Geothermal well two-phase flow wellbore pressure profile prediction method and device, application, electronic equipment, storage medium and computer program product

Abstract

The invention relates to the technical field of geothermal development, in particular to a geothermal well two-phase flow wellbore pressure profile prediction method and device, application, electronic equipment, a storage medium and a computer program product. The method comprises the following steps: constructing a pressure drop equation based on factors influencing the pressure drop of gas-liquid two-phase fluid in a shaft; wherein the factors influencing the fluid pressure drop in the shaft comprise fluid weight pressure drop in the shaft, friction pressure drop in the shaft, hydrostatic pressure change and acceleration pressure drop; optimizing the pressure drop equation to obtain a two-phase flow pressure profile prediction model in the shaft; and predicting the wellbore pressure profile of the two-phase flow geothermal well based on the in-wellbore two-phase flow pressure profile prediction model. According to the method, the pressure drop caused by multiple factors is considered, so that the calculation result is more accurate.

Description

Technical Field

[0001] This invention relates to the field of geothermal development technology, and in particular to a method, apparatus, application, electronic device, storage medium, and computer program product for predicting the pressure profile of a two-phase flow wellbore in a geothermal well. Background Technology

[0002] Geothermal wells face the challenge of modeling multiphase flows. While empirical models are used to predict pressure, their results are clearly inaccurate due to the complex two-phase flow within the geothermal well profile. Therefore, mechanical models and governing equations are increasingly being applied. In oil and gas wells, the set average temperature remains constant during production, but in geothermal wells, fluid flow faces heat losses within the wellbore. Therefore, establishing pressure distribution models in geothermal production requires using temperature variations as the basis for different enthalpy systems.

[0003] A typical two-phase vertical geothermal well is simplified as a conduit with superheated liquid at the bottom. However, as the fluid moves upward, the pressure of both decreases, causing temperature and pressure changes and a continuously increasing vapor fraction. Above the critical point, a two-phase zone (liquid-vapor) continues to flow toward the wellhead as mixing velocity and vapor increase. During upward flow, more vapor breaks off from the mixture and various flow states (bubbles, slugs, agitation, and annulus) become apparent in the wellbore. The different flow patterns encountered depend on the relative amounts of vapor and liquid velocities in the mixture. Determining the phase distribution in an upwardly inclined conduit is a complex problem due to the slippage between the vapor and liquid phases.

[0004] In pressure modeling of two-phase flows, it is necessary to consider the different flow regimes of the fluid in the wellbore. Most researchers attempt to simulate the pressure distribution in multiphase flows using different correlations to determine the vapor fraction or liquid holdup of the flow under different flow regimes encountered in the wellbore. However, the equations used to calculate the liquid percentage under various flow regimes have many limitations, such as the phase change of the flowing liquid in the wellbore, the wellbore geometry, and complex boundary conditions. Moreover, most of the main equations for calculating liquid holdup in two-phase flows are applicable to oil and gas flows, and have many limitations for geothermal wells. Furthermore, the components within different equations cannot achieve a transition between flow regimes, resulting in computational discontinuities. The transition from one flow regime to another is not abrupt but gradual. The model needs to account for the transitions between flow regimes, including flow rate parameters and mean rise velocity. The values ​​of flow parameters depend on the flow regime, well inclination, and flow direction.

[0005] In recent years, the development of numerical models and simulators has represented a significant shift in the prediction of pressure profiles for geothermal wells. Studies have found that using smaller flow rates in pipelines within geothermal systems can cause significant pressure losses and shock effects. Furthermore, the presence of CO2 in underground CO2 storage wells affects the critical depth, leading to calcite scaling within the wellbore. However, many models used to predict two-phase flow pressure gradients in production wells often neglect factors contributing to pressure drops during certain components of the production process. Most researchers focus only on frictional pressure drops, ignoring the pressure drop caused by pressure gradients resulting from head and acceleration during their derivation. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides a method, apparatus, application, electronic device, storage medium, and computer program product for predicting the pressure profile of a two-phase flow wellbore in a geothermal well. The invention provides the following technical solution:

[0007] In a first aspect of the present invention, a method for predicting the pressure profile of a two-phase flow wellbore in a geothermal well is provided, the method comprising:

[0008] Based on the factors affecting the pressure drop of gas-liquid two-phase fluids within the wellbore, a pressure drop equation is constructed. Among these factors, the pressure drop of fluids within the wellbore includes the weight pressure drop of the fluid within the wellbore, the frictional pressure drop within the wellbore, the hydrostatic pressure change, and the acceleration pressure drop.

[0009] The pressure drop equation is optimized to obtain a prediction model for the two-phase flow pressure profile inside the wellbore;

[0010] Based on the two-phase flow pressure profile prediction model in the wellbore, the wellbore pressure profile of a two-phase flow geothermal well is predicted.

