi-zone geometric model of the gas well. Based on the fracturing stimulation and reservoir heterogeneity, the shale / coal reservoir is divided into three flow zones:

[0131] High-permeability zone (HF zone) in hydraulic fracturing: This zone includes the main fracture formed by artificial fracturing and the high-conductivity channels filled with proppant. The permeability in this zone is high, reaching up to 10⁻⁶. -12 -10 -11 m 2 The main process involves two-phase Darcy flow of gas and water, and the adsorption / desorption effect is not considered.

[0132] Reservoir Stimulated Volume (SRV) Zone: This zone is where hydraulic fracturing induces secondary and microfractures, improving reservoir properties. It contains both matrix porosity and secondary fractures, and gas migration involves multiple mechanisms, including viscous flow, Knudsen diffusion, and surface diffusion, while also considering adsorption / desorption effects.

[0133] Unmodified reservoir zone (USRV zone): The pristine reservoir area far from the wellbore, unaffected by fracturing. The gas migration mechanism in this zone is similar to that in the SRV zone, but with weaker diffusion capacity.

[0134] 1. Establish a geometric model of the fracture network in a horizontal well segment: For the complex fracture network formed by segmented horizontal well modification, a branch fracture model in a rectangular coordinate system is established. The wellbore in the model is parallel to the y-direction. The HF region mainly consists of two parts: the main fracture and secondary fractures. The main fracture extends perpendicularly to the wellbore along the x-direction, with a length of... Width is Several secondary cracks flank the main crack, simulating a complex fishbone or dendritic network of cracks. These secondary cracks are symmetrical about the main crack and have a length of [missing information]. Width is An SRV region was formed around the HF region, and the length of the SRV region in the x-direction is [missing information]. The length in the y direction is A USRV region is formed around the SRV region, consisting of three regions: the upper, lower, and left sides of the SRV region. The length of the upper and lower USRV regions in the x-direction is... The length in the y direction is The length of the USRV region to the left of the SRV region in the x-direction is... The length in the y direction is .

[0135] 2. Establish a multi-zone composite geometric model for vertical wells: Establish a two-dimensional planar geometric model based on a rectangular coordinate system, as shown in the attached figure. Figure 2As shown, with the wellbore as the center, the formation is divided into three elliptical / rhomboid composite regions with different seepage characteristics: HF region (artificial fracture core region): The innermost rhomboid region of the model, representing the reach of the highly conductive artificial main fracture. Its half-length in the x-direction is x1, and its half-width in the y-direction is y1. SRV region (reservoir stimulation volume region): The elliptical region surrounding the HF region, representing the secondary fracture network formed through fracturing. Its half-length in the x-direction is x2, and its half-width in the y-direction is y2. USRV region (unstimulated original reservoir region): The outermost elliptical region of the model, representing the original formation unaffected by fracturing. Its half-length in the x-direction is x3, and its half-width in the y-direction is y3.

[0136] Step 3: Establish the governing equations for carbon isotope fractionation in a gas-water two-phase flow (GWF-CIF model). Based on mass conservation, momentum conservation, and the equation of state, establish the governing equations considering... 12 CH4 and 13 The governing equations for the carbon isotope fractionation of CH4-differential gas-liquid two-phase flow are applicable to the matrix regions of the SRV and USRV regions.

[0137] (1)

[0138] For the partial derivative with respect to time.

[0139] Equation coefficients in equation (1) , , , , , and Defined as:

[0140] (2)

[0141] (3)

[0142] (4)

[0143] In equations (1) to (4), and They are respectively 12 CH4 and 13 Partial pressure of CH4 in the gas phase, Pa; The pressure in the aqueous phase is Pa; and These are the saturation levels of the gas phase and the aqueous phase, respectively. ; For matrix porosity; and They are respectively 12 CH4 and13 The effective diffusion coefficient of CH4, m 2 / s; and The relative permeability of the aqueous phase and the gas phase; m represents absolute penetration rate. 2 ; and The viscosity of the aqueous phase and the gas phase are respectively, in Pa·s; The density of the aqueous phase is kg / m³. 3 ; The density of the aqueous phase at the reference pressure is taken as 1000 kg / m³. 3 ; Let be the compressibility coefficient of water, taken as 3.84 × 10⁻⁶. -10 1 / MPa; Capillary inlet pressure, Pa; For aperture distribution parameters; and These are the residual water saturation and residual gas saturation, respectively. and They are respectively 12 CH4 and 13 The Langmuir adsorption constant of CH4, 1 / Pa, is related to the following: ,in , ; Density of rock, kg / m³ 3 ; Let m be the volume of Langmuir. 3 / t; Let K be the reservoir temperature. This is the volume occupied by one mole of gas under standard conditions, 22.4 L / mol.

