Method for predicting productivity of water-producing gas well of water-driven gas reservoir

Abstract

The invention provides a method for predicting the productivity of a water-producing gas well of a water-driven gas reservoir, which enables a mine field to directly analyze and judge the influence of the activity of a formation water body on the productivity of the gas well. Based on a gas-water seepage theory and a material balance theory, parameters (water invasion constants) directly representing the active degree of a formation water body are introduced into a gas well productivity equation by utilizing gas well production dynamic data, a new productivity prediction model considering the influence of the high-speed non-darcy effect, the active degree of the water body and a skin coefficient on the productivity of the gas well is established, and the method belongs to an original innovative technology. According to the method, the productivity of the water-producing gas well of the water-driven gas reservoir under different water body active degrees can be quickly and conveniently determined by analyzing the model and utilizing gas well production dynamic data, so that gas field developers can timely adjust a gas well exploitation system according to the influence of different water body active degrees on the productivity of the gas well, and the production efficiency of the gas well is improved. And theoretical guidance and technical support are provided for formulating water control measures, delaying gas reservoir water invasion and improving the gas reservoir development effect.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of gas well productivity prediction, in particular to a water-drive gas reservoir water-producing gas well productivity prediction method, and more particularly to a water-drive gas reservoir water-producing gas well productivity prediction method considering the activity degree of water body. BACKGROUND

[0002] Among the gas reservoirs developed in China at present, nearly half of the gas reservoirs have active edge and bottom water. For example, among the about 500 gas reservoirs and gas-bearing structures in the Sichuan Basin, the number of water-drive gas reservoirs is nearly 250, accounting for about half of the total number of gas reservoirs. In the development process of water-drive gas reservoirs, as the water phase gradually invades the formation, gas-water two-phase seepage is formed in the formation, which increases the fluid seepage resistance and rapidly reduces the productivity of gas wells. The activity of underground water body seriously restricts the production increase of gas reservoirs. Accurate evaluation of the influence of the activity of underground water body on the productivity of gas wells is of great significance for the adjustment of gas well production system, the formulation of water control measures, the delay of water invasion of gas reservoirs, the promotion of gas well production increase and the improvement of the development effect of gas reservoirs.

[0003] However, in the current productivity prediction methods, some models only consider single-phase gas flow to establish the productivity prediction model, which is difficult to apply to the productivity prediction of water-drive gas reservoir water-producing gas wells. In the productivity prediction models considering the influence of water production on productivity, the production water-gas ratio is introduced or the liquid phase damage is considered as the deterioration of the permeability around the well to indirectly analyze the influence of the activity of formation water body on the productivity of gas wells, which is difficult to directly reflect the influence law of the activity of formation water body on the productivity of gas wells. Therefore, it is urgent to propose a calculation method directly considering the influence of water body activity on the productivity of water-drive gas reservoir water-producing gas wells to help reasonably predict the productivity of water-drive gas reservoir water-producing gas wells. SUMMARY

[0004] In view of the above problems, the purpose of the present application is to provide a calculation method directly considering the influence of the activity degree of water body on the productivity of water-drive gas reservoir water-producing gas wells, to solve the problem that the existing productivity calculation methods do not directly consider the influence of water body activity on the productivity of water-drive gas reservoir water-producing gas wells and are difficult to directly reflect the influence of formation water body on the productivity of gas wells, and to provide theoretical guidance and technical support for gas field developers to reasonably allocate production, formulate water control measures, delay water invasion of gas reservoirs and develop reasonable development schemes.

