A method for constructing a wellbore hydrate dynamic deposition and plugging prediction model

Abstract

The present application relates to the technical field of oil and gas development, and particularly relates to a kind of wellbore hydrate dynamic deposition blockage prediction model construction method, comprising S1, constructing wellbore hydrate dynamic blockage physical model;S2, constructing hydrate formation mathematical model in liquid film;S3, constructing hydrate formation and dynamic deposition mathematical model in liquid drop;S4, constructing water mass flow model in microelement;S5, constructing wellbore inner wall hydrate layer thickness and flow diameter model;S6, through time and space double iteration cycle, solve hydrate dynamic blockage prediction model, the technical scheme steps of the present application are clear, the prediction accuracy is high, can accurately predict the hydrate blockage degree at different well depth, according to the blockage degree, the safety hidden danger and economic loss caused by hydrate blockage in the process of natural gas development can be reasonably avoided.

Description

Technical Field

[0001] This invention relates to the field of oil and gas development technology, specifically to a method for constructing a prediction model for dynamic deposition and blockage of wellbore hydrates. Background Technology

[0002] Natural gas readily forms hydrates under high pressure and low temperature. Once formed, these hydrates accumulate at the bottom of pipelines, causing blockages that reduce flow or even wellbore closure, leading to serious safety hazards and substantial economic losses. Therefore, research on the dynamic deposition and blockage prediction of natural gas hydrates in wellbores is essential to mitigate the risks associated with hydrate formation during natural gas development.

[0003] The earliest domestic and international hydrate formation prediction models were calculated using empirical formulas. Later, scholars continued to develop new empirical formulas based on previous research results. However, the empirical formula method has poor accuracy in predicting hydrates containing acidic gases. Then, the Vdw-P model was developed. This model is based on classical adsorption theory. Its advantages are simple calculation and suitability for preliminary estimation of hydrate formation conditions in mines. Its disadvantages are low accuracy and very complex theory. The subsequent PP model, NR model, Du-Guo model and Chen-Guo model are all based on the Vdw-P model. The dynamic hydrate blockage prediction model established by Ji Guofa (2011) considers the diffusion shearing effect of hydrate particles and believes that hydrate blockage in the wellbore is mainly caused by diffusion shear deposition.

[0004] However, most of the current domestic and foreign hydrate prediction models are static prediction models, which mostly predict the conditions for hydrate formation. There is little research on dynamic deposition and blockage prediction models for hydrates. At the same time, the dynamic blockage law of hydrates under the conditions of annular mist flow during the production of high-pressure gas wells is not well understood, which makes it impossible to accurately predict the degree of hydrate blockage at different well depths. Summary of the Invention

[0005] The purpose of this invention is to provide a method for constructing a prediction model for dynamic deposition and blockage of hydrates in wellbores. Based on the mechanism of hydrate formation by liquid film and droplets, a mathematical model of dynamic hydrates by liquid film and droplets is constructed. At the same time, considering the consumption and supply of water in the wellbore, a mass flow rate model of water in a micro-element, a hydrate layer thickness model, and a flow diameter model are constructed, which can predict the degree of dynamic hydrate blockage at different well depths and at different times.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for constructing a prediction model for dynamic deposition and blockage of hydrates in wellbores includes the following steps:

[0008] S1. Construct a physical model of dynamic blockage of hydrates in the wellbore: The flow state in the wellbore is set as annular mist flow, and the liquid water in the wellbore exists in the form of liquid film and droplets. The liquid film adheres to the pipe wall, and the droplets are entrained in the gas phase. The entire wellbore is divided into micro-elements. The diameter of the wellbore pipe is D. The wellbore is divided into equidistant micro-elements with a length of dL and a corresponding time interval of dt. For each micro-element, a physical model of the flow distribution of droplets and liquid film is established.

[0009] S2. Construct a mathematical model for hydrate formation in a liquid film: Calculate the surface area A of the liquid film in the infinitesimal element. f With the rate of hydrate formation in the liquid film R gf Then, the mass m of hydrate formation in the liquid film was calculated. hf ;

[0010] S3. Constructing a mathematical model for hydrate formation in droplets: Based on droplet splitting theory, assuming the droplet size follows a normal distribution, and based on the carrying capacity E and the maximum carrying capacity E... m The surface area A of the droplet was calculated from the relationship. d The hydrate formation rate R in the droplet gd Then, the mass m of hydrate formation in the droplet was calculated. he ;

[0011] S4. Construct a mathematical model for the dynamic deposition of hydrates in droplets: based on the droplet deposition rate R... d Calculate the total amount of droplet deposition m during time dt. ld Then calculate the mass m of the hydrate particles deposited in the droplet within the infinitesimal element during the time interval dt. hd ;

[0012] S5. Construct a mass flow rate model for water in a micro-element: Calculate the total mass of water consumed in each micro-element within time dt. According to the law of conservation of mass, the amount of water consumed in each infinitesimal element is the sum of the amounts consumed by the liquid film and the droplets. Therefore, the mass flow rate of water in each infinitesimal element can be calculated.

[0013] S6. Construct a model for the thickness of the hydrate layer on the inner wall of the wellbore and the flow diameter: Calculate the thickness h of the hydrate layer on the pipe wall during time dt, and then calculate the flow diameter within the micro-element at the same location in the wellbore at different times.

[0014] S7. Solve the dynamic blockage prediction model for hydrates.

