Low-permeability gas reservoir productivity prediction method, storage medium and device

Abstract

The invention discloses a low-permeability gas reservoir productivity prediction method, a storage medium and a low-permeability gas reservoir productivity prediction device, and belongs to the technical field of low-permeability gas reservoir development. Based on the gas-water two-phase motion equation, establishing a gas phase productivity equation considering the high-speed non-darcy effect, the starting pressure gradient and the stress sensitive effect; establishing a water yield calculation formula considering the starting pressure gradient and the stress sensitive effect; the water-phase relative permeability is expressed on the basis of the relation between the gas-water relative permeability ratio and the water saturation; using a gas-water relative permeability model to express the gas-phase relative permeability considering the active degree of the water body; and substituting the gas phase relative permeability into the gas phase productivity equation. According to the method, the influence of the water body active degree, the starting pressure gradient and the stress sensitive effect on the productivity of the gas reservoir is considered, the multi-factor coupled productivity prediction model including formation water invasion is established, the technical problem that the productivity of the low-permeability gas reservoir is difficult to accurately predict through a traditional method is solved, and the development efficiency and economic benefits of the low-permeability gas reservoir are effectively improved.

Description

Technical Field

[0001] The present application belongs to the technical field of low permeability gas reservoir development, and in particular, relates to a method, storage medium and device for predicting the production capacity of a low permeability gas reservoir. Background Art

[0002] The permeability of low permeability gas reservoirs refers to the effective permeability between 0.1mD and 5mD, and the effective permeability of tight sandstone gas reservoirs is less than 0.1mD. As an important natural gas resource in my country, low permeability gas reservoirs are characterized by wide distribution and large reserves, and have broad development prospects. However, during the development process, they generally face the problem of water intrusion, which causes the fluid in the formation to change from single-phase flow to gas-water two-phase flow, significantly increases the gas phase seepage resistance, and then causes a sharp drop in gas well production capacity. In particular, the coupling effect of multiple factors such as groundwater activity, starting pressure gradient and stress sensitivity effect seriously restricts the efficient development of low permeability gas reservoirs. Therefore, accurate prediction of the production capacity of low permeability gas reservoirs has important engineering guidance significance for formulating reasonable water control measures, adjusting gas well production allocation and improving gas reservoir recovery.

[0003] The accuracy of existing low-permeability gas reservoir capacity prediction methods needs to be improved, and there are obvious limitations: on the one hand, the existing prediction models that consider the impact of water production often ignore the dynamic impact of water activity on gas reservoir capacity; on the other hand, the traditional single-phase seepage model cannot accurately describe the gas-water two-phase flow characteristics. Therefore, developing a capacity prediction method that comprehensively considers formation water intrusion into gas reservoirs and other multi-factor coupling has important theoretical value and practical significance for achieving accurate capacity prediction and scientific development of low-permeability water-bearing gas reservoirs. Summary of the invention

[0004] The present application aims to at least to some extent solve the technical problem of low accuracy in predicting gas reservoir production capacity. To this end, the present application provides a method, storage medium and device for predicting the production capacity of a low permeability gas reservoir, which can take into account the impact of water activity on the gas reservoir production capacity, and then establish a production capacity prediction model with multiple factors coupled including formation water intrusion, thereby solving the technical problem that traditional methods are difficult 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.

[0005] In a first aspect, an embodiment of the present application provides a method for predicting the productivity of a low permeability gas reservoir, comprising: Based on the gas-water two-phase motion equation, the production capacity equation and the underground water production formula of the gas well are established; Considering the activity of water bodies, the water invasion constant is established by the natural logarithm ratio of the water volume coefficient and the extraction degree; Based on the material balance principle, the relationship between water saturation, cumulative water intrusion and geological reserves is established, and the water volume coefficient is used to rewrite the water saturation relationship into a water intrusion constant. Through the relationship between the ratio of gas phase relative permeability and water phase relative permeability and water saturation, combined with the relationship between the ratio of gas phase relative permeability and water phase relative permeability and production water-gas ratio and condensate water-gas ratio, the relationship between water saturation and production water-gas ratio and condensate water-gas ratio is obtained, and the underground water production formula of gas well based on gas production and production water-gas ratio is established. Combine the gas well underground water production formula 1 and the gas well underground water production formula 2 to obtain the expression of water phase relative permeability including the water invasion constant; By substituting the water phase relative permeability including the water invasion constant into the Brooks-Corey model, the gas phase relative permeability including the water invasion constant is expressed; Substituting the gas phase relative permeability into the productivity equation, a productivity equation taking into account the activity of the water body is obtained, which is used to predict the productivity of low permeability gas reservoirs.

