A calculation method for wellbore pressure drop during the full life cycle of a shale gas horizontal well

Abstract

The present invention provides a method for calculating the wellbore pressure drop during the entire life cycle of a shale gas horizontal well, belonging to the technical field of oil and gas field development. Since the wellbore flow parameters vary greatly during different production stages of shale gas wells, casing production is adopted in the initial stage with high liquid production, and tubing production is adopted in the middle and late stages with relatively low production. However, the pressure models commonly used in engineering are difficult to accurately predict the wellbore pressure drop during the entire life cycle of shale gas wells. Therefore, in view of the production characteristics of shale gas wells, the present invention proposes a calculation model for the annular / non-annular flow pattern transition boundary considering the liquid-phase apparent velocity and pipeline inclination angle. Furthermore, by comprehensively considering factors such as gas / liquid-phase apparent velocity, inclination angle, and pipe diameter, pressure drop models for annular flow and non-annular flow are respectively established, obtaining a method for calculating the wellbore pressure drop during the entire life cycle of shale gas horizontal wells. This method has strong applicability to specific shale gas blocks, is simple 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.

Description

Technical Field

[0001] The present 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 whole life cycle of a shale gas horizontal well. Background Technique

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

[0003] In view of the production characteristics of shale gas wells, the commonly used pressure models in engineering are difficult to accurately predict the wellbore pressure drop at different production stages. The invention patent (CN113969779A) fits parameters using a large amount of on-site actual test data to establish a wellbore pressure calculation model for gas injection wells, which does not consider the change of flow pattern and is not applicable to production wells; the invention patent (CN104895560A) uses the Beggs-Brill model to calculate the wellbore pressure of deep-water test wells, focusing on the influence of inclination angle and is not applicable to 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 having poor applicability. In addition, the invention patent (CN111206919A) calculates the wellbore pressure of high-gas-production wells in long well sections using a conventional simple method considering the change of gas production with well depth in the reservoir section; the invention patent (CN118917227A) mainly considers the influence of condensate oil and proposes a method for calculating the wellbore pressure of water-bearing condensate gas wells. At present, there are almost no relevant reports on the calculation method of wellbore pressure drop for shale gas wells at different production stages, and the commonly used mechanism models only model for a single flow pattern (such as annular flow, Taylor slug flow), with a narrow applicable range for calculating the wellbore pressure drop of shale gas.

[0004] Therefore, in view of the production characteristics of shale gas horizontal wells, the present invention proposes a calculation model for the annular / non-annular flow pattern transition boundary considering the liquid-phase apparent velocity and pipeline inclination angle, respectively establishes the pressure drop models for annular flow and non-annular flow, and obtains a method for calculating the wellbore pressure drop during the whole life cycle of a shale gas horizontal well. This method has a wide applicable range, is simple to calculate and use, and has certain guiding significance for the production dynamic analysis and drainage gas production process optimization of shale gas horizontal wells. Summary of the Invention

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

[0006] A calculation method for the wellbore pressure drop during the entire life cycle of a shale gas horizontal well is as follows:

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

[0008] The superficial gas velocity v sg is:

[0009]

[0010] The superficial liquid velocity v sl is:

[0011]

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

[0013] Among them,

[0014]

[0015] The gas and liquid phase densities ρ g , ρ l under different pressure and temperature conditions are calculated as follows:

[0016]

[0017] ρ1 = 1000γ w (5).

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

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

[0020]

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

[0022] Compare the gas-phase apparent velocity v sg in Step 1 with the flow pattern transition boundary vcr of annular flow / non-annular flow:

[0023] If v sg < v cr , then the gas-phase apparent velocity v sg Under the production conditions, the flow pattern of the gas wellbore is judged as non-annular flow;

[0024] If v sg ≥ v cr , then the gas-phase apparent velocity v sg Under the production conditions, the flow pattern of the gas wellbore is judged as annular flow.

[0025] Step 3: Pressure drop calculation.

[0026] According to the judgment result of Step 2, the following formula is used to calculate the pressure drop for non-annular flow:

[0027]

[0028] where p is the pressure, Pa; z is the pipe length, 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, dimensionless.

