A method for determining the concentration of foaming agent in gas wellbore based on wellbore multiphase flow calculation

Abstract

The present invention provides a method for determining the concentration of a gas wellbore foaming agent based on wellbore multiphase flow calculation, and belongs to the technical field of oil and gas field development. The method includes: collecting gas well dynamic parameters, selecting a commonly used gas well productivity empirical formula in engineering to calculate the formation inflow curve; based on the two-phase flow Mukherjee & Brill model, introducing a foaming agent concentration coefficient, obtaining a friction resistance pressure drop and liquid holdup model, establishing a new foaming wellbore pressure drop model, and calculating the wellbore outflow curve; combining node system analysis, determining the stable production point of the gas well under different foaming agent concentrations, obtaining a regular curve of the foaming agent concentration coefficient and gas production change, determining the foaming agent entry concentration, and providing theoretical support for the on-site foam drainage gas production process.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and gas field development, and in particular relates to a method for determining the concentration of a gas wellbore foaming agent based on wellbore multiphase flow calculation. Background Art

[0002] In the later stage of gas well production, the gas well has the characteristics of low gas and liquid production. As the gas well continues to produce, the formation energy gradually decreases, the gas-carrying capacity weakens, and a large amount of liquid accumulates in the wellbore, which can easily cause flooding and shutdown. In order to effectively prevent and delay the phenomenon of liquid accumulation in gas wells, the foam drainage gas production process with low cost, quick effect and convenient operation is widely used in gas fields. The foam drainage gas production process is a drainage measure that uses foaming agents to mix with wellbore gas and liquid to form foam, thereby inhibiting the liquid from sliding off during the flow of wellbore fluid, changing the flow pattern, and reducing the bottom hole back pressure.

[0003] In the process of gas well production, accurate prediction of the wellbore mixed fluid flow pressure drop is crucial for the dynamic optimization of the process parameters of foam drainage gas wells. In the field of multiphase flow research, the wellbore pressure drop model mainly consists of two parts: friction resistance pressure drop and gravity pressure drop. For foam fluid, the friction resistance pressure drop between the fluid and the pipe wall and the liquid holdup calculation are extremely complex and particularly important. In addition, most of the existing wellbore pressure drop models are based on traditional two-phase flow theory and fail to fully consider the effect of foaming agent concentration on fluid flow characteristics. Therefore, developing a model that can accurately reflect the effect of foaming agent concentration on wellbore pressure drop is of great significance for optimizing foam drainage gas production technology.

[0004] The present invention provides a method for determining the concentration of a gas wellbore foaming agent based on wellbore multiphase flow calculation, and draws a formation inflow curve according to a gas well productivity formula commonly used in engineering. Based on the two-phase flow Mukherjee & Brill model, the critical gas flow velocity of the gas-liquid two-phase liquid film reversal is calculated, and the foaming agent concentration parameter is introduced to establish a friction resistance pressure drop and liquid holdup model. The polynomial coefficients are obtained through experimental fitting to form a new calculation method for the foam drainage gas wellbore pressure drop, and then the wellbore outflow curve is drawn. Combined with the node system analysis, the relationship curve between the foaming agent concentration coefficient and the gas production is obtained, so as to determine the optimal concentration of the foaming agent, and provide theoretical support for the on-site foam drainage gas production process. Summary of the invention

[0005] The present invention aims to provide a method for determining the concentration of a gas wellbore foam drainage agent based on wellbore multiphase flow calculation, so as to provide key theoretical support for the optimization design of on-site foam drainage gas production technology.

[0006] Step 1: Collect the wellbore structure data and production data of the gas well, including pipe inclination, inner diameter of the tubing, wellhead oil pressure, temperature, gas production, liquid production, liquid density, average formation pressure, foaming agent concentration, and foaming agent critical micelle concentration.

[0007] Step 2: Draw the formation inflow curve. Use the empirical formula for gas well productivity commonly used in engineering: (1) In the formula, Q SC is the gas production, m 3 / d; J is the gas production index, m 3 / (d×MPa); p r is the average formation pressure, MPa; p wf is the bottom hole flowing pressure, MPa.

