A productivity prediction method, storage medium and device for low-permeability gas reservoirs

Abstract

The present application discloses a productivity prediction method, a storage medium and a device for a low-permeability gas reservoir, belonging to the technical field of low-permeability gas reservoir development. Based on the gas-water two-phase motion equation, a gas-phase productivity equation considering the high-speed non-Darcy effect, the starting pressure gradient and the stress-sensitive effect is established; a water production calculation formula considering the starting pressure gradient and the stress-sensitive effect is established; based on the relationship between the gas-water relative permeability ratio and the water saturation, the water-phase relative permeability is expressed; using the gas-water relative permeability model, the gas-phase relative permeability considering the activity degree of the water body is expressed; the gas-phase relative permeability is brought into the above gas-phase productivity equation. The present application considers the influence of the activity degree of the water body, the starting pressure gradient and the stress-sensitive effect on the gas reservoir productivity, establishes a productivity prediction model coupled with multiple factors including formation water invasion, solves the technical problem that it is difficult to accurately predict the productivity of a low-permeability gas reservoir by traditional methods, and effectively improves the development efficiency and economic benefits of the low-permeability gas reservoir.

Description

Technical Field

[0001] This application belongs to the technical field of low-permeability gas reservoir development, and particularly relates to a method for predicting the productivity of a low-permeability gas reservoir, a storage medium, and a device. Background Art

[0002] The permeability of a low-permeability gas reservoir refers to an effective permeability ranging from 0.1 mD to 5 mD, and the effective permeability of a tight sandstone gas reservoir is less than 0.1 mD. As an important natural gas resource in China, low-permeability gas reservoirs are characterized by wide distribution and large reserves, and have broad development prospects. However, during the development process, the problem of water invasion is generally faced, resulting in the transformation of the fluid in the formation from single-phase flow to gas-water two-phase flow, significantly increasing the gas-phase seepage resistance, and further causing a sharp decline in the productivity of gas wells. In particular, the coupling effect of multiple factors such as underground water body activities, starting pressure gradient, and stress sensitivity effect severely restricts the efficient development of low-permeability gas reservoirs. Therefore, accurately predicting the productivity of low-permeability gas reservoirs has important engineering guiding significance for formulating reasonable water control measures, adjusting the gas well production allocation, and improving the gas reservoir recovery rate.

[0003] The accuracy of existing methods for predicting the productivity of low-permeability gas reservoirs needs to be improved, and there are obvious limitations: on the one hand, existing prediction models considering the influence of water production often ignore the dynamic influence of the water body activity degree on the productivity of the gas reservoir; on the other hand, traditional single-phase seepage models cannot accurately describe the characteristics of gas-water two-phase flow. Therefore, developing a comprehensive method for predicting the productivity considering the invasion of formation water into the gas reservoir and the coupling of other factors has important theoretical value and practical significance for realizing accurate productivity prediction and scientific development of low-permeability gas reservoirs with water. Summary of the Invention

[0004] This application aims to at least solve the technical problem of low accuracy in predicting the productivity of gas reservoirs to a certain extent. For this purpose, this application provides a method for predicting the productivity of a low-permeability gas reservoir, a storage medium, and a device, which can consider the influence of the water body activity degree on the productivity of the gas reservoir, and then can establish a productivity prediction model that couples multiple factors including the invasion of formation water, solve the technical problem that it is difficult for traditional methods to accurately predict the productivity of low-permeability gas reservoirs, and effectively improve the development efficiency and economic benefits of low-permeability gas reservoirs.

[0005] In a first aspect, an embodiment of this application provides a method for predicting the productivity of a low-permeability gas reservoir, including:

[0006] Based on the gas-water two-phase motion equation, establish a productivity equation and a first formula for the underground water production of a gas well;

[0007] Considering the water body activity degree, establish a water invasion constant through the natural logarithm ratio of the water storage volume coefficient to the recovery degree;

[0008] Based on the principle of material balance, establish the relationship between water saturation, cumulative water influx, and geological reserves, and rewrite it into a water saturation relationship containing the water influx constant through the water storage volume coefficient;

[0009] Through the relationship between the ratio of gas-phase relative permeability to water-phase relative permeability and water saturation, and combining the relationship between the ratio of gas-phase relative permeability to water-phase relative permeability and production gas-water ratio and condensate gas-water ratio, obtain the relationship between water saturation and production gas-water ratio and condensate gas-water ratio, and establish the second formula for underground water production of gas wells based on gas production and production gas-water ratio;

[0010] Simultaneously solve the first formula for underground water production of gas wells and the second formula for underground water production of gas wells to obtain the expression of water-phase relative permeability containing the water influx constant;

[0011] Through the Brooks-Corey model, substitute the water-phase relative permeability containing the water influx constant to represent the gas-phase relative permeability containing the water influx constant;

[0012] Substitute the gas-phase relative permeability into the productivity equation to obtain the productivity equation considering the activity degree of the water body, which is used to predict the productivity of low-permeability gas reservoirs.

[0013] In some embodiments, the productivity equation is the integral expression of the gas-phase motion equation and the water-phase motion equation in the reservoir flow region;

[0014] The gas phase is in high-speed non-Darcy flow. Considering the influence of the starting pressure gradient, the gas-phase motion equation is expressed as:

[0015]

[0016] The water phase is in Darcy flow, and the water-phase motion equation is expressed by the following formula:

[0017]

[0018] Where, p is the pressure at any point in the gas reservoir, Mpa; r is the radial distance from any point in the gas reservoir to the gas well, m; μ g is the viscosity of natural gas, mPa·s; k is the reservoir permeability, 10 -3 μm 2 ; k rg is the gas-phase relative permeability; is the gas-phase seepage velocity; β is the non-Darcy flow coefficient, m -1 , , m / s; ρ ց is the density of natural gas, kg / m3 , ; M air is the molar mass of air, g / mol; Z is the deviation factor of natural gas; R g is the gas constant; T is the formation temperature, in K; γ ց is the relative density of natural gas; λց is the starting pressure gradient of the gas phase; k rw is the relative permeability of the aqueous phase; μ w is the viscosity of formation water, mPa·s; is the seepage velocity of the aqueous phase, m / s; λ w is the starting pressure gradient of the aqueous phase, MPa / m.