[0144] For the artificial fracture region in the HF region, since the pore size is much larger than the molecular size, adsorption / desorption effects are not considered, let ,and 12 CH4 and 13 The diffusion coefficient of CH4 is the same. The governing equations simplify to:

[0145] (5)

[0146] Where the subscript F represents the HF region parameter, such as Porosity in the HF region.

[0147] Step 4: Couple with real gas effects. Consider the effects of temperature and pressure on the compressibility factor of methane gas. ,density and viscosity The impact.

[0148] 1. The gas compressibility factor was calculated using a polynomial fitting formula at different temperatures and pressures. :

[0149] (6)

[0150] In the formula, A function of temperature T:

[0151] (7)

[0152] 2. Gas density:

[0153] (8)

[0154] In the formula The molar mass of methane is 0.016 kg / mol. The gas constant is 8.314 J / mol·K.

[0155] 3. Gas viscosity is calculated using Lee's empirical formula:

[0156] (9)

[0157] In the formula, , and These are the parameters related to temperature and the molar mass of methane in the viscosity calculation formula.

[0158] Step 5: Couple the impact of effective stress evolution on reservoir properties. As gas wells produce, the decrease in pore pressure leads to an increase in effective stress, causing a decrease in porosity and permeability. Establish an effective stress model:

[0159] (1) Calculation of effective stress:

[0160] (10)

[0161] (11)

[0162] In the formula The effective stress is Pa; The overlying formation pressure is expressed in Pa. The rock correction factor is set to 1. ρ represents the pore pressure, in Pa.

[0163] (2) Porosity evolution:

[0164] The matrix porosity under effective stress is expressed as:

[0165] (12)

[0166] In the formula To take into account the stress-sensitive matrix porosity; K' represents the initial matrix porosity; K' represents the rock bulk modulus, in Pa. This is the initial time. For any time.

[0167] The matrix porosity under the combined influence of the adsorption layer and effective stress is expressed as:

[0168] (13)

[0169] in The average pore radius of the matrix is ​​given in meters (m). Let be the average pore radius under the influence of the adsorption layer, in meters (m). The diameter of a methane molecule is 0.38 nm. and They are respectively 12 CH4 and 13 CH4 coverage.

[0170] Step Six: Establish a multi-mechanism gas transport model. In the matrix pores, methane transport involves multiple mechanisms, including viscous flow, Knudsen diffusion, and surface diffusion. These are determined using the Knudsen number (Kn).

[0171] (14)

[0172] In the formula, Kn is the Knudsen number.

[0173] Combining the three transmission mechanisms with effective stress, 12 The apparent permeability of CH4 is:

[0174] (15)

[0175] In the formula, c is the mass balance constant, Pa; Langmuir pressure, MPa; m is the inherent permeability of the rock. 2 ;

[0176] In the formula, the first term inside the curly braces is the viscous flow contribution, the second term is the Knudsen diffusion contribution, and the third term is the surface diffusion contribution. The surface diffusion coefficient is related to the gas coverage. The relationship is:

[0177] (16)

[0178] in The surface diffusion coefficient at zero coverage For blocking parameters; 13 CH4 and 12 The ratio of the apparent diffusion coefficient of CH4 The range is 0.97 to 0.999.

[0179] Step 7: Establish a gas-water relative permeability model. Use an empirical formula for gas-water relative permeability applicable to coal / shale:

[0180] (17)

[0181] In the formula and These are the maximum relative permeability of the gas phase and the aqueous phase, respectively. , ; and The fitting index is set to 2; For effective water saturation, .

