Calculation method for considering gas channeling to wellhead under hydration heat, equipment and medium

Abstract

The invention relates to the technical field of entering of formation gas into a shaft and migration in the shaft after well cementation, and discloses a calculation method, equipment and medium for gas channeling to a wellhead under the consideration of hydration heat, and the calculation method comprises the following steps: based on the hydration effect of cement paste, establishing an annulus temperature transient model during the period of waiting for setting; solving the annular temperature transient model to obtain the cement paste temperature of each position in the cement paste; determining gas physical property parameters of corresponding positions in the cement paste based on the temperature of the cement paste; establishing a mathematical model of gas channeling to a wellhead based on the physical property parameters of the gas in combination with the characteristics of cement paste; and calculating the annulus pressure value generated by the gas channeling to the wellhead through the mathematical model of the gas channeling to the wellhead. According to the method, the gas seepage velocity equation is subjected to quasi-steady-state processing and discretization and then is solved through the iteration method, the method has the advantages of being high in calculation efficiency and good in convergence effect, and the annulus pressure value can be rapidly obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of formation gas entering the wellbore and migrating in the wellbore after cementing, and in particular to a calculation method, device and medium for gas channeling to the wellhead under hydration heat. BACKGROUND

[0002] Cementing operation is known for its large investment scale, significant risk coefficient, short operation cycle, high one-time operation requirement and system complexity. Its core goal is to achieve effective interlayer isolation, thereby consolidating the construction results of drilling operation, and ultimately ensuring the safe exploitation of oil and gas resources. However, in the initial stage of the setting of the cement slurry, due to the loss of weight of the cement slurry, the pore pressure will decrease significantly. When the pore pressure is less than the formation pressure, gas is likely to invade the cement slurry matrix under the action of pressure difference, and gradually enter the annulus, forming annular pressure, which poses a serious threat to the safe exploitation of oil and gas wells. Therefore, the gas channeling prevention ability of the cement slurry is undoubtedly a key factor in evaluating the performance of the oil and gas well cement.

[0003] During the gas invasion risk time of the cement slurry, gas has a high possibility of seepage in the cement slurry matrix driven by the pressure difference between the top and bottom, and then gradually migrates to the low pressure layer. When the gas successfully invades the cement slurry matrix, it has a high possibility of rising to the wellhead due to the buoyancy of the liquid cement slurry. However, considering the continuous release of heat during the hydration process of the cement slurry during the waiting-on-cement period, this will cause the temperature inside the matrix to rise, thereby affecting the hydration reaction process of the cement slurry. At the same time, the change in temperature will also have a significant impact on the physical properties of the gas, such as viscosity. Therefore, the process of gas rising to the wellhead cannot be simply regarded as a steady-state process. On the contrary, the interaction between the annulus temperature and the hydration of the cement slurry during the waiting-on-cement period must be fully considered, and the comprehensive influence of temperature on the hydration performance of the cement slurry and the annular gas must be analyzed to obtain the annular pressure value formed by the gas channeling to the wellhead under actual working conditions, so as to truly and accurately evaluate the gas channeling prevention ability of the cement slurry.

[0004] At present, there is relatively little numerical simulation research on the annular pressure phenomenon caused by gas channeling to the wellhead under the condition of hydration heat of the cement slurry. Existing research mainly focuses on the influence analysis of the hydration performance of the cement slurry during the waiting-on-cement period on the annular pressure after the gas channeling to the wellhead. In the article "Research on Key Performance and Evaluation Method of Gas Channeling Prevention Ability of Cement Slurry", a mathematical model of gas channeling to the wellhead is established, and a sensitivity factor analysis is carried out based on the hydration performance of the cement slurry. However, when dealing with the temperature change in the hydration process of the cement slurry and its influence on the physical properties of the annular gas, these parameters are usually solved by approximating them as constants. This makes it difficult to accurately and effectively apply the model to actual situations. SUMMARY

[0005] The application provides a calculation method, device and medium for gas channeling to a wellhead under hydration heat, which is based on hydration of cement slurry, and an annular space temperature transient model during cement slurry setting is established, so that the temperature distribution inside the cement slurry can be accurately obtained, the influence of temperature on gas physical parameters is further considered, and a mathematical model for gas channeling to the wellhead is established in combination with cement slurry characteristics, such as static gel strength transition time and other data, and the annular space pressure distribution characteristics during cement slurry setting are obtained.