[0011] Furthermore, the formula for the pressure drop equation is:

[0012]

[0013] In the formula, ρ m The density of a gas-liquid two-phase fluid mixture; g c f represents the conversion factor; m V represents the coefficient of friction of a gas-liquid two-phase mixture; m The velocity of the gas-liquid two-phase fluid mixture is represented by: D; the inner diameter of the tubing is represented by: P; the pressure inside the well casing is represented by: L; and the depth of the vertical well is represented by: g. csinθ The vertical component of gravitational acceleration is represented; t represents the production time. This indicates the pressure drop along the axial direction of the wellbore.

[0014] Further

[0015]

[0016] In the formula, A represents the cross-sectional area of ​​the gas-liquid two-phase fluid flow; q m ρ represents the mass flow rate of a gas-liquid two-phase fluid mixture. g ρ represents the density of steam. l ψ represents the liquid density; x represents the steam mass fraction; ψ represents the gas content of the wellbore cross section.

[0017] Furthermore,

[0018]

[0019] In the formula, c0 represents the flow coefficient; q m The mass flow rate of the gas-liquid two-phase fluid mixture is represented by ρ; x represents the mass fraction of steam; ρ represents the mass flow rate of the gas-liquid two-phase fluid mixture. g ρ represents the vapor density; A represents the flow cross-sectional area; l The value represents the liquid density; W, B, and y are all intermediate quantities; D represents the inner diameter of the oil pipe; σ represents the surface tension; g represents the acceleration due to gravity; V gb V represents the surface gas velocity required for the transition from bubble flow to slug flow; sb This represents the surface gas velocity required for the transition from annular flow to slug flow.

[0020] Furthermore, the pressure drop equation is optimized to obtain a prediction model for the two-phase flow pressure profile within the wellbore, including:

[0021] A pressure drop equation is constructed based on the liquid's own gravity, the friction of fluid flow, the resistance of gas accumulation, and the acceleration change of its own motion.

[0022] The pressure drop equation is calculated to obtain the fluid pressure equation along the length of the casing;

[0023] The fluid pressure equation along the casing length is integrally calculated to construct a two-phase flow pressure profile prediction model within the wellbore.

[0024] The two-phase flow pressure profile prediction model within the wellbore is further expressed as follows:

[0025]

[0026] In the formula, ρ l ψ represents the liquid density; ψ represents the gas content of the wellbore cross section; q m The mass flow rate of the gas-liquid two-phase fluid mixture is represented by ρ; x represents the mass fraction of steam; ρ represents the mass flow rate of the gas-liquid two-phase fluid mixture. g The value represents the vapor density; m represents the unit pressure drop due to fluid acceleration; z represents the unit pressure drop due to gas accumulation; P represents the pressure inside the well casing; L iIndicates the depth at the calculated location; L represents the depth of the vertical well; θ represents the angle between the well inclination and the horizontal; P wf represents the bottom hole pressure; e represents the unit pressure drop caused by friction.

[0027] Furthermore,

[0028]

[0029] In the formula, A represents the flow cross-sectional area; f m q represents the coefficient of friction of a gas-liquid two-phase mixture; m Indicates the mass flow rate of a gas-liquid two-phase mixture; g c denoted by conversion factor; d represents characteristic length; θ represents the angle between well inclination and horizontal; t represents production time.

[0030] Furthermore, based on the wellbore pressure profile prediction model for two-phase flow, the wellbore pressure profile of a two-phase flow geothermal well is predicted, including:

[0031] The flow regime of the gas-liquid two-phase mixture is determined based on the liquid density and vapor density inside the wellbore.

[0032] The wellbore pressure at the target depth is assigned based on the flow regime of the gas-liquid two-phase mixture.

[0033] Based on the assigned value, the enthalpy of the fluid at the target depth is obtained;

[0034] The steam mass fraction in the wellbore is obtained by calculating based on the liquid saturation enthalpy, the steam saturation enthalpy in the wellbore, and the fluid enthalpy at the target depth.

[0035] The pressure integral formula on the left side of the two-phase flow pressure profile prediction model in the wellbore is calculated based on the steam mass fraction to obtain the first calculated value at the target depth.

[0036] Substitute the value of the target depth into the depth formula on the right side of the two-phase flow pressure profile prediction model in the wellbore to obtain the second calculated value at the target depth.

[0037] When the difference between the first calculated value and the second calculated value is less than the threshold, the first calculated value is the wellbore pressure value at the target depth;

[0038] Based on the wellbore pressure value at the target depth, the wellbore pressure profile of the two-phase flow geothermal well is predicted.

[0039] Furthermore, when the difference between the first calculated value and the second calculated value is greater than or equal to the threshold, the wellbore pressure at the target depth is recalculated until the difference between the first calculated value and the second calculated value is less than the threshold.