[0008] According to the gas well production data, the productivity index is obtained by fitting using the least squares method. J , combined with the gas production parameter range, the bottom hole flowing pressure is calculated according to the empirical formula of gas well productivity, and the formation inflow curve of the relationship between bottom hole flowing pressure and gas production is obtained.

[0009] Step 3: Draw the wellbore outflow curve, and establish a foaming wellbore pressure drop model based on the wellbore structure data and production data obtained in step 1; combined with the gas production parameter range, given the wellhead oil pressure, calculate the bottomhole flow pressure based on the foaming wellbore pressure drop, and obtain the wellbore outflow curve showing the relationship between the bottomhole flow pressure and gas production.

[0010] The model building process is as follows:

[0011] a. Calculate the friction resistance pressure drop under bubble discharge conditions

[0012] (2) In the formula, is the friction resistance pressure drop, Pa / m; v SL is the liquid phase superficial velocity, m / s; f m is the friction coefficient, dimensionless; is the density of the mixture without slippage, kg / m 3 ; v m is the superficial velocity of the gas-liquid mixed phase, m / s; v cf is the critical gas flow velocity for gas-liquid two-phase film reversal, m / s; D is the inner diameter of the oil pipe, m; c 1 , c 2 , c 3 , c 4 are the polynomial coefficients obtained from experimental fitting; is the concentration coefficient of the foaming agent and is dimensionless.

[0013] The concentration coefficient of the foaming agent is expressed as:

[0014] (3) In the formula, CV The concentration of the foaming agent, mg / L; CMC is the critical micelle concentration of the foaming agent, mg / L.

[0015] The density of the no-slip mixture is:

[0016] (4) In the formula, r G is the gas density, kg / m 3 ; r L is the liquid density, kg / m 3 ; It is the liquid holdup without slippage and is dimensionless.

[0017] The non-slip liquid retention rate is:

[0018] (5)

[0019] The gas density under different pressure conditions is:

[0020] (6)

[0021] In the formula, r G is the gas density, kg / m 3 ; p is the pressure, MPa; M is the relative molecular mass of natural gas, g / mol; T is temperature, K; R is the ideal gas constant, (0.008314 atm·m 3 / (kmol·K)); Z is the deviation factor and is dimensionless.

[0022] The gas phase superficial velocity is:

[0023] (7)

[0024] The liquid phase superficial velocity is:

[0025] (8)

[0026] The superficial velocity of the gas-liquid mixture is:

[0027] (9)

[0028] In the formula, v SGis the gas phase superficial velocity, m / s; v SL is the liquid phase superficial velocity, m / s; v m is the superficial velocity of the gas-liquid mixed phase, m / s; Q SC is the gas production, m 3 / d; Q SL is the liquid production, m 3 / d; r SC is the gas density at normal pressure, kg / m 3 ; A is the cross-sectional area of ​​the pipe, m 2 .

[0029] The expression of the critical gas flow velocity for gas-liquid two-phase liquid film reversal is:

[0030] (10)

[0031] In the formula, r G is the gas density, kg / m 3 ; r L is the liquid density, kg / m 3 ; v SL is the liquid phase superficial velocity, m / s; g is the acceleration due to gravity, m / s 2 ; D is the inner diameter of the oil pipe, m; c 5 , c 6 are the coefficients of the polynomial obtained from the experimental fitting.

[0032] The calculation of friction coefficient is based on the friction relationship of Mukherjee & Brill model:

[0033] (11)

[0034] In the formula, k / D is the relative roughness of the tube wall, dimensionless; Re ns is the no-slip Reynolds number and is dimensionless.

[0035] The no-slip Reynolds number is:

[0036] (12)

[0037] In the formula, v m is the superficial velocity of the gas-liquid mixed phase, m / s; is the density of the mixture without slippage, kg / m 3 ; D is the inner diameter of the oil pipe, m; m ns is the viscosity of the no-slip mixture, Pa·s.