[0006] The application is achieved by the following technical solutions.

[0007] A calculation method for gas channeling to a wellhead under hydration heat, comprising:

[0008] A transient annular space temperature model during cement slurry setting is established based on hydration of the cement slurry;

[0009] The transient annular space temperature model is solved to obtain the cement slurry temperature at each position inside the cement slurry;

[0010] Gas physical parameters at the corresponding position inside the cement slurry are determined based on the cement slurry temperature;

[0011] A mathematical model for gas channeling to the wellhead is established based on the gas physical parameters in combination with cement slurry characteristics;

[0012] The annular space pressure value generated by gas channeling to the wellhead is calculated through the mathematical model for gas channeling to the wellhead.

[0013] As optimization, the transient annular space temperature model is specifically:

[0014]

[0015] wherein, T c is the cement slurry temperature; r w is the wellbore radius; U a is the total heat transfer coefficient between the annular space and the bottom layer; c c is the specific heat capacity of the cement slurry; p c is the density of the cement slurry; A a is the annular space cross-sectional area; T e is the formation temperature; r c is the casing radius; U c is the total heat transfer coefficient between the casing and the annular space; A c is the casing cross-sectional area; Q ∞ is the final hydration heat of the cement slurry; and a is the hydration degree, T fis the formation temperature at the jth axial grid position at the nth time step.

[0016] In some embodiments, the specific process of solving the annulus temperature transient model to obtain the cement slurry temperature at each position inside the cement slurry is as follows:

[0017] The spatial step size Ah and the time step size At of the wellbore axial direction are determined according to the length of the wellbore cementing section, and the number of axial grids and time grids are divided respectively, and the number of axial grids is J and the number of time grids is N;

[0018] The annulus temperature transient model is discretized, and the finite difference method is applied to solve the annulus temperature transient model to obtain the cement slurry temperature at each position inside the cement slurry, and the specific expression of the cement slurry temperature at each position inside the cement slurry is as follows:

[0019]

[0020] wherein, is the cement slurry temperature at the jth axial grid position at the n+1th time step; j ∈ [1, J], n ∈ [1, N-1], is the cement slurry temperature at the jth axial grid position at the nth time step; is the formation temperature at the jth axial grid position at the nth time step; is the casing temperature at the jth axial grid position at the nth time step; is the hydration degree at the jth axial grid position at the n+1th time step; is the hydration degree at the jth axial grid position at the nth time step. is the hydration degree at the jth axial grid position at the nth time step.

[0021] In some embodiments, the gas physical property parameters include gas viscosity and gas compressibility factor, and the formula of the gas viscosity is as follows:

[0022]

[0023] wherein, μ is the gas viscosity; M g is the molar mass, and p is the density of the gas;

[0024] The specific formula of the gas compressibility factor is as follows:

[0025]

[0026] wherein, Z is the gas compressibility factor; p r is the apparent contrast pressure; T r is the apparent contrast temperature; p r is the apparent contrast density.

[0027] In some embodiments, based on the gas property parameters and cement slurry characteristics, the specific process of establishing a mathematical model of gas channeling to the wellhead is as follows:

[0028] Based on the gas viscosity and gas compressibility factor, the seepage velocity q of the gas in the cement slurry matrix is calculated c ;

[0029] Based on the influence of the transient temperature of the cement slurry on the gas viscosity, N time steps and J space steps are divided, and the seepage velocity q c is discretized and solved to obtain a discrete gas seepage rate;

[0030] The real gas state equation of the annulus top gas column in N time steps is obtained;

[0031] The drilling fluid compression amount in N time steps is obtained;

[0032] According to the discrete gas seepage rate, the real gas state equation, and the drilling fluid compression amount, a channeling to the wellhead mathematical model is obtained.