[0040] In a second aspect of the invention, a device for predicting the pressure profile of a two-phase flow wellbore in a geothermal well is provided, the device comprising:

[0041] The construction unit is used to construct a pressure drop equation based on the factors affecting the pressure drop of the gas-liquid two-phase fluid in the wellbore; among which, the factors affecting the fluid pressure drop in the wellbore include the fluid weight pressure drop, the frictional pressure drop in the wellbore, the hydrostatic pressure change, and the acceleration pressure drop;

[0042] The acquisition unit is used to optimize the pressure drop equation and acquire a prediction model of the two-phase flow pressure profile in the wellbore.

[0043] The prediction unit is used to predict the wellbore pressure profile of a two-phase flow geothermal well based on a two-phase flow pressure profile prediction model within the wellbore.

[0044] Furthermore, the formula for the pressure drop equation is:

[0045]

[0046] In the formula, ρ m The density of a gas-liquid two-phase fluid mixture; g c f represents the conversion factor; m V represents the coefficient of friction of a gas-liquid two-phase mixture; m The velocity of the gas-liquid two-phase fluid mixture is represented by: D; the inner diameter of the tubing is represented by: P; the pressure inside the well casing is represented by: L; and the depth of the vertical well is represented by: g. csinθ The vertical component of gravitational acceleration is represented; t represents the production time. This indicates the pressure drop along the axial direction of the wellbore.

[0047] Furthermore, the pressure drop equation is optimized to obtain a prediction model for the two-phase flow pressure profile within the wellbore, including:

[0048] A pressure drop equation is constructed based on the liquid's own gravity, the friction of fluid flow, the resistance of gas accumulation, and the acceleration change of its own motion.

[0049] The pressure drop equation is calculated to obtain the fluid pressure equation along the length of the casing;

[0050] The fluid pressure equation along the casing length is integrally calculated to construct a two-phase flow pressure profile prediction model within the wellbore.

[0051] Furthermore, the two-phase flow pressure profile prediction model within the wellbore is expressed as follows:

[0052]

[0053] In the formula, ρ l ψ represents the liquid density; ψ represents the gas content of the wellbore cross section; q mThe mass flow rate of the gas-liquid two-phase fluid mixture is represented by ρ; x represents the mass fraction of steam; ρ represents the mass flow rate of the gas-liquid two-phase fluid mixture. g The value represents the vapor density; m represents the unit pressure drop due to fluid acceleration; z represents the unit pressure drop due to gas accumulation; P represents the pressure inside the well casing; L i Indicates the depth at the calculated location; L represents the depth of the vertical well; θ represents the angle between the well inclination and the horizontal; P wf represents the bottom hole pressure; e represents the unit pressure drop caused by friction.

[0054] In a third aspect of the invention, the method described above is provided for the application of predicting pressure profiles under water-water vapor flow conditions within a geothermal wellbore.

[0055] In a fourth aspect of the invention, an electronic device is provided, the electronic device comprising at least one processor and at least one memory, the memory being data-connected to the processor, wherein...

[0056] The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the method described above.

[0057] In a fifth aspect of the invention, a computer-storeable medium is provided, characterized in that the storage medium stores computer instructions, which, when executed by a processor, specifically perform the steps in the method described above.

[0058] In a sixth aspect of the invention, a computer program product is provided, comprising computer instructions, characterized in that, when the computer instructions are executed by a processor, they specifically perform the steps in the method described above.

[0059] The technical effects and advantages of this invention are as follows:

[0060] This invention proposes an improved model for predicting two-phase flow pressure profiles within geothermal wellbores. Current models consider various pressure-influencing factors, including fluid pressure drops due to build-up, friction within the wellbore, hydrostatic pressure, and acceleration pressure drop. Ignoring these calculation terms leads to an underestimation of pressure drop, affecting the accuracy of geothermal well pressure profile predictions. Furthermore, this model successfully captures the transition period at the start of production, a capability lacking in previous models. This invention considers pressure drop caused by multiple factors, resulting in more accurate calculations.

[0061] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures pointed out in the description and the drawings. Attached Figure Description

[0062] Figure 1 This is a flowchart of the geothermal well two-phase flow wellbore pressure profile prediction method provided in the embodiments of this application;

[0063] Figure 2 This is a schematic diagram of two-phase flow in a geothermal development well provided in an embodiment of this application;

[0064] Figure 3 This is a flowchart of the model calculation provided in the embodiments of this application;

[0065] Figure 4 This is a structural block diagram of an electronic device according to an embodiment of this application. Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] To address the shortcomings of existing technologies, this invention discloses a method for predicting the pressure profile of a two-phase flow wellbore in a geothermal well, such as... Figure 1 As shown, the method includes,

[0068] Step 1: Based on the factors affecting the pressure drop of the gas-liquid two-phase fluid in the wellbore, construct the pressure drop equation; among which, the factors affecting the fluid pressure drop in the wellbore include the fluid weight pressure drop, the frictional pressure drop in the wellbore, the hydrostatic pressure change, and the acceleration pressure drop;

[0069] Step 2: Optimize the pressure drop equation to obtain a prediction model for the two-phase flow pressure profile inside the wellbore;

[0070] Step 3: Based on the two-phase flow pressure profile prediction model in the wellbore, predict the wellbore pressure profile of the two-phase flow geothermal well.