[0005] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0006] A water-drive gas reservoir water-producing gas well productivity prediction method, characterized by using a water-drive gas reservoir non-liquid-accumulation water-producing gas well productivity equation considering the activity degree of water body for prediction, and the specific equation is as follows:

[0007]

[0008] wherein,

[0009]

[0010] In the formula: p wf is the average formation pressure and the bottom-hole flowing pressure; q gsc is the surface gas production of the gas well; μ g is the viscosity of natural gas; Z is the deviation factor of natural gas; T is the thermodynamic temperature of the formation; h is the effective thickness; r e , r w is the gas supply radius and the well radius; S is the skin factor; is the relative permeability of the gas phase corresponding to the irreducible water saturation; is the relative permeability of the water phase corresponding to the residual gas saturation; k abs is the absolute permeability.

[0011] The application provides a water-drive gas reservoir water-producing gas well productivity prediction method, which enables a mine field to directly analyze and judge the influence of formation water body activity on gas well productivity; based on gas-water seepage flow theory and material balance theory, a parameter (water invasion constant) directly representing the activity degree of a formation water body is introduced into a gas well productivity equation by using gas well production dynamic data, a new productivity prediction model considering the influence of high-speed non-Darcy effect, water body activity degree and skin factor on gas well productivity is established, and the application belongs to original innovation technology. The application is an analytical model, which can quickly and conveniently determine the productivity of a water-drive gas reservoir water-producing gas well under different water body activity degrees by using gas well production dynamic data, so that gas field developers can timely adjust a gas well production system, develop water control measures, delay water invasion of a gas reservoir and improve the development effect of the gas reservoir, and provide theoretical guidance and technical support.

[0012] Further, the water-drive gas reservoir non-liquid-accumulation water-producing gas well productivity equation considering the water body activity degree is established by introducing the relative permeability of the gas phase considering the influence of the water body activity degree into the planar radial pseudo-steady seepage binomial productivity equation considering the high-speed non-Darcy effect and formation pollution.

[0013] Further, the planar radial pseudo-steady seepage binomial productivity equation considering the high-speed non-Darcy effect and formation pollution is established based on gas-water seepage flow theory.

[0014] The planar radial pseudo-steady seepage binomial productivity equation considering the high-speed non-Darcy effect and formation pollution is:

[0015]

[0016] In the formula:

[0017]

[0018]

[0019] wherein the gas high-speed non-Darcy flow coefficient is calculated by the following formula:

[0020]

[0021] wherein: p wf is the average formation pressure and the bottom-hole flowing pressure; q gsc is the surface gas production of the gas well; μ g is the viscosity of the natural gas; Z is the deviation factor of the natural gas; T is the thermodynamic temperature of the formation; k is the reservoir permeability; k g is the effective permeability of the gas phase; h is the effective thickness; r e , r w is the gas supply radius and the well radius; S is the skin factor; γ g is the relative density of the natural gas; and β is the Forchheimei coefficient.

[0022] Further, the gas phase relative permeability considering the water body activity degree is calculated by the following method:

[0023] Step a: based on the material balance theory, the relationship between the water invasion constant and the formation water saturation is established;

[0024] Step b: the power function relationship between the gas-water relative permeability ratio and the water saturation, and the relationship between the gas-water relative permeability ratio and the production water-gas ratio are used to calculate the production water-gas ratio considering the condensate water-gas ratio;

[0025] Step c: the water phase relative permeability is calculated by using the pseudo-stable water production formula considering the formation pollution and the mine water production calculation formula;

[0026] Step d: based on step a, step b and step c, the water phase relative permeability considering the water body activity degree is calculated;

[0027] Step e: based on step d, the gas phase relative permeability considering the water body activity degree is calculated by combining the power function relationship of the relative permeability curve.