[0033] In some embodiments, the specific expression of the seepage velocity q of the gas in the cement slurry matrix is as follows: c

[0034]

[0035] Wherein, q c is the seepage velocity of the gas in the cement slurry matrix; C is a correction coefficient; k is the cement slurry permeability; p g is the gas layer pressure; p c is the top pressure of the cement slurry; T sc is the gas temperature under standard conditions; p sc is the gas pressure under standard conditions; L c is the length of the wellbore cementing section.

[0036] In some embodiments, the specific formula of the discrete gas seepage rate at time N is as follows:

[0037]

[0038] Wherein, n ∈ [1, N-1], is the gas seepage rate at time n+1; k n+1 is the cement slurry permeability at time n+1; is the cement slurry matrix pore pressure at position j at time n+1, is the cement slurry matrix pore pressure at position j-1 at time n+1; is the gas viscosity at position j at time n+1; ​Let Δh be the gas compressibility factor at position j at time n+1, Δh represent the spatial step size along the wellbore axis, and L represent the axial length of the wellbore. c This represents the height of the cement grout column.

[0039] In some embodiments, the real gas equation of state for the annular top column within the N time steps is specifically expressed as:

[0040]

[0041] Where, n∈[1,N-1], Let n be the amount of gas at the wellhead at time n; R is the increase in the amount of gas at the wellhead at time n+1; R is the universal gas constant; T wh This refers to the wellhead temperature. Let n be the annular pressure at time n+1; Let be the volume of gas at the wellhead at time n; This represents the increase in wellhead gas volume at time n+1.

[0042] In some embodiments, the increase in the amount of gas at the wellhead at time n+1 The specific formula is:

[0043]

[0044] in, Let Δt represent the gas seepage rate at time n+1, and Δt be the time step.

[0045] In some embodiments, the specific expression for the drilling fluid compression amount within N time steps is:

[0046]

[0047] Where, n∈[1,N-1], This represents the amount of drilling fluid compressed at time n+1. c represents the compressed volume of drilling fluid at time n+1. m Indicates the compressibility coefficient of the drilling fluid; This represents the volume of drilling fluid compressed at time n. This represents the annular pressure at time n.

[0048] In some embodiments, the mathematical model for reaching the wellhead is:

[0049]

[0050] in, This represents the annular pressure at time n+1; c represents the annular pressure at time n; mT represents the drilling fluid compressibility coefficient; R is the universal gas constant; T wh is the wellhead temperature; Z is the gas compressibility factor; represents the gas seepage rate at time t; Δt is the time step; T sc The gas temperature under standard conditions; This represents the volume of the air column at the nth time step. This represents the volume of drilling fluid at the nth time step. The total number of gas moles passing through the top of the cement column within n time steps. This represents the gas seepage rate at the i-th time step. Let be the pressure at the top of the cement slurry at the i-th time step. At the i-th time step, the gas is under pressure and temperature T c Under certain conditions, the compressibility factor, T c The temperature of the cement slurry; For the gas at time step n+1, the pressure and temperature T wh Compression factor under certain conditions.

[0051] The present invention also discloses an electronic device, including at least one processor and a memory communicatively connected to the at least one 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 a calculation method considering gas leakage to the wellhead under the aforementioned heat of hydration.

[0052] The present invention also discloses a storage medium storing a computer program, which, when executed by a processor, implements the aforementioned calculation method considering gas migration to the wellhead under the heat of hydration.

[0053] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0054] (1) Based on an in-depth study of the cement slurry hydration process, this invention fully considers the influence of annular temperature on the physical properties of the gas. By incorporating these influencing factors into the calculation conditions, this invention makes the simulation process closer to actual engineering conditions, thereby ensuring that the simulation results have higher feasibility and accuracy.

[0055] (2) The present invention performs quasi-steady-state processing on the gas seepage velocity equation, and solves iteratively after discretization. It has the characteristics of high computational efficiency and good convergence effect, and can obtain the annular pressure value (annular pressure value) relatively quickly. Attached Figure Description

[0056] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0057] Figure 1 This is a flowchart illustrating the method.

