A gas-water two-phase seepage prediction model and its establishment method and application

Abstract

The present invention discloses a gas-water two-phase seepage prediction model and its establishment method and application. The establishment method of the gas-water two-phase seepage prediction model includes the following steps: establishing the assumption conditions for gas-water two-phase seepage, and the assumption conditions include: the reservoir fluid is isothermal seepage; there are only gas and water phases in the gas reservoir; the influence of gravity and capillary force is ignored; the slip effect and starting pressure are not considered during the gas-water two-phase seepage; the oil phase, water-soluble gas and condensate water and their influence are not considered, the gas and water are linear Darcy seepage in the seepage process, and the reservoir fluid is composed of free gas and formation water; based on the assumption conditions, the gas-water two-phase seepage prediction model is established. The present invention can predict the future development capacity of a gas well only through actual production data, with high prediction efficiency, and compared with indoor experiments, it is closer to the actual production situation on site and the prediction result is more accurate.

Description

Technical Field

[0001] The invention relates to the technical field of gas reservoir development, and in particular to a gas-water two-phase seepage prediction model and an establishment method and application thereof. Background Art

[0002] my country is rich in gas resources. Based on the characteristics of gas reservoirs, the gas-water two-phase seepage prediction model is often used to predict production capacity. However, the existing research on gas-water two-phase seepage models is mostly based on multiphase flow. Although domestic and foreign scholars have successively introduced a number of gas-water two-phase flow binomial production capacity equations, the relative permeabilities under different water saturations in these equations are calibrated based on experimental data. In the actual production and development process, the formation conditions are a variable value and are not equivalent to indoor experiments. Therefore, they are subject to certain limitations in application. Summary of the invention

[0003] In view of the above problems, the present invention aims to provide a gas-water two-phase seepage prediction model and its establishment method and application.

[0004] The technical solution of the present invention is as follows:

[0005] On the one hand, a gas-water two-phase seepage prediction model and its establishment method and application are provided, comprising the following steps:

[0006] The assumptions for establishing gas-water two-phase seepage flow include:

[0007] (1) The reservoir fluid is isothermal seepage;

[0008] (2) There are only two phases in the gas reservoir: gas and water;

[0009] (3) Ignore the effects of gravity and capillary forces;

[0010] (4) The slip effect and starting pressure are not considered in the gas-water two-phase seepage;

[0011] (5) Without considering the oil phase, water-soluble gas and condensate water and their effects, the gas and water flow in the seepage process is linear Darcy seepage, and the reservoir fluid consists of free gas and formation water;

[0012] Based on the assumptions, the gas-water two-phase seepage prediction model is established.

[0013] Preferably, establishing the gas-water two-phase seepage prediction model specifically includes the following sub-steps:

[0014] According to Darcy's law of flow, the two-phase motion equation of gas and water is established;

[0015] According to the gas-water two-phase motion equation, a surface production formula for gas-water two-phase plane radial flow is obtained;

[0016] Integrating the plane radial flow surface yield formula and taking the skin coefficient into consideration, obtaining a modified formula of the plane radial flow surface yield formula;

[0017] Establishing a gas phase pseudo-pressure calculation model and a water phase pseudo-pressure calculation model, and obtaining abbreviated calculation models of the gas phase pseudo-pressure calculation model and the water phase pseudo-pressure calculation model;

[0018] Establishing a gas-water two-phase relative permeability calculation model, and obtaining a gas-water two-phase relative permeability ratio calculation model based on the gas-water two-phase relative permeability calculation model;

[0019] Establishing a calculation model for the production water-gas ratio, and combining the calculation model for the gas-water two-phase relative permeability ratio, obtaining a calculation model for the relationship between formation pressure and average water saturation;

[0020] Establish the dynamic balance equation under the condition of the original water saturation of the gas reservoir when there is no external water in the gas reservoir;

[0021] Establish a calculation model for average water saturation when there is no external water in the gas reservoir;

[0022] The calculation models of bottom hole pressure, formation water viscosity, formation water volume coefficient and PR equation were established respectively;

[0023] The formulas, equations and calculation models obtained from the above steps together constitute the gas-water two-phase seepage prediction model.