[0015] Furthermore, in step S2, the liquid film surface area A in the micro-element physical model... f The calculation formula is:

[0016] A f =πDdL;

[0017] Where: D is the pipe diameter, m; dL is the length of the infinitesimal element, m;

[0018] The hydrate formation rate R in the liquid film gf The calculation formula is:

[0019]

[0020] T sub =T eq -T s ;

[0021] Where: R gf M represents the hydrate formation rate in the liquid film, in mol / s; g is the average gas molar mass, g / mol; μ is the proportionality factor, representing the relative magnitude of the heat and mass transfer resistance, dimensionless; K1 and K2 are the kinetic rate constants; T s System temperature, K; T sub It is the supercooling temperature, K; T eq Let K be the hydrate equilibrium temperature under system pressure; A f Let m be the surface area of ​​the liquid film. 2 ;

[0022] The mass m of hydrate formation in the liquid film hf The calculation formula is:

[0023] m hf =MR gf dt;

[0024] Where: m hf R represents the mass of hydrate formed in the liquid film, in kg; M is the molecular mass of the hydrate, in g / mol; gf dt represents the hydrate formation rate in the liquid film (mol / s); dt is the time interval (s).

[0025] Further, in step S3, the carrying capacity E represents the content of droplets in the gas phase, defined as the ratio of the flow mass flow rate of droplets in the gas phase to the total flow mass flow rate of the liquid. The formula for calculating the carrying capacity E of droplets in the gas phase is:

[0026] E=W le / W l ;

[0027] W le The expression is:

[0028] W le =EW l ;

[0029] Where: E is the carrying capacity; W leW is the mass flow rate of the liquid droplets in the gas phase, kg / s. l The total mass flow rate of the liquid is kg / s; the carrying capacity E and the maximum carrying capacity E m The relationship is:

[0030]

[0031] Where: D is the inner diameter of the pipe, in meters; U g E is the gas flow velocity in m / s. m A represents the maximum carrying capacity. l It is a dimensionless constant, and its value at low pressure is approximately 8.8 × 10⁻⁶. -5 At high pressure, it is approximately 3.6 × 10⁻⁶. -5 σ is the surface tension, mN / m; ρ g The density of the gas is kg / m³. 3 ;ρ l The density of the liquid is kg / m³. 3 ;

[0032] The surface area A of the droplet d The calculation formula is:

[0033]

[0034] Among them: Q l and Q g These are the volumetric flow velocities of liquid and gas, respectively, with volumetric flow velocity in m. 3 / s; S is the ratio of droplet velocity to gas phase velocity, dimensionless; d 32 dL is the average droplet diameter of Sauter, in meters; dL is the length of the infinitesimal element, in meters.

[0035] According to droplet splitting theory, the maximum droplet size d in annular mist flow is... max The expression is:

[0036]

[0037] Where: ρ g The density is in the gas phase, kg / m³ 3 ;ρ l The density of the liquid phase is kg / m³. 3 μ l The viscosity of the liquid is Pa·s; μ g We is the gas phase viscosity, Pa·s; g For gas phase Weber number, Re g Re is the gas phase Reynolds number; l The liquid phase Reynolds number;

[0038] C w The expression is given under different Nμ values:

[0039] C W =0.028Nμ -4 / 5 Nμ≤1 / 15;

[0040] C W =0.25Nμ>1 / 15;

[0041] The expression for Nμ is:

[0042]

[0043] Assume the droplet size follows a normal distribution;

[0044] The average droplet diameter d of Sauter 32 The calculation formula is:

[0045]

[0046] Among them: We g For gas phase Weber number:

[0047]

[0048] Re g For gas phase Reynolds number:

[0049] Re g =ρ g U g D / μ g ;

[0050] Re l The liquid phase Reynolds number is:

[0051] Re l =ρ l U l D / μ l ;

[0052] The rate of hydrate formation R in droplets gf The calculation formula is:

[0053]

[0054] Where: M g The average molar mass of the gas is g / mol; μ is the proportionality factor, dimensionless; K1 and K2 are the kinetic rate constants; T s System temperature, K; T sub For supercooling, K; A d Let m be the surface area of ​​the droplet. 2 ;

[0055] The mass m of hydrate formation in the droplet heThe calculation formula is:

[0056] m he =MR gd dt;

[0057] Where: m he R is the mass of the hydrate formed in the droplet, in kg; M is the molecular mass of the hydrate, in g / mol; gd dt is the gas consumption rate in the droplet (mol / s); dt is the time interval (s).

[0058] Furthermore, in step S5, the droplet deposition rate R is calculated using the droplet flow rate. d The calculation formula is as follows:

[0059]

[0060] Where: R d The droplet deposition coefficient is expressed in kg / m³. 2 ·s; C is the droplet volume concentration, k d It is the radial velocity of the droplet along the tube wall, in m / s;

[0061] The k d The calculation formula is:

[0062]

[0063] set up Measuring the concentration of diluted droplets and under conditions of droplet-fluid transport equilibrium:

[0064]

[0065] Where: τ LF Characterizing the Lagrangian time constant of a fluid, It is the square of the velocity fluctuation of the gas in the direction perpendicular to the wall, the gas phase velocity. for:

[0066]

[0067] Where v * It is the friction speed:

[0068] v * =(τ i / ρ G ) 0.5 =U G (f i / 2) 0.5 ;

[0069] Among them: U G The gas flow rate is in m / s;

[0070] The Lagrangian time constant for gas phase flow is:

[0071]

[0072] Setting the inertial time constant of the fluid in annular mist flow When τ LF Greater than βτ LF The particles follow the fluid flow and σ p =σ G ;

[0073] Where the friction coefficient f i The calculation formula is:

[0074]

[0075] Where: f i ρ is the coefficient of friction, dimensionless; G The density is in the gas phase, kg / m³ 3 ;ρ L The density of the liquid phase is kg / m³. 3 W L The mass flow rate is expressed as kg / s; W G Re is the gas phase mass flow rate, kg / s; G μ is the gas phase Reynolds number. L The viscosity of the liquid is Pa·s; μ G Where is the gas phase viscosity, Pa·s;

[0076] Assuming the droplet distribution is the same in the gas phase within each micro-element, the total amount of droplets deposited over length dL in time dt is m. ld The calculation formula is:

[0077] m ld =R d A d ·dt=πk d CD·dL·dt;

[0078] Where: m he The mass of hydrate formed in the droplet is expressed in kg; m le Mass of droplets in the gas phase, kg; m ld Mass of droplet deposition in the gas phase, kg;

[0079] Combined with the mass flow rate W of droplets in the gas phase le expression;

[0080] mass m of droplets in the gas phase le The calculation formula is:

[0081] m le =W le dt;

[0082] The mass m of the hydrate particles deposited in the droplet within the infinitesimal element during time dt is... hd The calculation formula is:

[0083]

[0084] Where: m he The mass of hydrate formed in the droplet is expressed in kg; m le Mass of droplets in the gas phase, kg; m ld Mass of droplet deposition in the gas phase, kg;

[0085] The mass of hydrate particles deposited in the droplet within the infinitesimal element during time dt is further expressed as:

[0086]

[0087] Wherein: S d Let be the hydrate particle deposition coefficient, and let be a linear relationship between and . The calculation formula is:

[0088] S d =Av m +B;

[0089] Where: A and B are deposition constants, determined by fitting experimental data or field data; v m The velocity is the gas-liquid mixing velocity, in m / s; the mass of the gas-phase hydrate particles in each micro-element is... for:

[0090]

[0091] Where: m he The mass of hydrate formed in the droplet is expressed in kg; m hd The mass of the hydrate particles deposited in the droplet is expressed in kg; m nhe It is the mass of newly formed hydrate particles in a droplet within a micro-element, expressed in kg; m. he The mass of hydrate formed in the droplet is expressed in kg; m le Mass of droplets in the gas phase, kg; m ld Mass of droplet deposition in the gas phase, kg.

[0092] Furthermore, in step S5, the total water consumption mass in each infinitesimal element during time dt is... The calculation formula is:

[0093]

[0094] Where: m cl It is the total water consumption in the infinitesimal element, in kg; m ce It is the amount of water consumed in the droplet (kg); mcf This represents the water consumption in the liquid film, in kg; the subscript j indicates the distance step; the superscript i indicates the time step.

[0095] According to the law of conservation of mass, the supply, consumption, and production of water within each infinitesimal element satisfy the law of conservation of mass, and the mass flow rate of water within each infinitesimal element is... for:

[0096]

[0097] in: Let be the mass flow rate of water flowing into the j-th infinitesimal element at the i-th time step, in kg / s; Let be the mass of water consumed by the j-th infinitesimal element at the i-th time step, in kg; Let be the mass flow rate of water flowing into the (j+1)th infinitesimal element at the (i+1)th time step, in kg / s.

[0098] Further, in step S6, combining the mass expression for hydrate formation in the liquid film and the mass expression for hydrate particles deposited in the droplet, the thickness h of the hydrate layer on the pipe wall during time dt is calculated as follows:

[0099]

[0100] Where: ρ h The density of natural gas hydrate, kg / m³ 3 m hf The mass of hydrates formed in the liquid film is expressed in kg; m hd The mass of the hydrate formed in the droplet, in kg;

[0101] The flow diameter within each micro-element at different times for:

[0102]

[0103] Where i and i+1 represent the previous time and the next time, respectively, and j represents the same position in the wellbore.

[0104] Further, in step S7, the method for solving the dynamic blockage prediction model of hydrates is as follows: Numerical solution is performed through a dual iterative loop of the time interval dt and length interval dL for each micro-element, which yields the distribution of hydrates at different times and depths within the wellbore. When the flow diameter... When the value is less than 0, it indicates that the wellbore is completely blocked by hydrates. At this point, the cycle is terminated and the operation ends.

[0105] Based on the above technical solution, the embodiments of the present invention can produce at least the following technical effects:

[0106] (1) The present invention provides a method for constructing a prediction model of dynamic deposition blockage of hydrates in wellbore. Based on the mechanism of hydrate formation by liquid film and droplets, a mathematical model of dynamic hydrates by liquid film and droplets is constructed. At the same time, considering the consumption and supply of water in the wellbore, a mass flow rate model of water in micro-element, hydrate layer thickness and flow diameter model are constructed, which can predict the degree of dynamic hydrate blockage at different well depths and at different times.

