A method for predicting the temperature field of a wellbore-cavity-surrounding rock of a salt cavern helium storage

Abstract

The application discloses a kind of salt cavern helium storage wellbore-cavity-surrounding rock temperature field prediction method.Real-time monitoring salt cavern helium storage operation dynamics, including but not limited to wellhead pressure and injection-production rate and other data, based on the collected helium injection-production operation data, combined with the basic parameters of wellbore composite structure, the numerical calculation of helium flow and heat transfer equation is carried out;Again based on the prediction result of helium temperature field in wellbore, the convection law of helium in cavity is solved, and then the coupling heat transfer between cavity and surrounding rock is calculated, to realize the accurate prediction of wellbore-cavity-surrounding rock temperature field finally.

Description

Technical Field

[0001] This invention relates to the field of strategic energy material reserve technology, and in particular to a method for predicting the temperature field of the wellbore-cavity-surrounding rock in a salt cavern helium storage facility. Background Technology

[0002] Helium, a strategically scarce resource, is widely used as a pressurizing agent and booster in the aerospace industry, a coolant in the nuclear industry, and a protective gas in welding. Salt rock formations are excellent geological bodies for deep-earth energy storage, characterized by low permeability (less than 10). - 20 m 2 With its characteristics of low porosity (less than 1%), helium is widely used for natural gas storage in energy-consuming countries such as the United States, Europe, and China, and is also a major development direction for my country's large-scale helium storage. When conducting strategic helium storage through salt caverns, rapid helium injection and extraction lead to rapid temperature changes within the cavern cavity 9, resulting in continuous heat transfer between the helium and the surrounding rock, disturbing the original temperature field distribution of the surrounding rock. Since the physical and mechanical properties of salt rock are greatly affected by temperature, periodic temperature disturbances can generate excessive thermal stress within the cavity's surrounding rock, significantly increasing the risk of instability in the salt cavern cavity 9. Therefore, accurately predicting the temperature field distribution within the helium storage wellbore-cavity-surrounding rock during helium injection and extraction is crucial for optimizing injection and extraction parameters and ensuring the long-term stable operation of the cavity. Summary of the Invention

[0003] This invention provides a method for predicting the temperature field within the wellbore-cavity-surrounding rock of a salt cavern helium storage facility, which can accurately predict the temperature field distribution within the wellbore-cavity-surrounding rock during helium injection and production.

[0004] This invention provides a method for predicting the temperature field of a salt cavern helium storage wellbore-cavity-surrounding rock, comprising:

[0005] Obtain the pressure and flow velocity distribution within the wellbore during helium injection and production;

[0006] Based on the pressure and flow velocity distribution, the energy conservation equation and the heat transfer equation in the formation during helium injection and production are combined, and the above equations are differentially discretized using a fully implicit method. Combining the initial conditions and boundary conditions, the heat transfer equations of the wellbore and the formation are established in a unified tridiagonal solution matrix to achieve coupled solution of the temperature fields of the wellbore and the formation.

[0007] The solution results of the wellbore and formation temperature fields are used as the boundary conditions for the calculation, and the formula is applied. The temperature field inside the cavity was calculated; where ρ g C is the density of helium. g T is the specific heat capacity of helium. f Let r be the temperature of the helium gas, r be the distance from the formation to the center of the wellbore, and h be the temperature of the helium gas.g Let μ be the convective heat transfer coefficient of helium. jT C is the Joule-Thomson coefficient for helium. V,g where is the specific heat capacity of helium, and p is the pressure of helium.

[0008] Through formula The temperature field of the surrounding rock of the cavity was calculated; where ρ e C is the density of the formation. e For the specific heat capacity of the formation, T e λ represents the formation temperature. e is the thermal conductivity coefficient of the formation.