[0006] In some embodiments, the production capacity equation is an integral expression of the gas phase motion equation and the water phase motion equation in the reservoir flow region; The gas phase is a high-speed non-Darcy flow. Considering the influence of the starting pressure gradient, the gas phase motion equation is expressed as: The water phase is Darcy flow, and the water phase motion equation is expressed by the following formula: in, 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; m 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 percolation velocity; β is the non-Darcy flow coefficient, m -1 , , m / s; is the density of natural gas, kg / m 3 , ;M air is the molar mass of air, g / mol; is the relative density of natural gas; Initiate a pressure gradient for the gas phase; k rw is the relative permeability of water phase; m w is the formation water viscosity, mPa·s; is the water phase seepage velocity, m / s; l w is the starting pressure gradient of the water phase, MPa / m.

[0007] In some embodiments, in the gas phase motion equation and the water phase motion equation, the pressure sensitivity effect of the reservoir permeability changing with the formation pressure is considered to establish the equation: in, k is the reservoir permeability, 10 -3 μm 2 ; k i is the original permeability of the reservoir, 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.

[0008] In some embodiments, when integrating the equation of motion for the water phase, the average pressure Simplify the integral: in, p e is the boundary pressure, MPa; p wf is the bottom hole pressure, MPa; ψ w ( x ) is the pseudo-pressure function; m w is the formation water viscosity, mPa·s; k i is the original permeability of the reservoir, 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 air supply radius, m; r w is the well radius, m; l 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; p is the pressure at any point in the gas reservoir, MPa.

[0009] In some embodiments, the underground water production formula of the gas well is: in, 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 water phase; h is the effective thickness of the reservoir, m; ψ w ( x ) is the pseudo-pressure function; l 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 original formation pressure, MPa; p is the pressure at any point in the gas reservoir, MPa; r e is the air supply radius, m; r w is the well radius, m; m w is the formation water viscosity, mPa·s.

[0010] In some embodiments, the second formula for underground water production of a gas well is: in, q w is the underground water production of the gas well, m 3 / d; 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 cgris the condensate water-gas ratio, m 3 / 10 4 m 3 .

[0011] In some embodiments, the water invasion constant B is: in, oh is the water storage volume coefficient applicable to edge water, ; R is the degree of recovery; when 1≤B<2, the formation water is in an active state; when 2≤B<4, the formation water is in a secondary active state; when B≥4, the formation water is in an inactive state.

[0012] In some embodiments, the energy production equation taking into account the activity of the water body is: in, p e is the boundary pressure, MPa; p wf is the bottom hole pressure, MPa; ψ w ( x ) is the pseudo-pressure function; is the surface gas production, m 3 / d; a w is the intermediate calculation parameter, ; b w is the intermediate calculation parameter, ; c is the intermediate calculation parameter, ; m ց is the viscosity of natural gas, mPa·s; k i is the original permeability of the reservoir, 10 -3 μm 2 ; k rgw is the relative permeability of the gas phase taking into account the activity of the water body; 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 air supply radius, m; r wis 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); is the relative density of natural gas; Initiate a pressure gradient for the gas phase; is the average pressure in the gas reservoir.

[0013] In a second aspect, an embodiment of the present application provides a storage medium, wherein the storage medium stores a terminal program, and when the terminal program is executed, the method for predicting the production capacity of a low permeability gas reservoir as described above is performed.

[0014] In a third aspect, an embodiment of the present application provides a low permeability gas reservoir capacity prediction device, comprising a memory, a processor, and a computer program stored in the memory and executable in the processor, the computer program comprising steps corresponding to the low permeability gas reservoir capacity prediction method described above.