[0038] The viscosity of the no-slip mixture is:

[0039] (13) In the formula, m G is the gas phase viscosity, taking 2×10 -5 Pa·s; m L is the liquid viscosity, take 8×10 -4 Pa·s.

[0040] b. Establish bubble drainage liquid retention rate H foam

[0041] Based on the liquid holdup formula of the two-phase flow Mukherjee & Brill model, a liquid holdup model considering the concentration of the foaming agent is established, and the expression is: (14) In the formula, H foam It is the bubble drainage liquid retention rate defined in the present invention, %; H L is the two-phase liquid holdup of the Mukherjee & Brill model, %; F G is the gas phase apparent velocity converted using the Froude number, m / s; b 1 , b 2 , b 3 are the coefficients obtained from experimental fitting.

[0042] The two-phase liquid holdup of the Mukherjee & Brill model is: (15)

[0043] in:

[0044] (16)

[0045] In the formula, f(θ) is the function of the fitting tube inclination angle; N vg is the gas phase velocity criterion, dimensionless; N vl is the liquid phase velocity parameter, dimensionless; N L is the liquid phase viscosity, dimensionless; sis the gas-liquid surface tension, N / m, taken as 0.06; a 1 , a 2 , a 3 , a 4 , a 5 , a 6 are the polynomial coefficients obtained by fitting.

[0046] The gas phase apparent velocity converted using the Froude number is: (17)

[0047] c. Establish a foam drainage wellbore pressure drop model

[0048] The wellbore pressure drop model under the influence of foaming agent concentration is expressed as: (18) In the formula, i is the tube inclination angle, °; r m is the mixed density, kg / m 3 .

[0049] The mixed density is a function of the liquid holdup and is expressed as: (19) In the formula, H foam is the bubble drainage liquid retention rate, %; r L is the liquid density, kg / m 3 ; r G is the gas density, kg / m 3 .

[0050] Step 4: Based on the formation inflow curve and wellbore outflow curve obtained in steps 2 and 3, and based on the node system analysis, draw the relationship curve between the concentration coefficient of the foaming agent and the gas production to determine the optimal foaming agent concentration. The specific process is:

[0051] Given different foaming agent concentrations, different foaming agent concentration coefficients are calculated, and the wellbore outflow curves of the bottom hole pressure changing with gas production under different foaming agent concentrations are obtained; from the calculation results, it can be seen that the change law of the wellbore outflow curves with different foaming agent concentrations is consistent, and the bottom hole pressure first decreases and then increases with the increase of gas production; based on the node system analysis, the intersection of the formation inflow curve and the wellbore outflow curve is the stable production point of the gas well; according to the gas production corresponding to the stable production point under different foaming agent concentration coefficients, the relationship curve between the foaming agent concentration coefficient and the gas production is drawn, and the foaming agent concentration corresponding to the stable production point with the highest gas production is the optimal foaming agent injection concentration of the gas well. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 A technical roadmap for a method for determining the concentration of a gas wellbore foaming agent based on wellbore multiphase flow calculation;

[0053] Figure 2 Formation inflow / wellbore outflow graph;

[0054] Figure 3 Relationship curve between foaming agent concentration coefficient and gas production. DETAILED DESCRIPTION

[0055] 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.

[0056] like Figure 1 As shown, Figure 1 The present invention provides a method for determining the concentration of a gas wellbore foaming agent based on wellbore multiphase flow calculation. First, the gas wellbore structure data and production data are collected, and the formation inflow curve is calculated according to the gas well productivity empirical formula. Then, the critical gas flow velocity of the gas-liquid two-phase liquid film reversal is calculated. v cf , establish the bubble drainage friction resistance pressure drop formula, and establish a new liquid holdup model based on the liquid holdup formula of the two-phase flow Mukherjee & Brill model H foam . The gas well pressure drop formula considering the influence of the foaming agent concentration is obtained and used to draw the wellbore outflow curve. Based on the node system analysis, the intersection of the formation inflow curve and the wellbore outflow curve is the stable production point of the gas well. The stable production point of the gas well under different foaming agent concentrations is obtained. According to the gas production corresponding to the stable production point, the relationship curve between the foaming agent concentration coefficient and the gas production is drawn. The foaming agent concentration corresponding to the stable production point with the highest gas production is the optimal foaming agent injection concentration of the gas well.