[0029] Among them:

[0030] ρ m = ρ1H L + ρ g (1 - H L ) (8);

[0031] where H L is the liquid holdup, %. The following formula considering the effects of gas density, liquid density, gas-liquid surface tension, pipe inclination, gas velocity, liquid velocity and pipe diameter on the liquid holdup is used to calculate the liquid holdup:

[0032]

[0033] Among them:

[0034]

[0035] In the formula, f(θ) is the function of the inclination angle of the fitting pipe; k(D) is the function of the inner diameter of the fitting pipe; a1, a2, a3, b1, b2, b3 are the coefficients of the polynomial obtained by fitting; N g , N l are the gas and liquid phase velocity dimensionless numbers, dimensionless; σ is the gas-liquid surface tension, N / m, taking 0.06.

[0036] The calculation of the frictional resistance is based on the frictional resistance relationship of the M-B model:

[0037]

[0038] In the formula, k / D is the relative roughness of the pipe wall, dimensionless.

[0039] Among them, the no-slip Reynolds number is:

[0040]

[0041] In the formula, Re ns is the no-slip Reynolds number, dimensionless; ρ ns is the no-slip mixture density, kg / m 3 ; μ ns is the no-slip mixture viscosity, Pa·s.

[0042] The no-slip mixture density is:

[0043]

[0044] The no-slip mixture viscosity is:

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

[0046] In the formula, H Lns is the no-slip liquid holdup, %; μ g is the gas phase viscosity, taking 2×10 -5 Pa·s; μ l is the liquid phase viscosity, taking 8×10 -4 Pa·s.

[0047] The no-slip liquid holdup H Lns is:

[0048]

[0049] Gas-liquid mixing velocity v m is:

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

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

[0052]

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

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

[0055] ρ c = ρ g φ c + ρ1(1 - φ c ) (18).

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

[0057]

[0058] In the formula, FE is the droplet entrainment rate, in decimals.

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

[0060] FE = 1 - e [-0.125(ψ-1.5)] (20);

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

[0062] Among them:

[0063]

[0064] The shear stress τ wl between the pipe wall and the liquid film is:

[0065]

[0066] The interfacial friction coefficient $f_f$ is:

[0067] When $Re$ f ≤ 2300,

[0068]

[0069] When $Re$ f > 2300,

[0070]

[0071] where $\epsilon$ is the absolute roughness of the pipe wall, and it can be taken as 0.0152 mm.

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

[0073]

[0074] where $D$ f is the hydraulic diameter of the liquid film, in m.

[0075]

[0076] The liquid film velocity $v$ f is:

[0077]

[0078] In the formula, $\delta$ is the liquid film thickness, in m; $\overline{\delta}$ c is the average liquid film thickness, in m.

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

[0080]

[0081] The liquid film thickness equation is:

[0082] $\delta(\varphi,\theta)=(1 - \alpha\theta\cos\varphi)\overline{\delta}$ t (30);

[0083] The average liquid film thickness $\overline{\delta}$ c is:

[0084]

[0085] $\alpha$ is a relational expression regarding the inclination angle:

[0086]

[0087] The average liquid film thickness $\overline{\delta}$ of the vertical pipe t is:

[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-phase and liquid-phase Reynolds numbers Re sg 、Re sl are respectively:

[0090]

[0091] The gas-phase and liquid-phase Froude numbers Fr g 、Fr l are respectively:

[0092] Description of the Drawings

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

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

[0095] Figure 3 is the schematic diagram of the fitting curve of the liquid holdup with the pipe diameter;

[0096] Figure 4 is the schematic diagram of the annular flow model. Detailed Implementation Manner

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

[0098] As Figure 1 shown, Figure 1 is the flow chart for the calculation of the present invention. The present invention provides a method for calculating the wellbore pressure drop in the whole life cycle of a shale gas horizontal well. First, collect the gas well production data, including the well inclination angle θ, pipe diameter D, gas production rate Q g 、liquid production rate Q l 、pressure p, temperature T, and then calculate the gas-phase superficial velocity, liquid-phase superficial velocity, and gas-phase and liquid-phase densities. By comparing the gas-phase superficial velocity v sg calculated in step one and the critical gas flow velocity v cr, to judge the flow pattern in the gas well borehole, and then model non-annular flow and annular flow respectively. The core of the present invention lies in the judgment of the flow pattern in the wellbore and the process of establishing the pressure drop model for annular flow / non-annular flow.