[0009] Specifically, obtaining the pressure and flow velocity distribution within the wellbore during helium injection and production includes:

[0010] The mass conservation equation of gases and relation Combined, the pressure and flow velocity distribution within the wellbore during helium injection and production are obtained; where A is the wellbore diameter, ρ g Let F be the density of helium, v be the flow velocity of helium in the wellbore, z be the depth of the wellbore, and F be the density of helium. w θ is the frictional resistance of the helium flow, g is the acceleration due to gravity, and θ is the inclination angle of the wellbore.

[0011] Specifically, the energy conservation equation during the helium injection and production operation is as follows: Where A is the wellbore diameter, v is the flow velocity of helium gas in the wellbore, z is the wellbore depth, g is the acceleration due to gravity, and Q... e This represents the rate of heat transfer from the formation into the wellbore.

[0012] The heat transfer equation in the formation is: Where, ρ e C is the density of the formation. e For the specific heat capacity of the formation, T e λ represents the formation temperature. e is the thermal conductivity coefficient of the formation.

[0013] Specifically, the Q e Through formula Q e =2πrU we (T e,1 -T f ) is calculated; where U we T is the overall heat transfer coefficient between the wellbore and the formation. e,1 The temperature of the cavity wall.

[0014] Specifically, the U we Through formula The calculation yields h; where h tr is the convective heat transfer coefficient of the heat-collecting fluid. ti and r to These are the inner and outer diameters of the injection and production pipes, respectively, r oi and r oo These are the inner and outer diameters of the injection and production pipes, respectively, r ci and r co These are the inner and outer diameters of the casing, r. ces k is the outer diameter of the cement ring. w k t k cas and k ces These are the thermal conductivity coefficients of the annular water, the inner and outer injection / production pipes, the casing, and the cement sheath, respectively.

[0015] Specifically, the h g Through formula The calculation yields λ; where λ is the λ value. g μ is the thermal conductivity coefficient of helium. g τ is the viscosity of helium. g Let v be the internal tangential force of the helium gas, and v be the velocity vector of the helium gas.

[0016] Specifically, the v is expressed by the formula The calculation yields the result; where F is the gravity of helium and μ is the viscosity of helium.

[0017] Specifically, this also includes: determining whether the temperature field converges using the following formula:

[0018]

[0019] Where η, γ, and ω are the coefficients of the equation, and T k e,1 Let T be the temperature of the cavity wall at time k. k f Let T be the temperature of the helium gas inside the cavity at time k. k e,2 Let T be the temperature of the surrounding rock of the first unit grid in the direction from the cavity wall to the depth at time k. k-1 e,1 Let ε be the temperature of the cavity wall at time k-1, and ε be the convergence error.

[0020] In the formula, U hf R is the convective heat transfer coefficient of helium, r1 is the radius of the cavity wall, r0 is the cavity radius, and p k Let p be the helium pressure at time k. k-1 Let be the helium pressure at time k-1.

[0021] Specifically, this also includes: assembling and integrating temperature data of the wellbore, cavity, and surrounding rock, and outputting it in the form of cloud maps.

[0022] One or more technical solutions provided in this invention have at least the following technical effects or advantages:

[0023] Real-time monitoring of the operational dynamics of the salt cavern helium storage facility, including but not limited to wellhead pressure and injection / production rates, is performed. Based on the collected helium injection / production operation data and the basic parameters of the wellbore composite structure, numerical calculations of the helium flow and heat transfer equations are conducted. Then, based on the predicted helium temperature field within the wellbore, the convection law of helium within the cavity is solved, and the coupled heat transfer between the cavity and the surrounding rock is calculated, ultimately achieving accurate prediction of the temperature field of the wellbore-cavity-surrounding rock.