[0182] Step 8: Establish the relationship between capillary pressure and saturation. Capillary pressure The relationship with water saturation is as follows:

[0183] (18)

[0184] In the formula For the capillary inlet pressure, The aperture distribution parameter is taken as 0.5~2; Residual gas saturation; This represents the residual water saturation.

[0185] Step Nine: Consider the critical desorption pressure. The desorption of adsorbed gas is controlled by the reservoir pressure. When the reservoir pressure is higher than the critical desorption pressure ( At this pressure, the adsorbed gas remains stable and desorption does not occur. Desorption only begins when the reservoir pressure drops below the critical desorption pressure.

[0186] (19)

[0187] In the formula The critical desorption pressure is given in MPa.

[0188] Step 10: Set the initial conditions for the model. The specific initial conditions for each region are as follows:

[0189] (20)

[0190] in , middle These are the gas phases in the initial SRV region, USRV region, and HF region reservoirs, respectively. 12 Partial pressure of CH4, Pa; , middle These are the gas phases in the initial SRV region, USRV region, and HF region reservoirs, respectively. 13 Partial pressure of CH4, Pa; , middle These are the water phase pressures in the initial SRV, USRV, and HF reservoirs, respectively, in Pa; It is the initial reservoir pressure ( ), Pa; yes 13 CH4 and 12 The initial molar ratio of CH4; and These are the initial capillary pressures in the HF and matrix regions, respectively, in Pa; , and The value can be calculated based on the initial methane carbon isotope composition and the initial water saturation:

[0191] ;(twenty one)

[0192] in These are the initial carbon isotope values ​​of methane; The carbon isotope value of the standard sample; Capillary inlet pressure, Pa; and These are the effective water saturation levels in the HF and matrix regions, respectively. and These are the initial water saturation levels in the HF and matrix regions, respectively. and These are the residual water saturation and residual gas saturation in the HF region, respectively. and These are the residual water saturation and residual gas saturation in the matrix region, respectively.

[0193] Step 11: Set the model boundary conditions. On the wellbore wall... or noodles Set production boundaries at this point:

[0194] ;(twenty two)

[0195] In the formula The radius of the horizontal or vertical well, in meters (m). It is an exponential function obtained by fitting measured bottom flow pressure data, Pa; It is the fitting coefficient of the exponential function; It is the pressure corresponding to constant pressure production in the production well, in Pa.

[0196] Step 12: Numerical solution of the governing equations. Import the established geometric model, governing equations (1)-(5), variables (6)-(19) in the equations, initial conditions (20) and (21) and boundary conditions (22) into numerical simulation software (such as COMSOL Multiphysics or MATLAB PDE tool) for solution:

[0197] (1) Spatial discretization of the governing equations is performed using the finite element method (FEM) or the finite difference method (FDM).

[0198] (2) Use an implicit time stepping scheme (such as the backward Euler method or the Crank-Nicolson method) for time discretization. The time step Δt is adaptively adjusted according to the convergence. Initially, it can be 0.01-0.1 days, and later it can be increased to 1-10 days.

[0199] (3) The Newton-Raphson iterative method is used to solve the nonlinear equation system. The convergence criterion is that the relative residual is <10. -6 .

[0200] (4) The pressure field distribution at each time and spatial location was calculated: , and .

[0201] Step Thirteen: Calculate production dynamic parameters and isotope values. Based on the obtained pressure field, calculate the production dynamic parameters through volume integration and mass conservation. The cumulative gas production of the HF region, SRV region, USRV region, and all regions is given by the following formula:

[0202] (twenty three);

[0203] In the formula , and Porosity in the HF region, SRV region, and USRV region, respectively; and These represent the free HF region. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; and These represent free SRV regions. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; and These represent the free areas of the USRV region. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; and These represent the adsorption of SRV regions. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; and These represent the adsorption of USRV regions. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; For the total cumulative gas production across all regions, m 3 ; is the derivative within the corresponding region; h is the reservoir thickness, in meters;

[0204] The cumulative water production of the HF region, SRV region, USRV region, and all regions is calculated as follows:

[0205] (twenty four) ;

[0206] In the formula , , and The cumulative water production in m³ represents the total cumulative water production in the HF region, SRV region, USRV region, and all regions. 3 ; The density of water phase at atmospheric pressure is kg / m³. 3 ; The density of the aqueous phase is kg / m³. 3 ;

[0207] The carbon isotope value of methane in gas produced from deep shale / coal gas wells is given by the following formula:

[0208] (25);

[0209] The results are shown in Table 3.