[0019] In some embodiments, in the gas-phase motion equation and the aqueous-phase motion equation, the pressure-sensitive effect of reservoir permeability changing with formation pressure is considered, and the equation is established:

[0020]

[0021] where, k is the reservoir permeability, 10 -3 μm 2 ; k i is the original reservoir permeability, 10 -3 μm 2 ; p i is the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa; α is the stress sensitivity index, MPa -1 ; e is a mathematical constant.

[0022] In some embodiments, when integrating the aqueous-phase motion equation, the average pressure is used to simplify the integration:

[0023]

[0024] where, p e is the boundary pressure, MPa; p wf is the bottom-hole pressure, MPa; ψ w ( x ) is the pseudo-pressure function; μw is the formation water viscosity, mPa·s; k i is the original reservoir permeability, 10 -3 μm 2 ; k rw is the relative permeability of the water phase; q w is the underground water production of the gas well, m 3 / d; h is the effective thickness of the reservoir, m; r e is the gas supply radius, m; r w is the well radius, m; λ w is the starting pressure gradient of the water phase, MPa / m; e is a mathematical constant; α is the stress sensitivity index, MPa -1 ; p i is the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa.

[0025] In some embodiments, the formula for the underground water production of the gas well is:

[0026]

[0027] Wherein, q w is the underground water production of the gas well, m 3 / d; k i is the original reservoir permeability, 10 -3 μm 2 ; k rw is the relative permeability of the water phase; h is the effective thickness of the reservoir, m; ψ w ( x ) is the pseudo-pressure function; λ w is the starting pressure gradient of the water phase, MPa / m; e is a mathematical constant; α is the stress sensitivity index, MPa -1 ; p i is the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa; r e is the gas supply radius, m; r wis the well radius, m; μ w is the formation water viscosity, mPa·s; is the average pressure in the gas reservoir.

[0028] In some embodiments, the underground water production formula of the gas well is:

[0029]

[0030] Wherein, q w is the underground water production of the gas well, m 3 / d; q ց is the surface gas production, m 3 / d; B w is the formation water volume coefficient; W gr is the production water-gas ratio, m 3 / 10 4 m 3 ; W cgr is the condensate water-gas ratio, m 3 / 10 4 m 3 .

[0031] In some embodiments, the water invasion constant B is:

[0032]

[0033] Wherein, ω is the water storage volume coefficient applicable to edge water, ; R is the recovery factor; when 1≤B<2, the formation water body is in an active state, when 2≤B<4, the formation water body is in a sub-active state, and when B≥4, the formation water body is in an inactive state.

[0034] In some embodiments, the productivity equation considering the activity degree of the water body is:

[0035]

[0036] Wherein, p e is the boundary pressure, MPa; p wf is the bottom hole pressure, MPa; ψ w ( x ) is the pseudo-pressure function; q ց is the surface gas production, m 3 / d; a wis an intermediate calculation parameter, ; b w is an intermediate calculation parameter, ; c is an intermediate calculation parameter, ; μ ց is the natural gas viscosity, mPa·s; k i is the original reservoir permeability, 10 -3 μm 2 ; k rgw is the gas-phase relative permeability considering the water body activity degree; p sc is the pressure under standard conditions, MPa; T is the formation temperature, K ; Z is the natural gas deviation factor; T sc is the temperature under standard conditions, K; Z sc is the gas deviation factor under standard conditions; r e is the gas supply radius, m; r w is the well radius, m; α is the stress sensitivity index, MPa -1 ; p i is the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa; M air is the molar mass of air, g / mol; R g is the gas constant, MPa·m 3 / (mol·k); γ ց is the relative density of natural gas; λց is the gas-phase starting pressure gradient; is the average pressure in the gas reservoir.

[0037] In a second aspect, an embodiment of the present application provides a storage medium storing a terminal program, and when the terminal program is executed, the low-permeability gas reservoir productivity prediction method as described above is performed.

[0038] In a third aspect, an embodiment of the present application provides a low-permeability gas reservoir productivity prediction device, including a memory, a processor, and a computer program stored in the memory and executable in the processor, and the computer program includes steps corresponding to the low-permeability gas reservoir productivity prediction method as described above.

[0039] As can be seen from the above technical solutions, the beneficial effects of this application are as follows:

[0040] 1. In the method of this application, both gas-water two-phase flow is considered in the production capacity prediction, which can better simulate the actual production situation in low-permeability gas reservoirs. Considering water invasion, a water invasion constant is established through the water storage volume coefficient and the recovery degree to reflect the activity degree of the water body. Furthermore, the water saturation, water-phase relative permeability, and gas-phase relative permeability can be expressed as expressions related to the water invasion constant. At the same time, the relative permeability and material balance are combined. Finally, a permeability expression related to the activity degree of the water body is introduced into the production capacity equation, so that the influence of the activity degree of the water body on the production capacity of the gas reservoir can be considered. Since the production capacity equation can be based on multiple factors including the starting pressure gradient and stress sensitivity effect, a multi-factor coupled production capacity prediction model including formation water invasion can be established, solving the technical problem that it is difficult for traditional methods to accurately predict the production capacity of low-permeability gas reservoirs, and effectively improving the development efficiency and economic benefits of low-permeability gas reservoirs.

[0041] 2. In the storage medium of this application, by applying the production capacity prediction method in the storage medium, a storage medium is provided, which can be applied to a variety of electronic devices, and thus the rapid prediction of the production capacity of low-permeability gas reservoirs under the dynamic influence of water invasion can be realized.

[0042] 3. The device of this application executes the corresponding steps of the production capacity prediction method for low-permeability gas reservoirs through a computer program, and can quickly calculate the production capacity of low-permeability gas reservoirs. Through the device, the production capacity prediction can be quickly carried out relying on physical devices, and the production capacity prediction result can be obtained intuitively, providing a reliable production capacity prediction tool for gas field developers. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings required for description in the embodiments will be briefly introduced one by one below. Obviously, the accompanying drawings in the following description are some embodiments of this application. For those of ordinary skill in the art, other embodiments and accompanying drawings can be obtained based on these drawings without creative efforts. The block diagrams shown in the accompanying drawings are only functional entities, not necessarily corresponding to physically independent entities, that is: these functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices. The flowcharts shown in the accompanying drawings are only illustrative, not necessarily including all the contents and operations / steps, nor necessarily executed in the described order. For example, some operations / steps can be decomposed, and some operations / steps can be combined or partially combined. Therefore, the actual execution order may be changed according to the actual situation.

