Shale gas horizontal well full life cycle wellbore pressure drop calculation method

Abstract

The invention provides a shale gas horizontal well full life cycle wellbore pressure drop calculation method, and belongs to the technical field of oil and gas field development. The change range of wellbore flow parameters in different production stages of a shale gas well is large, casing production is adopted when the initial liquid yield is high, and oil pipe production is adopted when the middle and later yields are low. However, a common pressure model in engineering is difficult to accurately predict the shaft pressure drop of the shale gas well in the whole life cycle. Therefore, according to the shale gas well production characteristics, an annular / non-annular flow pattern transformation boundary calculation model considering the liquid phase apparent velocity and the pipeline inclination angle is provided, and then annular flow and non-annular flow pressure drop models are established by comprehensively considering factors such as the gas / liquid phase apparent velocity, the inclination angle and the pipe diameter; the method capable of calculating the well shaft pressure drop of the shale gas horizontal well in the full life cycle is obtained. The method is high in applicability for a specific shale gas block and easy and convenient to calculate and use, and has certain guiding significance for shale gas horizontal well production dynamic analysis and drainage and mining process optimization.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and gas field development, and mainly relates to a method for calculating the wellbore pressure drop during the entire life cycle of a shale gas horizontal well. Background Art

[0002] Shale gas is an important component of unconventional oil and gas, and its efficient development is of great significance for ensuring national energy security and promoting energy structure optimization. Accurately predicting shale gas wellbore pressure is the key to conducting gas well dynamic analysis and drainage gas production process design, and is crucial to increasing the economically recoverable reserves (EUR) of a single well and guiding the efficient development of gas fields. However, the production parameters of shale gas vary greatly in different life cycles. In the early stage, casing production is used, with high wellhead pressure, high gas and liquid production, and rapid pressure and production decline. In the middle and late stages, tubing production is used, with low wellhead pressure, low gas and liquid production, and a long production cycle. It is difficult to accurately predict the wellbore pressure drop in different production stages of shale gas wells.

[0003] In view of the production characteristics of shale gas wells, the pressure models commonly used in engineering are difficult to accurately predict the wellbore pressure drop in different production stages. The invention patent (CN113969779A) uses a large amount of actual field test data to fit parameters and establishes a wellbore pressure calculation model for gas injection wells. It does not consider the flow pattern changes and is not suitable for production wells; the invention patent (CN104895560A) uses the Beggs-Brill model to calculate the deepwater test wellbore pressure, focusing on the influence of the inclination angle, which is not suitable for shale gas wells; the invention patent (CN106777574A) directly uses the Mukherjee-Brill model to calculate the wellbore pressure of shale gas wells, without considering the production characteristics of shale gas wells, and has poor applicability. In addition, the invention patent (CN111206919A) considers the change of gas production in the reservoir section with the depth of the well and uses a conventional simple method to calculate the wellbore pressure of a high-yield gas well with a long well section; the invention patent (CN118917227A) mainly considers the influence of condensate oil and proposes a method for calculating the wellbore pressure of a water-containing condensate gas well. At present, there are almost no reports on the calculation method of the wellbore pressure drop of shale gas wells at different stages of production characteristics, and the commonly used mechanism model is only modeled for a single flow type (such as annular flow, Taylor slug flow), and the scope of application of shale gas wellbore pressure drop calculation is relatively narrow.

[0004] To this end, the present invention proposes a calculation model for the transition boundary of annular / non-annular flow pattern considering the liquid phase apparent velocity and pipeline inclination, and establishes annular flow and non-annular flow pressure drop models respectively, thereby obtaining a method for calculating the wellbore pressure drop during the whole life cycle of a shale gas horizontal well. The method has a wide range of applications, is easy to calculate and use, and has certain guiding significance for the production dynamic analysis of shale gas horizontal wells and the optimization of drainage and production processes. Summary of the invention

[0005] The purpose of the present invention is to accurately predict the wellbore pressure drop during the entire life cycle of a shale gas horizontal well, and to improve the pressure drop prediction accuracy by splitting the pressure drop model into two parts: annular flow and non-annular flow.

[0006] A method for calculating the wellbore pressure drop during the entire life cycle of a shale gas horizontal well, the specific steps of which are as follows:

[0007] Step 1: Calculation of fluid parameters. Collect the production data of gas wells in the target block, including well inclination θ, pipe diameter D, gas production Qg, liquid production Ql, pressure p, and temperature T, and calculate the relevant fluid parameters.

[0008] Gas phase superficial velocity v sg for:

[0009]

[0010] Liquid superficial velocity v sl for:

[0011]

[0012] Where D is the pipe diameter, m; Q g is the gas production, m 3 / s;Q l is the liquid production, m 3 / s; B g is the volume coefficient.