[0107] (2) The present invention provides a method for constructing a prediction model of dynamic deposition blockage of hydrates in wellbore. The technical solution of the present invention has clear steps and high prediction accuracy. It studies the dynamic blockage law of hydrates under the conditions of annular mist flow during the production process of high-pressure gas wells. It can accurately predict the degree of hydrate blockage at different well depths. According to the degree of blockage, it can reasonably avoid the safety hazards and economic losses caused by the formation of hydrate blockage during the natural gas development process. Attached Figure Description

[0108] Figure 1 This is a schematic diagram of the physical model of hydrate formation inside the wellbore according to an embodiment of the present invention;

[0109] Figure 2 This is a schematic diagram of liquid film atomization into droplets according to an embodiment of the present invention;

[0110] Figure 3 This is a schematic diagram of the deposition of hydrate particles in a droplet according to an embodiment of the present invention;

[0111] Figure 4 This is a schematic diagram of the consumption and supply of water (droplets + liquid film) in the wellbore according to an embodiment of the present invention;

[0112] Figure 5 This is a flowchart of the solution process for the dynamic blockage model of hydrates in an embodiment of the present invention;

[0113] Figure 6 This is a schematic diagram of the flow diameter at different well depths in the hydrate formation region according to an embodiment of the present invention;

[0114] Figure 7 This is a schematic diagram of the hydrate layer thickness at different well depths in the hydrate formation region of this invention. Detailed Implementation

[0115] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0116] Example: This embodiment of the invention provides a method for constructing a prediction model for dynamic deposition and blockage of hydrates in wellbores.

[0117] I. Construction of a Prediction Model for Dynamic Deposition and Blockage of Hydrates in Wellbores

[0118] S1. Construct a physical model of dynamic blockage by hydrates inside the wellbore:

[0119] The flow pattern inside the high-pressure gas wellbore is annular mist flow. Liquid water exists within the wellbore in the form of liquid films and droplets. The liquid films adhere to the wellbore wall, while the droplets are entrained in the gas phase. The constructed physical model involves dividing the entire wellbore into micro-elements and establishing a flow distribution model for droplets and liquid films for each micro-element. A schematic diagram of the physical model is shown below. Figure 1 As shown;

[0120] Its physical model makes the following assumptions:

[0121] (1) Divide the wellbore into equidistant infinitesimal elements of length dL, with a corresponding time interval of dt;

[0122] (2) The production process is a ring mist flow inside the wellbore, where the gas is the continuous phase and the water is the dispersed phase;

[0123] (3) Water exists in the form of a liquid film on the pipe wall and droplets entrained in the gas phase. The liquid film is continuously atomized into droplets.

[0124] (4) Both liquid films and droplets can form hydrates, and some of the hydrates formed by droplets are deposited inside the tube wall.

[0125] S2. Constructing a mathematical model for hydrate formation in liquid films:

[0126] From the established physical model of hydrate dynamic blockage, it can be seen that the height of the micro-element is dL, and the radius is the wellbore flow radius corresponding to the well depth; one of the forms in which water exists in the wellbore is a liquid film, which adheres to the inner side of the pipe wall. Therefore, the surface area of ​​the liquid film in the micro-element can be expressed as:

[0127] A f =πDdL;

[0128] In the formula: D is the inner diameter of the pipe, m; dL is the length of the infinitesimal element, m;

[0129] The hydrate formation rate R in the liquid film gf It can be expressed by the gas phase consumption rate formula as follows:

[0130]

[0131] T sub =T eq -T s ;

[0132] In the formula: Rgf M represents the gas consumption rate in the liquid film, i.e., the hydrate formation rate in the liquid film, expressed in mol / s. g is the average gas molar mass, g / mol; μ is the proportionality factor, representing the relative magnitude of the heat and mass transfer resistance, dimensionless; K1 and K2 are the kinetic rate constants; T s System temperature, K; T sub It is the supercooling temperature, K; T eq Let K be the hydrate equilibrium temperature under system pressure; A f Let m be the surface area of ​​the liquid film. 2 ;

[0133] The mass of hydrates formed in the liquid film can be expressed as:

[0134] m hf =MR gf dt;

[0135] Where: m hf R represents the mass of hydrate formed in the liquid film, in kg; M is the molecular mass of the hydrate, in g / mol; gf dt represents the gas consumption rate in the liquid film (mol / s); dt is the time interval (s).

[0136] S3. Construct a mathematical model for the formation and dynamic deposition of hydrates in droplets:

[0137] (1) Formation of hydrates in droplets:

[0138] Another form of water within the wellbore is as droplets entrained in the gas phase. The amount of droplets E carried in the gas phase is a result of liquid film atomization, where the liquid film atomizes into droplets, such as... Figure 2 As shown, the carrying capacity E represents the content of liquid droplets in the gas phase, defined as the proportion of the mass flow rate of the liquid droplets in the gas phase to the total mass flow rate of the liquid. The carrying capacity E can be expressed as:

[0139] E=W le / W l ;

[0140] W le It can be represented as:

[0141] W le =EW l ;

[0142] In the formula: W le W is the mass flow rate of the liquid droplets in the gas phase, kg / s. l The total mass flow rate of the liquid is expressed in kg / s.

[0143] The semi-empirical formula proposed by Pan and Hanratty (2002) can be used to obtain the carrying capacity E of the droplet in the gas phase and the maximum carrying capacity E.m The relationship is:

[0144]

[0145] In the formula: D is the inner diameter of the pipe, in meters; U g It is the gas flow rate in m / s; E m It is the maximum carrying capacity; A l It is a dimensionless constant, and its value at low pressure is approximately 8.8 × 10⁻⁶. -5 At high pressure, it is approximately 3.6 × 10⁻⁶. -5 σ is the surface tension, mN / m; ρ g It is the gas density, kg / m³ 3 ;ρ l It is the density of the liquid, kg / m³ 3 .