[0044] Figure 1The schematic flowchart of the embodiment of the productivity prediction method for low-permeability gas reservoirs according to the present invention is shown;

[0045] Figure 2 The fitting diagram of the gas-water relative permeability ratio and water saturation of the present invention applied to a low-permeability gas reservoir in the Sichuan Basin is shown; Specific embodiments

[0046] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the drawings corresponding to the specific embodiments of the present application. The following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the present application to be protected. The described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, various different configurations can be arranged and designed. All other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present application.

[0047] The present application will be described below in conjunction with the drawings and with reference to specific embodiments:

[0048] Please refer to Figure 1 , in the first aspect embodiment of the present application, a productivity prediction method for low-permeability gas reservoirs is provided. This productivity prediction method not only helps to optimize the single-well production allocation plan but also provides a scientific basis for formulating the overall development strategy of the gas reservoir. This productivity prediction method for low-permeability gas reservoirs is analyzed based on the following gas reservoir condition assumptions:

[0049] Seepage characteristic assumption: The gas phase follows high-speed non-Darcy flow, and the liquid phase obeys Darcy's law of flow;

[0050] Temperature characteristic assumption: Keep a constant temperature during the gas reservoir development process;

[0051] Reservoir characteristic assumption: The reservoir has isotropic characteristics;

[0052] Production characteristic assumption: After water invasion, the gas well is in a gas-water two-phase flow state, and no liquid accumulation is formed in the wellbore;

[0053] Mechanical characteristic assumption: Ignore the influence of gravity and capillary force on two-phase flow;

[0054] This productivity prediction method for low-permeability gas reservoirs includes:

[0055] S1. Based on the gas-water two-phase flow equations, establish the productivity equation and the first formula for the underground water production of gas wells. When establishing the productivity equation, the pseudo-pressure form can be used and then conventional corrections are made. Among them, the water-phase flow equation is integrated to obtain the first formula for the underground water production of gas wells. There is often a water body connected to the low-permeability gas reservoir. When the pressure wave propagates to the water body, formation water will invade the gas reservoir. Water invasion will hinder the flow path of natural gas and reduce the gas well production. Therefore, when predicting the productivity of low-permeability gas reservoirs, the gas-water two-phase flow needs to be considered.

[0056] S2. Considering the activity degree of the water body, establish the water invasion constant through the natural logarithm ratio of the water storage volume coefficient to the recovery degree. Establishing the water invasion constant, that is, water invasion constant = natural logarithm of the water storage volume coefficient / natural logarithm of the recovery degree, quantifies the index of the activity degree of the water body and can objectively evaluate the impact of water invasion on the exploitation of low-permeability gas reservoirs. The activity degree of the water body refers to the activity ability of formation water in the gas reservoir in a gas-producing well. Formation water invading the gas reservoir will occupy the gas flow channels, and these factors will affect the productivity of the gas well. Productivity refers to the gas production of a gas well in one day under the theoretical maximum pressure difference. Therefore, the activity degree of the water body needs to be considered to calculate the productivity of low-permeability gas reservoirs more accurately.

[0057] S3. Based on the material balance principle, establish the relationship between water saturation, cumulative water invasion volume and geological reserves, and rewrite it as a water saturation relationship containing the water invasion constant through the water storage volume coefficient. The material balance principle is one of the basic principles in reservoir engineering. It is based on the law of conservation of mass, that is, in a closed system, the total amount of matter remains unchanged during the reaction or flow process. The relationship between water saturation, cumulative water invasion volume and geological reserves is a conventionally established relationship. However, in this application, the water storage volume coefficient is introduced, so that when describing the expression of water saturation, cumulative water invasion volume and geological reserves, the water invasion constant is added, that is, the local expression about the water storage volume coefficient in this relationship is replaced by the water invasion constant.

[0058] S4. The relationship between the ratio of gas phase relative permeability and water phase relative permeability and water saturation is obtained by combining the relationship between the ratio of gas phase relative permeability and water phase relative permeability and the production water-gas ratio and condensate water-gas ratio to obtain the relationship between water saturation and the production water-gas ratio and condensate water-gas ratio, and the gas well underground water production formula 2 based on gas production and production water-gas ratio is established. The relationship between the ratio of gas phase relative permeability and water phase relative permeability and water saturation refers to the complex nonlinear relationship between the three, which has a certain coupling relationship. This relationship can be determined through experiments, and this similar relationship is relatively stable and is often used as an empirical formula for calculation in gas reservoir development. Similarly, the ratio of gas phase relative permeability and water phase relative permeability also has a certain coupling relationship with the production water-gas ratio and condensate water-gas ratio, and one side of the above two relationship formulas is the ratio of gas phase relative permeability to water phase relative permeability. In this way, the two formulas can be combined to establish an equation, and the gas production in the equation can be transformed into the gas well underground water production formula 2.

[0059] S5. Combine the gas well underground water production formula 1 and the gas well underground water production formula 2 to obtain an expression for the relative permeability of the water phase including the water invasion constant; that is, based on the two different expressions for the gas well underground water production, establish an equation for the gas well underground water production formula 1 and the gas well underground water production formula 2, and transform the equation to solve the expression for the relative permeability of the water phase, wherein the expression includes the water invasion constant.

[0060] S6. The Brooks-Corey model is used to express the relative permeability of the gas phase including the water invasion constant. The Brooks-Corey model is a classic model that describes the relationship between the relative permeability and saturation of multiphase fluids (such as water, gas, and oil) in porous media. The saturation power law function is used to characterize the flow characteristics of immiscible fluids. It is particularly suitable for reservoirs with non-uniform pore structures and can be used for numerical simulation of water phase movement and prediction of dynamic changes in the water phase. Based on the model, the gas-water relative permeability can be listed, and then the gas phase relative permeability can be determined by combining the normalized saturation.

