Three-phase flow gas content calculation method based on drift theory

Abstract

The invention provides a three-phase flow gas content calculation method based on a drift theory. Comprising the following steps: collecting a large amount of three-phase flow real test data including parameters such as flow velocity of each phase, pipeline inclination angle, viscosity of each phase, density of each phase, moisture content, pipe diameter, interphase interfacial tension and the like; the influence of factors such as gas-liquid flow velocity, pipe diameter, inclination angle, liquid phase viscosity, gas-liquid density ratio and gas content is considered, and a mathematical model of gas drift velocity is constructed; considering the influence of factors such as gas-liquid flow velocity, pipe diameter, inclination angle, liquid viscosity, gas-liquid density ratio, gas content and water content, and constructing a mathematical model of distribution parameters; performing parameter optimization solution on the model coefficient; and substituting the obtained optimization parameters into the mathematical model, and solving and calculating to obtain the gas content. The three-phase flow gas content calculation method based on the drift theory does not need to distinguish flow patterns, is wide in application range, is used for engineering and numerical simulation coupling calculation, and provides a thought for simply, conveniently and accurately predicting the three-phase flow gas content and the shaft pressure drop.

Description

Technical Field

[0001] The invention belongs to the technical field of gas well production, and in particular relates to a method for calculating the gas content of three-phase flow based on drift theory. Background Art

[0002] Three-phase flow is a co-flowing fluid system consisting of two immiscible liquid phases and a gas phase, which is commonly found in oil and gas field drilling, crude oil extraction and transportation. The three substances have very different physical properties, the phase interactions are highly complex, and the fluid flow is highly random, which poses a huge challenge to correctly understanding the flow laws of three-phase flow. Accurately obtaining the gas content and establishing an accurate three-phase flow wellbore flow model are important prerequisites for clarifying the wellbore flow laws, accurately controlling the wellbore pressure, and optimizing the production system.

[0003] At present, there are abundant research results on the flow law of two-phase flow, and there are many calculation models for gas content. However, the research on three-phase flow is far less than that on gas-liquid two-phase flow. A large number of literature surveys have found that the limited three-phase flow literature usually focuses on flow pattern and pressure drop, and often only involves specific pipe angles or fluid viscosity. There is a serious lack of high-precision models for calculating the gas content of three-phase flow. The models for dealing with three-phase flow include empirical models, homogeneous models and mechanism / numerical models. Empirical models are often limited to experimental conditions and are not very applicable. The homogeneous model does not consider the interaction between the two phases, and the error is large when dealing with laminar flow, annular flow and other flow patterns. The mechanism model establishes mechanical expressions based on the physical structure of different flow patterns, but the solution is difficult, and the model is discontinuous between flow pattern conversions, making it difficult to use for numerical calculations. The drift theory considers both the relative velocity between fluid phases and the distribution law of void fraction and flow velocity along the flow section. It has the advantages of simple model, continuous differentiability, and fast calculation speed, and can be used for numerical simulation and coupled calculation.

[0004] The present invention provides a method for calculating the gas content of three-phase flow based on drift theory, which does not need to distinguish flow types and has a wide range of applications. It can be used for engineering and numerical simulation coupling calculations, and provides ideas for simply and accurately predicting the gas content of three-phase flow and wellbore pressure drop. Summary of the invention

[0005] The purpose of the present invention is to provide a method for calculating the gas content of three-phase flow based on drift theory.

[0006] The present invention is achieved through the following technical solutions:

[0007] The present invention relates to a method for calculating the gas content of a three-phase flow based on drift theory, comprising the following steps:

[0008] Step 1: Collect a large amount of real test data of three-phase flow: flow velocity of each phase, pipe inclination, viscosity of each phase, density of each phase, water content, pipe diameter, and interphase interfacial tension parameters;

[0009] Step 2: Consider the influence of gas-liquid flow rate, pipe diameter, inclination angle, liquid viscosity, gas-liquid density ratio, and gas content, and construct a mathematical model of gas drift velocity:

[0010]