[0146] The surface area of ​​the droplet can be obtained from Aman's (2016) research as follows:

[0147]

[0148] In the formula: Q l and Q g These are the volumetric flow rates of liquids and gases, respectively, with volumetric flow rate in m. 3 / s; S is the ratio of droplet velocity to gas phase velocity, dimensionless; d 32 dL is the average droplet diameter of Sauter, in meters; dL is the length of the infinitesimal element, in meters.

[0149] According to the droplet splitting theory, the maximum droplet size in the annular mist flow can be expressed as:

[0150]

[0151] In the formula: ρ g The density is in the gas phase, kg / m³ 3 ;ρ l The density of the liquid phase is kg / m³. 3 μ l The viscosity of the liquid is Pa·s; μ g Where is the gas phase viscosity, Pa·s; Re g Re is the gas phase Reynolds number; l is the liquid phase Reynolds number.

[0152] C w The expression is given under different Nμ values:

[0153] C W =0.028Nμ -4 / 5 Nμ≤1 / 15

[0154] C W=0.25Nμ>1 / 15

[0155] The expression for Nμ is:

[0156]

[0157] Assuming the droplet size follows a normal distribution, the droplet size can be expressed as:

[0158]

[0159] In the formula: We g For the gas phase Weber number.

[0160]

[0161] Gas phase Reynolds number Re g The expression is:

[0162] Re g =ρ g U g D / μ g

[0163] Liquid phase Reynolds number Re l The expression is:

[0164] Re l =ρ l U l D / μ l

[0165] The hydrate formation rate in droplets can be expressed by the gas phase consumption rate formula as follows:

[0166]

[0167] Where: M g It is the average gas molar mass, g / mol; μ is the proportionality factor, dimensionless; K1 and K2 are two kinetic rate constants; T s It is the system temperature, K; T sub It refers to supercooling, K; A d Let m be the surface area of ​​the liquid film. 2 .

[0168] The mass of hydrate formed in the droplet is:

[0169] m he =MR gd dt

[0170] Where: m he R is the mass of the hydrate formed in the droplet, in kg; M is the molecular mass of the hydrate, in g / mol; gddt represents the gas consumption rate in the droplet (mol / s); dt is the time interval (s).

[0171] (2) Deposition of hydrates in droplets

[0172] Some of the hydrate particles in the gas phase can deposit and adhere to the pipe wall, while the rest will be entrained in the gas flow and move within the wellbore. The dynamic changes of hydrate particles deposition, detachment, and migration with the gas flow within the micro-element are considered, as illustrated in the schematic diagram below. Figure 3 As shown in the figure, the migration direction a represents the deposition of hydrate particles in the gas phase on the inner side of the pipe wall, and the migration direction b represents the hydrate particles in the liquid film that are not adhered to the pipe wall being carried back into the gas flow by the atomization effect of the liquid film.

[0173] Schadel (1990) proposed a method to calculate the droplet deposition rate (Rd) by studying the droplet flow rate. d The droplet deposition coefficient is expressed as follows:

[0174]

[0175] In the formula: R d The droplet deposition coefficient is kg / m 2 ·s; C is the droplet volume concentration, k d It is the radial velocity of the droplet along the tube wall, in m / s.

[0176] Radial flow velocity (k) d The calculation of ) refers to the method proposed by Pan and Hanratty (2002), and its expression is:

[0177]

[0178] In the formula: k d It is the radial velocity of the droplet along the tube wall, in m / s; k d The value depends primarily on the movement of the droplets.

[0179] set up Lee et al. (1989) measured the concentration of diluted droplets and the concentration under conditions of droplet-fluid transport equilibrium:

[0180]

[0181] In the formula: τ LF Characterizing the Lagrangian time constant of a fluid, It is the square of the velocity fluctuation of the gas in the direction perpendicular to the wall, and the gas phase flow velocity is:

[0182]

[0183] Where v *It is the friction speed, and its expression is:

[0184] v * =(τ i / ρ G ) 0.5 =U G (f i / 2) 0.5 ;

[0185] In the formula: U G ρ is the gas flow velocity, in m / s.

[0186] The Lagrangian time constant for gas-phase flow can be approximated as:

[0187]

[0188] For τ LF The inertial time constant of the specific fluid (βτ) LF In large cases, particles follow the fluid flow and σ p =σ G In the annular fog flow, it is usually set to...

[0189] Where the friction coefficient f i The calculation formula is:

[0190]

[0191] Where: f i ρ is the coefficient of friction, dimensionless; G The density is in the gas phase, kg / m³ 3 ;ρ L The density of the liquid phase is kg / m³. 3 W L The mass flow rate is expressed as kg / s; W G Re is the gas phase mass flow rate, kg / s; G μ is the gas phase Reynolds number. L The viscosity of the liquid is Pa·s; μ G Where is the gas phase viscosity, Pa·s;

[0192] Assuming the droplet distribution is uniform in the gas phase within each micro-element, the total amount of droplets deposited over length dL in time dt is:

[0193] m ld =R d A d ·dt=πk d CD·dL·dt;

[0194] Where: m he The mass of hydrate formed in the droplet is expressed in kg; m leMass of droplets in the gas phase, kg; m ld Mass of droplet deposition in the gas phase, kg.