[0024] Preferably, the gas-water two-phase motion equation includes:

[0025]

[0026]

[0027] Where: v g 、v w are the seepage velocities of gas phase and water phase, m / s; k rg , k rw and k are gas phase relative permeability, water phase relative permeability and reservoir absolute permeability, respectively. 2 ;μ g , μ w are respectively the gas phase and water phase viscosities, Pa·s; ▽ is the gradient operator; p is the pressure, MPa;

[0028] The surface production formula of the gas-water two-phase plane radial flow is:

[0029]

[0030]

[0031] Where: q g ,q w are respectively the surface production of gas phase and water phase plane radial flow, m 3 / d; r is the plane radial flow seepage radius, m; h is the reservoir thickness, m; B g , B w are the volume coefficients of gas phase and water phase, respectively, dimensionless;

[0032] The modified formula of the plane radial flow surface production formula is:

[0033]

[0034]

[0035] Where: r e is the seepage radius, m; r w is the well bottom radius, m; S a is the skin coefficient, dimensionless; p r 、p wf are the supply boundary pressure and bottom hole pressure, MPa, respectively;

[0036] The gas phase pseudo-pressure calculation model, the water phase pseudo-pressure calculation model and their abbreviated calculation models are:

[0037]

[0038]

[0039] q g =C.Δm(p) g (9)

[0040] q w =C.Δm(p) w (10)

[0041] Where: Δm(p) g , Δm(p) w are the pseudo pressures of the gas phase and water phase under pressure p, MPa; C is the capacity coefficient, dimensionless;

[0042] The gas-water two-phase relative permeability calculation model and the gas-water two-phase relative permeability ratio calculation model are respectively:

[0043]

[0044]

[0045]

[0046] Where: is the average water saturation of the formation, a decimal; D is the relative permeability coefficient, dimensionless;

[0047] The production water-gas ratio calculation model is:

[0048]

[0049] Where: R pwg is the production water-gas ratio, dimensionless; B g (p), B w (p) are the volume coefficients of the gas phase and water phase under pressure p; μ g (p), μ w (p) are the viscosities of the gas phase and water phase at pressure p, Pa·s;

[0050] The calculation model of the relationship between the formation pressure and the average water saturation is:

[0051]

[0052] The dynamic equilibrium equation is:

[0053]

[0054] Where: Z is the compression factor of the gas at pressure p, dimensionless; p i is the original formation pressure, MPa; Z i is the gas compression factor under original formation conditions, dimensionless; G p and G are the cumulative gas production and movable reserves of a single well, respectively. 3 ; W p is the cumulative water production, m 3 ; B gi is the volume coefficient of gas under original formation conditions, dimensionless;

[0055] The calculation model of the average water saturation is:

[0056]

[0057] Where: S wi is the initial water saturation of a single well, a decimal.

[0058] Preferably, the calculation model of the bottom hole pressure is:

[0059]

[0060] Where: p wf is the bottom hole pressure, MPa; p ts is the oil pipe pressure, MPa; γ g is the relative density of gas, dimensionless; H is the depth of the middle of the reservoir, m; Tav is the average temperature in the middle of the reservoir, K; Z av is the gas compressibility factor at the average reservoir pressure, dimensionless.

[0061] Preferably, the calculation model of the formation water viscosity is:

[0062] μ w =A(1.8×t w +32) B (19)

[0063]

[0064] B=f 5 +f 6 S 2 +f 7 S 2 ln(S)+f 8 S 3 (twenty one)

[0065] Where: μ w is the formation water viscosity, i.e. the water phase viscosity, Pa·s; A and B are both intermediate parameters; t w is the temperature of the formation water, °C; S is the mineralization of the formation water, 10 4 mg / L; f 1 to f 8 are fitting parameters.

[0066] Preferably, the calculation model of the formation water volume coefficient is:

[0067] B w =(1+ΔV wt )×(1+ΔV wp ) (twenty two)

[0068] ΔV wt =(f 9 +f 10 ×t w )(f 11 ×t w )+f 12 (twenty three)

[0069]

[0070] Where: B w is the formation water volume coefficient, i.e. the water phase volume coefficient, dimensionless; ΔV wt is the influence coefficient of temperature on aqueous solution; ΔV wp is the influence coefficient of pressure on aqueous solution; f 9 to f 12 All are fitting parameters; tw is the temperature of formation water, ℃; p is the pressure, MPa.

[0071] On the other hand, a gas-water two-phase seepage prediction model is also provided, and the gas-water two-phase seepage prediction model is established by any of the above-mentioned establishment methods.

[0072] On the other hand, there is also provided an application of a gas-water two-phase seepage prediction model in predicting formation parameters and / or production capacity. The gas-water two-phase seepage prediction model is the gas-water two-phase seepage prediction model described above, or is established by any of the above-mentioned establishment methods.