[0057] The core of the present invention is to establish a foam drainage wellbore pressure drop model.

[0058] (1) Calculation of friction resistance pressure drop under bubble drainage conditions

[0059] (1) In the formula, is the friction resistance pressure drop, Pa / m; v SL is the liquid phase superficial velocity, m / s; f m is the friction coefficient, dimensionless; is the density of the mixture without slippage, kg / m 3 ; v mis the superficial velocity of the gas-liquid mixed phase, m / s; v cf is the critical gas flow velocity for gas-liquid two-phase film reversal, m / s; D is the inner diameter of the oil pipe, m; c 1 , c 2 , c 3 , c 4 are the polynomial coefficients obtained from experimental fitting; is the concentration coefficient of the foaming agent and is dimensionless.

[0060] The concentration coefficient of the foaming agent is expressed as: (2) In the formula, CV The concentration of the foaming agent, mg / L; CMC is the critical micelle concentration of the foaming agent, mg / L.

[0061] The density of the no-slip mixture is: (3) In the formula, r G is the gas density, kg / m 3 ; r L is the liquid density, kg / m 3 ; It is the liquid holdup without slippage and is dimensionless.

[0062] The non-slip liquid retention rate is: (4)

[0063] The gas density under different pressure conditions is: (5) In the formula, r G is the gas density, kg / m 3 ; p is the pressure, MPa; M is the relative molecular mass of natural gas, g / mol; T is temperature, K; R is the ideal gas constant, (0.008314 atm·m 3 / (kmol·K)); Z is the deviation factor and is dimensionless.

[0064] The gas phase superficial velocity is: (6)

[0065] The liquid phase superficial velocity is: (7)

[0066] The superficial velocity of the gas-liquid mixture is: (8)

[0067] In the formula, v SG is the gas phase superficial velocity, m / s; v SL is the liquid phase superficial velocity, m / s; v m is the superficial velocity of the gas-liquid mixed phase, m / s; Q SC is the gas production, m 3 / d; Q SL is the liquid production, m 3 / d; r SC is the gas density at normal pressure, kg / m 3 ; A is the cross-sectional area of ​​the pipe, m 2 .

[0068] The expression of the critical gas flow velocity for gas-liquid two-phase liquid film reversal is: (9) In the formula, r G is the gas density, kg / m 3 ; r L is the liquid density, kg / m 3 ; v SL is the liquid phase superficial velocity, m / s; g is the acceleration due to gravity, m / s 2 ; D is the inner diameter of the oil pipe, m; c 5 , c 6 represents the coefficients of the polynomial obtained by experimental fitting.

[0069] The calculation of friction coefficient is based on the friction relationship of Mukherjee & Brill model: In formula (10), k / D is the relative roughness of the tube wall, dimensionless; Re ns is the no-slip Reynolds number and is dimensionless.

[0070] The no-slip Reynolds number is: (11) In the formula, v m is the superficial velocity of the gas-liquid mixed phase, m / s; is the density of the mixture without slippage, kg / m 3 ; D is the inner diameter of the oil pipe, m; m ns is the viscosity of the no-slip mixture, Pa·s.

[0071] The viscosity of the no-slip mixture is: (12) In the formula, m G is the gas phase viscosity, taking 2×10 -5 Pa·s; m L is the liquid viscosity, take 8×10 -4 Pa·s.

[0072] (2) Based on the liquid holdup formula of the two-phase flow Mukherjee & Brill model, a liquid holdup model considering the concentration of the foaming agent is established, and the expression is: (13) In the formula, H foam It is the bubble drainage liquid retention rate defined in the present invention, %; H L is the two-phase liquid holdup of the Mukherjee & Brill model, %; F G is the gas phase apparent velocity converted using the Froude number, m / s; b 1 , b 2 , b 3 are the coefficients obtained from experimental fitting.