[0015] It can be seen from the above technical solution that the beneficial effects of this application are: 1. The method of the present application takes both gas-water phase movement into consideration in capacity prediction, and can better simulate the actual mining situation in low permeability gas reservoirs. Taking water invasion into consideration, a water invasion constant is established through the water storage volume coefficient and the recovery degree to reflect the water body activity, and then the water saturation, water phase relative permeability, and gas phase relative permeability can be expressed as expressions about the water invasion constant. At the same time, the phase permeability and material balance are combined, and finally the permeability expression related to the water body activity is introduced into the capacity equation, and then the influence of the water body activity on the gas reservoir capacity can be considered. Since the capacity equation can be based on multiple factors including the starting pressure gradient and the stress sensitivity effect, a capacity prediction model with multiple factors coupled including formation water invasion can be established, so as to solve the technical problem that it is difficult for traditional methods to accurately predict the capacity of low permeability gas reservoirs, and effectively improve the development efficiency and economic benefits of low permeability gas reservoirs.

[0016] 2. The storage medium of the present application provides a storage medium by applying a capacity prediction method in the storage medium, so that the storage medium can be applied to a variety of electronic devices, thereby realizing rapid prediction of the capacity of low permeability gas reservoirs under the dynamic influence of water invasion.

[0017] 3. The device of the present application executes the corresponding steps of the method for predicting the production capacity of low permeability gas reservoirs through a computer program, and can quickly calculate the production capacity of low permeability gas reservoirs. The device can quickly predict the production capacity based on physical devices, and intuitively obtain the production capacity prediction results, providing a reliable production capacity prediction tool for gas field developers. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other embodiments and drawings can be obtained based on these drawings without creative work. The block diagrams shown in the drawings are only functional entities, which do not necessarily correspond to physically independent entities, that is, these functional entities can be implemented in software form, or in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices. The flowcharts shown in the drawings are only exemplary illustrations, and do not necessarily include all the contents and operations / steps, nor do they have to be executed in the order described. For example, some operations / steps can also be decomposed, and some operations / steps can be merged or partially merged, so the actual execution order may change according to the actual situation.

[0019] Figure 1 A schematic diagram of an embodiment of a method for predicting the productivity of a low permeability gas reservoir according to the present invention is shown; Figure 2 The present invention is applied to a low permeability gas reservoir in Sichuan Basin and a fitting diagram of the gas-water relative permeability ratio and water saturation; DETAILED DESCRIPTION

[0020] The following will be combined with the accompanying drawings corresponding to the specific implementation methods of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. The following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the present application for protection. The described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, various different configurations can be used to arrange and design. All other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0021] The present application is described below with reference to the accompanying drawings and specific embodiments: Please refer to Figure 1The first embodiment of the present application provides a method for predicting the production capacity of a low permeability gas reservoir, which not only helps to optimize the single well production allocation plan, but also provides a scientific basis for the formulation of the overall development strategy of the gas reservoir. The method for predicting the production capacity of a low permeability gas reservoir is analyzed based on the following assumptions about the gas reservoir conditions: Seepage characteristics assumption: the gas phase follows high-speed non-Darcy seepage flow, and the liquid phase obeys Darcy's seepage law; Temperature characteristics assumptions: Constant temperature conditions are maintained during gas reservoir development; Reservoir characteristics assumptions: The reservoir has isotropic characteristics; Production characteristics 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; Mechanical characteristics assumption: Ignore the effects of gravity and capillary force on two-phase seepage.

[0022] The low permeability gas reservoir productivity prediction method includes: S1. Based on the gas-water two-phase motion equation, the production capacity equation and the gas well underground water production formula 1 are established; when establishing the production capacity equation, it can be expressed in the form of pseudo-pressure, and then conventional corrections are performed, in which the water phase motion equation is integrated to obtain the gas well underground water production formula 1. Low permeability gas reservoirs are often connected to water bodies. 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 production of gas wells. Therefore, when predicting the production capacity of low permeability gas reservoirs, it is necessary to consider the gas-water two-phase flow.

[0023] S2. Considering the activity of water bodies, the water invasion constant is established through the ratio of the natural logarithm of the water volume coefficient and the degree of production; the water invasion constant is established, that is, the water invasion constant = the natural logarithm of the water volume coefficient / the natural logarithm of the degree of production. This quantifies the index of water body activity and can objectively evaluate the impact of water invasion on the exploitation of low permeability gas reservoirs. The activity of water bodies refers to the activity of formation water in the gas reservoir in water-producing gas wells. The invasion of formation water into the gas reservoir will occupy the gas flow channel. These factors will affect the production capacity of the gas well. The production capacity refers to the gas production of the gas well in one day under the theoretical maximum pressure difference. Therefore, it is necessary to consider the activity of water bodies in order to more accurately calculate the production capacity of low permeability gas reservoirs.