[0061] S7, substituting the gas phase relative permeability into the capacity equation, obtaining a capacity equation that takes into account the activity of the water body, and using it to predict the capacity of the low permeability gas reservoir. The original capacity equation is the capacity equation established in the above step S1. Substituting the gas phase relative permeability obtained in the above step into the original capacity equation, a new capacity equation can be obtained, and the capacity of the low permeability gas reservoir can be calculated and predicted by the new capacity equation.

[0062] The accuracy of existing productivity prediction methods for low-permeability gas reservoirs needs to be improved, and there are obvious limitations. On the one hand, existing prediction models considering the influence of water production often ignore the dynamic influence of water body activity on gas reservoir productivity and only focus on single factors such as starting pressure gradient or stress sensitivity effect. On the other hand, traditional single-phase seepage models cannot accurately describe the flow characteristics of gas-water two-phase flow. Therefore, existing productivity predictions for low-permeability gas reservoirs do not consider the activity of the water body, and water invasion will affect gas reservoir productivity, resulting in low accuracy of productivity prediction.

[0063] This application takes into account both gas-water two-phase movement in productivity prediction, which can better simulate the actual production situation in low-permeability gas reservoirs. Considering water invasion, a water invasion constant is established through the water storage volume coefficient and recovery degree to reflect the activity of the water body. Furthermore, water saturation, relative water permeability, and relative gas permeability can be expressed as expressions related to the water invasion constant. At the same time, relative permeability and material balance are combined. Finally, a permeability expression related to the activity of the water body is introduced into the productivity equation, thereby considering the influence of the activity of the water body on gas reservoir productivity. Since the productivity equation can be based on multiple factors including starting pressure gradient, stress sensitivity effect, etc., a productivity prediction model coupling multiple factors including formation water invasion can be established, solving the technical problem that traditional methods are difficult to accurately predict the productivity of low-permeability gas reservoirs, and effectively improving the development efficiency and economic benefits of low-permeability gas reservoirs. This method is applicable to the dynamic prediction and evaluation of productivity during the development of low-permeability gas reservoirs. At the same time, it can also be extended and applied to productivity prediction research in the development of unconventional natural gas resources such as low-permeability gas reservoirs and shale gas reservoirs, as well as related technical research on porous media seepage phenomena in oil and gas field development engineering.

[0064] In some embodiments, the productivity equation is the integral expression of the gas-phase motion equation and the water-phase motion equation in the reservoir flow region;

[0065] The gas phase is in high-speed non-Darcy flow. Considering the influence of the starting pressure gradient, the gas-phase motion equation is expressed as:

[0066]

[0067] The water phase is in Darcy flow, and the water-phase motion equation is expressed by the following formula:

[0068]

[0069] Where, p is the pressure at any point in the gas reservoir, Mpa; r is the radial distance from any point in the gas reservoir to the gas well, m; μ g is the viscosity of natural gas, mPa·s; k is the reservoir permeability, 10 -3 μm 2 ;k rg is the gas-phase relative permeability; is the gas-phase seepage velocity; β is the non-Darcy flow coefficient, m -1 , , m / s; ρ ց is the natural gas density, kg / m 3 , ; M air is the molar mass of air, g / mol; Z is the natural gas deviation factor; R g is the gas constant; T is the formation temperature, in K; γ ց is the relative density of natural gas; λց is the gas-phase starting pressure gradient; k rw is the water-phase relative permeability; μ w is the formation water viscosity, mPa·s; is the water-phase seepage velocity, m / s; λ w is the water-phase starting pressure gradient, MPa / m.

[0070] In some embodiments, during the development of a gas reservoir, as the reservoir pressure continues to decline, the stress-sensitive effect gradually appears, having a significant impact on the gas reservoir productivity. Therefore, in the gas-phase motion equation and the water-phase motion equation, to quantitatively characterize the relationship between the reservoir permeability and the formation pressure, considering the pressure-sensitive effect of the reservoir permeability changing with the formation pressure, the following equation based on the stress-sensitive effect is established:

[0071]

[0072] Wherein, k is the reservoir permeability, 10 -3 μm 2 ; k i is the original reservoir permeability, 10 -3 μm 2 ; p i is the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa; α is the stress-sensitive index, MPa -1 ; e is a mathematical constant.

[0073] Substituting Equation (3) into Equations (1) and (2) gives:

[0074]

[0075]

[0076] wherein, p is the pressure at any point in the gas reservoir, Mpa; r is the radial distance from any point in the gas reservoir to the gas well, m; μ g is the viscosity of natural gas, mPa·s; k i is the original permeability of the reservoir, 10 -3 μm 2 ; k rg is the relative permeability of the gas phase; k rw is the relative permeability of the water phase; e is a mathematical constant; p i is the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa; α is the stress sensitivity index, MPa -1 ; β is the non-Darcy flow coefficient, m -1 , ; ρ ց is the density of natural gas, kg / m 3 , ; Z is the gas deviation factor; R g is the gas constant; T is the formation temperature, in K; is the seepage velocity of the gas phase; λց is the starting pressure gradient of the gas phase; μ w is the viscosity of formation water, mPa·s; is the seepage velocity of the water phase, m / s; λ w is the starting pressure gradient of the water phase, MPa / m; k rw is the relative permeability of the water phase.

[0077] The seepage velocity of the gas phase in the formation can be expressed by the following formula:

[0078]

[0079] wherein, q ց is the gas production rate at the surface, m 3 / d;p sc is the pressure under standard conditions, MPa; T is the formation temperature, K ; Z is the gas deviation factor; p is the pressure at any point in the gas reservoir, Mpa; r is the radial distance from any point in the gas reservoir to the gas well, m; h is the effective thickness of the reservoir, m; T sc is the temperature under standard conditions, K; Z sc is the gas deviation factor under standard conditions.