[0099] (1) Based on the liquid film model theory, a prediction model for the flow pattern transition boundary for judging annular flow / non-annular flow considering the liquid phase apparent velocity and well inclination is proposed:

[0100]

[0101] In the formula, v cr is the critical gas flow velocity, m / s; v sl is the liquid phase apparent velocity, 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 apparent velocity v sg Under the production conditions, the flow pattern in the gas well borehole is judged as non-annular flow; if v sg ≥ v cr , then the gas phase apparent velocity v sg Under the production conditions, the flow pattern in the gas well borehole is judged as annular flow.

[0103] (2) According to the judgment result of step two, the following formula is used to calculate the pressure drop for non-annular flow:

[0104] Liquid holdup model:

[0105]

[0106] Where:

[0107]

[0108] Among them, f(θ) is a function fitting the well inclination, k(D) is a function fitting the inner diameter of the pipe, and a1, a2, a3, b1, b2, b3 are the coefficients of the polynomial obtained by fitting. The schematic diagrams of the fitting curves are respectively as Figure 2 , Figure 3 shown.

[0109] In the formula, N g , N l are the gas and liquid phase velocity criteria, dimensionless; σ is the gas-liquid surface tension, N / m, taking 0.06.

[0110] Friction model:

[0111]

[0112] In the formula, k / D is the relative roughness of the pipe wall, dimensionless.

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

[0114]

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

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

[0117] ρ c = ρ g φ c + ρ1(1 - φ c ) (6).

[0118] The shear stress τ wl between the pipe wall and the liquid film is:

[0119]

[0120] The cross-sectional areas A g 、A l occupied by the gas core and liquid film are respectively:

[0121]

[0122] The annular flow pressure drop model is based on the equation of the liquid film thickness δ and needs to be solved after giving geometric relations, velocities and closure relations. The liquid film thickness equation is:

[0123] δ(φ,θ) = (1 - αθcosφ)δ t (10);

[0124] The average liquid film thickness δ c is:

[0125]

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

[0127]

[0128] The average liquid film thickness δ t in the vertical pipe is:

[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 pattern and modeling separately, the calculation of wellbore pressure drop throughout the life cycle can be achieved.

[0131] Such as Figure 2 、 3 shown, Figure 2 is the fitting curve of the liquid holdup varying with the sine value of the angle, Figure 3 is the fitting curve of the liquid holdup varying with the 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 the variable.

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

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

[0134] (1) Aiming at the production characteristics of shale gas wells, a calculation model for the annular / non-annular flow pattern transition boundary considering the liquid-phase superficial velocity and pipe inclination is proposed. Furthermore, by comprehensively considering factors such as gas / liquid-phase superficial velocities, inclination, and pipe diameter, pressure drop models for annular flow and non-annular flow are established respectively, providing a calculation method for wellbore pressure drop throughout the life cycle of horizontal shale gas wells.