[0073] The two-phase liquid holdup of the Mukherjee & Brill model is: (14)

[0074] in: (15)

[0075] In the formula, f(θ) is the function of the fitting tube inclination angle; N vg is the gas phase velocity criterion, dimensionless; N vl is the liquid phase velocity parameter, dimensionless; N L is the liquid phase viscosity, dimensionless; s is the gas-liquid surface tension, N / m, taken as 0.06; a 1 , a 2 , a 3 , a 4 , a 5 , a 6 are the polynomial coefficients obtained by fitting.

[0076] The gas phase apparent velocity converted using the Froude number is: (16)

[0077] Finally, the wellbore pressure drop model under the influence of foaming agent concentration is obtained, and the expression is: (17) In the formula, i is the tube inclination angle, °; r m is the mixed density, kg / m 3 .

[0078] The mixed density is a function of the liquid holdup and is expressed as: (18) In the formula, H foam is the bubble drainage liquid retention rate, %; r L is the liquid density, kg / m 3 ; r G is the gas density, kg / m 3 .

[0079] like Figure 2 As shown, the formation inflow / wellbore outflow curve is drawn. The gas well productivity empirical formula commonly used in engineering is selected: (19) In the formula, Q SC is the gas production, m 3 / d; J is the gas production index, m 3 / (d×MPa); p r is the average formation pressure, MPa; p wf is the bottom hole flowing pressure, MPa.

[0080] Based on the measured data of gas well productivity test, the productivity index is obtained by fitting using the least squares method. J , combined with the gas production parameter range, the bottom hole flowing pressure is calculated according to the empirical formula of gas well productivity, and the formation inflow curve of the relationship between bottom hole flowing pressure and gas production is obtained.

[0081] Given different concentrations of foaming agent, calculate the different foaming agent concentration coefficients , , Given the wellhead oil pressure, the foam wellbore pressure drop model is used to calculate the wellbore outflow curve of the bottom hole flow pressure and gas production under different foaming agent concentrations. Based on the node system analysis, the intersection of the formation inflow and wellbore outflow curves is the stable production point of the gas well. , , Stable production point of gas well X1 , X 2 , X 3 .

[0082] like Figure 3 As shown, according to the stable production point X 1 , X 2 , X 3 The corresponding gas production Q 1 , Q 2 , Q 3 , draw the relationship curve between the concentration coefficient of the foaming agent and the gas production, the point with the highest gas production Q 1 The corresponding foaming agent concentration is the optimal foaming agent injection concentration for the gas well.

[0083] Compared with the shortcomings and deficiencies of the prior art, the present invention has the following beneficial effects:

[0084] (1) Under the conditions of foam drainage gas production, the influence of foaming agent concentration is fully considered, and a new formula for the wellbore pressure drop of gas wells under foam drainage gas production conditions is proposed.

[0085] (2) Combined with the node system analysis, according to the formation inflow / wellbore outflow curve, the relationship curve between the foaming agent concentration coefficient and the gas production is drawn to determine the concentration of the foaming agent, providing theoretical guidance for the on-site foam drainage gas production process.

