Annulus pressure calculation method and device, medium, equipment and product

Abstract

The invention relates to the technical field of annulus pressure calculation, in particular to an annulus pressure calculation method and device, a medium, equipment and a product, and the method comprises the steps: obtaining the temperatures of different depth points of cement paste; determining gas physical property parameters of different depth points through a gas physical property expression based on the temperatures of the different depth points of the cement paste; discretizing the seepage equation based on a preset axial node and a preset time node; a preset axial node is used as an outer circulation condition, a preset time node is used as an inner circulation condition, iterative calculation is conducted on the discrete seepage equation, and an annulus belt pressure value is obtained; the influence of the temperatures of different depth points of the cement paste on gas physical property parameters is fully considered, so that the simulation process is closer to actual conditions, the calculation efficiency is improved, and the annulus pressure value can be quickly obtained.

Description

Technical Field

[0001] This invention relates to the field of annular pressure calculation technology, and particularly to an annular pressure calculation method, apparatus, medium, equipment and product. Background Technology

[0002] Cementing is characterized by high investment, high risk, short operation time, one-time operation, and strong systematic nature. Its main purpose is to effectively isolate layers, consolidate drilling achievements, and ensure the safe extraction of oil and gas resources. However, in the early stages of cement slurry solidification, the pore pressure decreases due to weight loss. Under the influence of pressure differential, gas can penetrate the cement slurry matrix and then enter the annulus, causing annular pressure and adversely affecting the safe extraction of oil and gas wells. Therefore, the anti-gas channeling capability of cement slurry during the solidification period is an important factor affecting the evaluation of cement in oil and gas wells. The technical problem of how to calculate annular pressure exists in this field. Summary of the Invention

[0003] This invention provides a method, apparatus, medium, equipment, and product for calculating annular pressure, solving the technical problem of how to calculate annular pressure.

[0004] In a first aspect, the present invention provides a method for calculating annular pressure, the method comprising: obtaining the temperature at different depths of cement slurry; determining the gas property parameters at different depths based on the temperature at different depths of cement slurry through gas property expressions; discretizing the seepage equation based on preset axial nodes and time nodes; and iteratively calculating the discrete seepage equation using preset axial nodes as external circulation conditions and preset time nodes as internal circulation conditions to obtain the annular pressure value.

[0005] In some embodiments, the method further includes stopping the iteration when the sum of the iteratively calculated annular zone pressure and the drilling fluid hydrostatic column pressure is greater than the gas layer pressure.

[0006] In some embodiments, the gas physical properties include: gas viscosity; the gas physical properties at different depths are determined by gas physical property expressions based on the temperature at different depths of the cement slurry, including: obtaining the gas viscosity at different depths based on the cement slurry temperature, gas density, and molar mass by gas viscosity expressions.

[0007] In some embodiments, the gas physical property parameters include: gas compressibility factor; the gas physical property parameters at different depths are determined by gas physical property expressions based on the temperature at different depths of the cement slurry, including: obtaining the gas compressibility factor at different depths based on the apparent contrast temperature, apparent contrast density, and apparent contrast pressure through the gas compressibility factor expression.

[0008] In some embodiments, the number of axial nodes and the number of time nodes are determined based on the length of the cement grout sealing section, a preset time, and a preset step size.

[0009] In some embodiments, the step of iteratively calculating the discrete seepage equation to obtain the annular pressure value includes: obtaining a gas migration model to the wellhead based on the discrete seepage equation; and solving the gas migration model to obtain the annular pressure.

[0010] Secondly, the present invention provides an annular pressure calculation device, comprising: a temperature acquisition module for acquiring the temperature at different depths of cement slurry; a property acquisition module for determining the gas property parameters at different depths based on the temperature at different depths of cement slurry using gas property expressions; a model construction module for discretizing the seepage equation based on preset axial nodes and time nodes; and a pressure calculation module for iteratively calculating the discrete seepage equation using preset axial nodes as the outer circulation condition and preset time nodes as the inner circulation condition to obtain the annular pressure value.

[0011] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, comprises the steps of the annular pressure calculation method of any of the above aspects.

[0012] Fourthly, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the annular pressure calculation method according to any of the above aspects.

[0013] Fifthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the annular pressure calculation method according to any of the above aspects.