[0195] Combined with the mass flow rate W of droplets in the gas phase le The expression for the mass m of the droplet in the gas phase. le The expression is:

[0196] m le =W le dt;

[0197] The mass of the hydrate particles deposited in the droplet during the infinitesimal time dt is:

[0198]

[0199] Where: m he The mass of hydrate formed in the droplet is expressed in kg; m le Mass of droplets in the gas phase, kg; m ld Mass of droplet deposition in the gas phase, kg.

[0200] The mass of hydrate particles deposited in the droplet within the infinitesimal element during time dt can be further expressed as:

[0201]

[0202] In the formula: S d The deposition coefficient of hydrate particles is related to the flow velocity. Experiments have shown that it has a linear relationship with the flow velocity, which can be expressed as:

[0203] S d =Av m +B

[0204] In the formula: A and B are deposition constants, determined by fitting experimental data or field data; v m The velocity is the gas-liquid mixing velocity, in m / s. The mass of the gas-phase hydrate particles in each micro-element is:

[0205]

[0206] Where: m he The mass of hydrate formed in the droplet is expressed in kg; m hd The mass of the hydrate particles deposited in the droplet is expressed in kg; m nhe It is the mass of newly formed hydrate particles in a droplet within a micro-element, expressed in kg; m. he The mass of hydrate formed in the droplet is expressed in kg; m le Mass of droplets in the gas phase, kg; m ld Mass of droplet deposition in the gas phase, kg.

[0207] S4. Construct a mass flow rate model for water in a micro-element:

[0208] As hydrates continuously form within the wellbore, the water inside is constantly consumed. Unconsumed water is produced at the wellhead along with gas, while water is continuously supplied from the bottom of the well. Therefore, the supply, consumption, and production of water within each micro-element must satisfy the law of conservation of mass. The process of water consumption, supply, and production within the wellbore is as follows: Figure 4 As shown.

[0209] The amount of water consumed within each infinitesimal element is the sum of the water consumed by the liquid film and the water consumed by the droplets. Therefore, the total mass of water consumed in each infinitesimal element during time dt is:

[0210]

[0211] Where: m cl It is the total water consumption in the infinitesimal element, in kg; m ce It is the amount of water consumed in the droplet (kg); m cf This represents the water consumption in the liquid film, in kg; the subscript j indicates the distance step; the superscript i indicates the time step.

[0212] According to the law of conservation of mass, the mass flow rate of water in each infinitesimal element is:

[0213]

[0214] In the formula: Let be the mass flow rate of water flowing into the j-th infinitesimal element at the i-th time step, in kg / s; Let be the mass of water consumed by the j-th infinitesimal element at the i-th time step, in kg; Let be the mass flow rate of water flowing into the (j+1)th infinitesimal element at the (i+1)th time step, in kg / s.

[0215] S5. Construct a model for the thickness of the hydrate layer on the inner wall of the wellbore and the flow diameter:

[0216] The liquid film and droplets form hydrates and deposit on the pipe wall. The hydrate layer in each micro-element continuously increases along the pipe. Combining equations (2-3) and (2-29), the thickness (h) of the hydrate layer on the pipe wall during time dt can be obtained as follows:

[0217]

[0218] In the formula: ρ h The density of natural gas hydrate, kg / m³ 3 ;m hf The mass of hydrates formed in the liquid film is expressed in kg; m hd The mass of the hydrate formed in the droplet is expressed in kg.

[0219] Therefore, the flow diameter within each infinitesimal element at different times is:

[0220]

[0221] In the formula: i and i+1 represent the previous time and the next time, respectively, and j represents the same position in the wellbore.

[0222] S6. Solve the hydrate dynamic blockage prediction model through dual iterative loops of time and space:

[0223] Because the dynamic blockage model of hydrates is nonlinear, an iterative loop is used for numerical solution. The entire wellbore is divided into micro-elements. By iterating through the time interval dt and length interval dL of each micro-element, the distribution of hydrates at different times and depths in the wellbore can be obtained. When the flow diameter is less than 0, the wellbore is completely blocked by hydrates. At this point, the loop is terminated and the calculation ends.

[0224] The solution process for the dynamic blockage model of hydrates is as follows: Figure 5 As shown.

[0225] II. Model Application and Case Analysis:

[0226] According to on-site production data, well A has hydrate blockage in its wellbore. Well A has a daily gas production of 146,000 cubic meters / day and a daily water production of 2.3 tons / day. The wellhead pressure is 65 MPa, the wellhead temperature is 8.1℃, and the bottom temperature is 138℃.

[0227] The gas composition of the separator in Well A is shown in the table below.

[0228] Table 1A Separator Gas Components

[0229] Components Content (mol%) <![CDATA[CO2]]> 1.8590 <![CDATA[N2]]> 1.5380 <![CDATA[C1]]> 94.0600 <![CDATA[C2]]> 2.1691 <![CDATA[C3]]> 0.2282 <![CDATA[iC4]]> 0.0482 <![CDATA[nC4]]> 0.0480 <![CDATA[iC5]]> 0.0228 <![CDATA[nC5]]> 0.0123 <![CDATA[C6]]> 0.0144

[0230] Based on the aforementioned basic data from Well A, simulation calculations yielded the following results: distribution of the flow diameter and hydrate layer throughout the wellbore. Figure 6-7 As shown.

[0231] Therefore, the well depth greater than 471m is the safe production operation window, and the well depth between 0 and 471m is the hydrate formation area. As time increases, the amount of hydrate formation and deposition increases, and the flow diameter becomes smaller and smaller. The model calculates that the location of the most severe hydrate blockage is at a well depth of 198m, and the model prediction results are consistent with the field conditions.