[0073] Preferably, when the gas-water two-phase seepage prediction model is used to predict formation parameters, the following steps are included:

[0074] S1: Calculate the gas viscosity, compressibility factor and gas volume of the target gas well at different pressures under formation temperature conditions according to the PR equation;

[0075] S2: Calculate the formation water viscosity under reservoir conditions based on the formation water mineralization of the target gas well produced water and the calculation model of formation water viscosity;

[0076] S3: Calculate the formation water volume coefficient under reservoir conditions according to the calculation model of the formation water volume coefficient;

[0077] S4: Based on the known cumulative water production, cumulative gas production, movable reserves of a single well, gas volume coefficient under original reservoir conditions, and p i / Z i , and the formation water volume coefficient obtained in step S3, combined with the dynamic balance equation, to calculate the p / Z of the formation at time t;

[0078] S5: Calculate the formation pressure p of the gas well at time t based on the p / Z calculated in step S4 and the compression factor of the gas at different pressures obtained in step S1;

[0079] S6: Calculate the gas volume coefficient of the gas well at time t and pressure p according to the volume of the gas at different pressures obtained in step S1;

[0080] S7: Based on the known original water saturation, cumulative water production, movable reserves of a single well, and gas volume coefficient under the original conditions of the reservoir, the average water saturation of the gas well at time t is calculated in combination with the calculation model of the average water saturation;

[0081] S8: Calculate the water-gas ratio of the target gas well at time t according to the daily water production and daily gas production of the target gas well at time t;

[0082] S9: Calculate the gas-water two-phase relative permeability ratio of the gas well at time t based on the formation water viscosity obtained in step S2, the formation water volume coefficient obtained in step S3, the gas viscosity obtained in step S1, the gas volume coefficient obtained in step S6, and the water-gas ratio obtained in step S8 in combination with the production water-gas ratio calculation model;

[0083] S10: Calculate the relative permeability coefficient based on the average water saturation obtained in step S7 and the gas-water two-phase relative permeability ratio obtained in step S9 in combination with a gas-water two-phase relative permeability ratio calculation model;

[0084] S11: According to the relative permeability coefficient obtained in step S10, the relative permeability of the gas-water two-phase at different average water saturations is calculated in combination with a gas-water two-phase relative permeability calculation model, thereby obtaining a gas-water relative permeability curve during the actual production process of the target gas well;

[0085] S12: Obtaining an average formation pressure according to the oil pressure and the formation pressure, and obtaining an average formation compression factor under the condition of the average formation pressure through the compression factors under different pressures obtained in step S1;

[0086] S13: according to the average formation compression factor obtained in step S12, combined with the relative density of gas, the depth of the middle part of the reservoir and the reservoir temperature, the bottom hole pressure of the gas well at time t is calculated by using a bottom hole pressure calculation model;

[0087] S14: The water phase pseudo-pressure is calculated based on the formation water volume coefficient, formation water viscosity, formation pressure, bottom hole pressure and water phase relative permeability in combination with a water phase pseudo-pressure calculation model.

[0088] Preferably, when the gas-water two-phase seepage prediction model is used to predict production capacity, in addition to steps S1-S14, the following steps are further included:

[0089] S15: fitting the daily water production data of the target gas well through the abbreviated calculation model of the water phase pseudo-pressure to obtain the productivity coefficient of the target gas well, and predicting the future water production of the target gas well according to the productivity coefficient;

[0090] S16: Based on the gas-water relative permeability curve of the target gas well and in combination with the calculation model of the relationship between formation pressure and average water saturation, the water-gas ratio of the gas well is obtained by back-calculation;

[0091] S17: predicting the future gas production of the target gas well according to the water-gas ratio obtained in step S16 and the future water production predicted in step S15;

[0092] S18: predicting the cumulative gas production and cumulative water production of the target gas well at time t based on the predicted daily gas production and daily water production at different production times;

[0093] S19: Assuming the oil pressure of subsequent gas well development, repeat steps S7 and S12-S18 to predict the future average formation water saturation, formation pressure, daily gas production, cumulative gas production and cumulative water production of the target gas well.

[0094] The beneficial effects of the present invention are:

[0095] The present invention starts with the production data that is most easily obtained on site, and establishes a gas-water two-phase seepage prediction model based on the gas-water two-phase stable seepage theory; the future development capacity of the gas well can be predicted only through actual production data, with high prediction efficiency, and compared with indoor experiments, it is closer to the actual production situation on site, and the prediction result is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0097] Figure 1 A schematic diagram of a calculation flow for predicting production capacity using the present invention according to a specific embodiment;

[0098] Figure 2 It is a schematic diagram of the prediction result of gas-water relative permeability curve in a specific embodiment;

[0099] Figure 3 This is a schematic diagram of a prediction result of daily gas production of a gas well in a specific embodiment;