[0024] S3. Based on the material balance principle, the relationship between water saturation and cumulative water intrusion and geological reserves is established, and the water storage volume coefficient is used to rewrite it into a water saturation relationship that includes a water intrusion constant. The material balance principle is one of the basic principles in oil and gas 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 and cumulative water intrusion and geological reserves is a conventionally established relationship, but in this application, a water storage volume coefficient is introduced, so that when describing the expression of water saturation and cumulative water intrusion and geological reserves, the water intrusion constant is added, that is, the local expression of the water storage volume coefficient in the relationship is replaced by the water intrusion constant.

[0025] 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.

[0026] 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.

[0027] 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.

[0028] 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.

[0029] The accuracy of existing low-permeability gas reservoir capacity prediction methods needs to be improved, and there are obvious limitations: on the one hand, the existing prediction models that consider the impact of water production often ignore the dynamic impact of water activity on gas reservoir capacity, and only focus on single factors such as the start-up pressure gradient or stress sensitivity effect; on the other hand, the traditional single-phase seepage model cannot accurately describe the gas-water two-phase flow characteristics. Therefore, the existing low-permeability gas reservoir capacity prediction does not take into account the water activity, and water invasion will affect the gas reservoir capacity, which in turn leads to low accuracy of capacity prediction.

[0030] This application takes both gas and water phase movement into account in the capacity prediction, and can better simulate the actual mining situation in low permeability gas reservoirs. Considering water invasion, the water invasion constant is established by the water volume coefficient and the recovery degree to reflect the water activity, and then the water saturation, water phase relative permeability, and gas phase relative permeability can be expressed as expressions about the water invasion constant. At the same time, the phase permeability and material balance are combined, and finally the permeability expression related to the water activity is introduced into the capacity equation, so that the influence of water activity on the gas reservoir capacity can be considered. Since the capacity equation can be based on multiple factors including the starting pressure gradient and the stress sensitivity effect, a capacity prediction model with multiple factors coupled including formation water invasion can be established, which solves the technical problem that traditional methods are difficult to accurately predict the capacity of low permeability gas reservoirs, and effectively improves the development efficiency and economic benefits of low permeability gas reservoirs. This method is suitable for the dynamic prediction and evaluation of capacity in the development process of low permeability gas reservoirs, and can also be extended to the capacity prediction research in the development of unconventional natural gas resources such as low permeability gas reservoirs and shale gas reservoirs, as well as the related technical research on porous media seepage phenomena in oil and gas field development projects.

[0031] In some embodiments, the production capacity equation is an integral expression of the gas phase motion equation and the water phase motion equation in the reservoir flow region; The gas phase is a high-speed non-Darcy flow. Considering the influence of the starting pressure gradient, the gas phase motion equation is expressed as: The water phase is Darcy flow, and the water phase motion equation is expressed by the following formula: in, 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; mg 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 percolation velocity; β is the non-Darcy flow coefficient, m -1 , , m / s; is the density of natural gas, kg / m 3 , ;M air is the molar mass of air, g / mol; is the relative density of natural gas; Initiate a pressure gradient for the gas phase; k rw is the relative permeability of water phase; m w is the formation water viscosity, mPa·s; is the water phase seepage velocity, m / s; l w is the starting pressure gradient of the water phase, MPa / m.

[0032] In some embodiments, during the development of gas reservoirs, as the reservoir pressure continues to drop, the stress sensitivity effect gradually emerges, which has a significant impact on the gas reservoir productivity. Therefore, in the gas phase motion equation and the water phase motion equation, in order to quantitatively characterize the relationship between the reservoir permeability and the formation pressure, the pressure sensitivity effect of the reservoir permeability changing with the formation pressure is considered, and the following equation based on the stress sensitivity effect is established: in, k is the reservoir permeability, 10 -3 μm 2 ; k i is the original permeability of the reservoir, 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.

[0033] Substituting formula (3) into formula (1) and (2), we can obtain: in, 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; m 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 gas phase relative permeability; k rw is the relative permeability of 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 , ; is the density of natural gas, kg / m 3 , ; is the gas phase percolation velocity; Initiate a pressure gradient for the gas phase; m w is the formation water viscosity, mPa·s; is the water phase seepage velocity, m / s; l w is the water phase starting pressure gradient, MPa / m; k rw is the relative permeability of water phase.