[0028] A water drive gas reservoir water-gas well productivity prediction method, comprising the following steps:

[0029] Step 1: based on the gas-water seepage theory, a planar radial pseudo-stable seepage binomial productivity equation considering the high-speed non-Darcy effect and the formation pollution is established;

[0030] Step 2: based on the material balance theory, the relationship between the water invasion constant and the formation water saturation is established;

[0031] Step 3: The relationship between the gas-water relative permeability ratio and the water-gas ratio is combined with the power function relationship between the gas-water relative permeability ratio and the water saturation, so that the water-gas ratio considering the condensate water-gas ratio is represented;

[0032] Step 4: The water phase relative permeability is represented by using the pseudo-stable water production formula considering the formation pollution and the field water production calculation formula;

[0033] Step 5: The water phase relative permeability considering the water body activity degree is represented based on steps 2, 3 and 4;

[0034] Step 6: The gas phase relative permeability considering the influence of the water body activity degree is represented based on step 5 and the power function relationship of the relative permeability curve;

[0035] Step 7: The gas phase relative permeability considering the influence of the water body activity degree is brought into step 1, and the water-drive gas reservoir un-liquid-filled water-gas well productivity equation considering the water body activity degree is established.

[0036] Finally, the water-drive gas reservoir un-liquid-filled water-gas well productivity prediction method considering the high-speed non-Darcy effect, the water body activity degree and the skin factor is established.

[0037] The above steps can be changed according to the actual situation, and the technical scheme can be completed.

[0038] The water-drive gas reservoir water-gas well productivity prediction method provided by the application can directly analyze and judge the influence of the formation water body activity on the gas well productivity; based on the gas-water seepage theory and the material balance theory, the parameter (water invasion constant) directly representing the formation water body activity degree is introduced into the gas well productivity equation by using the gas well production dynamic data, a new productivity prediction model considering the influence of the high-speed non-Darcy effect, the water body activity degree and the skin factor on the gas well productivity is established, and the application belongs to the original innovation technology. The application is an analytical model, the gas well production dynamic data is used, the water-drive gas reservoir water-gas well productivity under different water body activity degrees can be quickly and conveniently determined, so that the gas field development personnel can timely adjust the gas well production system, develop the water control measures, delay the water invasion of the gas reservoir and improve the development effect of the gas reservoir, and the application provides the theoretical guidance and technical support.

[0039] Further, in step 1, the planar radial pseudo-stable seepage binomial productivity equation considering the high-speed non-Darcy effect and the formation pollution is formula (1):

[0040]

[0041] In formula (1), the following conditions are met:

[0042]

[0043] The gas high-speed non-Darcy flow coefficient is calculated by formula (4):

[0044]

[0045] In the formula: p wf is the average formation pressure and well bottom flow pressure, MPa; q gsc is the gas well ground gas production, m 3 / d; μ g is the natural gas viscosity, mPa·s; Z is the natural gas deviation factor; T is the thermodynamic temperature of the formation, K; k is the reservoir permeability, 10 -3 μm 2 ; k rg is the gas phase relative permeability; h is the effective thickness, m; r e , r w is the gas supply radius and well radius, m; S is the skin factor; γ g is the relative density of natural gas; β is the Forchheimei coefficient, m -1 .

[0046] Further, in step 2, the water invasion constant and the relationship between the formation water saturation is:

[0047] Based on the principle of material balance, when considering the influence of edge and bottom water, the water production gas well development to a certain moment should meet the following principles: cumulative production of natural gas and cumulative production of formation water underground volume = volume expansion of underground natural gas + volume expansion of rock and bound water + formation water invasion volume; Specifically, as formula (5):

[0048]

[0049] In the formula: G p is the cumulative gas production, m 3 ; B g is the natural gas volume factor; W p is the cumulative water production, m 3 ; B w is the formation water volume factor; G is the dynamic reserves of gas reservoir, m 3 ; B gi is the natural gas volume factor under the initial pressure; S wi is the irreducible water saturation; C w is the formation water compression coefficient, MPa -1 ; C f is the rock skeleton compression coefficient, MPa -1 ; ΔP is the gas well production pressure difference, MPa; W e is the current water invasion of gas reservoir, m 3 .

[0050] From formula (5) can be obtained:

[0051]

[0052] The left side of formula (6) is the increment of the formation water saturation at the current time, and the formation water saturation at the current time can be expressed as formula (7):

[0053]

[0054] In the formula: Sw is the water saturation at the current time.