[0086] Obviously, the above 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 determining the concentration of a gas wellbore foaming agent based on wellbore multiphase flow calculation, characterized in that: The main steps include: Step 1: Collect the wellbore structure data and production data of the gas well, including pipe inclination, inner diameter of the oil pipe, wellhead oil pressure, temperature, gas production, liquid production, liquid density, average formation pressure, foaming agent concentration, and foaming agent critical micelle concentration; Step 2: Draw the formation inflow curve and use the empirical formula for gas well productivity commonly used in engineering: In the formula, Q SC is the gas production, m 3 / d; J is the gas production index, m 3 / (d·MPa); p r is the average formation pressure, MPa; p wf is the bottom hole flowing pressure, MPa; According to the gas well production data, the productivity index J is obtained by fitting using the least square method. Combined with the gas production parameter range, the bottom hole flowing pressure is calculated according to the gas well productivity empirical formula, and the formation inflow curve of the relationship between the bottom hole flowing pressure and gas production is obtained; Step 3: Draw the wellbore outflow curve, and establish a foaming wellbore pressure drop model based on the wellbore structure data and production data obtained in step 1; combine the gas production parameter range, give the wellhead oil pressure, calculate the bottom hole flow pressure based on the foaming wellbore pressure drop, and obtain the wellbore outflow curve of the relationship between the bottom hole flow pressure and the gas production; Step 4: Based on the formation inflow curve and wellbore outflow curve obtained in steps 2 and 3, and based on the node system analysis, draw a curve of the relationship between the concentration coefficient of the foaming agent and the gas production to determine the optimal foaming agent injection concentration.

2. A method for determining the concentration of a gas wellbore foaming agent based on wellbore multiphase flow calculation according to claim 1, characterized in that: In step 3, calculate the friction resistance pressure drop under the bubble discharge condition: In the formula, is the friction resistance pressure drop, Pa / m; v SL is the liquid phase apparent velocity, m / s; f m is the friction coefficient, dimensionless; ρ ns is the density of the mixture without slippage, kg / m 3 ;v m is the superficial velocity of the gas-liquid mixture, m / s; v cf is the critical gas velocity of gas-liquid two-phase liquid film reversal, m / s; D is the inner diameter of the oil pipe, m; c1, c2, c3, c4 are the polynomial coefficients obtained by experimental fitting; α is the concentration coefficient of the foaming agent, dimensionless; The expression of the critical gas flow velocity for gas-liquid two-phase liquid film reversal is: In the formula, ρ G is the gas density, kg / m 3 ; ρ L is the liquid density, kg / m 3 ;v SL is the apparent velocity of the liquid phase, m / s; g is the acceleration due to gravity, m / s 2 ; D is the inner diameter of the oil pipe, m; c5 and c6 are the coefficients of the polynomial obtained by experimental fitting.

3. A method for determining the concentration of a gas wellbore foaming agent based on wellbore multiphase flow calculation according to claim 1, characterized in that: In step 3, establish the bubble drainage liquid holdup H foam : Based on the liquid holdup formula of the two-phase flow Mukherjee & Brill model, a liquid holdup model considering the concentration of the foaming agent is established, and the expression is: In the formula, H foam is the bubble drainage liquid retention rate, %; H L is the two-phase liquid holdup of the Mukherjee & Brill model, %; F G is the gas phase apparent velocity converted by Froude number, m / s; b1, b2, b3 are coefficients obtained by experimental fitting; α is the foaming agent concentration coefficient, dimensionless.

4. A method for determining the concentration of a gas wellbore foaming agent based on wellbore multiphase flow calculation according to claim 1, characterized in that: Step 4: Determine the optimal concentration of the foaming agent. The specific process is as follows: In the combined step 2, the empirical formula of gas well productivity is used to calculate the formation inflow curve of the relationship between bottomhole flow pressure and gas production; in the combined step 3, the wellbore outflow curve of the relationship between bottomhole flow pressure and gas production is calculated using the foam wellbore pressure drop model. Given different foaming agent concentrations, different foaming agent concentration coefficients are calculated to obtain the wellbore outflow curve of the bottomhole flow pressure changing with gas production under different foaming agent concentrations; from the calculation results, it can be seen that the change law of the wellbore outflow curves of different foaming agent concentrations is consistent, and the bottomhole flow pressure first decreases and then increases with the increase of gas production; based on the node system analysis, the intersection of the formation inflow curve and the wellbore outflow curve is the stable production point of the gas well; according to the gas production corresponding to the stable production point under different foaming agent concentration coefficients, a curve of the change relationship between the foaming agent concentration coefficient and the gas production is drawn, and the foaming agent concentration corresponding to the stable production point with the highest gas production is the optimal foaming agent injection concentration of the gas well.

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