[0024] This invention enables real-time and accurate prediction of the temperature field of the entire wellbore, cavity, and surrounding rock by simply installing a helium injection and production monitoring device on the ground. Based on a comprehensive theoretical model and limited real-time ground monitoring data, this invention achieves precise temperature field prediction with simple calculations and a scientifically sound approach. Attached Figure Description

[0025] Figure 1 A flowchart illustrating the method for predicting the temperature field of a salt cavern helium storage wellbore-cavity-surrounding rock provided in an embodiment of the present invention;

[0026] Figure 2 This is a schematic diagram of grid division in an embodiment of the present invention;

[0027] Figure 3 This is a schematic diagram of the structure of a prediction system built based on the prediction method for the temperature field of a salt cavern helium storage wellbore-cavity-surrounding rock provided in the embodiments of the present invention;

[0028] Figure 4 This is a schematic diagram illustrating the working principle of a prediction system built based on the prediction method for the temperature field of a salt cavern helium storage wellbore-cavity-surrounding rock provided in an embodiment of the present invention.

[0029] Among them, 1. Helium flow meter; 2. Wellhead pressure gauge; 3. Injection and production inner pipe; 4. Casing; 5. Cement sheath; 6. B annulus; 7. Injection and production outer pipe; 8. A annulus; 9. Salt cavern cavity; 10. Cavity surrounding rock; 11. Signal transmission optical cable; 12. Signal decoder; 13. Terminal wellbore-cavity-surrounding rock temperature field calculation system. Detailed Implementation

[0030] This invention provides a method for predicting the temperature field within the wellbore-cavity-surrounding rock of a salt cavern helium storage facility, which can accurately predict the temperature field distribution within the wellbore-cavity-surrounding rock during helium injection and production.

[0031] The technical solutions in the embodiments of the present invention are designed to achieve the above-mentioned technical effects, and the overall concept is as follows:

[0032] Real-time monitoring of the operational dynamics of the salt cavern helium storage facility, including but not limited to wellhead pressure and injection / production rates, is performed. Based on the collected helium injection / production operation data and the basic parameters of the wellbore composite structure, numerical calculations of the helium flow and heat transfer equations are conducted. Then, based on the predicted helium temperature field within the wellbore, the convection law of helium within the cavity is solved, and the coupled heat transfer between the cavity and the surrounding rock is calculated, ultimately achieving accurate prediction of the temperature field of the wellbore-cavity-surrounding rock.

[0033] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0034] See Figure 1 The method for predicting the temperature field of a salt cavern helium storage wellbore-cavity-surrounding rock provided in this embodiment of the invention includes:

[0035] Step S110: Obtain the pressure and flow velocity distribution within the wellbore during helium injection and production;

[0036] This step is described in detail to obtain the pressure and flow velocity distribution within the wellbore during helium injection and production, including:

[0037] The mass conservation equation of gases The relationship (quantitative relationship between the pressure of gas in unsteady flow within a wellbore and the changes in hydrostatic pressure, frictional pressure drop, and kinetic energy). Combined, the pressure and flow velocity distribution within the wellbore during helium injection and production are obtained; where A is the wellbore diameter in meters. 2 ;ρ g Helium density, kg / m³ 3 v is the flow velocity of helium gas in the wellbore, in m / s, which can be measured by a helium flow meter at the wellhead; t is time, in seconds; z is the wellbore depth, in meters; F w The frictional resistance of helium flow is N; g is the acceleration due to gravity, m / s². 2 θ is the inclination angle of the wellbore, in degrees.

[0038] Step S120: Based on the pressure and flow velocity distribution, the energy conservation equation during helium injection and production operation and the heat transfer equation in the formation are combined, and the above equations are differentially discretized using a fully implicit method; combined with the initial conditions and boundary conditions, the heat transfer equations of the wellbore and the formation are established in a unified tridiagonal solution matrix to achieve coupled solution of the temperature fields of the wellbore and the formation.