[0034] The seepage velocity of gas in the formation can be expressed by the following formula: in, is the surface gas production, m 3 / d; p sc is the pressure under standard conditions, MPa; T is the formation temperature, K ; Z is the natural 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.

[0035] In some embodiments, equation (6) is substituted into equation (4) to integrate the gas phase motion equation while using the average pressure By simplifying the integral, we can obtain the correlation between pressure and underground water production in the gas phase: in, p e is the boundary pressure, MPa; p wf is the bottom hole pressure, MPa; ψ w ( x ) is the pseudo-pressure function; ; m g is the viscosity of natural gas, mPa·s; p sc is the pressure under standard conditions, MPa; T is the formation temperature, K ; Z is the natural gas deviation factor; r e is the air 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 gas phase relative permeability; 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; is the surface gas production, m 3 / 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; is the relative density of natural gas; R g is the gas constant, MPa·m 3 / (mol·k); Start a pressure gradient for the gas phase.

[0036] In some embodiments, equation (6) is substituted into equation (5) to integrate the equation of motion for the water phase, while using the average pressure Simplifying the integral, we get the correlation between pressure and underground water production of the water phase: in, p e is the boundary pressure, MPa; p wf is the bottom hole pressure, MPa; ψ w ( x ) is the pseudo-pressure function; ; m w is the formation water viscosity, mPa·s; k i is the original permeability of the reservoir, 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 air supply radius, m; r w is the well radius, m; l 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 original formation pressure, MPa; p is the pressure at any point in the gas reservoir, MPa.

[0037] In some implementations, formula (8) is rewritten to obtain formula 1 for underground water production of a gas well: in, 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 ; krw is the relative permeability of water phase; h is the effective thickness of the reservoir, m; ; l 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 original formation pressure, MPa; p is the pressure at any point in the gas reservoir, MPa; r e is the air supply radius, m; r w is the well radius, m; m w is the formation water viscosity, mPa·s.

[0038] According to the material balance principle, the current water saturation of the formation can be expressed by the following formula: in, S w is water saturation; S wi is the bound water saturation; G is geological reserves, 10 8 m 3 ; W e is the cumulative water intrusion, 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.

[0039] In the study of water invasion mechanism of gas reservoirs, the water volume coefficient is introduced to quantitatively characterize the degree of formation water invasion. oh As an evaluation indicator, it is defined as: in, oh is the water storage volume coefficient applicable to edge water; G is geological reserves, 10 8 m 3 ; W e is the water intrusion, 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.

[0040] In some implementations, after studying the relationship between water invasion and gas reservoir recovery, it is found that there is a certain relationship between the water volume coefficient and the recovery degree, that is, the water invasion constant B is: in, oh is the water storage volume coefficient applicable to edge water, ; R is the degree of recovery; when 1≤B<2, the formation water is in an active state; when 2≤B<4, the formation water is in a secondary active state; when B≥4, the formation water is in an inactive state.

[0041] Combining formulas (10), (11) and (12), we get: in, S w is water saturation; S wi is the bound water saturation; R is the recovery degree; B is the water invasion constant.

[0042] There is an empirical relationship between the ratio of gas phase relative permeability, water phase relative permeability, and water saturation: in, k rg is the gas phase relative permeability; k rw is the relative permeability of water phase; a、b are the fitting coefficients respectively; S w is water saturation; e Is a mathematical constant.

[0043] At the same time, the ratio of gas phase relative permeability to water phase relative permeability has the following relationship with the production water-gas ratio and the condensate water-gas ratio: in, k rg is the gas phase relative permeability; k rw is the relative permeability of water phase; is the viscosity of natural gas, mPa·s; Bg is the gas volume coefficient; m w is the formation water viscosity, mPa·s; 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 .

[0044] Substituting formula (14) into formula (15) yields: in, 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 ; is the viscosity of natural gas, mPa·s; B g is the gas volume coefficient; m 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.

[0045] 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: in, q w is the underground water production of the gas well, m 3 / d; is the surface gas production, m 3 / d; B w is the formation water volume coefficient; Wgr 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 .