[0071] It should be noted that the following assumptions are made in the derivation of the two-phase flow pressure profile prediction model in the wellbore in this invention:

[0072] ①The current model is only applicable to water-steam flow.

[0073] ②The external work done by the working fluid is zero.

[0074] ③ The physical properties of the fluid are functions of temperature and pressure, and the thermal conductivity of the fluid and the surrounding rock strata is constant.

[0075] ④ The heat loss in the wellbore is due to heat conduction to the surrounding rock; convective heat loss is negligible.

[0076] like Figure 2 The figure shows a schematic diagram of two-phase flow in a geothermal development well in a specific embodiment of the present invention. As can be seen from the figure, the wellbore passes through slug flow, bubble flow, unidirectional flow and reservoir sequentially from the wellhead to the bottom of the well. The bottom pressure of the reservoir is set to the bottom pressure, and the two-phase flow contains bubbles.

[0077] In a specific embodiment of the present invention, step 1: construct a pressure drop equation based on the factors affecting the pressure drop of the gas-liquid two-phase fluid in the wellbore; wherein, the total pressure drop of water and its hot vapor at a given flow velocity in the cross-section of the wellbore flowing through the vertical well consists of the following parts: pressure drop due to fluid weight, pressure drop due to friction, pressure drop due to acceleration, and pressure drop due to the accumulation in the wellbore.

[0078] The formula for the pressure drop equation is:

[0079]

[0080] In the formula, ρ m Density of a gas-liquid two-phase fluid mixture, expressed in kg / m³ 3 g c f represents the conversion factor, which is dimensionless; m V represents the coefficient of friction of a gas-liquid two-phase fluid mixture, and is dimensionless; m The velocity of the gas-liquid two-phase fluid mixture is expressed in m / s; D represents the inner diameter of the tubing in m; P represents the pressure inside the well casing in Pa; L represents the depth of the vertical well in m; g csinθ This represents the vertical component of gravitational acceleration; t represents the production time, in hours. This indicates the pressure drop along the axial direction of the wellbore.

[0081] In a specific embodiment of the present invention, step 2: optimizing the pressure drop equation to obtain a prediction model of the two-phase flow pressure profile in the wellbore, including:

[0082] The pressure drop equation is calculated to obtain the fluid pressure equation along the length of the casing;

[0083] The fluid pressure equation along the casing length is integrally calculated to construct a two-phase flow pressure profile prediction model within the wellbore.

[0084] In a specific embodiment of the present invention:

[0085] The density of the gas-liquid two-phase mixture is:

[0086] ρ m =ρ g F g +ρ l (1-F g (2)

[0087] In the formula, ρ g This indicates the density of steam, in kg / m³. 2 ;ρ l This indicates the density of the liquid, in kg / m³. 3 ;F g This represents the volume fraction of in-situ steam and is dimensionless.

[0088] The given steam volume fraction F g It can be written as:

[0089]

[0090] In the formula, V sg V represents the surface velocity of steam, in m / s; c0 represents the flow coefficient, a dimensionless quantity; Φ This represents the average rising velocity of the bubble, in m / s;

[0091] A flowing gas-liquid mixture can be written as:

[0092] V m =V sg +V sl (4)

[0093]

[0094] Substituting equations (5) and (6) into equation (4) yields equation (7), as follows:

[0095]

[0096] In the formula, V sl A represents the surface velocity of the liquid, in m / s; A represents the flow cross-sectional area, in m². 2 x represents the mass fraction of steam; q m This indicates the mass flow rate of the two-phase mixture, in kg / s.

[0097] The average rate of ascent is given by the following formula:

[0098] V Φ =W(1.53-By) (8)

[0099] In the formula, V_Φ represents the average rising velocity of the bubble, m / s; W, B, and y all represent intermediate quantities.

[0100]

[0101] In the formula, D represents the inner diameter of the oil pipe, in meters; σ represents the surface tension, in N / m.

[0102]

[0103] g represents gravitational acceleration; ρ l This indicates the density of the liquid, in kg / m³. 2 ;ρ g This indicates the density of steam, in kg / m³. 2 σ represents surface tension, N / m.

[0104]

[0105] In the formula, V gb V represents the surface gas velocity required for the transition from bubble flow to slug flow; sb This represents the surface gas velocity required for the transition from annular flow to slug flow.

[0106] Substituting equations (5), (7), and (8) into equation (3) yields:

[0107]

[0108] Substituting equation (12) into equation (2) and simplifying:

[0109]

[0110] make:

[0111] Substituting equations (7) and (13) into equation (1):

[0112]

[0113] make:

[0114]

[0115] Equation (15) becomes:

[0116]

[0117]

[0118] Apply variable separation along the sleeve length direction:

[0119]

[0120] Consider P = P wf (Bottomhole pressure), where L is the depth from the bottom of the well to the bottom of the well under the boundary conditions and the integral equation at any point. The two-phase flow pressure profile prediction model inside the wellbore is obtained as follows:

[0121]

[0122] In equation (21), several parameters are functions of pressure, ρ g ρ l qm 1 and 2 are parameters that vary with pressure and are unknown, while the rest are known quantities; therefore, it is difficult to solve using analytical equations. Numerical calculation methods are used to iteratively solve equation (21).