[0100] Figure 4 It is a schematic diagram of the prediction result of the cumulative gas production of a gas well in a specific embodiment;

[0101] Figure 5 It is a schematic diagram of the prediction result of the cumulative water production of a gas well in a specific embodiment;

[0102] Figure 6 It is a schematic diagram of the prediction results of the average water saturation of the formation according to a specific embodiment. DETAILED DESCRIPTION

[0103] The present invention is further described below in conjunction with the accompanying drawings and embodiments. It should be noted that, in the absence of conflict, the embodiments in this application and the technical features in the embodiments can be combined with each other. It should be noted that, unless otherwise specified, all technical and scientific terms used in this application have the same meanings as those generally understood by those of ordinary skill in the art to which this application belongs. The words "including" or "comprising" and the like used in the disclosure of the present invention mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0104] In one aspect, the present invention provides a gas-water two-phase seepage prediction model, wherein the gas-water two-phase seepage prediction model is established by the following steps:

[0105] The assumptions for establishing gas-water two-phase seepage flow include:

[0106] (1) The reservoir fluid is isothermal seepage;

[0107] (2) There are only two phases in the gas reservoir: gas and water;

[0108] (3) Ignore the effects of gravity and capillary forces;

[0109] (4) The slip effect and starting pressure are not considered in the gas-water two-phase seepage;

[0110] (5) Without considering the oil phase, water-soluble gas and condensate water and their effects, the gas and water flow in the seepage process is linear Darcy seepage, and the reservoir fluid consists of free gas and formation water;

[0111] Based on the assumptions, the gas-water two-phase seepage prediction model is established, which specifically includes the following sub-steps:

[0112] (1) According to Darcy's law of permeability, a gas-water two-phase motion equation is established; the gas-water two-phase motion equation includes:

[0113]

[0114]

[0115] Where: v g 、v w are the seepage velocities of gas phase and water phase, m / s; k rg , k rw and k are gas phase relative permeability, water phase relative permeability and reservoir absolute permeability, respectively. 2 ;μ g , μ w are respectively the gas phase and water phase viscosities, Pa·s; ▽ is the gradient operator; p is the pressure, MPa;

[0116] (2) According to the gas-water two-phase motion equation, the surface production formula of the gas-water two-phase plane radial flow is obtained; the surface production formula of the gas-water two-phase plane radial flow is:

[0117]

[0118]

[0119] Where: q g ,q w are respectively the surface production of gas phase and water phase plane radial flow, m 3 / d; r is the plane radial flow seepage radius, m; h is the reservoir thickness, m; B g , B w are the volume coefficients of gas phase and water phase, respectively, dimensionless;

[0120] (3) Integrating the plane radial flow surface yield formula and taking the skin coefficient into consideration, a correction formula of the plane radial flow surface yield formula is obtained; the correction formula of the plane radial flow surface yield formula is:

[0121]

[0122]

[0123] Where: r e is the seepage radius, m; r w is the well bottom radius, m; S a is the skin coefficient, dimensionless; p r 、p wf are the supply boundary pressure and bottom hole pressure, MPa, respectively;

[0124] (4) establishing a gas phase pseudo-pressure calculation model and a water phase pseudo-pressure calculation model, and obtaining abbreviated calculation models of the gas phase pseudo-pressure calculation model and the water phase pseudo-pressure calculation model;

[0125] The gas phase pseudo-pressure calculation model, the water phase pseudo-pressure calculation model and their abbreviated calculation models are:

[0126]

[0127]

[0128] q g =C.Δm(p) g (9)

[0129] q w =C.Δm(p) w (10)

[0130] Where: Δm(p)g , Δm(p) w are the pseudo pressures of the gas phase and water phase under pressure p, MPa; C is the capacity coefficient, dimensionless;

[0131] (5) establishing a gas-water two-phase relative permeability calculation model, and obtaining a gas-water two-phase relative permeability ratio calculation model based on the gas-water two-phase relative permeability calculation model;

[0132] The gas-water two-phase relative permeability calculation model and the gas-water two-phase relative permeability ratio calculation model are respectively:

[0133]

[0134]

[0135]

[0136] Where: is the average water saturation of the formation, a decimal; D is the relative permeability coefficient, dimensionless;

[0137] (6) establishing a calculation model for the production water-gas ratio, and combining it with the calculation model for the gas-water two-phase relative permeability ratio to obtain a calculation model for the relationship between formation pressure and average water saturation;

[0138] The production water-gas ratio calculation model is:

[0139]

[0140] Where: R pwg is the production water-gas ratio, dimensionless; B g (p), B w (p) are the volume coefficients of the gas phase and water phase under pressure p; μ g (p), μ w (p) are the viscosities of the gas phase and water phase at pressure p, Pa·s;