[0046] Combining equations (9) and (17), the relative permeability of the water phase can be expressed as follows: in, k rw is the relative permeability of water phase; m w is the formation water viscosity, mPa·s; B w is the formation water volume coefficient; is the surface gas production, m 3 / d; r e is the air 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 original permeability of the reservoir, 10 -3 μm 2 ; h is the effective thickness of the reservoir, m; ; l 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 original formation pressure, MPa; is the average pressure of the gas reservoir, MPa.

[0047] Substituting formula (13) and formula (16) into formula (18), we can obtain: in, is the intermediate calculation parameter; is the viscosity of natural gas, mPa·s; B g is the gas volume coefficient; is the surface gas production, m 3 / d; r e is the air supply radius, m; r w is the well radius, m; k i is the original permeability of the reservoir, 10 -3 μm 2 ; h is the effective thickness of the reservoir, m; ; l 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 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.

[0048] From the Brooks-Corey model, we know that the relative permeability of gas and water can be expressed as: 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 w All are Corey index; 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.

[0049] Combining equations (19), (20) and (21), we can obtain the gas phase relative permeability considering the activity of the water body: 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 w Both are Corey indexes.

[0050] In some embodiments, by substituting formula (22) into formula (7), the production capacity equation considering the water body activity, the starting pressure gradient and the stress sensitivity effect is: in, p e is the boundary pressure, MPa; p wf is the bottom hole pressure, MPa; ψ w ( x ) is the pseudo-pressure function; is the surface gas production, m 3 / d; a w is the intermediate calculation parameter, ; b w is the intermediate calculation parameter, ; c is the intermediate calculation parameter, ; m ց is the viscosity of natural gas, mPa·s; k i is the original permeability of the reservoir, 10 -3 μm 2 ; k rgw is the relative permeability of the gas phase taking into account the activity of the water body; 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; re is the air 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); is the relative density of natural gas; Initiate a pressure gradient for the gas phase; is the average pressure in the gas reservoir.

[0051] Please refer to Figure 2 , taking a low permeability gas reservoir in Sichuan Basin as an example: the initial formation pressure of the water-producing gas well in the gas reservoir is 40.21MPa, the formation temperature is 95.71℃, and the initial formation permeability is 4.65´10 -3 μm 2 , porosity is 4.72%, effective thickness is 52.27 m, relative density of natural gas is 0.5902, and stress sensitivity coefficient is 0.0214 MPa -1 , the gas phase starting pressure is 0.001MPa / m, and the water phase starting pressure gradient is 0.003MPa / m. Combined with relevant literature, the water invasion constant is calculated to be 2.47, and the fitting relationship between the gas-water relative permeability ratio and water saturation is shown in Figure 2 By combining the production dynamic data of the well with the above parameters and using the established low permeability gas reservoir capacity calculation method, the open flow rate of the well is calculated to be 17.14´10 4 m 3 / d, and the unimpeded flow rate of the well test is 18.57´10 4 m 3 / d compared, the relative error is only 7.71%, which is relatively small and meets the requirements of engineering application. Based on the actual core test phase permeability curve of the gas reservoir, the ratio of gas phase relative permeability to water phase relative permeability and water saturation are fitted to obtain the fitting coefficient a is 97239, the fitting coefficient b The method of this application can directly use the on-site production dynamic data for rapid calculation, effectively realize the accurate prediction of production capacity, and then timely optimize the production system according to different water body activity levels, starting pressure gradients and stress sensitivity effect conditions, formulate targeted water control and management measures, and improve the single well production capacity.

[0052] The second aspect of the present application provides a storage medium, which is a readable storage medium, and the readable storage medium stores a terminal program. When the terminal program is executed, the method, storage medium and device for predicting the production capacity of low permeability gas reservoirs as in any of the above embodiments are performed. If the module / unit integrated in the terminal device is implemented in the form of a software functional unit and sold or used as an independent product, the terminal program can be stored in a readable storage medium. Based on this understanding, the present application implements all or part of the process of the method in the above embodiment, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a readable storage medium. When the computer program is executed by a processor, the steps of each method in the above embodiment can be implemented. When the computer program is executed by the processor, the specific implementation of each step and the technical effect produced are the same as those in the above method embodiment. For brief description, the parts not mentioned in this embodiment can refer to the corresponding content in the above method embodiment. 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, thereby realizing the rapid prediction of the production capacity of low permeability gas reservoirs under the dynamic influence of water invasion.