[0232] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for constructing a prediction model for dynamic deposition and blockage of hydrates in wellbores, characterized in that, Includes the following steps: S1. Construct a physical model of dynamic blockage of hydrates in the wellbore: The flow state in the wellbore is set as annular mist flow, and the liquid water in the wellbore exists in the form of liquid film and droplets. The liquid film adheres to the pipe wall, and the droplets are entrained in the gas phase. The entire wellbore is divided into micro-elements. The diameter of the wellbore pipe is D. The wellbore is divided into equidistant micro-elements with a length of dL and a corresponding time interval of dt. For each micro-element, a physical model of the flow distribution of droplets and liquid film is established. S2. Construct a mathematical model for hydrate formation in a liquid film: calculate the surface area of ​​the liquid film in the infinitesimal element. Rate of hydrate formation in liquid film Then, the mass of hydrate formed in the liquid film was calculated. ; S3. Constructing a mathematical model for hydrate formation in droplets: Based on droplet splitting theory, assuming the droplet size follows a normal distribution, and based on the amount of hydrate carried... With maximum carrying capacity The surface area of ​​the droplet was calculated using the relationship. hydrate formation rate in droplets Then, the mass of hydrate formed in the droplet was calculated. ; S4. Construct a mathematical model for the dynamic deposition of hydrates in droplets: based on the droplet deposition rate. Calculate the total amount of droplet deposition during time dt. Then calculate the mass of hydrate particles deposited in the droplet within the infinitesimal element during time dt. ; S5. Construct a mass flow rate model for water in a micro-element: Calculate the total mass of water consumed in each micro-element within time dt. According to the law of conservation of mass, the amount of water consumed in each infinitesimal element is the sum of the amounts consumed by the liquid film and the droplets. Therefore, the mass flow rate of water in each infinitesimal element can be calculated. ; S6. Construct a model for the thickness of the hydrate layer on the inner wall of the wellbore and the flow diameter: Calculate the thickness of the hydrate layer on the pipe wall during time dt. Then, the flow diameter within the micro-element at the same location within the wellbore at different times is calculated. ; S7. Solve the dynamic blockage prediction model for hydrates; In step S5, the d t The total mass of water consumed in each infinitesimal element within a given time period for: ； in: m cl It is the total water consumption in the micro-element, in kg; m ce It is the amount of water consumed in the droplet (in kg); m cf This is the amount of water consumed in the liquid film, in kg; subscript j Indicates the distance step size; superscript i Indicates the time step; According to the law of conservation of mass, the supply, consumption, and production of water within each infinitesimal element satisfy the law of conservation of mass, and the mass flow rate of water within each infinitesimal element is... for: ； in: For the first j The infinitesimal element is in the first... i Mass flow rate of water at a time step, kg / s; For the first j The infinitesimal element is in the first... i Mass of water consumed at each time step, kg; For the first j +1 infinitesimal elements in the... i+ Mass flow rate of water at one time step, kg / s.

2. The method for constructing a prediction model for dynamic deposition and blockage of wellbore hydrates according to claim 1, characterized in that, In step S2, the liquid film surface area in the micro-element physical model The calculation formula is: ； in: The diameter of the pipe is in meters (m). Let be the length of the infinitesimal element, in meters (m). The hydrate formation rate in the liquid film The calculation formula is: ； ； in: The hydrate formation rate in the liquid film is expressed in mol / s. The average molar mass of the gas is expressed in g / mol. is a scaling factor, representing the relative magnitude of heat and mass transfer resistance, and is dimensionless. and The kinetic rate constant; Let K be the system temperature. It is the supercooled temperature, K; T eq Let K be the hydrate equilibrium temperature under system pressure. Let m be the surface area of ​​the liquid film. 2 ; The mass of hydrates formed in the liquid film The calculation formula is: ； in: m hf The mass of hydrates formed in the liquid film, in kg; It is the molecular weight of the hydrate, in g / mol; R gf The rate of hydrate formation in the liquid film is mol / s; d t The time interval is s.