[0011] Where V d is the gas drift velocity, m / s; α g is the gas content, dimensionless; y1, y2, y3 are all model coefficients, dimensionless; N θ 、N σ 、N μ They are angle influence term, density and interfacial tension influence term, and liquid viscosity influence term, dimensionless; g is gravitational acceleration, m / s 2 ; D is the hydraulic diameter of the pipe, mm; θ is the pipe angle, °; v m is the mixed fluid flow rate, m / s; ρ l , g , are respectively the liquid phase density and the gas phase density, kg / m 3 ; σ l is the gas-liquid surface tension, N / m; μ l is the liquid viscosity, pa·s;

[0012] Step 3: Consider the effects of gas-liquid flow rate, pipe diameter, inclination angle, liquid viscosity, gas-liquid density ratio, gas content, and water content, and construct a mathematical model of distribution parameters:

[0013]

[0014] In formula (5), C0 is the distribution coefficient, dimensionless; x1, x2, x3, x4, x5, a, b, c, d are all model coefficients, dimensionless; β g is the injected gas void fraction, dimensionless; Re m is the Reynolds number of the mixed fluid, dimensionless; f w is the moisture content, dimensionless;

[0015] Step 4: Optimize the parameters of the model coefficients x1, x2, x3, x4, x5, a, b, c, d, y1, y2, and y3;

[0016] Step 5: Substitute the obtained optimization parameters into the mathematical model established in steps 2 and 3, and use the Newton iteration method to solve and calculate to obtain the gas content.

[0017] Preferably, in step 4, the parameter optimization solution of the model coefficients x1, x2, x3, x4, x5, a, b, c, d, y1, y2, and y3 is performed as follows:

[0018] The objective function (6) is established, and the optimization function fminunc in Matlab is used to solve the model coefficients x1, x2, x3, x4, x5, a, b, c, d, y1, y2, and y3:

[0019]

[0020] In formula (6), α g,i,cal , α g,i,cal are the model-calculated gas content and the measured gas content, dimensionless; is the objective function, dimensionless; n is the number of data points, dimensionless; i is the sequence number, dimensionless.

[0021] Preferably, the coefficient vector for the parameter optimization solution is X=[x1,x2,x3,x4,x5,y1,y2,y3,a,b,c,d] T , use the optimization function [x,fval]=fminunc[f,x0,options] in Matlab to write a program script to obtain the optimal solution of the parameter vector.

[0022] Preferably, in step 5, the specific method of solving the calculation using the Newton iteration method is as follows: the drift velocity and distribution coefficient model established is used to establish a solution equation (7) for the gas content rate based on the drift theory:

[0023] f(α g )=C0(α g )v m +V d (α g )-v sg / α g (7)

[0024] Formula (7) is about the gas content α g The implicit nonlinear equation of is solved by Newton iteration method, and the iteration format is established: α g (k+1)=α g (k)-f(α g (k)) / f′(α g (k)), set the initial value of the iteration: α g (0) = 0.5v sg / v m , if f(α g (k))|<10 -5 , the accuracy requirement is met, the iteration is terminated, the calculation is completed, and the gas content α is output g Final result, otherwise continue to iterate;

[0025] In formula (7), v sgis the superficial gas velocity, m / s; k is the number of iterations, dimensionless.

[0026] Preferably, the specific method of solving the calculation using the Newton iteration method is as follows:

[0027] First establish the iteration format:

[0028] α g (k+1)=α g (k)-f(α g (k)) / f′(α g (k)) (8)

[0029] In formula (8), v sg is the superficial gas velocity, m / s; k is the number of iterations, dimensionless;

[0030] Then set the initial value of iteration: α g (0) = 0.5v sg / v m , if f(α g (k))|<10 -5 , the accuracy requirement is met, the iteration is terminated, the calculation is completed, and the gas content α is output g This is the final gas content result. Otherwise, continue iterating until the accuracy requirement is met and output the solved gas content α g .

[0031] The present invention has the following advantages:

[0032] The present invention provides a method for calculating the gas content of three-phase flow based on drift theory, which does not need to distinguish flow types and has a wide range of applications. It can be used for engineering and numerical simulation coupling calculations, and provides ideas for simply and accurately predicting the gas content of three-phase flow and wellbore pressure drop. DETAILED DESCRIPTION

[0033] The present invention is described in detail below in conjunction with specific embodiments. It should be noted that the following embodiments are only further descriptions of the present invention, but the protection scope of the present invention is not limited to the following embodiments.