[0210] Table 3 Dynamic parameters and isotope values

[0211]

[0212] Step Fourteen: Construct the objective function and perform historical data fitting. The cumulative gas production calculated in Step Thirteen will be used to model this process. Cumulative water production , and carbon isotope values ​​of methane By comparing the data with the field measurement data, a multi-objective optimization function is constructed.

[0213] (26)

[0214] In the formula: For multi-parameter optimization objectives; , , The weighting coefficients for each item can be set according to the reliability of the data and the focus of the fit. It is recommended... , , ; , , These represent the number of observation points for each type of data; , and These represent the model-calculated values ​​of cumulative gas production, cumulative water production, and methane carbon isotope value at any given time. , and These represent the field-observed values ​​of cumulative gas production, cumulative water production, and methane carbon isotope values ​​at any given time. An optimization algorithm (such as the BobyQA algorithm, genetic algorithm, or particle swarm optimization algorithm) is used to solve the problem. The minimum value determines the optimal values ​​for the following undetermined parameters:

[0215] Table 4 Optimized Data Results

[0216]

[0217] During the optimization process, some parameters can be fixed based on core test or well logging interpretation results, reducing the number of optimization variables and improving the stability of the fit.

[0218] Step 15: Verify the quality of historical fitting. Substitute the optimized parameters into the model, and calculate the cumulative gas production, cumulative water production, and methane carbon isotope value calculated by the model using formulas (23), (24), and (25). Combine the field monitoring data to draw a comparison chart of the fitting curve and the measured data, such as... Figure 3 As shown. If the average fit R 2 If the value is greater than 0.8, the fitting effect is considered good, and the next steps of production prediction and gas production ratio evaluation can be carried out.

[0219] (1) Cumulative gas production fitting curve: The vertical axis represents the cumulative gas production (m³). 3 The horizontal axis represents production time t (day), and the calculated and measured values ​​are overlaid to calculate the goodness of fit R. 2 Requires R 2 >0.85.

[0220] (2) Cumulative water production fitting curve: The vertical axis represents the cumulative water production (m³). 3The x-axis represents production time t (days), and the goodness-of-fit R is calculated. 2 Requires R 2 >0.85.

[0221] (3) Methane carbon isotope fitting curve: The vertical axis represents the methane carbon isotope value in the produced gas (‰), and the horizontal axis represents the production time t (day). The calculated values ​​from the model and the measured values ​​are superimposed to display the model calculation and the goodness of fit R. 2 Requires R 2 >0.8.

[0222] If the fitting quality does not meet the requirements, the parameter range or weighting coefficients need to be adjusted. Repeat step fourteen until a satisfactory fit is obtained.

[0223] Step Sixteen: Predict the gas well's full lifecycle production capacity and EUR. Based on the optimal parameters determined by historical fitting, extend the model calculation time to the gas well's economic limit (e.g., 20-30 years) to predict the full lifecycle production dynamics:

[0224] (1) Predict the cumulative gas production over 20 years (or 30 years) (20yr) is the EUR (final recoverable reserves) of the gas well. Figure 4 The image shows the EUR (Estimated Ultimate Recovery) prediction results. By fitting measured data, the recoverable reservoirs of future gas wells are predicted.

[0225] (2) Predicting daily gas production (t) and daily water production (t) The curve of change over time can be used to identify the duration of the steady-production period, the declining production period, and the final production period, such as Figure 5 As shown. (Through) Figure 5 We know that the production stage of a gas well can be determined by combining the methane carbon isotope values ​​during the gas well production process.

[0226] (3) Predict the long-term evolution trend of methane carbon isotope values ​​and identify the three stages of isotope fractionation:

[0227] (A) Stage I (early stable period): Rapid production of fracture gas, with relatively stable carbon isotope values ​​of methane;

[0228] (B) Phase II (Medium-term decline): Matrix free gas dominates production, and the carbon isotope value of methane gradually decreases;

[0229] (C) Stage III (late rising phase): Desorption of adsorbed gas dominates the output, and the carbon isotope value of methane gradually increases.