[0014] This invention provides a method, apparatus, medium, equipment, and product for calculating annular pressure. The method includes: obtaining the temperature at different depths of cement slurry; determining the gas property parameters at different depths based on the temperature of the cement slurry using gas property expressions; discretizing the seepage equation based on preset axial nodes and time nodes; iteratively calculating the discretized seepage equation using preset axial nodes as external circulation conditions and preset time nodes as internal circulation conditions to obtain the annular pressure value; fully considering the influence of the temperature at different depths of cement slurry on the gas property parameters, making the simulation process closer to actual conditions; the discretization and iterative calculation of the seepage equation improves the calculation efficiency and enables rapid acquisition of the annular pressure value. Attached Figure Description

[0015] The invention will now be described in more detail with reference to embodiments and the accompanying drawings:

[0016] Figure 1 This is a flowchart illustrating a method for calculating annular pressure according to an embodiment of this application;

[0017] Figure 2 This is a schematic diagram of the structure of an annular pressure calculation device provided in an embodiment of this application;

[0018] Figure 3 This is a flowchart illustrating a method for calculating gas leakage to the wellhead considering the temperature at different depths of cement slurry, as provided in an embodiment of this application.

[0019] Figure 4 This is a schematic diagram illustrating gas leakage to the wellhead, provided in an embodiment of this application.

[0020] Figure 5 This is a schematic diagram of the gas compressibility factor at different depths of cement slurry provided in an embodiment of this application;

[0021] Figure 6 This is a schematic diagram of gas viscosity at different depths of cement slurry provided in an embodiment of this application;

[0022] Figure 7 This is a schematic diagram of an annular pressure under the consideration of simultaneous gas intrusion of cement slurry with different permeabilities, provided by an embodiment of this application;

[0023] Figure 8 This is a schematic diagram of annular pressure under different gas intrusion times provided in an embodiment of this application.

[0024] In the accompanying drawings, the same parts are referred to by the same reference numerals, and the drawings are not drawn to scale. Detailed Implementation

[0025] To enable those skilled in the art to better understand the present invention and to fully understand and implement the process of how the present invention uses technical means to solve technical problems and achieve corresponding technical effects, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. The embodiments of the present invention and the various features therein can be combined with each other without conflict, and the resulting technical solutions are all within the protection scope of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0026] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0027] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0028] Cementing is characterized by high investment, high risk, short operation time, one-time operation, and strong systematic nature. Its main purpose is to effectively isolate layers, consolidate drilling achievements, and ensure the safe extraction of oil and gas resources. However, in the early stages of cement slurry solidification, the pore pressure decreases due to weight loss. Under the influence of pressure differential, gas can penetrate the cement slurry matrix and then enter the annulus, causing annular pressure and adversely affecting the safe extraction of oil and gas wells. Therefore, the anti-gas channeling capability of cement slurry during the solidification period is an important factor affecting the evaluation of cement in oil and gas wells. The technical problem of how to calculate annular pressure exists in this field.

[0029] The technical solution of this application will be described below with reference to specific embodiments.

[0030] Example One

[0031] Figure 1 This is a flowchart illustrating a method for calculating annular pressure according to an embodiment of this application, as shown below. Figure 1 As shown, in the technical solution of this embodiment, an annular pressure calculation method is provided. The method includes: obtaining the temperature at different depths of cement slurry; determining the gas property parameters at different depths based on the temperature at different depths of cement slurry through gas property expressions; discretizing the seepage equation based on preset axial nodes and time nodes; iteratively calculating the discrete seepage equation with preset axial nodes as external circulation conditions and preset time nodes as internal circulation conditions to obtain the annular pressure value.

[0032] In annular pressure detection during oil drilling cementing, the accurate calculation of annular pressure values ​​is a challenge. Existing technologies struggle to accurately account for the influence of cement slurry temperatures at different depths on gas properties, leading to inaccurate annular pressure calculations. This embodiment addresses this issue by first acquiring the temperatures of the cement slurry at different depths, achieved through wellbore structure design and on-site measurements. Then, based on these temperatures, gas properties at different depths are determined using the gas property expressions described later, including gas viscosity and compressibility factor. Next, the flow equation is discretized based on preset axial and time nodes. The number of time and axial grids is determined, simplifying the transient process into a quasi-steady-state process for solution. Finally, using preset axial nodes as the outer circulation condition and preset time nodes as the inner circulation condition, the discrete flow equation is iteratively calculated to obtain the annular pressure value. This approach fully considers the influence of cement slurry temperatures at different depths on gas properties, making the simulation process more closely resemble actual conditions. Discretization and iterative calculation of the seepage equation improve computational efficiency and enable rapid acquisition of annular pressure values. For example, in practical cementing projects, accurate calculation of annular pressure values ​​allows for better evaluation of the cement slurry's ability to prevent gas channeling, providing an important basis for optimizing the cement slurry system.