[0058] Figure 2 A schematic diagram showing gas leaking into the wellhead;

[0059] Figure 3 The annular pressure values ​​are given under conditions considering and not considering the heat release of hydration in this invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0061] First, this invention obtains the basic performance parameters of cement slurry during the curing period, the actual wellbore structural dimensions, and the physical properties of the annular gas based on field cementing construction data. Based on the principle of energy conservation and the theory of heat exchange within the wellbore, and considering the heat exchange mechanism between the annular cement slurry and the casing wall and wellbore wall in the radial direction during the curing period, as well as the heat release during cement slurry hydration, a transient annular temperature model is established. The finite difference method is used to solve this mathematical model, determining initial and boundary conditions, dividing the data into cells, discretizing the equations, and using an iterative method to obtain the temperature distribution characteristics inside the cement slurry during the curing period. Further considering the influence of annular temperature on the physical properties of the gas, a mathematical model of gas migration to the wellhead is established by combining the real gas state equation and the gas seepage rate calculation equation. Taking into account the influence of formation temperature at different depths on the initial temperature of the cement slurry and the differences in hydration rates, the model is discretized, and an iterative method is used to obtain the annular pressure under actual working conditions.

[0062] like Figure 1 As shown, in one embodiment, the present invention provides a calculation method considering gas migration to the wellhead under the heat of hydration, comprising:

[0063] S1. Based on the hydration of cement paste, a transient model of the annular temperature during the setting period is established; this transient model of the annular temperature is... Figure 1 The annular cement slurry heat conduction model.

[0064] The specific steps are as follows:

[0065] Initial condition assignment: Based on the actual wellbore structure and casing size data, input the wellbore size, casing size, and cemented section depth for each well opening (actual wellbore structure dimensions); simultaneously, determine the density of drilling fluid and cement slurry, as well as the parameters required for calculating cement slurry permeability, static cementitious strength, porosity, and hydration degree (basic performance parameters of cement slurry); in addition, provide the downhole temperature, wellhead temperature, formation pressure, and thermophysical parameters of each component (physical property parameters of annular gas).

[0066] (1) Based on the principle of energy conservation and the theory of heat exchange inside the wellbore during the condensation period, the factors affecting the annular temperature are: ① heat exchange between the radial annulus and the casing wall and the well wall; ② heat release during cement slurry hydration; ③ changes in the internal energy of the annular cement slurry itself.

[0067] Therefore, the annular temperature transient model is as follows:

[0068]

[0069] Among them, T c r represents the temperature of the cement slurry. w U is the radius of the wellbore; a c is the overall heat transfer coefficient between the annulus and the bottom layer; c ρ is the specific heat capacity of cement slurry; c Density of cement paste; A a T is the cross-sectional area of ​​the annulus. e Formation temperature; r c U is the radius of the casing; c A is the overall heat transfer coefficient between the casing and the annulus; c Q is the cross-sectional area of ​​the casing; ∞ α represents the final heat of hydration of the cement paste; α represents the degree of hydration, T f The temperature of the interfacial formation.

[0070] S2. Solve the annular temperature transient model to obtain the cement slurry temperature at various locations within the cement slurry. Specifically, set the initial cement slurry temperature as the formation temperature, and use the finite difference method to solve the discretized annular temperature transient model to obtain the temperature distribution within the cement slurry mass during the setting period. Here, the cement slurry temperature at each location within the cement slurry is... Figure 1 The discretized heat transfer model in the model.

[0071] In some embodiments, the specific process of solving the annular temperature transient model to obtain the cement slurry temperature at various locations inside the cement slurry is as follows:

[0072] The spatial step Δh and time step Δt of the wellbore axial direction are determined based on the length of the wellbore sealing section, and the number of axial grids and time grids are divided respectively. Let the number of axial grids be J and the number of time grids be N; one grid corresponds to one step am.

[0073] The annular temperature transient model is discretized, with the initial temperature of the cement slurry set as the formation temperature. The finite difference method is then used to solve the annular temperature transient model to obtain the cement slurry temperature at various locations within the cement slurry. The specific representation of the cement slurry temperature at each location within the cement slurry is as follows:

[0074]

[0075] in, Let J be the temperature of the cement slurry at the j-th axial grid position at time n+1; j∈[1, J], n∈[1, N-1]. Let be the temperature of the cement slurry at the j-th axial grid position at time n; Let be the formation temperature at the j-th axial grid position at time n; Let be the temperature inside the casing at the j-th axial grid position at time n; The degree of hydration at the j-th axial grid position at time n+1; Let be the degree of hydration at the j-th axial grid position at time n.