[0055] The water storage volume coefficient ω is expressed as formula (8):

[0056]

[0057] In the formula: ω is the water storage volume coefficient of the gas reservoir.

[0058] The water storage volume coefficient and the recovery degree have a relationship as formula (9):

[0059]

[0060] In the formula: B is the water influx constant; R is the recovery degree of the gas reservoir.

[0061] By combining formula (7) to formula (9), we get:

[0062] S w = R B (1-S wi )+S wi (10)

[0063] Further, in step 3, the production water-gas ratio considering the condensate water-gas ratio is: in the gas-water relative permeability curve, the ratio of the gas-water two-phase relative permeability krg / krw and the water saturation has the following relationship:

[0064]

[0065] In the formula: K rw is the water phase relative permeability; K rg is the gas phase relative permeability; a, b are the fitting coefficients of the relative permeability curve.

[0066] When considering the condensate water-gas ratio, the production water-gas ratio and the relative permeability have the following relationship:

[0067]

[0068] μ w is the formation water viscosity, mPa·s; B w is the formation water volume coefficient; W grFor production water-gas ratio, m 3 / 10 4 m 3 ; W cgr For condensate water-gas ratio, m 3 / 10 4 m 3 .

[0069] Solving equation (11) and equation (12) gives:

[0070]

[0071] Further, in step 4, the water phase relative permeability is expressed by using the pseudo-stable water production rate formula considering formation pollution and the field water production rate calculation formula, and the pseudo-stable water production rate formula considering formation pollution of the water drive gas reservoir is:

[0072]

[0073] In the formula: q w For gas well subterranean water production rate, m 3 / d; k w For water phase effective permeability, 10 -3 μm 2 ; μ w For formation water viscosity, mPa·s.

[0074] According to the field water production rate calculation formula, the gas well water production rate formula considering condensate water is:

[0075] q w = q gsc B w (W gr -W cgr )×10 -4 (15)

[0076] In the formula: B w For formation water volume coefficient; W gr For production water-gas ratio, m 3 / 10 4 m 3 ; W cgr For condensate water-gas ratio, m 3 / 10 4 m 3 .

[0077] Solving equation (14) and equation (15) gives:

[0078]

[0079] In the formula: k abs For absolute permeability, 10 -3μm 2 ; k rw is the relative permeability of water phase.

[0080] Further, in step 5, the relative permeability of water phase considering the activity of water body is expressed as:

[0081] Substitute equation (13) into equation (17) and let the right side term be:

[0082]

[0083] Further, in step 6, the relative permeability of gas phase considering the influence of the activity of water body is expressed as:

[0084] The relative permeability of gas and water phases can be expressed by the Brooks-Corey model

[0085]

[0086] where S w * is the normalized wet phase saturation, i.e.

[0087]

[0088] In the formula: is the relative permeability of water phase corresponding to residual gas saturation; is the relative permeability of gas phase corresponding to irreducible water saturation; n w , n g is the Corey index; is the normalized water phase saturation; S w is the reservoir water saturation; S wc , S gr are the irreducible water saturation and the residual gas saturation, respectively.

[0089] By combining equations (18)-(21), we have

[0090]

[0091] Further, in step 7, the relative permeability of gas phase considering the influence of the activity of water body is brought into step 1 to establish the productivity equation of a water production gas well in a water-drive gas reservoir considering the activity of water body, i.e.

[0092]

[0093] where

[0094]

[0095] Through the above derivation, based on the material balance theory and the gas-water seepage theory, a parameter (water invasion constant) representing the activity degree of the formation water is introduced into the gas well productivity equation, a new productivity prediction model considering the high-speed non-Darcy effect, skin factor and the activity degree of the formation water affecting the gas well productivity is established, and the influence of the activity degree of the formation water on the gas well productivity is analyzed.