[0053] In a third aspect of the present application, a low permeability gas reservoir capacity prediction device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable in the processor, wherein the computer program comprises the steps corresponding to the above-mentioned low permeability gas reservoir capacity prediction method, storage medium, and device, such as a computing program. When the processor executes the computer program, the steps in the above-mentioned method embodiment are implemented, such as Figure 1 The steps shown; or, when the processor executes the computer program, the functions of each module / unit in the embodiment of the above-mentioned device are realized, such as fast calculation. It should be understood that the device of each embodiment of the present application can be implemented based on a memory and a processor, each memory is used to store a computer program for executing the above-mentioned method of the present application, and the processor executes the above-mentioned computer program, so that the device implements the method of each of the above-mentioned embodiments. By executing the steps corresponding to the method for predicting the capacity of a low permeability gas reservoir through a computer program, the capacity of a low permeability gas reservoir can be quickly calculated, and the device can rely on physical devices to quickly predict the capacity, intuitively obtain the capacity prediction results, and provide a reliable capacity prediction tool for gas field developers.

[0054] In some embodiments, the computer program can be divided into one or more modules / units, one or more modules / units are stored in a memory and executed by a processor to complete the method of the present application. One or more modules / units can be instruction segments of a series of computer programs that complete specific functions, 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 only schematic. For example, the division of modules or units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed. At the same time, the direct coupling or indirect coupling or communication connection between the components that make up the device / terminal device can be through some interfaces, and the connection can be electrical, mechanical or other forms. The above-mentioned modules or units can be integrated in a processor, can exist physically alone, or can be integrated or combined with two or more units; the above-mentioned modules or units can be implemented in the form of hardware or in the form of software functional units.

[0055] In some embodiments, the above-mentioned device can be a desktop computer, a notebook, an industrial computer, a PDA, a tablet computer or other mobile terminal, as well as a computer device such as a cloud server, and is not limited to which operating system is installed. The device may include, but is not limited to: a processor and a memory. Those skilled in the art will understand that the example of the low permeability gas reservoir capacity prediction device does not constitute a limitation on the device, and may include more or fewer components than shown in the figure, or combine certain components, or different components. For example, the device may also include input devices, output devices, network access devices, buses, etc., and may also include a display screen for intuitively displaying calculation results.

[0056] Regarding the specific implementation of this application, it should be noted that: 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 the methods, devices (systems), and computer program products according to the embodiments of the present application. In the description of the present application, the processor can be a central processing unit (CPU), a single-chip microcomputer (MCU), a graphics processor (GPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC) or a field programmable gate array (FPGA), and can also be other general-purpose processors, programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc. The processor is the control center of the X device / terminal device, and uses various interfaces and lines to connect the various parts of the entire X device / terminal device. In the description of the present application, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form, etc. Computer-readable storage media may include any entity or device that can carry computer program code, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory, random access memory, electrical carrier signal, telecommunication signal, software distribution media or other recording media, etc.

[0057] In the description of the present application, the terms "include", "comprises" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, device or readable storage medium including a series of elements includes not only those elements, but also includes other elements that are not explicitly listed and are consistent with the concept of the present application, or also includes elements inherent to such process, method, device or readable storage medium. In the absence of further restrictions, the elements defined by the sentence "comprises a ..." do not exclude the presence of additional elements in the process, method, device or readable storage medium including the elements.

[0058] In the description of the present application, the descriptions of reference terms such as "some embodiments", "optional embodiments", "examples", "specific examples", "optional examples" or "optional embodiments" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiments or examples 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 do not necessarily refer to the same embodiments or examples. 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 may combine and combine the different embodiments or examples described in this specification.

[0059] In addition, the technical solutions between the various embodiments can be combined with each other, but it must be based on the ability of ordinary technicians in the field to implement. Although the embodiments of the present application have been shown and described, these embodiments can be changed, modified, replaced and modified in various ways without departing from the principles and purpose of the present application. Ordinary technicians in the field can understand that according to the technical inspirations disclosed in the present application, various other specific changes and combinations of embodiments that do not depart from the essence of the present application are made, which are still within the scope of protection defined by the claims of the present invention and their equivalent technical solutions.

[0060] At the same time, the technical solutions between the various embodiments can be combined with each other, but they must be based on the fact that they can be implemented by ordinary technicians in this field. When the combination of technical solutions is mutually contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by this application.