[0123] Geothermal wells experience water evaporation within the wellbore, unlike oil and gas production where the temperature is relatively constant. Therefore, enthalpy is crucial; thus, equation (22) must be solved to accurately predict the pressure profile by obtaining the enthalpy of the fluid rising through the wellbore at different depths. Equation (22) needs to be substituted into equation (21) for calculation.

[0124] The steam mass fraction x is calculated by combining enthalpy and pressure, as shown in the following equation:

[0125]

[0126] In the formula, J represents the enthalpy; h represents the saturated enthalpy of the gas-liquid two-phase fluid mixture; h g The vapor saturation enthalpy is expressed in J / kg; σ represents surface tension; h l The enthalpy of liquid saturation is expressed in J / kg; V represents volume; g c denoted by the conversion factor, dimensionless; Q represents the heat transfer rate per unit wellbore length, J / hm, where a positive value indicates heat gain during injection, and a negative value indicates heat loss during production; W T The volumetric flow rate is expressed in m³ / h; v represents the fluid velocity. This represents the velocity gradient, in m / s.

[0127] Q = L R W T C p (T f -T ei )

[0128]

[0129] In the formula, LR represents the relaxation length parameter, m -1 Cp represents the specific heat capacity of water, in J / (kg℃); W T T represents volumetric flow rate, m³ / h; f T represents fluid temperature, expressed in °C. ei Represents the undisturbed formation temperature at any depth, expressed in °C; C p The specific heat capacity of water is expressed in J / (kg℃); r to U represents the outer radius of the oil pipe, in meters (m). to Represents the overall heat transfer coefficient, J / hm 2 ℃; T D The value represents the temperature at a certain depth, which is dimensionless; Ke represents the Earth's thermal conductivity, W / mK.

[0130] In a specific embodiment of the present invention, step 3, predicting the wellbore pressure profile of a two-phase flow geothermal well based on a wellbore pressure profile prediction model, includes:

[0131] Step 301: Determine the flow regime of the gas-liquid two-phase mixture based on the liquid density and vapor density inside the wellbore;

[0132] Step 302: Assign a value to the wellbore pressure at the target depth based on the flow regime of the gas-liquid two-phase mixture;

[0133] Step 303: Based on the assigned value, obtain the enthalpy of the fluid at the target depth;

[0134] Step 304: Calculate the steam mass fraction in the wellbore based on the liquid saturation enthalpy, the vapor saturation enthalpy in the wellbore, and the fluid enthalpy at the target depth.

[0135] Step 305: Calculate the pressure integral formula on the left side of the two-phase flow pressure profile prediction model in the wellbore based on the steam mass fraction, and obtain the first calculated value at the target depth.

[0136] Step 306: Substitute the value of the target depth into the depth formula on the right side of the two-phase flow pressure profile prediction model in the wellbore to obtain the second calculated value at the target depth.

[0137] Step 307: When the difference between the first calculated value and the second calculated value is less than the threshold, the first calculated value is the wellbore pressure value at the target depth; or when the difference between the first calculated value and the second calculated value is greater than or equal to the threshold, the wellbore pressure at the target depth is recalculated until the difference between the first calculated value and the second calculated value is less than the threshold.

[0138] Step 308: Wellbore pressure value at the target depth, predicting the wellbore pressure profile of the two-phase flow geothermal well.

[0139] In one specific embodiment of the present invention, combined with Figure 3 The operational steps for predicting the wellbore pressure profile of a two-phase flow geothermal well are as follows:

[0140] Input parameters: wellbore size, flow rate, bottom hole pressure; then determine the steam fraction x;

[0141] Based on the known liquid density ρ l ρ vapor density g Calculate the Reynolds number Re to determine the flow regime of the gas-liquid mixture; based on the flow regime, determine three flow mechanisms for the bottom hole fluid: among which,

[0142] For laminar flow (Reynolds number less than 2300), refer to the Taylor vertical tube gas-liquid two-phase flow pattern transformation boundary diagram and empirical formulas.

[0143] Transitional flow (2300-4000) is based on the Taylor vertical tube gas-liquid two-phase flow pattern transformation boundary diagram and empirical formulas.

[0144] For turbulent flow (greater than 4000), refer to the Taylor vertical tube gas-liquid two-phase flow pattern transformation boundary diagram and empirical formulas.

[0145] Calculate the flow rate based on different flow regimes;

[0146] Calculate the Reynolds number of a gas-liquid mixture:

[0147]

[0148] In the formula, Λ represents an intermediate variable; Re m Represents the Reynolds number, dimensionless; μ m V represents the dynamic viscosity of a fluid; m The velocity of the steam-liquid mixture is expressed in m / s; d represents the characteristic length; and ε represents the slip ratio (the ratio of gas velocity to liquid velocity).