[0039] Specifically, the energy conservation equation during helium injection and production is as follows: Where A is the diameter of the wellbore, C V,g The specific heat capacity of helium is J / (kg·℃); T fTemperature of helium, °C; μ jT denoted by , where is the Joule-Thomson coefficient of helium; v is the flow velocity of helium in the wellbore; z is the wellbore depth; g is the acceleration due to gravity; and Q is the velocity of helium. e Q is the rate of heat transfer from the formation into the wellbore, expressed in W / m; where Q e Through formula Q e =2πrU we (T e,1 -T f ) is calculated; where U we The overall heat transfer coefficient between the wellbore and the formation, W / (m³). 2 ·℃); T e,1 The temperature of the cavity wall (surrounding rock numbered 1).

[0040] It should be noted here that, see Figure 2 The formation is divided into N cell grids along the depth direction, labeled 0, 1, 2, 3…N; and M cell grids along the depth direction, labeled 0, 1, 2, 3…M. Therefore, the entire formation contains M×N cell grids.

[0041] It should also be noted that an injection / production outer pipe 7, casing 4, and cement sheath 5 are sequentially installed between the inner injection / production pipe 3 and the formation. The casing layers differ at different well depths. For example... Figure 3 As shown, the shallow layer has two layers of casing, the middle layer has one layer of casing, and the bottom layer has no casing. U we Through formula The calculation yields h; where h t The convective heat transfer coefficient of the heat-collecting fluid is expressed in W / (m³). 2 ·℃); r ti and r to These are the inner and outer diameters of the injection / production inner tube 3, respectively, in meters (m); r. oi and r oo These are the inner and outer diameters of the injection / production outer pipe 7, respectively, in meters (m); r. ci and r co These are the inner and outer diameters of sleeve 4, respectively, in meters (m) and r. ces The outer diameter of cement ring 5 is in meters (m); k w k t k cas and k ces The thermal conductivity coefficients (W·m) of the annular water, injection and production pipes, casing 4, and cement ring 5 are respectively. -1 ·℃ -1 In the above formula, the terms on the right side of the equal sign represent the heat transfer coefficient components of the inner injection / production pipe 3, the A annulus 8, the outer injection / production pipe 7, the B annulus 6, the casing 4, and the cement ring 5, respectively.

[0042] The heat transfer equation in the formation is: Where, ρ e The density of the formation is kg / m³. 3 C e ρ is the specific heat capacity of the formation, J / (kg·℃); r is the distance from the formation to the center of the wellbore, m; T e λ represents the formation temperature in °C. e ν is the thermal conductivity of the formation, W / (m·℃).

[0043] Step S120 is explained in detail below:

[0044] Equation Q e =2πrU we (T e,1 -T f Substitute into the equation The implicit discretization scheme of the wellbore heat transfer equation is as follows:

[0045]

[0046] The above equation (1) can be further simplified to:

[0047]

[0048] in,

[0049]

[0050] The implicit discretization scheme for the heat transfer equation of the formation is:

[0051]

[0052] Equation (5) above can be simplified to:

[0053]

[0054] in,

[0055] Furthermore, the heat transfer equations between the wellbore and the formation can be assembled into the following form:

[0056] A×B=C (8)

[0057] in,

[0058]

[0059]

[0060] Numerical solutions to the temperature fields of the wellbore and formation can be obtained through matrix operations.

[0061] Step S130: Use the solution results of the wellbore and formation temperature fields as the boundary conditions for the calculation, and apply the formula... The temperature field inside the cavity was calculated; where ρ g C is the density of helium. g T is the specific heat capacity of helium. f Let r be the temperature of the helium gas, r be the distance from the formation to the center of the wellbore, and h be the temperature of the helium gas. g ρ is the convective heat transfer coefficient of helium, W / (m·℃); μ jT C is the Joule-Thomson coefficient for helium. V,g ρ is the specific heat capacity of helium, and p is the helium pressure in Pa, which can be measured by a wellhead pressure gauge.