[0230] (4) Plot a sensitivity analysis diagram for EUR to assess the impact of key parameters (such as Langmuir volume, critical desorption pressure, and initial water saturation) on EUR. Figure 6 As shown. Figure 6 As shown, sensitivity analysis can clarify the main controlling factors for EUR in deep / shale gas wells.

[0231] Step 17: Calculate the dynamic production ratio of adsorbed gas and free gas. Based on the prediction results of Step 16, quantitatively evaluate the production contribution of adsorbed gas and free gas:

[0232] 1. Cumulative gas production ratio:

[0233] (27)

[0234] In the formula Represents the proportion of free gas in the cumulative gas production at any given time; This represents the proportion of adsorbed gas in the cumulative produced gas at any given time. and Representing the cumulative gas production of free gas and adsorbed gas in all regions at any given time, m 3 .

[0235] 2. Instantaneous gas production ratio:

[0236] (28)

[0237] In the formula Represents the instantaneous proportion of free gas. This represents the instantaneous proportion of adsorbed gas. and Represent the gas production rates of free gas and adsorbed gas in all regions at any given time, m 3 / s.

[0238] 3. Plot the output ratio evolution curve, such as... Figure 7 As shown. Using Figure 7 We can determine how many years free gas dominates the gas production rate, how many years it takes for free gas to begin to replace free gas as the dominant gas; and how many years it takes for the contribution of adsorbed gas to exceed that of free gas in terms of total gas output.

[0239] Plot a graph with production time t as the x-axis. and The curves showing changes over time can be used to identify the transition point from free gas dominance to adsorbed gas dominance.

[0240] Plot a graph with production time t as the x-axis. and The deposition curves visually demonstrate the contribution ratio of the two gases.

[0241] Step 18: Identify the relationship between isotopic fractionation inflection points and the transition of gas production mechanisms. Analyze the methane carbon isotope value curve and the production ratio curve. Correspondence: Combining Figure 6 and Figure 3 The third figure in the diagram is used to analyze the correspondence between the isotope and gas production ratio curves:

[0242] 1. Determine the two key inflection points of the methane carbon isotope value curve:

[0243] (1) t1: The moment when the carbon isotope value of methane changes from stable to decreasing during the transition from stage I to stage II;

[0244] (2) t2: The moment when the methane carbon isotope value changes from decreasing to increasing during the transition from stage II to stage III (minimum point);

[0245] 2. Analyze the gas generation mechanism at times t1 and t2:

[0246] (1) At time t1, compare the gas production contributions of the HF region, SRV region and USRV region to identify the moment when the matrix gas begins to be produced in large quantities.

[0247] (2) At time t2, compare and At time t2, when the isotopic minimum occurs, it is the critical period for the conversion of free gas into adsorbed gas.

[0248] 3. Establish the correspondence between the inflection point of isotope fractionation and the timing of production enhancement measures:

[0249] (1) If the current stage is at the end of stage I or the beginning of stage II, it means that the production of fracture gas is nearing its end. You can consider reducing the casing pressure or adjusting the working system to slow down the decline.

[0250] (2) If the current stage is transitioning from stage II to stage III (methane carbon isotope value is close to the minimum value), it indicates that the degree of free gas recovery is relatively high, which is a favorable time to implement CO2 displacement or secondary fracturing.

[0251] (3) If the current stage has been entered, it means that the adsorbed gas has become the main contributor, and the desorption conditions should be optimized (such as further reducing the pressure and increasing the temperature).