[0149]

[0150]

[0151] Then calculate

[0152] Then the steam density ρ g Liquid density ρ l The mass flow rate q of a gas-liquid two-phase fluid mixture is expressed as follows. m The steam mass fraction x and the gas content ψ of the well section are substituted into formula (21) to calculate the pressure at a certain depth: First, assume a value and substitute it into formula (21). If the difference between the left and right sides of the equation is less than 5% of the right side, the pressure value at that depth is obtained. Otherwise, change the assumed value and recalculate.

[0153] The properties of the working fluid affected by pressure include: the coefficient of friction f of the gas-liquid two-phase mixture. m The density ρ of a gas-liquid two-phase fluid mixture m In-situ steam volume fraction F g The heat transfer rate Q per unit well length and the saturated enthalpy h of the gas-liquid two-phase fluid mixture.

[0154] The present invention also provides a device for predicting the pressure profile of a two-phase flow wellbore in a geothermal well, the device comprising,

[0155] The construction unit is used to construct a pressure drop equation based on the factors affecting the pressure drop of the gas-liquid two-phase fluid in the wellbore; among which, the factors affecting the fluid pressure drop in the wellbore include the fluid weight pressure drop, the frictional pressure drop in the wellbore, the hydrostatic pressure change, and the acceleration pressure drop;

[0156] The acquisition unit is used to optimize the initial pressure drop model and acquire a prediction model of the two-phase flow pressure profile in the wellbore.

[0157] The prediction unit is used to predict the wellbore pressure profile of a two-phase flow geothermal well based on a two-phase flow pressure profile prediction model within the wellbore.

[0158] In one specific embodiment of the present invention, the formula for the pressure drop equation is:

[0159]

[0160] In the formula, ρ m Density of a gas-liquid two-phase fluid mixture, expressed in kg / m³ 3 g c f represents the conversion factor, which is dimensionless; m V represents the coefficient of friction of a gas-liquid two-phase fluid mixture, dimensionless; m The velocity of the gas-liquid two-phase fluid mixture is expressed in m / s; D represents the inner diameter of the tubing in m; P represents the pressure inside the well casing in Pa; L represents the depth of the vertical well in m; g csinθ This represents the vertical component of gravitational acceleration; t represents the production time, in hours. This indicates the pressure drop along the axial direction of the wellbore.

[0161] In a specific embodiment of the present invention, optimizing the initial pressure drop model to obtain a predictive model of the two-phase flow pressure profile within the wellbore includes:

[0162] A pressure drop equation is constructed based on the liquid's own gravity, the friction caused by fluid flow, the resistance caused by gas accumulation, and the acceleration change of its own motion.

[0163] The initial pressure drop model is calculated to obtain the fluid pressure equation along the length of the casing;

[0164] The fluid pressure equation along the casing length is integrally calculated to construct a two-phase flow pressure profile prediction model within the wellbore.

[0165] In a specific embodiment of the present invention, the two-phase flow pressure profile prediction model in the wellbore is expressed as follows:

[0166]

[0167] Regarding the apparatus in the above embodiments, the specific manner in which each unit performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0168] The present invention also provides the application of the method described above in predicting pressure profiles under water-water vapor flow conditions within geothermal wellbores.

[0169] Based on the above disclosure, the present invention also provides an electronic device. For example... Figure 4 As shown, the electronic device of this disclosure includes at least one processor electrically connected to the present invention and at least one memory electrically connected to the processor, wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method steps as executed by the controller above.

[0170] The readable storage medium provided in this application is a computer-readable storage medium, which stores computer-readable program instructions (i.e., a computer program) for performing the above-described methods. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as the beneficial effects of the methods provided in the above embodiments, and will not be repeated here.

[0171] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the method steps described above. Compared with the prior art, the beneficial effects of the computer program product provided in this application are the same as those of the methods provided in the above embodiments, and will not be repeated here.

[0172] The technical solution of the present invention will be further described below with reference to specific embodiments.

[0173] Combination Figure 3 To verify the accuracy of the calculation model, pressure values ​​at ten different depths were calculated and compared with measured values ​​from a case study well in the Dagang Oilfield. The well has a vertical depth of 2223m and a casing diameter of 198.7mm. The bottomhole pressure is 8.54MPa, and the flow rate is 22.68m³ / h. 3 / h.

[0174] Assuming a bottom hole pressure of 3.2 MPa, obtain h and h' from the known charts. l and h g Substitute the numerical value into the formula to obtain the value of steam mass fraction x:

[0175]

[0176] Liquid density ρ l=857.1kg / m 3

[0177] Gas density ρ g =17kg / m 3

[0178] Calculate the Reynolds number of a gas-liquid mixture

[0179] The value of ε / d is calculated based on the wellbore dimensions and fluid velocity.