[0062] Specifically, h g Through formula It can be calculated; where λ g ρ is the thermal conductivity of helium, W / (m·℃); μ g Where τ is the viscosity of helium, Pa·s; g The internal force of helium gas is given by: v is the velocity vector of helium gas, in Pa; where v is expressed by the formula... The calculation yielded the following: where F is the gravity of helium, N; and μ is the viscosity of helium.

[0063] Step S140: Using the formula The temperature field of the surrounding rock 10 of the cavity was calculated.

[0064] To ensure the accuracy of the prediction results, the following method is also used to determine whether the temperature field has converged:

[0065]

[0066] Where η, γ, and ω are the coefficients of the equation, and T k e,1 Let T be the temperature of the cavity wall (the surrounding rock numbered 1) at time k. k f Let T be the temperature of the helium gas inside the cavity at time k. k e,2 Let T be the temperature of the surrounding rock in the first unit grid (numbered 2) at time k, from the cavity wall in the depth direction. k-1 e,1 Let ε be the temperature of the cavity wall (the surrounding rock numbered 1) at time k-1, and ε be the convergence error.

[0067] In the formula, U hfR is the convective heat transfer coefficient of helium, r1 is the radius of the cavity wall, r0 is the cavity radius, and p k Let p be the helium pressure at time k. k-1 Let be the helium pressure at time k-1.

[0068] In order to output the obtained prediction results, the following steps are also included: assembling and integrating the temperature data of the wellbore, cavity and surrounding rock to obtain two matrices. Matrices 1 and 2 record the temperature and position of each grid point in the wellbore, cavity and surrounding rock respectively, and output them in the form of cloud map.

[0069] See Figure 3 and Figure 4 The prediction system built based on the prediction method of the temperature field of salt cavern helium storage wellbore-cavity-surrounding rock provided in the embodiments of the present invention includes: a helium flow meter 1, a wellhead pressure gauge 2, a signal transmission optical cable 11, and a signal decoder 12; the helium flow meter 1 and the wellhead pressure gauge 2 are installed on the wellhead surface manifold for real-time monitoring of helium injection and production rates and wellhead pressure; the signal transmission optical cable 11 is shallowly buried below the ground for monitoring signal transmission and transmitting the collected pressure and flow signals to the signal decoder 12; the signal decoder 12 is installed in the central control room of the well site for signal decoding and remote transmission to the terminal system. During the helium injection and production operation, the injection and production inner pipe 3 realizes the injection and production exchange between the surface manifold and the underground salt cavern gas storage 9; the well-hole-cavity-surrounding rock temperature field calculation system 13 of the terminal system can be further divided into a well-hole temperature field prediction system and a cavity-surrounding rock temperature field prediction system. The well-hole temperature field prediction system performs numerical calculations of the helium flow and heat transfer equations based on the received helium injection and production operation data and the basic parameters of the well-hole composite structure; the cavity-surrounding rock temperature field prediction system solves the convection law of helium in the cavity based on the received helium temperature field prediction results, and then calculates the coupled heat transfer between the cavity and the surrounding rock, ultimately realizing the accurate calculation of the well-hole-cavity-surrounding rock temperature field.