[0076] S3. Determine the gas physical property parameters at the corresponding location inside the cement slurry based on the temperature of the cement slurry;

[0077] In some embodiments, the gas physical properties include gas viscosity and gas compressibility factor.

[0078] The gas viscosity in the annulus is determined based on the transient temperature of the cement slurry. Specifically, the Lee-Gonzalez-Eakin method is used to determine the gas viscosity, and the formula for the gas viscosity is as follows:

[0079]

[0080] Where μ is the gas viscosity; M g Let ρ be the molar mass of the gas, and ρ be the density of the gas.

[0081] The compressibility factor of the annular gas is calculated based on the transient temperature of the cement slurry. Specifically, the formula for the gas compressibility factor is as follows:

[0082]

[0083] Where Z is the gas compressibility factor; p r For visual contrast pressure; T r For apparent contrast temperature; ρ rFor apparent contrast density.

[0084] S4. Based on the gas physical properties and cement slurry characteristics, establish a mathematical model for gas migration to the wellhead;

[0085] In some embodiments, the specific process of establishing a mathematical model for gas migration to the wellhead based on the gas physical properties and cement slurry characteristics is as follows:

[0086] S4.1 Calculate the gas seepage velocity qx within the cement paste matrix based on the gas viscosity and gas compressibility factor; specifically, the gas seepage velocity q... c That is Figure 1 A calculation model for the seepage velocity of gas in cement slurry matrix.

[0087] In some embodiments, the gas seepage velocity q within the cement paste matrix c The specific expression is:

[0088]

[0089] Where, q c ρ is the gas permeation rate within the cement paste matrix; C is the correction factor; k is the cement paste permeability; p g p is the gas layer pressure; c The pressure at the top of the cement grout; T sc p represents the gas temperature under standard conditions. sc L represents the gas pressure under standard conditions. c This refers to the length of the wellbore sealing section.

[0090] S4.2 Based on the influence of the transient temperature of cement slurry on the viscosity of gas, divide the flow rate into N time steps and J spatial steps, and discretize the flow rate to obtain the discrete gas flow rate.

[0091] In some embodiments, considering the influence of the transient temperature of the cement slurry on the gas viscosity, the gas seepage velocity calculation model is discretized, dividing it into N time steps and J spatial steps (where N and J represent the same meaning as the number of time grids being N and the number of axial grids being J), simplifying the transient process into a quasi-steady-state process for solution. The specific formula for the discrete gas seepage rate within time N is as follows:

[0092]

[0093] Where, n∈[1,N-1], k is the gas seepage rate at time n+1; n+1 Let n be the cement slurry permeability at time n+1; Let be the pore pressure of the cement paste matrix at position j at time n+1. The pore pressure of the cement paste matrix at position j-1 at time n+1; Let J be the gas viscosity at position j at time n+1; Let Δh be the gas compressibility factor at position j at time n+1, Δh represent the spatial step size along the wellbore axis, and L represent the axial length of the wellbore. c This refers to the length of the wellbore sealing section, i.e., the height of the cement slurry column.

[0094] S4.3 Obtain the real gas state equations for the annular top column within N time steps;

[0095] In some embodiments, the real gas equation of state for the annular top column within the N time steps is specifically expressed as:

[0096]

[0097] Where, n∈[1,N-1], Let n be the amount of gas at the wellhead at time n; R is the increase in the amount of gas at the wellhead at time n+1; R is the universal gas constant; T wh This refers to the wellhead temperature. Let n be the annular pressure at time n+1; Let be the volume of gas at the wellhead at time n; This represents the increase in wellhead gas volume at time n+1.

[0098] S4.4 Obtain the drilling fluid compression within N time steps;

[0099] In some embodiments, the specific expression for the drilling fluid compression amount within N time steps is:

[0100]

[0101] Where, n∈[1,N-1], This represents the amount of drilling fluid compressed at time n+1. c represents the compressed volume of drilling fluid at time n+1. m Indicates the compressibility coefficient of the drilling fluid; This represents the volume of drilling fluid compressed at time n. This represents the annular pressure at time n.