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

[0136] The above is only the research idea of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A calculation method for wellbore pressure drop during the full life cycle of a shale gas horizontal well, characterized in that, It includes the following steps: Step 1: Fluid parameter calculation. Collect the production data of gas wells in the target block, including well inclination angle θ, pipe diameter D, gas production rate Q g , liquid production rate Q l , pressure p, temperature T, and calculate the relevant fluid parameters; Superficial gas velocity v sg is as follows: Liquid-phase apparent velocity v sl is as follows: Where D is the pipe diameter, in m; Q g is the gas production rate, in m 3 / s; Q l is the liquid production rate, in m 3 / s; B g is the volume coefficient; Among them, Gas and liquid phase densities ρ under different pressure and temperature conditions g and ρ l The calculation formula is as follows: ρ1 = 1000γ w Where ρ g and ρ l are the gas and liquid phase densities, kg / m 3 ; p is the pressure, Pa; γ g is the relative density of the gas phase, taken as 0.65; γ w is the relative density of the liquid phase, taken as 1.02; Z g is the natural gas deviation factor, taken as 0.94; T is the temperature, K; Step 2: Flow pattern judgment. Based on the liquid film model theory, a prediction model for the flow pattern transition boundary of annular flow / non-annular flow considering the liquid phase superficial velocity and well inclination angle is proposed: where, v cr is the critical gas velocity, m / s; v sl is the apparent liquid velocity, m / s; g is the acceleration of gravity, m / s 2 ; θ is the well inclination angle, °; Compare the superficial gas velocity v in Step 1 sg with the flow pattern transition boundary v between annular flow and non-annular flow cr : If v sg <v cr , then the superficial gas 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 superficial velocity v sg under production conditions, the flow pattern in the gas wellbore is judged to be annular flow; Step 3: Model annular flow and non-annular flow respectively, and calculate the pressure drop according to the judgment results of Step 2; Modeling of non-annular flow: where p is the pressure, Pa; z is the pipe length, m; ρ m is the gas-liquid mixed density, kg / m 3 ; v m is the gas-liquid velocity, m / s; f m is the friction coefficient, dimensionless; Modeling of annular flow: For the annular flow pressure drop model, the combined momentum balance equation of the gas core and liquid film is used for calculation: Where, A l and A g are the cross-sectional areas occupied by the liquid film and the gas core, m 2 ; S l is the wetted perimeter of the pipe cross-section, m; τ wl is the shear stress between the pipe wall and the liquid film, N / m 2 ; ρ c is the density of the gas-liquid mixture in the gas core.

2. The method for calculating the wellbore pressure drop during the full life cycle of a shale gas horizontal well according to claim 1, wherein In step three, the gas-liquid mixed density ρ m is as follows: ρ m = ρ l H L + ρ g (1 - H L ) where H L is the liquid holdup, %, and the liquid holdup is calculated using the following formula that takes into account the effects of gas density, liquid density, gas-liquid surface tension, pipe inclination angle, gas flow velocity, liquid flow velocity, and pipe diameter on the liquid holdup: Where: In the formula, a1, a2, a3, b1, b2, b3 are the coefficients of the polynomial fitted according to experimental data; N g 、N l are the gas and liquid phase velocity criteria, dimensionless; σ is the gas-liquid surface tension, N / m; The calculation of frictional resistance is based on the frictional resistance relationship of the M-B model: In the formula, k / D is the relative roughness of the pipe wall, dimensionless; Among them, the no-slip Reynolds number is: where Re ns is the non-slip Reynolds number, dimensionless; ρ ns is the non-slip mixture density, kg / m 3 ; μ ns is the non-slip mixture viscosity, Pa·s; The no-slip mixture density is: The no-slip mixture viscosity is: μ ns = (1 - H Lns )μ g + H Lns μ l where H Lns is the non-slip liquid holdup, %; μ g is the gas-phase viscosity, taking 2×10 -5 Pa·s; μ l is the liquid-phase viscosity, taking 8×10 -4 Pa·s; Non-slip holdup H Lns is as follows: Gas-liquid mixing velocity v m is as follows: v m = v sl + v sg 。 3. The method for calculating the wellbore pressure drop during the full life cycle of a shale gas horizontal well according to claim 2, characterized in that, In step 3, the cross-sectional areas A g and A l occupied by the gas core and the liquid film are respectively: where FE is the droplet entrainment rate, in decimal, and Φ c is the void fraction, and its relationship with the droplet entrainment rate FE is as follows: The liquid film thickness equation is: δ(φ,θ) = (1 - αφ cos φ)δ t Average liquid film thickness δ c is as follows: α is a relationship about the inclination angle: Average liquid film thickness δ of vertical tube t is as follows: δ t = 7.165Re sg -1.07 Re sl 0.48 Fr g 0.24 Fr1 -0.24 D Among them, the gas-phase and liquid-phase Reynolds numbers Re sg , Re sl are respectively: Gas and liquid phase Froude numbers Fr g 、Fr l are respectively:

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