[0141] The calculation model of the relationship between the formation pressure and the average water saturation is:

[0142]

[0143] (7) Establishing a dynamic balance equation under the condition of the original water saturation of the gas reservoir when there is no external water in the gas reservoir; the dynamic balance equation is:

[0144]

[0145] Where: Z is the compression factor of the gas at pressure p, dimensionless; p i is the original formation pressure, MPa; Zi is the gas compression factor under original formation conditions, dimensionless; G p and G are the cumulative gas production and movable reserves of a single well, respectively. 3 ; W p is the cumulative water production, m 3 ; B gi is the volume coefficient of gas under original formation conditions, dimensionless;

[0146] (8) Establishing a calculation model for average water saturation when there is no external water body in the gas reservoir; the calculation model for average water saturation is:

[0147]

[0148] Where: S wi is the initial water saturation of a single well, a decimal.

[0149] (9) Establish the calculation models of bottom hole pressure, formation water viscosity, formation water volume coefficient and PR equation respectively;

[0150] In a specific embodiment, the calculation model of the bottom hole pressure is:

[0151]

[0152] Where: p wf is the bottom hole pressure, MPa; p ts is the oil pipe pressure, MPa; γ g is the relative density of gas, dimensionless; H is the depth of the middle of the reservoir, m; T av is the average temperature in the middle of the reservoir, K; Z av is the gas compressibility factor at the average reservoir pressure, dimensionless.

[0153] The calculation model of the formation water viscosity is:

[0154] μ w =A(1.8×t w +32) B (19)

[0155]

[0156] B=f 5 +f 6 S 2 +f 7 S 2 ln(S)+f 8 S 3 (twenty one)

[0157] Where: μ wis the formation water viscosity, i.e. the water phase viscosity, Pa·s; A and B are both intermediate parameters; t w is the temperature of the formation water, °C; S is the mineralization of the formation water, 10 4 mg / L; f 1 to f 8 are fitting parameters.

[0158] The calculation model of the formation water volume coefficient is:

[0159] B w =(1+ΔV wt )×(1+ΔV wp ) (twenty two)

[0160] ΔV wt =(f 9 +f 10 ×t w )(f 11 ×t w )+f 12 (twenty three)

[0161]

[0162] Where: B w is the formation water volume coefficient, i.e. the water phase volume coefficient, dimensionless; ΔV wt is the influence coefficient of temperature on aqueous solution; ΔV wp is the influence coefficient of pressure on aqueous solution; f 9 to f 12 All are fitting parameters; t w is the temperature of formation water, ℃; p is the pressure, MPa.

[0163] It should be noted that, in addition to the calculation method used in the above embodiment, other calculation methods of bottom hole pressure, formation water viscosity, and formation water volume coefficient in the prior art can also be applied to the present invention. In addition, the PR equation is a prior art, and the specific equation is not repeated here.

[0164] (10) The formulas, equations and calculation models obtained from the above steps together constitute the gas-water two-phase seepage prediction model.

[0165] On the other hand, the present invention also provides an application of the gas-water two-phase seepage prediction model in predicting formation parameters and / or production capacity.

[0166] When the gas-water two-phase seepage prediction model is used to predict formation parameters, the following steps are included:

[0167] S1: Calculate the gas viscosity, compressibility factor and gas volume of the target gas well at different pressures under formation temperature conditions according to the PR equation;

[0168] S2: Calculate the formation water viscosity under reservoir conditions based on the formation water mineralization of the target gas well produced water and the calculation model of formation water viscosity;

[0169] S3: Calculate the formation water volume coefficient under reservoir conditions according to the calculation model of the formation water volume coefficient;

[0170] S4: Based on the known cumulative water production, cumulative gas production, movable reserves of a single well, gas volume coefficient under original reservoir conditions, and p i / Z i , and the formation water volume coefficient obtained in step S3, combined with the dynamic balance equation, to calculate the p / Z of the formation at time t;

[0171] S5: Calculate the formation pressure p of the gas well at time t based on the p / Z calculated in step S4 and the compression factor of the gas at different pressures obtained in step S1;

[0172] S6: Calculate the gas volume coefficient of the gas well at time t and pressure p according to the volume of the gas at different pressures obtained in step S1;

[0173] S7: Based on the known original water saturation, cumulative water production, movable reserves of a single well, and gas volume coefficient under the original conditions of the reservoir, the average water saturation of the gas well at time t is calculated in combination with the calculation model of the average water saturation;