[0034] Example

[0035] This embodiment relates to a method for calculating the gas content of a three-phase flow based on drift theory, comprising the following steps:

[0036] Step 1: Collect a large amount of real test data of three-phase flow: flow velocity of each phase, pipe inclination, viscosity of each phase, density of each phase, water content, pipe diameter, interfacial tension between phases and other parameters;

[0037] Step 2: Considering the influence of factors such as gas-liquid flow rate, pipe diameter, inclination angle, liquid viscosity, gas-liquid density ratio, and gas content, a mathematical model of gas drift velocity is constructed:

[0038]

[0039] Where V d is the gas drift velocity, m / s; α g is the gas content, dimensionless; y1, y2, y3 are all model coefficients, dimensionless; N θ 、N σ 、N μ They are angle influence term, density and interfacial tension influence term, and liquid viscosity influence term, dimensionless;

[0040] g is the acceleration due to gravity, m / s 2 ; D is the hydraulic diameter of the pipe, mm; θ is the pipe angle, °; v m is the mixed fluid flow rate, m / s; ρ l , g , are respectively the liquid phase density and the gas phase density, kg / m 3 ; σ l is the gas-liquid surface tension, N / m; μ l is the liquid viscosity, pa·s;

[0041] Step 3: Consider the influence of factors such as gas-liquid flow rate, pipe diameter, inclination angle, liquid viscosity, gas-liquid density ratio, gas content, water content, etc., and construct a mathematical model of distribution parameters:

[0042]

[0043] Where C0 is the distribution coefficient, dimensionless; x1, x2, x3, x4, x5, a, b, c, d are all model coefficients, dimensionless; β g is the injected gas void fraction, dimensionless; Re m is the Reynolds number of the mixed fluid, dimensionless; f w is the moisture content, dimensionless;

[0044] Step 4: Optimize the parameters of the model coefficients x1, x2, x3, x4, x5, a, b, c, d, y1, y2, and y3.

[0045] First, the objective function formula (6) is established. The criterion for establishing the objective function is to minimize the error between the calculated gas content and the measured gas content. Therefore, we have:

[0046]

[0047] In formula (6), α g,i,cal , α g,i,mea are the model-calculated gas content and the measured gas content, dimensionless; is the objective function, dimensionless; n is the number of data points, dimensionless; i is the sequence number, dimensionless.

[0048] Among them, the coefficient vector to be solved is X = [x1,x2,x3,x4,x5,y1,y2,y3,a,b,c,d] T , use the optimization function [x,fval]=fminunc[f,x0,options] in Matlab to write a program script to achieve the optimization solution of the parameter vector.

[0049] Step 5: Substitute the obtained optimization parameters into the mathematical model established in steps 2 and 3, and use the Newton iteration method to solve and calculate to obtain the gas content. According to the drift theory, the drift velocity and distribution coefficient model established are used to establish the solution relationship of the gas content:

[0050] f(α g )=C0(α g )v m +V d (α g )-v sg / α g (7)

[0051] Since formula (7) is about the gas content α g It is an implicit nonlinear equation, so the Newton iteration method must be used to solve it. The solution steps are as follows:

[0052] First establish the iteration format:

[0053] α g (k+1)=α g (k)-f(α g (k)) / f′(α g (k)) (8)

[0054] In formula (8), v sg is the superficial gas velocity, m / s; k is the number of iterations, dimensionless.

[0055] Then set the initial value of the iteration: α g (0) = 0.5v sg / v m , if |f(α g (k))|<10 -5 , the accuracy requirement is met, the iteration is terminated, the calculation is completed, and the gas content α is output g This is the final gas content result. Otherwise, continue iterating until the accuracy requirement is met and output the solved gas content α g .

[0056] The present invention relates to a method for calculating the gas content of three-phase flow based on drift theory, which does not need to distinguish flow types and has a wide range of applications. It can be used for engineering and numerical simulation coupling calculations, and provides ideas for simply and accurately predicting the gas content of three-phase flow and wellbore pressure drop.

[0057] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art may make various modifications or variations within the scope of the claims, which will not affect the essence of the present invention.