[0102] Based on the above theory, the amount of gas that leaks to the wellhead (the increase in the amount of gas at the wellhead) can be calculated as follows:

[0103]

[0104] in, Let n+1 be the increase in the amount of gas at the wellhead. Let Δt represent the gas seepage rate at time n+1, and Δt be the time step.

[0105] S4.5. Based on the discrete gas seepage rate, the real gas state equation, and the drilling fluid compression, a mathematical model for the gas flowing to the wellhead is obtained.

[0106] In some embodiments, the mathematical model for reaching the wellhead is:

[0107]

[0108] in, This represents the annular pressure at time n+1; c represents the annular pressure at time n; m T represents the drilling fluid compressibility coefficient; R is the universal gas constant; T wh is the wellhead temperature; Z is the gas compressibility factor; Δt is the time step; T sc The gas temperature under standard conditions; This represents the volume of the air column at the nth time step. This represents the drilling fluid volume at the nth time step. The total number of gas moles passing through the top of the cement column within n time steps. This represents the gas seepage rate at the i-th time step. Let be the pressure at the top of the cement slurry at the i-th time step. At the i-th time step, the gas is under pressure and temperature T c Under certain conditions, the compressibility factor, T c The temperature of the cement slurry; For the gas at time step n+1, the pressure and temperature T wh Compression factor under certain conditions.

[0109] S5. Calculate the annular pressure value generated by gas leakage to the wellhead using the mathematical model of gas leakage to the wellhead.

[0110] When calculating the annular pressure value (annular zone pressure value) at the wellhead, it is calculated iteratively based on the time grid and the spatial grid. When gas channeling has not ended, it is iterated along the time and axial space until the gas channeling ends. At this time, the annular pressure value at the wellhead is the final annular pressure value.

[0111] The present invention will be further described in detail below using a high-pressure gas well as an example, in conjunction with the accompanying drawings. However, the present invention is not limited to the following example.

[0112] A calculation method considering gas migration to the wellhead under the heat of hydration includes the following steps:

[0113] (1) Based on the cementing design and geological design, the properties of the cement slurry and annular working fluid, surface temperature, formation temperature, and wellbore structure were obtained. The well depth is 5087m, and the drilling fluid density is 2.32g / cm³. 3 The drilling fluid compressibility coefficient is 1.0e-6 / psi, and the cement slurry density is 2.35 g / cm³. 3 The formation pressure and temperature are 85 MPa and 128℃, respectively. The wellhead and top cement slurry column temperatures are 23.4℃ and 112℃, respectively. The wellbore diameter is 0.1524m, the casing diameter is 0.1197m, the casing wall thickness is 12.7mm, the drilling depth is 5087m, the cemented section is 4400m~5085m, and the cemented section length is 685m.

[0114] (2) Determine the axial direction and time step, with an axial step of 30m and a time step of 1min;

[0115] (3) Based on the annular temperature transient model established above, the transient temperature of the cement slurry matrix and the gas viscosity are obtained;

[0116] (4) Using axial node j as the outer circulation condition and time node n as the inner circulation condition, the hydration degree, transient temperature and seepage equation of each part of the cement slurry along the axial direction are discretized.

[0117] (5) Obtain the degree of hydration at time node n and spatial node j based on the on-site construction data, and obtain the cement slurry temperature distribution by combining the transient annular temperature model, and solve for the annular gas viscosity. As the gas continuously rises to the wellhead, the annular pressure increases. When the sum of the annular pressure and the drilling fluid hydrostatic pressure exceeds the formation pressure, circulation stops.

[0118] (6) Obtain the annular pressure value of gas reaching the wellhead.

[0119] This method is used to obtain the pressurized annulus zone at the wellhead under conditions of hydration release, such as... Figure 3 As shown, comparing the annular pressure obtained by this scheme considering the heat release condition of hydration with that without considering the heat release condition of hydration, it can be seen that the gas reaches the wellhead earlier under the condition of considering the heat release condition of cement slurry hydration than under the condition without considering the heat release condition of hydration, and the annular pressure is lower than that under the condition without considering the heat release condition of hydration. Therefore, if the original formation temperature is used as a condition to calculate the annular pressure of gas reaching the wellhead, this temperature is lower than the actual cement slurry matrix temperature, which will cause a large error in the calculation of the annular pressure. If the annular pressure is calculated under the condition of considering the heat release condition of cement slurry hydration, this temperature condition meets the downhole operating conditions and the annular pressure under the actual operating conditions is obtained.