[0080] In some embodiments, substituting Equation (6) into Equation (4), integrating the gas-phase motion equation, and simultaneously using the average pressure to simplify the integration, a correlation between pressure and the underground water production of the gas phase is obtained:

[0081]

[0082] wherein, p e is the boundary pressure, MPa; p wf is the bottom-hole pressure, MPa; ψ w ( x ) is the pseudo-pressure function; ; μ g is the natural gas viscosity, mPa·s; p sc is the pressure under standard conditions, MPa; T is the formation temperature, K ; Z is the gas deviation factor; r e is the gas supply radius, m; r w is the well radius, m; k i is the original permeability of the reservoir, 10 -3 μm 2 ; k rg is the relative permeability of the gas phase; h is the effective thickness of the reservoir, m; T sc is the temperature under standard conditions, K; Z sc is the gas deviation factor under standard conditions; q ց is the surface gas production, m3 / d; p i is the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa; α is the stress sensitivity index, MPa -1 ; e is a mathematical constant; M air is the molar mass of air, g / mol; γ ց is the relative density of natural gas; R g is the gas constant, MPa·m 3 / (mol·k); λց is the starting pressure gradient of the gas phase.

[0083] In some embodiments, substituting Equation (6) into Equation (5), integrating the water-phase motion equation, and simplifying the integration using the average pressure to obtain the correlation between pressure and the underground water production of the water phase:

[0084]

[0085] where, p e is the boundary pressure, MPa; p wf is the bottom-hole pressure, MPa; ψ w ( x ) is the pseudo-pressure function; ; μ w is the formation water viscosity, mPa·s; k i is the original reservoir permeability, 10 -3 μm 2 ; k rw is the relative permeability of the water phase; q w is the underground water production of the gas well, m 3 / d; h is the effective thickness of the reservoir, m; r e is the gas supply radius, m; r w is the well radius, m; λ w is the starting pressure gradient of the water phase, MPa / m; e is a mathematical constant; α is the stress sensitivity index, MPa -1 ; p iis the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa; is the average pressure in the gas reservoir.

[0086] In some embodiments, by rewriting formula (8), the first formula for the underground water production of a gas well can be obtained:

[0087]

[0088] where q w is the underground water production of the gas well, m 3 / d; k i is the original permeability of the reservoir, 10 -3 μm 2 ; k rw is the relative permeability of the water phase; h is the effective thickness of the reservoir, m; ; λ w is the starting pressure gradient of the water phase, MPa / m; e is a mathematical constant; α is the stress sensitivity index, MPa -1 ; p i is the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa; r e is the gas supply radius, m; r w is the well radius, m; μ w is the viscosity of formation water, mPa·s.

[0089] According to the principle of material balance, the current water saturation of the formation can be expressed by the following formula:

[0090]

[0091] where S w is the water saturation; S wi is the irreducible water saturation; G is the geological reserves, 10 8 m 3 ; W e is the cumulative water influx, 10 4 m 3 ; W p is the cumulative water production, 10 4 m3 ; B w is the formation water volume factor; B gi is the original gas volume factor.

[0092] In the study of the mechanism of water invasion in gas reservoirs, to quantitatively characterize the degree of formation water invasion, the water storage volume factor ω is introduced as an evaluation index, and its definition is:

[0093]

[0094] where, ω is the water storage volume factor applicable to edge water; G is the geological reserve, 10 8 m 3 ; W e is the water invasion volume, 10 4 m 3 ; W p is the cumulative water production, 10 4 m 3 ; B w is the formation water volume factor; B gi is the original gas volume factor.

[0095] In some embodiments, after studying the water invasion of the gas reservoir and the production degree of the gas reservoir, it is found that there is a certain relationship between the water storage volume factor and the production degree, that is, the water invasion constant B is:

[0096]

[0097] where, ω is the water storage volume factor applicable to edge water, ; R is the production degree; when 1 ≤ B < 2, the formation water body is in an active state, when 2 ≤ B < 4, the formation water body is in a sub-active state, and when B ≥ 4, the formation water body is in an inactive state.

[0098] Combining formulas (10), (11) and (12) gives:

[0099]

[0100] where, S w is the water saturation; S wi is the irreducible water saturation; R is the production degree; B is the water invasion constant.

[0101] There is the following empirical relationship between the ratio of gas-phase relative permeability to water-phase relative permeability and water saturation:

[0102]

[0103] Wherein, k rg is the gas-phase relative permeability; k rw is the water-phase relative permeability; a, b are fitting coefficients respectively; S w is the water saturation; e is a mathematical constant.

[0104] Meanwhile, the ratio of gas-phase relative permeability to water-phase relative permeability also has the following relationship with the production gas-water ratio and condensate gas-water ratio:

[0105]

[0106] Wherein, k rg is the gas-phase relative permeability; k rw is the water-phase relative permeability; μ ց is the natural gas viscosity, mPa·s; B g is the gas volume factor; μ w is the formation water viscosity, mPa·s; B w is the formation water volume factor; W gr is the production gas-water ratio, m 3 / 10 4 m 3 ; W cgr is the condensate gas-water ratio, m 3 / 10 4 m 3 .

[0107] Substituting formula (14) into formula (15) gives:

[0108]

[0109] Wherein, W gr is the production gas-water ratio, m 3 / 10 4 m 3 ; W cgr is the condensate gas-water ratio, m 3 / 104 m 3 ; μ ց is the viscosity of natural gas, mPa·s; B g is the gas volume coefficient; μ w is the formation water viscosity, mPa·s; B w is the formation water volume coefficient; S w is water saturation; e is a mathematical constant; a, b are the fitting coefficients respectively; S w is the water saturation.

[0110] In some embodiments, according to the mine water production calculation formula, the formation water production can be calculated from the gas production and the production water-gas ratio, that is, the gas well underground water production formula 2 is:

[0111]

[0112] in, q w is the underground water production of the gas well, m 3 / d; q ց is the surface gas production, m 3 / d; B w is the formation water volume coefficient; W gr is the production water-gas ratio, m 3 / 10 4 m 3 ; W cgr is the condensate water-gas ratio, m 3 / 10 4 m 3 .