Claims

1. A method for calculating the gas content of three-phase flow based on drift theory, characterized in that: The following steps are involved: Step 1: Collect a large amount of real test data of three-phase flow: flow velocity of each phase, pipe inclination, viscosity of each phase, density of each phase, water content, pipe diameter, and interphase interfacial tension parameters; Step 2: Construct a mathematical model of gas drift velocity based on the effects of gas-liquid flow rate, pipe diameter, inclination angle, liquid viscosity, gas-liquid density ratio, and gas holdup: Where V d is the gas drift velocity, m / s; α g is the gas content, dimensionless; y1, y2, y3 are all model coefficients, dimensionless; N θ 、N σ 、N μ They are angle influence term, density and interfacial tension influence term, and liquid viscosity influence term, dimensionless; g is gravitational acceleration, m / s 2 ; D is the hydraulic diameter of the pipe, mm; θ is the pipe angle, °; v m is the mixed fluid flow rate, m / s; ρ l , g , are respectively the liquid phase density and the gas phase density, kg / m 3 ; σ l is the gas-liquid surface tension, N / m; μ l is the liquid viscosity, pa·s; Step 3: Construct a mathematical model of distribution parameters based on the influence of gas-liquid flow rate, pipe diameter, inclination angle, liquid viscosity, gas-liquid density ratio, gas content, and water content: Where, C0 is the distribution coefficient, dimensionless; x1, x2, x3, x4, x5, a, b, c, d are all model coefficients, dimensionless; β g is the injected gas void fraction, dimensionless; Re m is the Reynolds number of the mixed fluid, dimensionless; f w is the moisture content, dimensionless; Step 4: Optimize the parameters of the model coefficients x1, x2, x3, x4, x5, a, b, c, d, y1, y2, and y3; Step 5: Substitute the obtained optimization parameters into the mathematical model established in steps 2 and 3, and use the Newton iteration method to solve and calculate to obtain the gas content.

2. The method for calculating the gas content of three-phase flow based on drift theory according to claim 1, characterized in that: In step 4, the model coefficients x1, x2, x3, x4, x5, a, b, c, d, y1, y2, and y3 are optimized as follows: The objective function (6) is established, and the optimization function fminunc in Matlab is used to solve the model coefficients x1, x2, x3, x4, x5, a, b, c, d, y1, y2, and y3: In formula (6), α g,i,cal , α g,i,cal are the model-calculated gas content and the measured gas content, dimensionless; is the objective function, dimensionless; n is the number of data points, dimensionless; i is the sequence number, dimensionless.

3. A method for calculating the gas content of three-phase flow based on drift theory as claimed in claim 2, characterized in that: The coefficient vector of the parameter optimization solution is X = [x1, x2, x3, x4, x5, y1, y2, y3, a, b, c, d] T , use the optimization function [x,fval]=fminunc[f,x0,options] in Matlab to write a program script to obtain the optimal solution of the parameter vector.

4. The method for calculating the gas content of three-phase flow based on drift theory according to claim 1, characterized in that: In step 5, the specific method of solving the calculation using the Newton iteration method is as follows: the drift velocity and distribution coefficient model established is used to establish the gas content rate solution equation (7) based on the drift theory: f(a g )=C0(a g )v m +V d (a g )-v sg a g (7) Formula (7) is about the gas content α g The implicit nonlinear equation of is solved by Newton iteration method, and the iteration format is established: α g (k+1)=α g (k)-f(α g (k)) / f′(α g (k)), set the initial value of iteration: α g (0) = 0.5v sg / v m , if f(α g (k))<10 -5 , the accuracy requirement is met, the iteration is terminated, the calculation is completed, and the gas content α is output g final result, otherwise continue to iterate; in formula (7), v sg is the superficial gas velocity, m / s; k is the number of iterations, dimensionless.

5. A method for calculating the gas content of three-phase flow based on drift theory as claimed in claim 4, characterized in that: The specific method of solving the calculation using the Newton iteration method is as follows: First establish the iteration format: a g (k+1)=a g (k)-f(a g (k)) / f′(α g (k)) (8) In formula (8), v sg is the superficial gas velocity, m / s; k is the number of iterations, dimensionless; Then set the initial value of iteration: α g (0) = 0.5v sg / v m , if f(α g (k))<10 -5 , the accuracy requirement is met, the iteration is terminated, the calculation is completed, and the gas content α is output g , which is the final gas content result. Otherwise, continue to iterate until the accuracy requirement is met and output the solved gas content α g .

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