[0120] In summary, this invention considers the influence of the heat of hydration during the cement slurry setting period on gas seepage, establishes a gas migration model to the wellhead, determines the boundary conditions of the model, and solves for the gas migration annular pressure at the wellhead.

[0121] In some embodiments, an electronic device is also disclosed, including at least one processor and a memory communicatively connected to the at least one 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 a calculation method considering gas leakage to the wellhead under the heat of hydration as described above.

[0122] In some embodiments, a storage medium is also disclosed storing a computer program that, when executed by a processor, implements the aforementioned calculation method considering gas migration to the wellhead under hydration heat.

[0123] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A calculation method considering gas migration to the wellhead under the heat of hydration, characterized in that, include: Based on the hydration of cement slurry, a transient model of annular temperature during the setting period was established. Solve the annular temperature transient model to obtain the cement slurry temperature at various locations inside the cement slurry; The gas physical properties of the corresponding location inside the cement slurry are determined based on the temperature of the cement slurry. Based on the gas physical properties and cement slurry characteristics, a mathematical model for gas migration to the wellhead is established. The annular pressure value generated by gas leakage to the wellhead is calculated using the mathematical model described above.

2. The calculation method for considering gas migration to the wellhead under the heat of hydration as described in claim 1, characterized in that, The specific transient model of annular temperature is as follows: Among them, T c r represents the temperature of the cement slurry. w U is the radius of the wellbore; a c is the overall heat transfer coefficient between the annulus and the formation; c ρ is the specific heat capacity of cement slurry; c Density of cement paste; A a T is the cross-sectional area of ​​the annulus. e Temperature at the wellbore-formation interface; r c U is the radius of the casing; c A is the overall heat transfer coefficient between the casing and the annulus; c Q is the cross-sectional area of ​​the casing; ∞ α represents the final heat of hydration of the cement paste; α represents the degree of hydration, T f The temperature of the interfacial formation.

3. The calculation method for considering gas migration to the wellhead under the heat of hydration as described in claim 2, characterized in that, The specific process of solving the annular temperature transient model to obtain the cement slurry temperature at various locations inside the cement slurry is as follows: The spatial step Δh and time step Δt of the wellbore axis are determined based on the length of the wellbore sealing section, and the number of axial grids and time grids are divided respectively. Let the number of axial grids be J and the number of time grids be N. The annular temperature transient model is discretized, and the finite difference method is applied to solve the annular temperature transient model to obtain the cement slurry temperature at each location inside the cement slurry. The specific expression of the cement slurry temperature at each location inside the cement slurry is as follows: in, Let J be the temperature of the cement slurry at the j-th axial grid position at time n+1; j∈[1, J], n∈[1, N-1]. Let be the temperature of the cement slurry at the j-th axial grid position at time n; Let be the formation temperature at the j-th axial grid position at time n; Let be the temperature inside the casing at the j-th axial grid position at time n; The degree of hydration at the j-th axial grid position at time n+1; Let be the degree of hydration at the j-th axial grid position at time n.

4. The calculation method for considering gas migration to the wellhead under the heat of hydration as described in claim 3, characterized in that, The gas physical properties include gas viscosity and gas compressibility factor, and the formula for gas viscosity is: Where μ is the gas viscosity; M g Here, ρ is the molar mass, and ρ is the density of the gas. The specific formula for the gas compressibility factor is as follows: Where Z is the gas compressibility factor; p r For visual contrast pressure; T r For apparent contrast temperature; ρ r For apparent contrast density.