[0096] In summary, by adopting the technical scheme, the present application has the following beneficial effects:

[0097] The present application provides a water-drive gas reservoir water-producing gas well productivity prediction method, which can directly analyze and judge the influence of the formation water activity on the gas well productivity; based on the gas-water seepage theory and the material balance theory, the parameter (water invasion constant) directly representing the activity degree of the formation water is introduced into the gas well productivity equation by using the gas well production dynamic data, a new productivity prediction model considering the high-speed non-Darcy effect, the activity degree of the formation water and the skin factor affecting the gas well productivity is established, which belongs to the original innovative technology. The present application is an analytical model, which can quickly and conveniently determine the water-drive gas reservoir water-producing gas well productivity under different activity degrees of the formation water by using the gas well production dynamic data, thereby providing theoretical guidance and technical support for the gas field development personnel to timely adjust the gas well production system, develop water control measures, delay water invasion of the gas reservoir and improve the development effect of the gas reservoir according to the influence of different activity degrees of the formation water on the gas well productivity. BRIEF DESCRIPTION OF DRAWINGS

[0098] Figure 1 It is a physical model schematic diagram.

[0099] Figure 2 It is a relative permeability ratio and water saturation relationship diagram.

[0100] Figure 3 It is a water invasion constant influence diagram on the gas well productivity.

[0101] Figure 4 It is a permeability influence diagram on the gas well productivity.

[0102] Figure 5 It is an effective thickness influence diagram on the gas well productivity. DETAILED DESCRIPTION

[0103] The present application will be described in detail below with reference to the accompanying drawings.

[0104] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application, and are not used to limit the present application.

[0105] EXAMPLE

[0106] Physical models and assumptions, specifically as follows: Figure 1 As shown.

[0107] The following assumptions are made regarding the gas reservoir conditions: ① The gas phase satisfies high-velocity non-Darcy flow, and the liquid phase satisfies Darcy's law of flow; ② The gas reservoir is at a constant temperature; ③ The reservoir is horizontal, homogeneous, and of uniform thickness; ④ Gas and water are produced simultaneously in the gas well, with no liquid accumulation; ⑤ The effects of gravity and capillary force on fluid flow are ignored.

[0108] Derivation of Capacity Forecasting Method

[0109] Step 1: Based on the gas-water seepage theory, establish a planar radial quasi-steady seepage binomial productivity equation that considers high-speed non-Darcy effect and formation contamination.

[0110] Step 2: Based on the material balance theory, establish the relationship between the water erosion constant and the formation water saturation;

[0111] Step 3: Using the power function relationship between the gas-water relative permeability ratio and water saturation, combined with the relationship between the gas-water relative permeability ratio and the production water-gas ratio, the production water-gas ratio considering the condensate water-gas ratio is expressed.

[0112] Step 4: Using the pseudo-steady water production formula that takes into account formation contamination and the mine water production calculation formula, express the relative permeability of the water phase;

[0113] Step 5: Based on Steps 2, 3, and 4, express the relative permeability of the water phase considering the water body activity level;

[0114] Step 6: Based on Step 5, and combined with the power function relationship of the relative permeability curve, express the relative permeability of the gas phase considering the influence of the water body activity level;

[0115] Step 7: Substitute the relative permeability of the gas phase, which takes into account the influence of water activity, into Step 1 to establish the production capacity equation for water-driven gas reservoirs without liquid accumulation.

[0116] Finally, a method for predicting the production capacity of water-driven gas reservoirs without liquid accumulation was established, taking into account the high-speed non-Darcy effect, water activity level, and skin coefficient.