[0174] S8: Calculate the water-gas ratio of the target gas well at time t according to the daily water production and daily gas production of the target gas well at time t;

[0175] S9: Calculate the gas-water two-phase relative permeability ratio of the gas well at time t based on the formation water viscosity obtained in step S2, the formation water volume coefficient obtained in step S3, the gas viscosity obtained in step S1, the gas volume coefficient obtained in step S6, and the water-gas ratio obtained in step S8 in combination with the production water-gas ratio calculation model;

[0176] S10: Calculate the relative permeability coefficient based on the average water saturation obtained in step S7 and the gas-water two-phase relative permeability ratio obtained in step S9 in combination with a gas-water two-phase relative permeability ratio calculation model;

[0177] S11: According to the relative permeability coefficient obtained in step S10, the relative permeability of the gas-water two-phase at different average water saturations is calculated in combination with a gas-water two-phase relative permeability calculation model, thereby obtaining a gas-water relative permeability curve during the actual production process of the target gas well;

[0178] S12: Obtaining an average formation pressure according to the oil pressure and the formation pressure, and obtaining an average formation compression factor under the condition of the average formation pressure through the compression factors under different pressures obtained in step S1;

[0179] S13: according to the average formation compression factor obtained in step S12, combined with the relative density of gas, the depth of the middle part of the reservoir and the reservoir temperature, the bottom hole pressure of the gas well at time t is calculated by using a bottom hole pressure calculation model;

[0180] S14: The water phase pseudo-pressure is calculated based on the formation water volume coefficient, formation water viscosity, formation pressure, bottom hole pressure and water phase relative permeability in combination with a water phase pseudo-pressure calculation model.

[0181] When the gas-water two-phase seepage prediction model is used to predict production capacity, in addition to steps S1-S14, the following steps are also included:

[0182] S15: fitting the daily water production data of the target gas well through the abbreviated calculation model of the water phase pseudo-pressure to obtain the productivity coefficient of the target gas well, and predicting the future water production of the target gas well according to the productivity coefficient;

[0183] S16: Based on the gas-water relative permeability curve of the target gas well and in combination with the calculation model of the relationship between formation pressure and average water saturation, the water-gas ratio of the gas well is obtained by back-calculation;

[0184] S17: predicting the future gas production of the target gas well according to the water-gas ratio obtained in step S16 and the future water production predicted in step S15;

[0185] S18: predicting the cumulative gas production and cumulative water production of the target gas well at time t based on the predicted daily gas production and daily water production at different production times;

[0186] S19: Assuming the oil pressure of subsequent gas well development, repeat steps S7 and S12-S18 to predict the future average formation water saturation, formation pressure, daily gas production, cumulative gas production and cumulative water production of the target gas well.

[0187] In a specific embodiment, taking a gas well as an example, the gas-water two-phase seepage prediction model of the present invention is used to predict its formation parameters and production capacity at a certain time in the future. The specific technical route is as follows: Figure 1 The prediction results of the gas-water relative permeability curve are shown in Figure 2 The daily gas production prediction results are shown in Figure 3 The cumulative gas production prediction results are shown in Figure 4 The cumulative water production prediction results are shown in Figure 5 The prediction results of the average water saturation of the formation are shown in Figure 6 As shown. Figure 3-6It can be seen that the data predicted by the present invention is consistent with the actual production data, with an error of less than 3%, meeting the engineering requirements and having significant progress compared with the prior art.

[0188] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for establishing a gas-water two-phase seepage prediction model. It is characterized in that The following steps are involved: The assumptions for establishing gas-water two-phase seepage flow include: (1) The reservoir fluid is isothermal seepage; (2) There are only two phases in the gas reservoir: gas and water; (3) Ignore the effects of gravity and capillary forces; (4) The slip effect and starting pressure are not considered in the gas-water two-phase seepage; (5) Without considering the oil phase, water-soluble gas and condensate water and their effects, the gas and water flow in the seepage process is linear Darcy seepage, and the reservoir fluid consists of free gas and formation water; Based on the assumptions, the gas-water two-phase seepage prediction model is established, which specifically includes the following sub-steps: According to Darcy's law of flow, the air-water two-phase motion equation is established; According to the gas-water two-phase motion equation, a surface production formula for gas-water two-phase plane radial flow is obtained; Integrating the plane radial flow surface yield formula and taking the skin coefficient into consideration, obtaining a modified formula of the plane radial flow surface yield formula; Establishing a gas phase pseudo-pressure calculation model and a water phase pseudo-pressure calculation model, and obtaining abbreviated calculation models of the gas phase pseudo-pressure calculation model and the water phase pseudo-pressure calculation model; Establishing a gas-water two-phase relative permeability calculation model, and obtaining a gas-water two-phase relative permeability ratio calculation model based on the gas-water two-phase relative permeability calculation model; Establishing a calculation model for the production water-gas ratio, and combining the calculation model for the gas-water two-phase relative permeability ratio, obtaining a calculation model for the relationship between formation pressure and average water saturation; When there is no external water in the gas reservoir, the dynamic equilibrium equation is established only under the condition of the original water saturation of the gas reservoir; Establish a calculation model for average water saturation when there is no external water in the gas reservoir; The calculation models of bottom hole pressure, formation water viscosity, formation water volume coefficient and PR equation were established respectively; The formulas, equations and calculation models obtained from the above steps together constitute the gas-water two-phase seepage prediction model.