[0113] Combining equations (9) and (17), the relative permeability of the water phase can be expressed as follows:

[0114]

[0115] in, k rw is the relative permeability of water phase; μ w is the formation water viscosity, mPa·s; B w is the formation water volume coefficient; q ց is the surface gas production, m 3 / d; r e is the gas supply radius, m; r w is the well radius, m; W gr is the production water-gas ratio, m 3 / 10 4 m 3 ; W cgr is the condensate water-gas ratio, m 3 / 10 4 m 3 ; k i is the initial reservoir permeability, 10 -3 μm 2 ; h is the effective thickness of the reservoir, m; ; λ w is the water-phase starting pressure gradient, MPa / m; e is a mathematical constant; α is the stress sensitivity index, MPa -1 ; p i is the initial formation pressure, MPa; is the average pressure of the gas reservoir, Mpa.

[0116] Substituting Equation (13) and Equation (16) into Equation (18), we get:

[0117]

[0118] where is an intermediate calculation parameter; μ ց is the viscosity of natural gas, mPa·s; B g is the gas volume factor; q ց is the surface gas production rate, m 3 / d; r e is the gas supply radius, m; r w is the well radius, m; k i is the initial reservoir permeability, 10 -3 μm 2 ; h is the effective thickness of the reservoir, m; ; λ w is the water-phase starting pressure gradient, MPa / m; e is a mathematical constant; αis the stress sensitivity index, MPa -1 ; p i is the original formation pressure, MPa; is the average pressure of the gas reservoir, MPa; S w is water saturation; S wi is the bound water saturation; a, b are fitting coefficients respectively; R is the recovery degree; B is the water invasion constant.

[0119] From the Brooks-Corey model, we know that the relative permeability of gas and water can be expressed as:

[0120]

[0121] in, k rg is the gas phase relative permeability; k rw is the relative permeability of water phase; is the gas phase relative permeability corresponding to irreducible water saturation; is the relative permeability of water phase corresponding to the residual gas saturation; n ց , n w All are Corey indexes; S w * is the normalized wetting phase saturation, ; S w is the reservoir water saturation; S wc is the bound water saturation; S gr is the residual gas saturation.

[0122] Combining equations (19), (20) and (21), we can obtain the gas phase relative permeability considering the activity of the water body:

[0123]

[0124] in, k rgw is the relative permeability of the gas phase taking into account the activity of the water body; is the gas phase relative permeability corresponding to irreducible water saturation; is the parameter in formula (19); is the relative permeability of water phase corresponding to the residual gas saturation; n ց , n wThey are all Corey indices.

[0125] In some embodiments, substituting Equation (22) into Equation (7), the productivity equation considering the water body activity, starting pressure gradient, and stress sensitivity effect is:

[0126]

[0127] Wherein, p e is the boundary pressure, MPa; p wf is the bottom-hole pressure, MPa; ψ w ( x ) is the pseudo-pressure function; q ց is the surface gas production, m 3 / d; a w is an intermediate calculation parameter, ; b w is an intermediate calculation parameter, ; c is an intermediate calculation parameter, ; μ ց is the natural gas viscosity, mPa·s; k i is the original reservoir permeability, 10 -3 μm 2 ; k rgw is the gas-phase relative permeability considering the water body activity; p sc is the pressure under standard conditions, MPa; T is the formation temperature, K ; Z is the natural gas deviation factor; T sc is the temperature under standard conditions, K; Z sc is the gas deviation factor under standard conditions; r e is the gas supply radius, m; r w is the well radius, m; α is the stress sensitivity index, MPa -1 ; p i is the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa; M air is the molar mass of air, g / mol; R gis the gas constant, MPa·m 3 / (mol·k); γ ց is the relative density of natural gas; λց is the gas-phase starting pressure gradient; is the average pressure in the gas reservoir.

[0128] Please refer to Figure 2 , taking a low-permeability gas reservoir in the Sichuan Basin as an example for illustration: The initial formation pressure of the gas-producing and water-producing well in the gas reservoir is 40.21 MPa, the formation temperature is 95.71 °C, the initial formation permeability is 4.65x10 -3 μm 2 , the porosity is 4.72%, the effective thickness is 52.27 m, the relative density of natural gas is 0.5902, the stress sensitivity coefficient is 0.0214 MPa -1 , the gas-phase starting pressure is 0.001 MPa / m, and the water-phase starting pressure gradient value is 0.003 MPa / m. Combining relevant literature, the water invasion constant is calculated to be 2.47. The fitting relationship between the ratio of gas-water relative permeability and water saturation is shown in Figure 2 . Through the production performance data of this well combined with the above parameters, using the established productivity calculation method for low-permeability gas reservoirs, the open flow potential of this well is calculated to be 17.14x10 4 m 3 / d. Compared with the open flow potential of 18.57x10 4 m 3 / d from well testing, the relative error is only 7.71%, and the relative error is small, meeting the requirements of engineering applications. Based on the actual core test relative permeability curves of this gas reservoir, fitting the ratio of gas-phase relative permeability to water-phase relative permeability and water saturation, the fitting coefficient a is 97239, and the fitting coefficient b is 21.25. Using the method of this application, it can directly use the on-site production performance data for rapid calculation, effectively achieve accurate prediction of productivity, and then be able to optimize the production system in a timely manner according to different water activity levels, starting pressure gradients, and stress sensitivity effects, formulate targeted water control and water treatment measures, and improve the productivity of single wells.

[0129] In the embodiment of the second aspect of the present application, a storage medium is provided. The storage medium is a readable storage medium, and the readable storage medium stores a terminal program. When the terminal program is executed, it performs the low-permeability gas reservoir productivity prediction method, storage medium, and device as described in any of the above embodiments. If the modules / units integrated in the terminal device are implemented in the form of software functional units and sold or used as independent products, the terminal program can be stored in a readable storage medium. Based on this understanding, all or part of the processes of implementing the method in the above embodiments of the present application can also be completed by instructing relevant hardware through a computer program. The computer program can be stored in the readable storage medium. When the computer program is executed by a processor, the steps of each method in the above embodiments can be implemented. When the computer program is executed by the processor, the specific implementation and the technical effects generated by each step are the same as those in the foregoing method embodiments. For the sake of brief description, for the parts not mentioned in this embodiment, reference can be made to the corresponding content in the foregoing method embodiments. By applying the productivity prediction method in the storage medium, a storage medium is provided, which can be applied to various electronic devices, thereby realizing the rapid prediction of the productivity of low-permeability gas reservoirs under the dynamic influence of water invasion.