[0117] The planar radial pseudo-steady seepage binomial productivity equation for conventional gas wells considering formation contamination is as follows:

[0118]

[0119] In the formula

[0120]

[0121] The high-velocity non-Darcy flow coefficient of gas is calculated using the following formula:

[0122]

[0123] wherein: pwf is the average formation pressure and the bottom hole flowing pressure, MPa; qgsc is the surface gas production of the gas well, m 3 / d; μg is the viscosity of natural gas, mPa·s; Z is the deviation factor of natural gas; T is the thermodynamic temperature of the formation, K; kg is the effective gas permeability, 10 -3 μm 2 ; h is the effective thickness, m; re, rw are the gas supply radius and the well radius, m; S is the skin factor (such as mechanical skin); γ g is the relative density of natural gas; β is the Forchheimei coefficient, m -1 .

[0124] Based on the principle of material balance, when the influence of edge and bottom water is considered, the water production gas well development at a certain time should meet the following principles: cumulative output of natural gas and cumulative output of formation water underground volume = volume expansion of underground natural gas + volume expansion of rock and bound water + formation water invasion volume. Therefore:

[0125]

[0126] From formula (5), the following formula can be obtained:

[0127]

[0128] wherein, C w is the isothermal compressibility, MPa -1 ; C f is the compressibility of rock, MPa -1 ; ΔP is the production pressure difference of the gas well.

[0129] The left side of formula (6) is the increment of the formation water saturation at the current time, and the formation water saturation at the current time can be expressed as:

[0130]

[0131] The water storage volume coefficient ω is expressed as:

[0132]

[0133] According to the previous research, the water storage volume coefficient and the recovery degree have the following relationship:

[0134]

[0135] wherein: B is the water invasion constant

[0136] By combining formula (7) to formula (9), the following formula is obtained:

[0137] S w = R B (1-S wi )+S wi (10)

[0138] Previous studies have found that in the gas-water relative permeability curve, the ratio of gas-water relative permeability krg / krw and water saturation exists the following relationship:

[0139]

[0140] When considering the condensate water-gas ratio, the production water-gas ratio and the relative permeability exist the following relationship:

[0141]

[0142] The simultaneous equations (11), (12) are:

[0143]

[0144] The pseudo-steady water production formula of water drive gas reservoir considering formation pollution is:

[0145]

[0146] In the formula: q w is the underground water production of gas well, m 3 / d; k w is the effective permeability of water phase, 10 -3 μm 2 ; μ w is the viscosity of formation water, mPa·s.

[0147] According to the formula of field water production, the water production formula of gas well considering condensate water is:

[0148] q w =q gsc B w (W gr -W cgr )×10 -4 (15)

[0149] In the formula: 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 .

[0150] The simultaneous equations (14), (15) can express the relative permeability of water phase as

[0151]

[0152] where k abs is the absolute permeability, 10 -3 μm 2 ; k rw is the relative permeability of water phase.

[0153] Substitute equation (13) into equation (17) and let the right side be:

[0154]

[0155] Substitute equation (10) into equation (17) to get:

[0156]

[0157] The relative permeability of gas and water phases can be represented by the Brooks-Corey model

[0158]

[0159] where S w * is the normalized wetting phase saturation, i.e.

[0160]

[0161] where: is the relative permeability of water phase corresponding to residual gas saturation; is the relative permeability of gas phase corresponding to irreducible water saturation; n is the normalized water phase saturation; Sw is the reservoir water saturation; Swc and Sgr are the irreducible water saturation and residual gas saturation, respectively.

[0162] Substitute equations (18) to (21) to get:

[0163]

[0164] Substitute equation (22) into equation (1) to get the water drive gas reservoir productivity prediction model considering the water body activity:

[0165]

[0166] where

[0167]

[0168] Through the above derivation, based on the material balance theory and the gas and water seepage theory, a parameter (water invasion constant) representing the activity degree of formation water is introduced into the gas well productivity equation, a new productivity prediction model considering the high-speed non-Darcy effect, skin factor and the influence of the activity degree of formation water on the gas well productivity is established, and the influence of the activity degree of formation water on the gas well productivity is analyzed.