2. The method for establishing a gas-water two-phase seepage prediction model according to claim 1, It is characterized in that The gas-water two-phase motion equation includes: Where: v g 、v w are the seepage velocities of gas phase and water phase, m / s; k rg , k rw and k are gas phase relative permeability, water phase relative permeability and reservoir absolute permeability, respectively. 2 ;μ g , μ w are respectively the gas phase and water phase viscosities, Pa·s; ▽ is the gradient operator; p is the pressure, MPa; The surface production formula of the gas-water two-phase plane radial flow is: Where: q g ,q w are respectively the surface production of gas phase and water phase plane radial flow, m 3 / d; r is the plane radial flow seepage radius, m; h is the reservoir thickness, m; B g , B w are the volume coefficients of gas phase and water phase, respectively, dimensionless; The modified formula of the plane radial flow surface production formula is: Where: r e is the seepage radius, m; r w is the well bottom radius, m; S a is the skin coefficient, dimensionless; p r 、p wf are the supply boundary pressure and bottom hole pressure, MPa, respectively; The gas phase pseudo-pressure calculation model, the water phase pseudo-pressure calculation model and their abbreviated calculation models are: q g =C.Δm(p) g (9) q w =C.Δm(p) w (10) Where: Δm(p) g , Δm(p) w are the pseudo pressures of the gas phase and water phase under pressure p, MPa; C is the capacity coefficient, dimensionless; The gas-water two-phase relative permeability calculation model and the gas-water two-phase relative permeability ratio calculation model are respectively: Where: is the average water saturation of the formation, a decimal; D is the relative permeability coefficient, dimensionless; The production water-gas ratio calculation model is: Where: R pwg is the production water-gas ratio, dimensionless; B g (p), B w (p) are the volume coefficients of the gas phase and water phase under pressure p; μ g (p), μ w (p) are the viscosities of the gas phase and water phase at pressure p, Pa·s; The calculation model of the relationship between the formation pressure and the average water saturation is: The dynamic equilibrium equation is: Where: Z is the compression factor of the gas at pressure p, dimensionless; p i is the original formation pressure, MPa; Z i is the gas compression factor under original formation conditions, dimensionless; G p and G are the cumulative gas production and movable reserves of a single well, respectively. 3 ; W p is the cumulative water production, m 3 ; B gi is the volume coefficient of gas under original formation conditions, dimensionless; The calculation model of the average water saturation is: Where: S wi is the initial water saturation of a single well, a decimal.

3. The method for establishing a gas-water two-phase seepage prediction model according to claim 1 or 2, It is characterized in that The calculation model of the bottom hole pressure is: Where: p wf is the bottom hole pressure, MPa; p ts is the oil pipe pressure, MPa; γ g is the relative density of gas, dimensionless; H is the depth of the middle of the reservoir, m; T av is the average temperature in the middle of the reservoir, K; Z av is the gas compressibility factor at the average reservoir pressure, dimensionless.

4. The method for establishing a gas-water two-phase seepage prediction model according to claim 1 or 2, It is characterized in that The calculation model of the formation water viscosity is: m w =A(1.8×t w +32) B (19) B=f 5 +f 6 S 2 +f 7 S 2 ln(S)+f 8 S 3 (21) Where: μ w is the formation water viscosity, i.e. the water phase viscosity, Pa·s; A and B are both intermediate parameters; t w is the temperature of the formation water, ℃; S is the mineralization of the formation water, 10 4 mg / L; f 1 to f 8 are fitting parameters.