5. The calculation method for considering gas migration to the wellhead under the heat of hydration as described in claim 4, characterized in that, The specific process of establishing a mathematical model for gas migration to the wellhead based on the aforementioned gas physical properties and cement slurry characteristics is as follows: The gas seepage velocity q in the cement paste matrix is ​​calculated based on the gas viscosity and gas compressibility factor. c ; Based on the influence of cement slurry transient temperature on gas viscosity, N time steps and J spatial steps are defined to measure the seepage velocity q. c Discretization is performed to obtain discrete gas percolation rates; Obtain the real gas equation of state for the annular top column within N time steps; Obtain the drilling fluid compression within N time steps; A mathematical model for the gas flow to the wellhead is obtained based on discrete gas flow rates, the real gas equation of state, and drilling fluid compressibility.

6. The calculation method for considering gas migration to the wellhead under the heat of hydration as described in claim 5, characterized in that, The gas seepage velocity q in the cement paste matrix c The specific expression is: Where, q c ρ is the gas permeation rate within the cement paste matrix; C is the correction factor; k is the cement paste permeability; p g p is the gas layer pressure; c The pressure at the top of the cement grout; T sc p represents the gas temperature under standard conditions. sc L represents the gas pressure under standard conditions. c This refers to the length of the wellbore sealing section.

7. The calculation method for considering gas migration to the wellhead under the heat of hydration as described in claim 6, characterized in that, The specific formula for the discrete gas seepage rate at time N is: Where, n∈[1,N-1], k is the gas seepage rate at time n+1; n+1 Let n be the cement slurry permeability at time n+1; Let be the pore pressure of the cement paste matrix at position j at time n+1. The pore pressure of the cement paste matrix at position j-1 at time n+1; Let J be the gas viscosity at position j at time n+1; Let Δh be the gas compressibility factor at position j at time n+1, Δh represent the spatial step size along the wellbore axis, and L represent the axial length of the wellbore. c This refers to the length of the wellbore sealing section.

8. The calculation method for considering gas migration to the wellhead under the heat of hydration as described in claim 7, characterized in that, The real gas state equation for the annular top column within the N time steps is specifically expressed as follows: Where, n∈[1,N-1], Let n be the amount of gas at the wellhead at time n; R is the increase in the amount of gas at the wellhead at time n+1; R is the universal gas constant; T wh The wellhead temperature; The annular pressure at time n+1; Let be the volume of gas at the wellhead at time n; This represents the increase in wellhead gas volume at time n+1.

9. The calculation method for considering gas migration to the wellhead under the heat of hydration as described in claim 8, characterized in that, The increase in the amount of gas at the wellhead at time n+1 The specific formula is: in, Let Δt represent the gas seepage rate at time n+1, and Δt be the time step.

10. The calculation method for considering gas migration to the wellhead under the heat of hydration as described in claim 9, characterized in that, The specific expression for the drilling fluid compression rate within N time steps is: Where, n∈[1,N-1], This represents the amount of drilling fluid compressed at time n+1. c represents the volume of drilling fluid compressed at time n+1. m Indicates the compressibility coefficient of the drilling fluid; This represents the volume of drilling fluid compressed at time n. This represents the annular pressure at time n.

11. The calculation method for considering gas migration to the wellhead under the heat of hydration as described in claim 10, characterized in that, The mathematical model for the wellhead traversal is as follows: in, This represents the annular pressure at time n+1; Represents the annular pressure at time n; represents c. m T represents the drilling fluid compressibility coefficient; R is the universal gas constant; T wh Z is the wellhead temperature; Z is the gas compressibility factor; represents the gas seepage rate at time t; Δt is the time step; T sc The gas temperature under standard conditions; This represents the volume of the air column at the nth time step. This represents the drilling fluid volume at the nth time step. The total number of gas moles passing through the top of the cement column within n time steps. This represents the gas seepage rate at the i-th time step. Let be the pressure at the top of the cement slurry at the i-th time step. At the i-th time step, the gas is under pressure and temperature T c Under certain conditions, the compressibility factor, T c The temperature of the cement slurry; For the gas at time step n+1, the pressure and temperature T wh Compression factor under certain conditions.

12. An electronic device, characterized in that, It includes at least one processor and a memory communicatively connected to the at least one 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 a calculation method for considering gas migration to the wellhead under the heat of hydration as described in any one of claims 1 to 11.

13. A storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements a calculation method for gas migration to the wellhead under the heat of hydration, as described in any one of claims 1 to 11.

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