3. The method for constructing a prediction model for dynamic deposition and blockage of wellbore hydrates according to claim 1, characterized in that, In step S3, the carrying amount E The content of droplets in the gas phase is defined as the proportion of the mass flow rate of droplets in the gas phase to the total mass flow rate of the liquid, representing the amount of droplets carried in the gas phase. The calculation formula is: ； W le The expression is: ； in: E It refers to the carrying capacity; W le The mass flow rate of the liquid droplets in the gas phase is kg / s; W l The total mass flow rate of the liquid is expressed in kg / s. The carrying capacity E With maximum carrying capacity E m The relationship is: ； in: D The inner diameter of the pipe is in meters (m). U g The gas flow rate is m / s; E m This represents the maximum carrying capacity. A l It is a dimensionless constant, and its value at low pressure is 8.8 × 10⁻⁶. -5 At high pressure, it is 3.6 × 10 -5 ; Surface tension, mN / m; The density of the gas is kg / m³. 3 ; The density of the liquid is kg / m³. 3 ; Surface area of ​​droplets A d The calculation formula is: ； in: Q l and Q g These are the volumetric flow rates of liquid and gas, respectively, with volumetric flow rate in m. 3 / s; S The ratio of droplet velocity to gas phase velocity is dimensionless. d 32 d is the average droplet diameter of Sauter, in meters (m); L It is the length of the infinitesimal element, in meters (m). According to droplet splitting theory, the maximum droplet size in annular mist flow is... d max The expression is: ； in: The density is in the gas phase, kg / m³ 3 ; The density of the liquid phase is kg / m³. 3 ; The viscosity of the liquid is Pa·s; Where is the gas phase viscosity, Pa·s; For gas phase Weber number, The gas phase Reynolds number; The liquid phase Reynolds number; C w In different The expression under the condition of value is: C W =0.028Nμ -4 / 5 Nμ≤1 / 15; ； The expression is: ； Assume the droplet size follows a normal distribution; The average droplet diameter of Sauter d 32 The calculation formula is: ； in: For gas phase Weber number: ； For gas phase Reynolds number: ； The liquid phase Reynolds number is: ； hydrate formation rate in droplets The calculation formula is: ； in: M g The average molar mass of the gas is expressed in g / mol. μ It is a proportionality factor, dimensionless; K 1 and K 2 represents the kinetic rate constant; T s Let K be the system temperature. T sub Supercooling, K; A d Let m be the surface area of ​​the droplet. 2 ; The mass of hydrates formed in the droplets m he The calculation formula is: ； in: m he The mass of hydrate formed in the droplet, in kg; M It is the molecular weight of the hydrate, in g / mol; R gd The gas consumption rate in the droplet is mol / s; d t The time interval is s.

4. The method for constructing a prediction model for dynamic deposition and blockage of wellbore hydrates according to claim 1, characterized in that, In step S4, the droplet deposition rate is calculated using the droplet flow rate. R d : ； in: R d The droplet deposition coefficient is expressed in kg / m³. 2 ·s; C It is the volume concentration of the droplets. k d It is the radial velocity of the droplet along the tube wall, in m / s; The k d The calculation formula is: ； set up Measuring the concentration of diluted droplets and under conditions of droplet-fluid transport equilibrium: ； in: Characterizing the Lagrangian time constant of a fluid, It is the square of the velocity fluctuation of the gas in the direction perpendicular to the wall, the gas phase velocity. for: ； in v * It is the friction speed: ； in: U G The gas flow rate is in m / s; The Lagrangian time constant for gas phase flow is: ； Setting the inertial time constant of the fluid in annular mist flow ; when Greater than The particles follow the fluid flow and ; Among them, the coefficient of friction The calculation formula is: ； in: The coefficient of friction is dimensionless. The density is in the gas phase, kg / m³ 3 ; The density of the liquid phase is kg / m³. 3 ; W L The value is the liquid phase mass flow rate, in kg / s; W G The mass flow rate is in the gas phase, kg / s; R e G The gas phase Reynolds number; μ L The viscosity of the liquid is Pa·s; Where is the gas phase viscosity, Pa·s; Assuming the droplet distribution is the same in the gas phase within each micro-element, the total amount of droplets deposited over length dL in time dt is... The calculation formula is: ； in: m he The mass of hydrate formed in the droplet, in kg; m le Mass of droplets in the gas phase, kg; m ld Mass of droplet deposition in the gas phase, kg; Combined with the mass flow rate of droplets in the gas phase W le expression; mass of droplets in the gas phase m le The calculation formula is: ； In the infinitesimal element d t Mass of hydrate particles deposited in droplets within a time period The calculation formula is: ； in: m he The mass of hydrate formed in the droplet, in kg; m le Mass of droplets in the gas phase, kg; m ld Mass of droplet deposition in the gas phase, kg; micro element body d t The mass of hydrate particles deposited in the droplet within a given time period is further expressed as: ； in: S d Let be the hydrate particle deposition coefficient, and let be a linear relationship between and . The calculation formula is: ； in: A and B This is the deposition constant, determined by fitting experimental data or field data; v m The velocity is the gas-liquid mixing velocity, in m / s; The mass of the gas phase hydrate particles in each micro-element for: ； in: m he The mass of hydrate formed in the droplet, in kg; m hd The mass of the hydrate particles deposited in the droplet is expressed in kg. m nhe It is the mass of newly formed hydrate particles in a micro-element, expressed in kg; m he The mass of hydrate formed in the droplet, in kg; m le Mass of droplets in the gas phase, kg; m ld Mass of droplet deposition in the gas phase, kg.

5. The method for constructing a prediction model for dynamic deposition and blockage of wellbore hydrates according to claim 1, characterized in that, In step S6, the thickness of the hydrate layer on the pipe wall during time dt is calculated by combining the mass expression for hydrate formation in the liquid film and the mass expression for hydrate particles deposited in the droplet. h for: ； in: The density of natural gas hydrate, kg / m³ 3 ; m hf The mass of hydrates formed in the liquid film, in kg; m hd The mass of the hydrate formed in the droplet is expressed in kg. The flow diameter within each micro-element at different times for: ； Where i and i+1 represent the previous time and the next time, respectively, and j represents the same position in the wellbore.

6. The method for constructing a prediction model for dynamic deposition and blockage of wellbore hydrates according to claim 1, characterized in that, In step S7, the method for solving the hydrate dynamic blockage prediction model is as follows: Numerical solution is performed through a dual iterative loop of the time interval dt and length interval dL for each micro-element, which yields the hydrate distribution at different times and depths within the wellbore. When the flow diameter... When the value is less than 0, it indicates that the wellbore is completely blocked by hydrates. At this point, the cycle is terminated and the operation ends.

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