Claims

1. A quantitative evaluation method for shale gas and coal-fired gas production based on a gas-water two-phase flow isotopic fractionation model, comprising the following steps: (1) Collect basic data of gas wells: Collect basic geological and engineering data of target deep shale or coal gas wells, including reservoir basic parameters, fracturing parameters, production dynamic data and wellhead gas isotope data; (2) Establish a multi-zone geometric model for gas wells: establish a segmented fracture network geometric model for horizontal wells and a multi-zone composite geometric model for vertical wells; based on the fracturing and reservoir heterogeneity, divide shale or coal reservoirs into three flow zones: the hydraulic fracturing high-permeability zone (HF zone), the reservoir stimulation volume zone (SRV zone), and the unstimulated reservoir zone (USRV zone); (3) Establish the governing equations for carbon isotope fractionation in gas-water two-phase flow, i.e., the GWF-CIF model: Based on mass conservation, momentum conservation, and the equation of state, establish the governing equations considering... 12 CH4 and 13 The governing equations for the carbon isotope fractionation of CH4-differential gas-liquid two-phase flow; This set of equations applies to the matrix regions of both the SRV and USRV regions: (1)； For the partial derivative with respect to time; Equation coefficients in equation (1) , , , , , and Defined as: (2)； (3)； (4)； In equations (1) to (4), and They are respectively 12 CH4 and 13 Partial pressure of CH4 in the gas phase, Pa; The pressure in the aqueous phase is Pa; and These are the saturation levels of the gas phase and the aqueous phase, respectively. ; For matrix porosity; and They are respectively 12 CH4 and 13 The effective diffusion coefficient of CH4, m 2 / s; and The relative permeability of the aqueous phase and the gas phase; m represents absolute penetration rate. 2 ; and The viscosity of the aqueous phase and the gas phase are respectively, in Pa·s; The density of the aqueous phase is kg / m³. 3 ; The density of the aqueous phase at the reference pressure is taken as 1000 kg / m³. 3 ; Let be the compressibility coefficient of water, taken as 3.84 × 10⁻⁶. -10 1 / MPa; Capillary inlet pressure, Pa; For aperture distribution parameters; and These are the residual water saturation and residual gas saturation, respectively. and They are respectively 12 CH4 and 13 The Langmuir adsorption constant of CH4, 1 / Pa, is related to the following: ,in , ; Density of rock, kg / m³ 3 ; Let m be the volume of Langmuir. 3 / t; Let K be the reservoir temperature. The volume occupied by a unit amount of gas under standard conditions is 22.4 L / mol. It is the gas constant; For the artificial crack zone in the HF region, let ,and 12 CH4 and 13 The diffusion coefficient of CH4 is the same. The governing equations simplify to: (5)； The subscript F indicates the HF region parameter. Porosity in the HF region; (4) Coupled with real gas effects: Considering the effect of temperature and pressure on the compressibility factor of methane gas ,density and viscosity The impact; (5) The effect of coupled effective stress evolution on reservoir properties: As gas wells produce, the pore pressure decreases, leading to an increase in effective stress, which in turn causes a decrease in porosity and permeability. An effective stress model is established. (6) Establish a multi-mechanism gas transport model; (7) Establish a relative permeability model of air and water; (8) Establish the relationship between capillary pressure and saturation; (9) Consider the critical desorption pressure: the desorption of adsorbed gas is controlled by the reservoir pressure; when the reservoir pressure is higher than the critical desorption pressure, the adsorbed gas remains stable and will not desorb. Desorption will only begin when the reservoir pressure drops below the critical desorption pressure. (10) Set the initial conditions for the model; (11) Set the boundary conditions for the model; (12) Numerical solution of the governing equations; import the geometric model, governing equations, variables, initial conditions and boundary conditions established above into numerical simulation software for solution; (13) Calculate production dynamic parameters and isotope values: Based on the pressure field obtained by the solution, calculate the production dynamic parameters by volume integration and mass conservation; (14) Construct the objective function for historical fitting: The cumulative gas production calculated by the model in step (13) is used to perform historical fitting. Cumulative water production , and carbon isotope values ​​of methane By comparing the data with the field measurement data, a multi-objective optimization function is constructed; (15) Verify the quality of historical fitting: Substitute the optimized parameters into the model and plot the fitting curve and the actual data comparison graph; (16) Predicting the full life cycle production capacity and EUR of gas wells: Based on the optimal parameters determined by historical fitting, the model calculation time is extended to the economic limit of gas wells to predict the production dynamics of the entire life cycle. (17) Calculate the dynamic production ratio of adsorbed gas and free gas; (18) Identify the relationship between the isotope fractionation inflection point and the gas production mechanism conversion.