[0070] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0071] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for predicting the temperature field of a salt cavern helium storage wellbore-cavity-surrounding rock, characterized in that, include: Obtain the pressure and flow velocity distribution within the wellbore during helium injection and production; Based on the pressure and flow velocity distribution, the energy conservation equation and the heat transfer equation in the formation during helium injection and production are combined, and the above equations are differentially discretized using a fully implicit method. Combining the initial conditions and boundary conditions, the heat transfer equations of the wellbore and the formation are established in a unified tridiagonal solution matrix to achieve coupled solution of the temperature fields of the wellbore and the formation. The solution results of the wellbore and formation temperature fields are used as the boundary conditions for the calculation, and the formula is applied. The temperature field inside the cavity was calculated; where, ρ g C is the density of helium. g The specific heat capacity of helium. T f Let r be the temperature of the helium gas, and r be the distance from the formation to the center of the wellbore. h g Let be the convective heat transfer coefficient of helium. μ jT The Joule-Thomson coefficient for helium. C V,g where is the specific heat capacity of helium, and p is the pressure of helium. Through formula The temperature field of the surrounding rock of the cavity was calculated; where ρ e C is the density of the formation. e For the specific heat capacity of the formation, T e λ represents the formation temperature. e The thermal conductivity coefficient of the stratum; The acquisition of pressure and flow velocity distribution within the wellbore during helium injection and production includes: The mass conservation equation of gases and relation Combined, the pressure and flow velocity distribution within the wellbore during helium injection and production were obtained; among them, A The diameter of the wellbore. ρ g The density of helium gas. v The velocity of helium gas in the wellbore. z For wellbore depth, F w For the frictional resistance of helium flow, g It is the acceleration due to gravity. θ The inclination angle of the wellbore; The energy conservation equation during the helium injection and production operation is as follows: ;in, A The diameter of the wellbore. v The velocity of helium gas in the wellbore. z For wellbore depth, g It is the acceleration due to gravity. Q e This represents the rate of heat transfer from the formation into the wellbore. The heat transfer equation in the formation is: ;in, ρ e For the density of the formation, C e For the specific heat capacity of the formation, T e For the formation temperature, λ e The thermal conductivity coefficient of the stratum; It also includes: determining whether the temperature field converges using the following formula: in, η , γ and ω The coefficients of the equation are... T k e,1 Let K be the temperature of the cavity wall at time k. T k f Let K be the temperature of the helium gas inside the cavity at time k. T k e,2 Let K be the temperature of the surrounding rock of the first unit grid in the depth direction from the cavity wall at time k. T k-1 e,1 Let K be the temperature of the cavity wall at time k-1. ε This is the convergence error; In the formula, U hf R is the convective heat transfer coefficient of helium, r1 is the radius of the cavity wall, r0 is the cavity radius, and p k Let p be the helium pressure at time k. k-1 Let be the helium pressure at time k-1.

2. The method for predicting the temperature field of a salt cavern helium storage wellbore-cavity-surrounding rock as described in claim 1, characterized in that, The Q e Through formula Calculated; where, U we The overall heat transfer coefficient between the wellbore and the formation. T e,1 The temperature of the cavity wall.

3. The method for predicting the temperature field of a salt cavern helium storage wellbore-cavity-surrounding rock as described in claim 2, characterized in that, The U we Through formula Calculated; where, h t The convective heat transfer coefficient of the heat-collecting fluid is denoted as . r ti and r to These are the inner and outer diameters of the injection and production pipes, respectively. r oi and r oo These are the inner and outer diameters of the injection and production pipes, respectively. r ci and r co These are the inner and outer diameters of the sleeve, respectively. r ces The outer diameter of the cement ring. k w , k t , k cas and k ces These are the thermal conductivity coefficients of the annular water, the inner and outer injection / production pipes, the casing, and the cement sheath, respectively.

4. The method for predicting the temperature field of a salt cavern helium storage wellbore-cavity-surrounding rock as described in claim 1, characterized in that, The h g Through formula Calculated; where, λ g is the thermal conductivity coefficient of helium. μ g The viscosity of helium gas. τ g The internal tangential force of helium gas. v is the velocity vector of helium gas.

5. The method for predicting the temperature field of a salt cavern helium storage wellbore-cavity-surrounding rock as described in claim 4, characterized in that, The v Through formula Calculated; where, F For the gravity of helium, μ The viscosity of helium gas is given.

6. The method for predicting the temperature field of the wellbore-cavity-surrounding rock of a salt cavern helium storage facility as described in any one of claims 1-5, characterized in that, Also includes: Temperature data of the wellbore, cavity, and surrounding rock are assembled and integrated, and output in the form of cloud maps.

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