[0130] In the embodiment of the third aspect of the present application, a low-permeability gas reservoir productivity prediction device is provided, including a memory, a processor, and a computer program stored in the memory and operable on the processor. The computer program includes the steps corresponding to the low-permeability gas reservoir productivity prediction method, storage medium, and device as described above. For example, a calculation program. When the processor executes the computer program, the steps in the above method embodiments are implemented. For example Figure 1 the steps shown; or when the processor executes the computer program, the functions of each module / unit in the above device embodiment are implemented, such as rapid calculation. It should be understood that the devices in the embodiments of the present application can be implemented based on the memory and the processor. Each memory is used to store the computer program for executing the above method of the present application. The processor executes the above computer program, so that the device implements the methods of the above various embodiments. By executing the steps corresponding to the low-permeability gas reservoir productivity prediction method through the computer program, the productivity of the low-permeability gas reservoir can be quickly calculated. Through the device, the productivity prediction can be quickly carried out relying on physical devices, and the productivity prediction result can be intuitively obtained, providing a reliable productivity prediction tool for gas field developers.

[0131] In some embodiments, a computer program may be divided into one or more modules / units, which are stored in a memory and executed by a processor to implement the method of the present application. One or more modules / units may be a series of instruction segments of a computer program for performing a specific function, and the instruction segments are used to describe the execution process of the computer program in the above-mentioned device. The embodiments described above are merely illustrative. For example, the division of modules or units is only a logical function division, and there may be other division methods in actual implementation. For example, multiple units or components may be combined or integrated into another device, or some features may be ignored or not executed. At the same time, the direct coupling, indirect coupling or communication connection between the components of the device / terminal device may be through some interfaces, and the connection may be electrical, mechanical or other forms. The above-mentioned modules or units may be integrated in a processor, may exist physically alone, or two or more units may be integrated or combined; the above-mentioned modules or units may be implemented in the form of hardware or in the form of software functional units.

[0132] In some embodiments, the above-mentioned device may be a desktop computer, a notebook, an industrial computer, a personal digital assistant, a tablet computer or other mobile terminals, as well as a computer device such as a cloud server, regardless of the operating system it is equipped with. The device may include, but is not limited to: a processor and a memory. Those skilled in the art can understand that the examples of the low-permeability gas reservoir productivity prediction device do not limit the device, and it may include more or fewer components than shown in the figure, or combine certain components, or different components. For example, the device may further include an input device, an output device, a network access device, a bus, etc., or further include a display screen for intuitively displaying the calculation results.

[0133] Regarding the specific implementation manners of the present application, it should be noted that:

[0134] In the description of the present application, the embodiments of the present application can be implemented by electronic hardware, computer program products, or a combination of computer software and electronic hardware, and are described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. In the description of the present application, the processor may be a central processing unit (CPU), a microcontroller unit (MCU), a graphics processing unit (GPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or a field-programmable gate array (FPGA), or may also be other general-purpose processors, programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc. The processor is the control center of the X device / terminal device, and connects various parts of the entire X device / terminal device through various interfaces and lines. In the description of the present application, the computer program includes computer program code, and the computer program code may be in the form of source code, object code, executable file, or some intermediate form, etc. The computer-readable storage medium may include any entity or device capable of carrying the computer program code, such as a USB flash drive, a mobile hard disk, a magnetic disk, an optical disc, a computer memory, a read-only memory, a random access memory, an electrical carrier signal, a telecommunication signal, a software distribution medium, or other recording media, etc.

[0135] In the description of the present application, the term "comprising", "including", or any other variant thereof is intended to cover a non-exclusive inclusion, such that a process, method, device, or readable storage medium comprising a series of elements includes not only those elements but also other elements not expressly listed that are consistent with the concept of the present application, or further includes elements inherent to such process, method, device, or readable storage medium. Without further limitation, an element defined by the statement "comprising one..." does not exclude the presence of additional elements in the process, method, device, or readable storage medium comprising the element.

[0136] In the description of the present application, the description with reference to terms such as "some embodiments", "optional embodiments", "examples", "specific examples", "optional examples", or "optional embodiments" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application, but do not mean that these embodiments illustrate and describe all possible forms of the present invention. In this specification, the schematic representations of the above terms are not necessarily directed to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0137] In addition, the technical solutions between various embodiments can be combined with each other, but it must be based on the ability of those of ordinary skill in the art to implement. Although the embodiments of the present application have been shown and described, various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and purposes of the present application. Those of ordinary skill in the art can understand that various other specific changes and combinations of embodiments made according to these technical revelations disclosed in the present application and not departing from the essence of the present application are still within the protection scope defined by the claims of the present invention and their equivalent technical solutions.

[0138] At the same time, the technical solutions between various embodiments can be combined with each other, but it must be based on the ability of those of ordinary skill in the art to implement. When the combination of technical solutions results in contradictions or is impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the protection scope required by the present application.

Claims

1. A productivity prediction method for low-permeability gas reservoirs, characterized in that Comprising: Based on the gas-water two-phase flow equations, establish a productivity equation and the first formula for the underground water production of a gas well; Considering the activity degree of the water body, establish a water influx constant through the ratio of the water storage volume coefficient to the natural logarithm of the recovery degree; Based on the material balance principle, establish a relationship between the water saturation, the cumulative water influx, and the geological reserves, and rewrite it into a water saturation relationship containing the water influx constant through the water storage volume coefficient; Through the relationship between the ratio of the gas-phase relative permeability to the water-phase relative permeability and the water saturation, and combining the relationship between the ratio of the gas-phase relative permeability to the water-phase relative permeability and the production gas-water ratio and the condensate gas-water ratio, obtain the relationship between the water saturation and the production gas-water ratio and the condensate gas-water ratio, and establish the second formula for the underground water production of a gas well based on the gas production and the production gas-water ratio; Simultaneously solve the first formula for the underground water production of a gas well and the second formula for the underground water production of a gas well to obtain an expression for the water-phase relative permeability containing the water influx constant; Through the Brooks-Corey model, substitute the water-phase relative permeability containing the water influx constant to represent the gas-phase relative permeability containing the water influx constant; Substitute the gas-phase relative permeability into the productivity equation to obtain a productivity equation considering the activity degree of the water body, which is used to predict the productivity of a low-permeability gas reservoir.