[0180]

[0181]

[0182] Then calculate

[0183] The intermediate function at 3.2 MPa is obtained using formula (20):

[0184]

[0185] The calculated pressure value was then obtained by integration, which was 3.1097. The error range between this value and the assumed value of 3.2 was less than 5%, so the calculation ended.

[0186] If the value is within the error range, the calculation ends; if the value is outside the error range, change the initial input value and repeat the above process until the result meets the requirements.

[0187] The calculation results are shown in Table 1.

[0188] Table 1 Calculation Results

[0189]

[0190]

[0191] As shown in Table 1, the calculation error remains at around 5%, which meets the engineering error standards.

[0192] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the pressure profile of a two-phase flow wellbore in a geothermal well, characterized in that, The method includes, Based on the factors affecting the pressure drop of gas-liquid two-phase fluids within the wellbore, a pressure drop equation is constructed. Among these factors, the pressure drop of fluids within the wellbore includes the weight pressure drop of the fluid within the wellbore, the frictional pressure drop within the wellbore, the hydrostatic pressure change, and the acceleration pressure drop. The pressure drop equation is optimized to obtain a prediction model for the two-phase flow pressure profile inside the wellbore; Based on the two-phase flow pressure profile prediction model in the wellbore, the wellbore pressure profile of a two-phase flow geothermal well is predicted.

2. The method for predicting the pressure profile of a two-phase flow wellbore in a geothermal well according to claim 1, characterized in that, The formula for the pressure drop equation is: In the formula, ρ m The density of a gas-liquid two-phase fluid mixture; g c f represents the conversion factor; m V represents the coefficient of friction of a gas-liquid two-phase mixture; m The velocity of the gas-liquid two-phase fluid mixture is represented by: D; the inner diameter of the tubing is represented by: P; the pressure inside the well casing is represented by: L; and the depth of the vertical well is represented by: g. csinθ The vertical component of gravitational acceleration is represented; t represents the production time. This indicates the pressure drop along the axial direction of the wellbore.

3. The method for predicting the pressure profile of a two-phase flow wellbore in a geothermal well according to claim 2, characterized in that, In the formula, A represents the cross-sectional area of ​​the gas-liquid two-phase fluid flow; q m ρ represents the mass flow rate of a gas-liquid two-phase fluid mixture. g ρ represents the density of steam. l ψ represents the liquid density; x represents the steam mass fraction; ψ represents the gas content of the wellbore cross section.

4. The method for predicting the pressure profile of a two-phase flow wellbore in a geothermal well according to claim 3, characterized in that, In the formula, c0 represents the flow coefficient; q m The mass flow rate of the gas-liquid two-phase fluid mixture is represented by ρ; x represents the mass fraction of steam; ρ represents the mass flow rate of the gas-liquid two-phase fluid mixture. g ρ represents the vapor density; A represents the flow cross-sectional area; l The value represents the liquid density; W, B, and y are all intermediate quantities; D represents the inner diameter of the oil pipe; σ represents the surface tension; g represents the acceleration due to gravity; V gb V represents the surface gas velocity required for the transition from bubble flow to slug flow; sn This represents the surface gas velocity required for the transition from annular flow to slug flow.

5. The method for predicting the pressure profile of a two-phase flow wellbore in a geothermal well according to claim 1, characterized in that, The pressure drop equation is optimized to obtain a prediction model for the two-phase flow pressure profile inside the wellbore, including: A pressure drop equation is constructed based on the liquid's own gravity, the friction of fluid flow, the resistance of gas accumulation, and the acceleration change of its own motion. The pressure drop equation is calculated to obtain the fluid pressure equation along the length of the casing; The fluid pressure equation along the casing length is integrally calculated to construct a two-phase flow pressure profile prediction model within the wellbore.

6. The method for predicting the pressure profile of a two-phase flow wellbore in a geothermal well according to claim 4 or 5, characterized in that, The prediction model for the two-phase flow pressure profile within the wellbore is expressed as follows: In the formula, ρ l ψ represents the liquid density; ψ represents the gas content of the wellbore cross section; q m The mass flow rate of the gas-liquid two-phase fluid mixture is represented by ρ; x represents the mass fraction of steam; ρ represents the mass flow rate of the gas-liquid two-phase fluid mixture. g The value represents the vapor density; m represents the unit pressure drop due to fluid acceleration; z represents the unit pressure drop due to gas accumulation; P represents the pressure inside the well casing; L i Indicates the depth at the calculated location; L represents the depth of the vertical well; θ represents the angle between the well inclination and the horizontal; P wf represents the bottom hole pressure; e represents the unit pressure drop caused by friction.

7. The method for predicting the pressure profile of a two-phase flow wellbore in a geothermal well according to claim 6, characterized in that, In the formula, A represents the flow cross-sectional area; f m q represents the coefficient of friction of a gas-liquid two-phase mixture; m Indicates the mass flow rate of a gas-liquid two-phase mixture; g c denoted by conversion factor; d represents characteristic length; θ represents the angle between well inclination and horizontal; t represents production time.