[0013] in,

[0014]

[0015] Density of gas and liquid phase under different pressure and temperature conditions ρ g , l The calculation formula is:

[0016]

[0017] ρ1=1000γ w (5).

[0018] In the formula, ρ g , l is the density of gas and liquid phase, kg / m 3 ; p is pressure, Pa; γ g is the relative density of the gas phase, which is taken as 0.65; γ w is the relative density of the liquid phase, which is taken as 1.02; Z g is the natural gas deviation coefficient, which is taken as 0.94; T is the temperature, K.

[0019] Step 2: Flow pattern judgment. Based on the liquid film model theory, a flow pattern transition boundary prediction model for judging annular flow / non-annular flow is proposed, which takes into account the liquid phase apparent velocity and well inclination:

[0020]

[0021] In the formula, v cr is the critical gas velocity, m / s; v sl is the apparent velocity of the liquid phase, m / s; g is the acceleration due to gravity, m / s 2 ; θ is the well inclination, °.

[0022] Compare the gas phase superficial velocity v in step 1 sg And the flow pattern transition limit vcr of annular flow / non-annular flow:

[0023] If v sg <v cr , then the gas phase superficial velocity v sg Under production conditions, the flow pattern in the gas wellbore is judged to be non-annular flow;

[0024] If v sg ≥v cr , then the gas phase superficial velocity v sg Under production conditions, the flow pattern in the gas wellbore is judged to be annular flow.

[0025] Step 3: Calculate the pressure drop.

[0026] According to the judgment result of step 2, the pressure drop is calculated for non-annular flow using the following formula:

[0027]

[0028] Where p is pressure, Pa; z is the length of the pipeline, m; ρ m is the gas-liquid mixture density, kg / m 3 ;v m is the gas-liquid velocity, m / s; f m is the friction coefficient and is dimensionless.

[0029] in:

[0030] ρ m =ρ1H L +ρ g (1-H L ) (8);

[0031] In the formula, H L is the liquid holdup, %. The liquid holdup is calculated using the following formula that takes into account the effects of gas density, liquid density, gas-liquid surface tension, tube inclination, gas flow rate, liquid flow rate and tube diameter on the liquid holdup:

[0032]

[0033] in:

[0034]

[0035] Where f(θ) is the function of the fitting tube inclination angle; k(D) is the function of the fitting tube inner diameter; a1, a2, a3, b1, b2, b3 are the coefficients of the fitted polynomial; N g 、N l is the velocity coefficient of gas and liquid phase, dimensionless; σ is the gas-liquid surface tension, N / m, taken as 0.06.

[0036] The calculation of friction resistance is based on the MB model friction resistance relationship:

[0037]

[0038] Where k / D is the relative roughness of the tube wall and is dimensionless.

[0039] The no-slip Reynolds number is:

[0040]

[0041] In the formula, Re ns is the no-slip Reynolds number, dimensionless; ρ ns is the density of the mixture without slippage, kg / m 3 ;μ ns is the viscosity of the no-slip mixture, Pa·s.

[0042] The density of the no-slip mixture is:

[0043]

[0044] The viscosity of the no-slip mixture is:

[0045] μ ns =(1-H Lns )μ g +H Lns μ1 (14);

[0046] In the formula, H Lns is the liquid retention rate without slippage, %; μ g is the gas phase viscosity, taking 2×10 -5 Pa·s; μ l is the liquid viscosity, take 8×10 -4 Pa·s.

[0047] No slip hold-up rate H Lns for:

[0048]

[0049] Gas-liquid mixing speed v m for:

[0050] v m =v s1 +v sg (16).

[0051] For the annular flow pressure drop model, the combined momentum balance formula of the gas core and the liquid film is used for calculation:

[0052]

[0053] In the formula, A l , A g is the cross-sectional area of ​​the liquid film and gas core, m 2 ; S l is the wetted perimeter of the pipe section, m; τ wl is the shear stress between the tube wall and the liquid film, N / m 2 .

[0054] Among them, the density of the gas-liquid mixture in the gas core ρc is:

[0055] ρ c =ρ g φ c +ρ1(1-φ c ) (18).

[0056] Φ c is the void ratio, and its relationship with the droplet entrainment rate FE is:

[0057]

[0058] Where FE is the droplet entrainment rate, a decimal.

[0059] The entrainment rate FE is given by the Wallis correlation:

[0060] FE=1-e [-0.125(ψ-1.5)] (20);

[0061] Where ψ is a coefficient related to gas superficial velocity, gas viscosity, gas / liquid density and surface tension.

[0062] in:

[0063]

[0064] Shear stress τ between tube wall and liquid film wl for:

[0065]

[0066] The interfacial friction coefficient ff is:

[0067] When Re f ≤2300,

[0068]

[0069] When Re f >2300 hours,

[0070]

[0071] Among them, ε is the absolute roughness of the tube wall, which can be taken as 0.0152mm.