2. The productivity prediction method for low-permeability gas reservoirs according to claim 1, wherein The productivity equation is the integral expression of the gas-phase flow equation and the water-phase flow equation in the reservoir flow region; The gas phase is in high-speed non-Darcy flow. Considering the influence of the starting pressure gradient, the gas-phase flow equation is expressed as: The water phase is in Darcy flow, and the water-phase flow equation is expressed by the following formula: wherein, p is the pressure at any point in the gas reservoir, Mpa; r is the radial distance from any point in the gas reservoir to the gas well, m; μ g is the viscosity of natural gas, mPa·s; k is the reservoir permeability, 10 -3 μm 2 ; k rg is the relative permeability of the gas phase; is the seepage velocity of the gas phase; β is the non-Darcy flow coefficient, m -1 , , m / s; ρ ց is the density of natural gas, kg / m 3 , ; M air is the molar mass of air, g / mol; Z is the gas deviation factor; R g is the gas constant; T is the formation temperature, in K; γ ց is the relative density of natural gas; λց is the starting pressure gradient of the gas phase; k rw is the relative permeability of the water phase; μ w is the viscosity of formation water, mPa·s; is the seepage velocity of the water phase, m / s; λ w is the starting pressure gradient of the water phase, MPa / m.

3. The productivity prediction method for low-permeability gas reservoirs according to claim 2, wherein In the gas-phase flow equation and the water-phase flow equation, considering the pressure-sensitive effect of the reservoir permeability changing with the formation pressure, establish an equation: Among them, k is the reservoir permeability, 10 -3 μm 2 ; k i is the initial reservoir permeability, 10 -3 μm 2 ; p i is the initial formation pressure, MPa; p is the pressure at any point in the gas reservoir, MPa; α is the stress sensitivity index, MPa -1 ; e is a mathematical constant.

4. The productivity prediction method for low-permeability gas reservoirs according to claim 2, wherein When integrating the aqueous phase motion equation, the average pressure is used simultaneously Simplify the integration: Wherein, p e is the boundary pressure, MPa; p wf is the bottom-hole pressure, MPa; ψ w ( x ) is the pseudo-pressure function; μ w is the formation water viscosity, mPa·s; k i is the original reservoir permeability, 10 -3 μm 2 ; k rw is the relative permeability of water phase; q w is the underground water production of the gas well, m 3 / d; h is the effective thickness of the reservoir, m; r e is the gas supply radius, m; r w is the well radius, m; λ w is the starting pressure gradient of water phase, MPa / m; e is a mathematical constant; α is the stress sensitivity index, MPa -1 ; p i is the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa.

5. The productivity prediction method for low-permeability gas reservoirs according to claim 1, characterized in that The first formula for the underground water production of a gas well is: Wherein, q w is the underground water production of the gas well, m 3 / d; k i is the original permeability of the reservoir, 10 -3 μm 2 ; k rw is the relative permeability of the aqueous phase; h is the effective thickness of the reservoir, m; ψ w ( x ) is the pseudo-pressure function; λ w is the starting pressure gradient of the aqueous phase, MPa / m; e is a mathematical constant; α is the stress sensitivity index, MPa -1 ; p i is the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa; r e is the gas supply radius, m; r w is the well radius, m; μ w is the formation water viscosity, mPa·s; is the average pressure in the gas reservoir.

6. The productivity prediction method for low-permeability gas reservoirs according to claim 5, wherein, The second formula for the underground water production of a gas well is: Among them, q w is the underground water production of the gas well, m 3 / d; q ց is the surface gas production, m 3 / d; B w is the formation water volume coefficient; W gr is the production water-gas ratio, m 3 / 10 4 m 3 ; W cgr is the condensate water-gas ratio, m 3 / 10 4 m 3 .

7. The productivity prediction method for low-permeability gas reservoirs according to claim 1, characterized in that The water influx constant B is: Among them, ω is the water storage volume coefficient applicable to edge water, ; G is the geological reserve, 10 8 m 3 ; W e is the cumulative water influx, 10 4 m 3 ; W p is the cumulative water production, 10 4 m 3 ; B w is the formation water volume coefficient; B gi is the original gas volume coefficient; R is the recovery factor; when 1 ≤ B < 2, the formation water body is in an active state, when 2 ≤ B < 4, the formation water body is in a sub-active state, and when B ≥ 4, the formation water body is in an inactive state.

8. The productivity prediction method for low-permeability gas reservoirs according to any one of claims 1-7, characterized in that The productivity equation considering the activity degree of the water body is: wherein, p e is the boundary pressure, MPa; p wf is the bottom-hole pressure, MPa; ψ ( x ) is the pseudo-pressure function; q ց is the gas production rate at the surface, m 3 / d; a w is an intermediate calculation parameter, ; b w is an intermediate calculation parameter, ; c is an intermediate calculation parameter, ; μ ց is the natural gas viscosity, mPa·s; k i is the original reservoir permeability, 10 -3 μm 2 ; k rgw is the relative permeability of the gas phase considering the activity of the water body; p sc is the pressure under standard conditions, MPa; T is the formation temperature, K ; Z is the gas deviation factor; T sc is the temperature under standard conditions, K; Z sc is the gas deviation factor under standard conditions; r e is the gas supply radius, m; r w is the well radius, m; α is the stress sensitivity index, MPa -1 ; p i is the original formation pressure, MPa; p is the pressure at any point in the gas reservoir, Mpa; M air is the molar mass of air, g / mol; R g is the gas constant, MPa·m 3 / (mol·k); γ ց is the relative density of natural gas; λց is the starting pressure gradient of the gas phase; is the average pressure in the gas reservoir.

9. A storage medium storing a terminal program, characterized in that, When the terminal program is executed, perform the productivity prediction method for a low-permeability gas reservoir as described in any one of claims 1-8.

10. A productivity prediction device for a low-permeability gas reservoir, comprising a memory, a processor, and a computer program stored in the memory and operable on the processor, characterized in that, The computer program includes the steps corresponding to the productivity prediction method for a low-permeability gas reservoir as described in any one of claims 1-8.

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