[0169] Example calculation

[0170] It is known that the formation pressure of a water drive gas reservoir production gas well H1 in Sichuan Basin is 32.47 MPa, the formation temperature is 132.66 ℃, the permeability is 8.16×10-3 μm2, the porosity is 4.25%, the effective thickness is 34.88 m, the skin factor is -1.37, the relative density of natural gas is 0.6355, and the supply radius is 800 m. The water invasion constant of the well is calculated by the water invasion constant method to be 2.64. The open flow capacity of the well is calculated by the method established by the present application using the production dynamic data of the well to be 53.98×104 m3 / d, which is compared with the open flow capacity of 56.39×104 m3 / d obtained by the field test, and the relative error is only 4.27%, which is small and meets the engineering application requirements. Details are shown in the following table. Figure 2 The relative permeability ratio versus the water saturation relationship diagram. Figure 3 The water invasion constant versus the gas well productivity influence diagram.

[0171] Previous studies show that when the water invasion constant 1≤B<2, the formation water is in an active state, when the water invasion constant 2≤B<4, the formation water is in a sub-active state, and when the water invasion constant B≥4, the formation water is not active. Therefore, according to the present application, the water invasion constant is designed to be 1, 2, 3, 4 and 5 respectively, which is brought into the present application for iterative calculation to analyze the influence of the water invasion constant on the gas well productivity. Figure 3 The water invasion constant versus the gas well productivity influence diagram, as shown in the following table. Figure 3 It can be seen that as the water invasion constant decreases, i.e. the activity degree of formation water increases, the gas well productivity decreases significantly, and as the activity degree of formation water increases, the decrease amplitude of the gas well productivity increases. In the development process of the water drive gas reservoir, timely analysis of the influence of the activity of formation water on the gas well productivity is of great significance for the adjustment of gas well production system, the formulation of water control measures, the delay of water invasion of the gas reservoir, the promotion of gas well production and the improvement of the development effect of the gas reservoir.

[0172] According to the present application, different permeabilities are designed to calculate the gas well productivity under different permeabilities by the present application to analyze the influence of the permeability on the gas well productivity. Figure 4 The permeability versus the gas well productivity influence diagram, as shown in the following table. Figure 4 It can be seen that as the permeability increases, the gas well productivity shows a magnitude growth, which shows that the influence of the permeability on the gas well productivity is particularly significant.

[0173] According to the present application, effective thicknesses of 10 m, 20 m, 30 m, 40 m and 50 m are designed, and the gas well productivity under different effective thicknesses is calculated by using the present application, Figure 5 The figure of effective thickness versus gas well productivity is obtained from Figure 5 It can be seen that the gas well productivity increases rapidly with the increase of the effective thickness, and in the development process of the gas reservoir, the gas well should pass through the formation with larger effective thickness as much as possible.

[0174] The above merely describes the preferred embodiments of the present application, and is not used to limit the present application, and any modification, equivalent replacement and improvement within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for predicting deliverability of a watered gas well in a water-drive gas reservoir, characterized by, The water production capacity equation of the water-drive gas reservoir un-liquid-filled water production gas well considering the water activity degree is established by bringing the gas phase relative permeability considering the water activity degree into the binomial productivity equation of the planar radial pseudo-steady seepage flow considering the high-speed non-Darcy effect and the formation pollution. The binomial productivity equation of the planar radial pseudo-steady seepage flow considering the high-speed non-Darcy effect and the formation pollution is established based on the gas-water seepage theory. where: p wf is the average formation pressure and the bottom-hole flowing pressure; q gsc is the surface gas production rate of the gas well; μ g is the viscosity of the natural gas; Z is the deviation factor of the natural gas; T is the thermodynamic temperature of the formation; b is the fitting coefficient of the relative permeability curve; h is the effective thickness; r e , r w is the gas supply radius and the well radius; S is the skin factor; is the relative permeability of the gas phase corresponding to the irreducible water saturation; is the relative permeability of the water phase corresponding to the residual gas saturation; k abs is the absolute permeability; n w , n g is the Corey index.