2. The quantitative evaluation method for shale gas and coal-fired gas production based on a gas-water two-phase flow isotopic fractionation model according to claim 1, characterized in that: In step (2) mentioned above: A. Establishing a geometric model of the fracture network in a horizontal well segment: For the complex fracture network formed by segmented horizontal well modification, a branch fracture model in a rectangular coordinate system is established. The model wellbore is parallel to the y-direction. The HF region consists of a main fracture and secondary fractures. The main fracture extends perpendicularly to the wellbore along the x-direction, with a length of... Width is Several secondary cracks flank the main crack, simulating a complex fishbone or dendritic network of cracks. These secondary cracks are symmetrical about the main crack and have a length of [missing information]. Width is An SRV region was formed around the HF region, and the length of the SRV region in the x-direction is [missing information]. The length in the y direction is A USRV region is formed around the SRV region, consisting of three regions: the upper, lower, and left sides of the SRV region. The length of the upper and lower USRV regions in the x-direction is... The length in the y direction is The length of the USRV region to the left of the SRV region in the x-direction is... The length in the y direction is ; B. Establish a multi-zone composite geometric model for vertical wells: Establish a two-dimensional planar geometric model based on a rectangular coordinate system. With the wellbore as the center, divide the formation into three elliptical or rhomboid composite zones with different seepage characteristics: HF zone: The rhomboid zone located at the innermost part of the model, representing the range of the artificial main fracture with high conductivity. Its half-length in the x-direction is x1, and its half-width in the y-direction is y1; SRV zone: an elliptical region surrounding the HF zone, representing the secondary fracture network formed by fracturing; its half-length in the x-direction is x2, and its half-width in the y-direction is y2; USRV zone: the outermost elliptical region of the model, representing the original strata unaffected by fracturing. Its half-length in the x-direction is x3, and its half-width in the y-direction is y3.

3. The quantitative evaluation method for shale gas and coal-fired gas production based on a gas-water two-phase flow isotopic fractionation model according to claim 1, characterized in that: In step (4) mentioned above: (1) The gas compressibility factor was calculated using a polynomial fitting formula at different temperatures and pressures. : (6)； In the formula, A function of temperature T: (7) ; (2) Gas density: (8) ; In the formula The molar mass of methane is 0.016 kg / mol. The gas constant is 8.314 J / mol·K; (3) Gas viscosity is expressed using Lee's empirical formula: (9)； In the formula, , and These are the parameters related to temperature and the molar mass of methane in the viscosity calculation formula.

4. The quantitative evaluation method for shale gas and coal-fired gas production based on a gas-water two-phase flow isotopic fractionation model according to claim 1, characterized in that: In step (5) mentioned above: (1) Calculation of effective stress: (10)； (11)； In the formula The effective stress is Pa; The overlying formation pressure is expressed in Pa. The rock correction factor is set to 1. Pore ​​pressure, Pa; (2) Porosity evolution: The matrix porosity under effective stress is expressed as: (12)； In the formula To take into account the stress-sensitive matrix porosity; K' represents the initial matrix porosity; K' represents the rock bulk modulus, in Pa. This is the initial time. For any time; The matrix porosity under the combined influence of the adsorption layer and effective stress is expressed as: (13)； in The average pore radius of the matrix is ​​given in meters (m). Let be the average pore radius under the influence of the adsorption layer, in meters (m). The diameter of a methane molecule is 0.38 nm. and They are respectively 12 CH4 and 13 CH4 coverage.

5. The quantitative evaluation method for shale gas and coal-fired gas production based on a gas-water two-phase flow isotopic fractionation model according to claim 1, characterized in that: In steps (6) and (7) mentioned above: (1) Establishment of a multi-mechanism gas transport model: In the matrix pores, methane transport involves multiple mechanisms, including viscous flow, Knudsen diffusion, and surface diffusion, which are determined by the Knudsen number Kn. (14)； In the formula, Kn is the Knudsen number; Combining the three transmission mechanisms with effective stress, 12 The apparent permeability of CH4 is: （15）； In the formula, c is the mass balance constant, Pa; Langmuir pressure, MPa; m is the inherent permeability of the rock. 2 ; In the formula, the first term inside the curly braces is the viscous flow contribution, the second term is the Knudsen diffusion contribution, and the third term is the surface diffusion contribution. The surface diffusion coefficient is related to the gas coverage. The relationship is: (16)； in The surface diffusion coefficient at zero coverage For blocking parameters; 13 CH4 and 12 The ratio of the apparent diffusion coefficient of CH4 The range is 0.97 to 0.999; (2) Establishment of the gas-water relative permeability model: An empirical formula for gas-water relative permeability applicable to coal / shale is adopted: (17)； In the formula and These are the maximum relative permeability of the gas phase and the aqueous phase, respectively. , ; and The fitting index is set to 2; For effective water saturation, .