Claims

1. A method for predicting the productivity of a low permeability gas reservoir, characterized in that: include: Based on the gas-water two-phase motion equation, the production capacity equation and the underground water production formula of the gas well are established; Considering the activity of water bodies, the water invasion constant is established by the natural logarithm ratio of the water volume coefficient and the extraction degree; Based on the material balance principle, the relationship between water saturation, cumulative water intrusion and geological reserves is established, and the water volume coefficient is used to rewrite the water saturation relationship into a water intrusion constant. Through the relationship between the ratio of gas phase relative permeability and water phase relative permeability and water saturation, combined with the relationship between the ratio of gas phase relative permeability and water phase relative permeability and production water-gas ratio and condensate water-gas ratio, the relationship between water saturation and production water-gas ratio and condensate water-gas ratio is obtained, and the underground water production formula of gas well based on gas production and production water-gas ratio is established. Combine the gas well underground water production formula 1 and the gas well underground water production formula 2 to obtain the expression of water phase relative permeability including the water invasion constant; By substituting the water phase relative permeability including the water invasion constant into the Brooks-Corey model, the gas phase relative permeability including the water invasion constant is expressed; Substituting the gas phase relative permeability into the productivity equation, a productivity equation taking into account the activity of the water body is obtained, which is used to predict the productivity of low permeability gas reservoirs.

2. The method for predicting the productivity of low permeability gas reservoirs according to claim 1, characterized in that: The production capacity equation is an integral expression of the gas phase motion equation and the water phase motion equation in the reservoir flow region; The gas phase is a high-speed non-Darcy flow. Considering the influence of the starting pressure gradient, the gas phase motion equation is expressed as: The water phase is Darcy flow, and the water phase motion equation is expressed by the following formula: in, 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 percolation velocity; β is the non-Darcy flow coefficient, m -1 , , m / s; is the density of natural gas, kg / m 3 , ;M air is the molar mass of air, g / mol; is the relative density of natural gas; Initiate a pressure gradient for the gas phase; k rw is the relative permeability of water phase; μ w is the formation water viscosity, mPa·s; is the water phase seepage velocity, m / s; λ w is the starting pressure gradient of the water phase, MPa / m.

3. The method for predicting the productivity of low permeability gas reservoirs according to claim 2, characterized in that: In the gas phase motion equation and the water phase motion equation, the pressure sensitivity effect of reservoir permeability changing with formation pressure is considered and the equation is established: in, k is the reservoir permeability, 10 -3 μm 2 ; k i is the original permeability of the reservoir, 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.

4. The method for predicting the productivity of low permeability gas reservoirs according to claim 2, characterized in that: When integrating the water phase motion equation, the average pressure Simplify the integral: in, 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 permeability of the reservoir, 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 air 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.

5. The method for predicting the productivity of low permeability gas reservoirs according to claim 1, characterized in that: The underground water production formula of the gas well is: in, 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 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 air supply radius, m; r w is the well radius, m; μ w is the formation water viscosity, mPa·s.

6. The method for predicting the productivity of low permeability gas reservoirs according to claim 5, characterized in that: The second formula for underground water production of the gas well is: in, q w is the underground water production of the gas well, m 3 / d; 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 method for predicting the productivity of low permeability gas reservoirs according to claim 1, characterized in that: The water intrusion constant B is: in, ω is the water storage volume coefficient applicable to edge water, ; R is the degree of recovery; when 1≤B<2, the formation water is in an active state; when 2≤B<4, the formation water is in a secondary active state; when B≥4, the formation water is in an inactive state.

8. The method for predicting the productivity of low permeability gas reservoirs according to any one of claims 1 to 7, characterized in that: The production capacity equation considering the activity of water body is: in, p e is the boundary pressure, MPa; p wf is the bottom hole pressure, MPa; ψ ( x ) is the pseudo-pressure function; is the surface gas production, m 3 / d; a w is the intermediate calculation parameter, ; b w is the intermediate calculation parameter, ; c is the intermediate calculation parameter, ; is the viscosity of natural gas, mPa·s; k i is the original permeability of the reservoir, 10 -3 μm 2 ; k rgw is the relative permeability of the gas phase taking into account the activity of the water body; 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 air 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); is the relative density of natural gas; Initiate a pressure gradient for 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, the method for predicting the productivity of a low permeability gas reservoir as described in any one of claims 1-8 is performed.

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

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