2. The method for predicting deliverability of a watered gas well in a watered gas reservoir according to claim 1, characterized in that, The binomial productivity equation of the planar radial pseudo-steady seepage flow considering the high-speed non-Darcy effect and the formation pollution is:

3. The method for predicting deliverability of a watered gas well in a water- drive gas reservoir according to claim 2, characterized in that, In the formula, the high-speed non-Darcy flow coefficient of the gas is calculated by the following formula:

4. The water-drive gas reservoir water production gas well productivity prediction method according to claim 2, characterized in that, The gas phase relative permeability considering the water activity degree is calculated by the following method: Step a: based on the material balance theory, the relationship between the water invasion constant and the formation water saturation is established; where: p wf is the average formation pressure and the bottom-hole flowing pressure; q gsc is the surface gas production of the gas well; μ g is the viscosity of the natural gas; Z is the deviation factor of the natural gas; T is the thermodynamic temperature of the formation; k is the reservoir permeability; k g is the effective permeability of the gas phase; h is the effective thickness; r e , r w is the gas supply radius and the well radius; S is the skin factor; γ g is the relative density of the natural gas; and β is the Forchheimei coefficient. Step b: the production water-gas ratio considering the condensate water-gas ratio is calculated by using the power function relationship between the gas-water relative permeability ratio and the water saturation, and the relationship between the gas-water relative permeability ratio and the production water-gas ratio; Step c: the water phase relative permeability is calculated by using the pseudo-steady water production formula considering the formation pollution and the field water production calculation formula; Step d: the water phase relative permeability considering the water activity degree is calculated based on step a, step b and step c; Step e: the gas phase relative permeability considering the water activity degree is calculated by combining the power function relationship of the phase permeability curve based on step d. In step a, the relationship between the water invasion constant and the formation water saturation is: In step b, the production water-gas ratio considering the condensate water-gas ratio is: In step c, the water phase relative permeability is represented by using the pseudo-steady water production formula considering the formation pollution and the field water production calculation formula:

5. The method for predicting deliverability of a watered gas well in a watered gas reservoir according to claim 4, characterized in that, In step d, the water phase relative permeability considering the water activity degree is represented as: S w = R B (1-S wi )+S wi ; where S w is the formation water saturation; S wi is the irreducible water saturation; B is the water influx constant; and R is the gas reservoir recovery.

6. The method for predicting deliverability of a watered gas well in a watered gas reservoir according to claim 5, wherein, In step e, the gas phase relative permeability considering the water activity degree is represented by combining the power function relationship of the phase permeability curve: where: μ g is the natural gas viscosity; B g is the natural gas volume factor; μ w is the formation water viscosity; B w is the formation water volume factor; W gr is the produced water gas ratio; W cgr is the condensate water gas ratio; a, b are the relative permeability curve fitting coefficients; S w is the formation water saturation.

7. The method of predicting deliverability of a watered gas well in a watered gas reservoir of claim 6, wherein, ​ where: μ w is the formation water viscosity; B w is the formation water volume factor; q gsc is the surface gas rate of the gas well; k abs is the absolute permeability; k rw is the water phase relative permeability; μ w is the formation water viscosity; B w is the formation water volume factor; W gr is the produced water gas ratio; W cgr is the condensate water gas ratio; p wf is the average formation pressure and the bottom hole flowing pressure; r e , r w is the gas supply radius and the well radius; S is the skin factor.

8. The method for predicting deliverability of a watered gas well in a watered gas reservoir according to claim 7, characterized in that, ​ 9. The method for predicting deliverability of a watered gas well in a water-drive gas reservoir according to claim 8, wherein, ​ wherein is the relative permeability of the gas phase corresponding to the irreducible water saturation; is the relative permeability of the water phase corresponding to the residual gas saturation; n w , n g is the Corey exponent.

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