6. The quantitative evaluation method for shale gas and coal-fired gas production based on a gas-water two-phase flow isotopic fractionation model according to claim 1, characterized in that: As mentioned above: in step (8) Capillary pressure The relationship with water saturation is as follows: (18)； In the formula For the capillary inlet pressure, The aperture distribution parameter is 0.5~2; Residual gas saturation; This represents the residual water saturation.

7. The quantitative evaluation method for shale gas and coal gas production based on a gas-water two-phase flow isotopic fractionation model according to claim 1, characterized in that: In step (9) mentioned above: 12 CH4 and 13 The coverage of CH4 is as follows: (19)； In the formula The critical desorption pressure is given in MPa.

8. The quantitative evaluation method for shale gas and coal-fired gas production based on a gas-water two-phase flow isotopic fractionation model according to claim 1, characterized in that: In steps (10) and (11): (1) Setting initial conditions for the model: The specific initial conditions for each region are as follows: (20)； in , middle These are the gas phases in the initial SRV region, USRV region, and HF region reservoirs, respectively. 12 Partial pressure of CH4, Pa; , middle These are the gas phases in the initial SRV region, USRV region, and HF region reservoirs, respectively. 13 Partial pressure of CH4, Pa; , middle These are the water phase pressures in the initial SRV, USRV, and HF reservoirs, respectively, in Pa; It is the initial reservoir pressure Pa; yes 13 CH4 and 12 The initial molar ratio of CH4; and These are the initial capillary pressures in the HF and matrix regions, respectively, in Pa; , and The value can be calculated based on the initial methane carbon isotope composition and the initial water saturation: (21)； in This is the initial carbon isotope value of methane; The carbon isotope value of the standard sample; Capillary inlet pressure, Pa; and These are the effective water saturation levels in the HF and matrix regions, respectively. and These are the initial water saturation levels in the HF and matrix regions, respectively. and These are the residual water saturation and residual gas saturation in the HF region, respectively. and These are the residual water saturation and residual gas saturation in the matrix region, respectively. (2) Set the model boundary condition L on the well wall. or noodles Set production boundaries at this point: (22)； In the formula The radius of the horizontal or vertical well, in meters (m). It is an exponential function obtained by fitting measured bottom flow pressure data, Pa; It is the fitting coefficient of the exponential function; It is the pressure corresponding to constant pressure production in the production well, in Pa.

9. The quantitative evaluation method for shale gas and coal-fired gas production based on a gas-water two-phase flow isotopic fractionation model according to claim 1, characterized in that: In step (13): The cumulative gas production of the HF region, SRV region, USRV region, and all regions is given by the following formula: (23)； In the formula , and Porosity in the HF region, SRV region, and USRV region, respectively; and These represent the free HF region. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; and These represent free SRV regions. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; and These represent the free areas of the USRV region. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; and These represent the adsorption of SRV regions. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; and These represent the adsorption of USRV regions. 12 CH4 and 13 The cumulative gas production of CH4, m 3 ; For the total cumulative gas production across all regions, m 3 ; is the derivative within the corresponding region; h is the reservoir thickness, in meters; The cumulative water production of the HF region, SRV region, USRV region, and all regions is calculated as follows: (24)； In the formula , , and The cumulative water production in m³ represents the total cumulative water production in the HF region, SRV region, USRV region, and all regions. 3 ; The density of water phase at atmospheric pressure is kg / m³. 3 ; The density of the aqueous phase is kg / m³. 3 ; The carbon isotope value of methane in gas produced from deep shale / coal gas wells is given by the following formula: （25）。

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