[0072] Liquid film Reynolds number Re f It can be calculated from the liquid film velocity, liquid density and viscosity:

[0073]

[0074] Among them, D f is the hydraulic diameter of the liquid film, m.

[0075]

[0076] Liquid film velocity v f for:

[0077]

[0078] Where, δ is the thickness of the liquid film, m; δ c is the average liquid film thickness, m.

[0079] The cross-sectional area A occupied by the gas core and liquid film g , A l They are:

[0080]

[0081] The liquid film thickness equation is:

[0082] δ(φ,θ)=(1-αθcosφ)δ t (30);

[0083] Average film thickness δ c for:

[0084]

[0085] α is the relationship between the inclination angle and the tilt angle:

[0086]

[0087] Average liquid film thickness of vertical tube δ t for:

[0088] δ t =7.165Re sg -1.07 Re sl 0.48 Fr g 0.24 Fr1 -0.24 D (33);

[0089] Among them, the gas and liquid phase Reynolds number Re sg 、Re sl They are:

[0090]

[0091] Froude number of gas and liquid phase g , Fr l They are:

[0092] BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 This is a flow chart for calculating wellbore pressure drop;

[0094] Figure 2 It is a schematic diagram of the fitting curve of liquid holdup versus sine value of angle;

[0095] Figure 3 It is a schematic diagram of the fitting curve of liquid holdup versus tube diameter;

[0096] Figure 4 Schematic diagram of the annular flow model. DETAILED DESCRIPTION

[0097] In order to make the purpose and calculation process of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings to highlight the advantages of the present invention.

[0098] like Figure 1 As shown, Figure 1 The present invention provides a method for calculating the wellbore pressure drop during the entire life cycle of a shale gas horizontal well. First, the gas well production data is collected, including the well inclination angle θ, the pipe diameter D, and the gas production Q. g Liquid production Q l , pressure p, temperature T, and then calculate the gas phase apparent velocity, liquid phase apparent velocity, gas and liquid phase density. By comparing the gas phase apparent velocity v calculated in step 1 sg and the critical gas velocity v calculated in step 2 cr, to determine the flow pattern of the gas wellbore, and then to model the non-annular flow and annular flow respectively. The core of the present invention lies in the process of determining the flow pattern of the wellbore and establishing the annular flow / non-annular flow pressure drop model.

[0099] (1) Based on the liquid film model theory, a prediction model for determining the transition boundary of annular flow / non-annular flow is proposed, which takes into account the liquid phase apparent velocity and well inclination:

[0100]

[0101] In the formula, v cr is the critical gas velocity, m / s; v sl is the apparent velocity of the liquid phase, m / s; g is the acceleration due to gravity, m / s 2 ; θ is the well inclination, °.

[0102] If v sg <v cr , then the gas phase superficial velocity v sg Under production conditions, the flow pattern of the gas wellbore is judged to be non-annular flow; if v sg ≥v cr , then the gas phase superficial velocity v sg Under production conditions, the flow pattern in the gas wellbore is judged to be annular flow.

[0103] (2) Based on the judgment result of step 2, the pressure drop is calculated for non-annular flow using the following formula:

[0104] Liquid holdup model:

[0105]

[0106] in:

[0107]

[0108] Among them, f(θ) is the function of the fitting tube inclination angle, k(D) is the function of the fitting tube inner diameter, a1, a2, a3, b1, b2, b3 are the coefficients of the fitted polynomial, and the schematic diagrams of the fitting curves are as follows: Figure 2 , Figure 3 shown.

[0109] Where N g 、N l is the velocity coefficient of gas and liquid phase, dimensionless; σ is the gas-liquid surface tension, N / m, taken as 0.06.

[0110] Friction model:

[0111]

[0112] Where k / D is the relative roughness of the tube wall and is dimensionless.

[0113] For the annular flow pressure drop model, the combined momentum balance formula of the gas core and the liquid film is used for calculation:

[0114]

[0115] In the formula, A l , A g is the cross-sectional area of ​​the liquid film and gas core, m 2 ; S l is the wetted perimeter of the pipe section, m; τ wl is the shear stress between the tube wall and the liquid film, N / m 2 ;

[0116] Among them, the density of the gas-liquid mixture in the gas core ρc is:

[0117] ρ c =ρ g φ c +ρ1(1-φ c ) (6).