5. The method for establishing a gas-water two-phase seepage prediction model according to claim 1 or 2, It is characterized in that The calculation model of the formation water volume coefficient is: B w =(1+ΔV wt )×(1+ΔV wp ) (22) ΔV wt =(f 9 +f 10 ×t w )(f 11 ×t w )+f 12 (23) ΔV wp =-5.0987×10 -7 p×(t w +17.78)-6.54435×10 -9 p 2 ×(t w +17.78) (24) -5.20574×10 -5 p-4.74029×10 -6 p 2 Where: B w is the formation water volume coefficient, i.e. the water phase volume coefficient, dimensionless; ΔV wt is the influence coefficient of temperature on aqueous solution; ΔV wp is the influence coefficient of pressure on aqueous solution; f 9 to f 12 All are fitting parameters; t w is the temperature of formation water, ℃; p is the pressure, MPa.

6. A method for predicting formation parameters and / or production capacity, It is characterized in that The prediction is performed using a gas-water two-phase seepage prediction model established by the establishment method described in any one of claims 1 to 5.

7. The method for predicting formation parameters and / or productivity according to claim 6, It is characterized in that When predicting formation parameters, the following steps are involved: S1: Calculate the gas viscosity, compressibility factor and gas volume of the target gas well at different pressures under formation temperature conditions according to the PR equation; S2: Calculate the formation water viscosity under reservoir conditions based on the formation water mineralization of the target gas well produced water and the calculation model of formation water viscosity; S3: Calculate the formation water volume coefficient under reservoir conditions according to the calculation model of the formation water volume coefficient; S4: Based on the known cumulative water production, cumulative gas production, movable reserves of a single well, gas volume coefficient under original reservoir conditions, and p i / Z i , and the formation water volume coefficient obtained in step S3, combined with the dynamic balance equation, to calculate the p / Z of the formation at time t; S5: Calculate the formation pressure p of the gas well at time t based on the p / Z calculated in step S4 and the compression factor of the gas at different pressures obtained in step S1; S6: Calculate the gas volume coefficient of the gas well at time t and pressure p according to the volume of the gas at different pressures obtained in step S1; S7: Based on the known original water saturation, cumulative water production, movable reserves of a single well, and gas volume coefficient under the original conditions of the reservoir, the average water saturation of the gas well at time t is calculated in combination with the calculation model of the average water saturation; S8: Calculate the water-gas ratio of the target gas well at time t according to the daily water production and daily gas production of the target gas well at time t; S9: Calculate the gas-water two-phase relative permeability ratio of the gas well at time t based on the formation water viscosity obtained in step S2, the formation water volume coefficient obtained in step S3, the gas viscosity obtained in step S1, the gas volume coefficient obtained in step S6, and the water-gas ratio obtained in step S8 in combination with the production water-gas ratio calculation model; S10: Calculate the relative permeability coefficient based on the average water saturation obtained in step S7 and the gas-water two-phase relative permeability ratio obtained in step S9 in combination with a gas-water two-phase relative permeability ratio calculation model; S11: According to the relative permeability coefficient obtained in step S10, the relative permeability of the gas-water two-phase at different average water saturations is calculated in combination with a gas-water two-phase relative permeability calculation model, thereby obtaining a gas-water relative permeability curve during the actual production process of the target gas well; S12: Obtaining an average formation pressure according to the oil pressure and the formation pressure, and obtaining an average formation compression factor under the condition of the average formation pressure through the compression factors under different pressures obtained in step S1; S13: according to the average formation compression factor obtained in step S12, combined with the relative density of gas, the depth of the middle part of the reservoir and the reservoir temperature, the bottom hole pressure of the gas well at time t is calculated by using a bottom hole pressure calculation model; S14: The water phase pseudo-pressure is calculated based on the formation water volume coefficient, formation water viscosity, formation pressure, bottom hole pressure and water phase relative permeability in combination with a water phase pseudo-pressure calculation model.

8. The method for predicting formation parameters and / or productivity according to claim 7, It is characterized in that When predicting production capacity, in addition to steps S1-S14, the following steps are also included: S15: fitting the daily water production data of the target gas well through the abbreviated calculation model of the water phase pseudo-pressure to obtain the productivity coefficient of the target gas well, and predicting the future water production of the target gas well according to the productivity coefficient; S16: Based on the gas-water relative permeability curve of the target gas well and in combination with the calculation model of the relationship between formation pressure and average water saturation, the water-gas ratio of the gas well is obtained by back-calculation; S17: predicting the future gas production of the target gas well according to the water-gas ratio obtained in step S16 and the future water production predicted in step S15; S18: predicting the cumulative gas production and cumulative water production of the target gas well at time t based on the predicted daily gas production and daily water production at different production times; S19: Assuming the oil pressure of subsequent gas well development, repeat steps S7 and S12-S18 to predict the future average formation water saturation, formation pressure, daily gas production, cumulative gas production and cumulative water production of the target gas well.

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