8. The method for predicting the pressure profile of a two-phase flow wellbore in a geothermal well according to claim 6, characterized in that, Based on the wellbore pressure profile prediction model for two-phase flow, the wellbore pressure profile of a two-phase flow geothermal well is predicted, including: The flow regime of the gas-liquid two-phase mixture is determined based on the liquid density and vapor density inside the wellbore. The wellbore pressure at the target depth is assigned based on the flow regime of the gas-liquid two-phase mixture. Based on the assigned value, the enthalpy of the fluid at the target depth is obtained; The steam mass fraction in the wellbore is obtained by calculating based on the liquid saturation enthalpy, the steam saturation enthalpy in the wellbore, and the fluid enthalpy at the target depth. The pressure integral formula on the left side of the two-phase flow pressure profile prediction model in the wellbore is calculated based on the steam mass fraction to obtain the first calculated value at the target depth. Substitute the value of the target depth into the depth formula on the right side of the two-phase flow pressure profile prediction model in the wellbore to obtain the second calculated value at the target depth. When the difference between the first calculated value and the second calculated value is less than the threshold, the first calculated value is the wellbore pressure value at the target depth; Based on the wellbore pressure value at the target depth, the wellbore pressure profile of the two-phase flow geothermal well is predicted.

9. The method for predicting the pressure profile of a two-phase flow wellbore in a geothermal well according to claim 8, characterized in that, When the difference between the first calculated value and the second calculated value is greater than or equal to the threshold, the wellbore pressure at the target depth is recalculated until the difference between the first calculated value and the second calculated value is less than the threshold.

10. A device for predicting the pressure profile of a two-phase flow wellbore in a geothermal well, characterized in that, The device includes, The construction unit is used to construct a pressure drop equation based on the factors affecting the pressure drop of the gas-liquid two-phase fluid in the wellbore; among which, the factors affecting the fluid pressure drop in the wellbore include the fluid weight pressure drop, the frictional pressure drop in the wellbore, the hydrostatic pressure change, and the acceleration pressure drop; The acquisition unit is used to optimize the pressure drop equation and acquire a prediction model of the two-phase flow pressure profile in the wellbore. The prediction unit is used to predict the wellbore pressure profile of a two-phase flow geothermal well based on a two-phase flow pressure profile prediction model within the wellbore.

11. The geothermal well two-phase flow wellbore pressure profile prediction device according to claim 10, characterized in that, The formula for the pressure drop equation is: In the formula, ρ m The density of a gas-liquid two-phase fluid mixture; g c f represents the conversion factor; m V represents the coefficient of friction of a gas-liquid two-phase mixture; m The velocity of the gas-liquid two-phase fluid mixture is represented by: D; the inner diameter of the tubing is represented by: P; the pressure inside the well casing is represented by: L; and the depth of the vertical well is represented by: g. csinθ The vertical component of gravitational acceleration is represented; t represents the production time. This indicates the pressure drop along the axial direction of the wellbore.

12. The geothermal well two-phase flow wellbore pressure profile prediction device according to claim 11, characterized in that, The pressure drop equation is optimized to obtain a prediction model for the two-phase flow pressure profile inside the wellbore, including: A pressure drop equation is constructed based on the liquid's own gravity, the friction of fluid flow, the resistance of gas accumulation, and the acceleration change of its own motion. The pressure drop equation is calculated to obtain the fluid pressure equation along the length of the casing; The fluid pressure equation along the casing length is integrally calculated to construct a two-phase flow pressure profile prediction model within the wellbore.

13. The geothermal well two-phase flow wellbore pressure profile prediction device according to claim 12, characterized in that, The prediction model for the two-phase flow pressure profile within the wellbore is expressed as follows: In the formula, ρ l ψ represents the liquid density; ψ represents the gas content of the wellbore cross section; q m The mass flow rate of the gas-liquid two-phase fluid mixture is represented by ρ; x represents the mass fraction of steam; ρ represents the mass flow rate of the gas-liquid two-phase fluid mixture. g The value represents the vapor density; m represents the unit pressure drop due to fluid acceleration; z represents the unit pressure drop due to gas accumulation; P represents the pressure inside the well casing; L i Indicates the depth at the calculated location; L represents the depth of the vertical well; θ represents the angle between the well inclination and the horizontal; P wf represents the bottom hole pressure; e represents the unit pressure drop caused by friction.

14. The application of the method as described in any one of claims 1-9 in predicting pressure profiles under water-water vapor flow conditions within a geothermal wellbore.

15. An electronic device comprising at least one processor and at least one memory, the memory being data-connected to the processor, wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-9.

16. A computer-storable medium, characterized in that, The storable medium stores computer instructions, which, when executed by a processor, specifically perform the steps of the method as described in any one of claims 1-9.

17. A computer program product comprising computer instructions, characterized in that, When the computer instructions are executed by the processor, they specifically perform the steps in the method as described in any one of claims 1-9.

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