[0118] Shear stress τ between tube wall and liquid film wl for:

[0119]

[0120] The cross-sectional area A occupied by the gas core and liquid film g , A l They are:

[0121]

[0122] The annular flow pressure drop model is an equation based on the liquid film thickness δ, which needs to be solved after given geometric relationships, velocity and closure relationships. The liquid film thickness equation is:

[0123] δ(φ,θ)=(1-αθcosφ)δ t (10);

[0124] Average film thickness δ c for:

[0125]

[0126] Among them, α is the relationship about the inclination angle:

[0127]

[0128] Average liquid film thickness of vertical tube δ t for:

[0129] δ t =7.165Resg -1.07 Re sl 0.48 Fr g 0.24 Fr1 -0.24 D (13);

[0130] By dividing the flow patterns and modeling them separately, the calculation of the wellbore pressure drop over the entire life cycle can be realized.

[0131] like Figure 2 , 3 As shown, Figure 2 is the fitting curve of the change of liquid holdup with the sine value of angle, Figure 3 It is the fitting curve of the change of liquid holdup with pipe diameter. The fitting relationship is a quadratic function with a high degree of fitting. And the liquid holdup shows a trend of increasing first and then decreasing with the increase of variables.

[0132] like Figure 4 As shown, Figure 4 Schematic diagram of annular flow model. As can be seen from the figure, the gas carries the liquid droplets through the center of the annular liquid film, and the liquid exists in two forms: a flowing liquid film and droplets entrained in the gas core. Unlike vertical pipe flow, in inclined and horizontal pipe flow, the liquid film around the pipe wall is not uniform. Generally speaking, the bottom liquid film is thicker than the top liquid film. For the convenience of research, the average liquid film δc is introduced here. The average liquid film is the average value of the thickest liquid film at the bottom and the thinnest liquid film at the top.

[0133] Compared with the existing pressure drop calculation model, the advantages of the present invention are:

[0134] (1) According to the production characteristics of shale gas wells, a calculation model for the transition boundary of annular / non-annular flow pattern considering the liquid phase superficial velocity and pipeline inclination is proposed. Then, the annular flow and non-annular flow pressure drop models are established respectively by comprehensively considering factors such as gas / liquid phase superficial velocity, inclination and pipe diameter. This provides a method for calculating the wellbore pressure drop during the entire life cycle of shale gas horizontal wells.

[0135] (2) Compared with the existing pressure drop prediction model, the calculation process of the present invention is simpler and does not require the writing of complex computer programs to assist in the calculation.

[0136] The above description is only the research idea of ​​the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating the wellbore pressure drop during the entire life cycle of a shale gas horizontal well, characterized in that: The steps include: Step 1: Collect production data of gas wells in the target area, including well inclination θ, pipe diameter D, and gas production Q g Liquid production Q l , pressure p, temperature T, calculate the gas phase apparent velocity, liquid phase apparent velocity, gas and liquid phase density; Step 2: Propose a prediction model for the flow pattern transition boundary between annular flow and non-annular flow, which takes into account the liquid phase superficial velocity and pipeline inclination, and judge the flow pattern of shale gas wellbore; Step 3: Model the annular flow and non-annular flow separately, and calculate the pressure drop based on the judgment results of step 2.

2. The method for calculating the wellbore pressure drop during the entire life cycle of a shale gas horizontal well according to claim 1, characterized in that: Step 2 proposes a prediction model for the flow pattern transition boundary between annular flow and non-annular flow, taking into account the liquid phase apparent velocity and well inclination: Compare the gas phase superficial velocity v in step 1 sg and the critical gas velocity v calculated in step 2 cr : If v sg <v cr , then the gas phase superficial velocity v sg Under production conditions, the flow pattern in the gas wellbore is judged to be non-annular flow; If v sg ≥v cr , then the gas phase superficial velocity v sg Under production conditions, the flow pattern in the gas wellbore is judged to be annular flow.

3. The method for calculating the wellbore pressure drop during the entire life cycle of a shale gas horizontal well according to claim 1, characterized in that: In step 3, the non-annular flow holdup model is fitted with the tube inclination angle and the tube inner diameter: in: Where a1, a2, a3, b1, b2, b3 are the coefficients of the polynomial fitted according to the experimental data; N g 、N l is the velocity parameter of gas and liquid phase, dimensionless; σ is the gas-liquid surface tension, N / m.

4. The method for calculating the wellbore pressure drop during the entire life cycle of a shale gas horizontal well according to claim 1, characterized in that: In step 3, the annular flow pressure drop model is an equation based on the liquid film thickness δ, which needs to be solved after given geometric relationships, velocity and closure relationships. The liquid film thickness equation is: δ(φ,θ)=(1-θcosφ)δ t in: d t =7.165Re sg -1.07 Re s1 0.48 Fr g 0.24 Fr1 -0.24 D Average liquid film δ c It is the average value of the sum of the thickest liquid film at the bottom and the thinnest liquid film at the top: α is the relationship between the inclination angle. When 0≤θ<30°, α is 0.0287; when 30°≤θ<90°, α is 0.55θ -868 .

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