[0033] Example Two

[0034] Based on the above embodiments, the method further includes: stopping the iteration when the sum of the iteratively calculated annular zone pressure value and the drilling fluid static column pressure is greater than the gas layer pressure.

[0035] In calculating the annular zone pressure, a reasonable stopping condition needs to be determined to avoid unnecessary waste of computational resources and ensure the accuracy of the calculation results. In this embodiment, an iteration stopping condition is added based on the previous embodiment. The iteration stops when the sum of the iteratively calculated annular zone pressure and the drilling fluid hydrostatic pressure exceeds the gas layer pressure. By setting a reasonable stopping condition, computational resources can be effectively saved and computational efficiency improved. Simultaneously, the accuracy of the calculation results is ensured, avoiding errors caused by over-calculation. In actual cementing engineering, timely stopping of unnecessary calculations provides timely and accurate annular zone pressure values ​​for engineering decisions. For example, when the calculated annular zone pressure value approaches the stopping iteration condition, corresponding measures can be taken in advance, such as adjusting the cement slurry formula or increasing the cementing pressure, to prevent excessive annular zone pressure and ensure cementing quality and safe oil and gas well production.

[0036] Example Three

[0037] Based on the above embodiments, the gas physical properties include: gas viscosity; the gas physical properties at different depths are determined by gas physical property expressions based on the temperature at different depths of the cement slurry, including: the gas viscosity at different depths is obtained by gas viscosity expressions based on the cement slurry temperature, gas density, and molar mass.

[0038] Accurately determining the gas viscosity at different depths is one of the key issues in calculating annular pressure. Existing technologies have shortcomings in considering the influence of cement slurry temperature at different depths on gas viscosity, leading to inaccurate annular pressure calculation results. This embodiment clarifies the method for determining the gas viscosity component of the gas physical property parameters. Based on cement slurry temperature, gas density, and molar mass, the gas viscosity at different depths is obtained through a gas viscosity expression. By accurately obtaining these parameters, the gas viscosity at different depths can be calculated more accurately. In the actual calculation process, the temperature at different depths of the cement slurry is first obtained based on the wellbore structure design and field measurement data. Then, parameters such as gas density and molar mass are substituted into the gas viscosity expression for calculation. This method allows for more accurate determination of the gas viscosity at different depths, improving the accuracy of annular pressure calculation. In oil drilling and cementing processes, accurate gas viscosity values ​​are crucial for assessing the gas seepage rate within the cement slurry matrix. For example, when the gas viscosity is low, the gas seepage rate within the cement slurry matrix may be accelerated, thereby increasing the risk of annular pressure. Accurate calculation of gas viscosity allows for better prediction of annular pressure variations, providing a basis for taking appropriate preventative measures. Furthermore, refining the method for determining gas viscosity also helps improve the reliability and practicality of the overall annular pressure calculation method.

[0039] Example Four

[0040] Based on the above embodiments, the gas physical property parameters include: gas compressibility factor; the gas physical property parameters at different depths are determined by gas physical property expressions based on the temperature at different depths of cement slurry, including: obtaining the gas compressibility factor at different depths by gas compressibility factor expressions based on apparent contrast temperature, apparent contrast density and apparent contrast pressure.

[0041] Accurately determining the gas compressibility factor at different depths is crucial when calculating annular pressure. Existing technologies have limitations in considering the influence of cement slurry temperature at different depths on the gas compressibility factor, leading to inaccurate annular pressure calculations. In this embodiment, the gas compressibility factor at different depths is obtained based on apparent contrast temperature, apparent contrast density, and apparent contrast pressure using a gas compressibility factor expression. Accurately obtaining these parameters allows for more accurate calculation of the gas compressibility factor at different depths. In the actual calculation process, the temperature at different depths of the cement slurry is first obtained based on the wellbore structure design and field measurement data. Then, parameters such as apparent contrast temperature, apparent contrast density, and apparent contrast pressure are substituted into the gas compressibility factor expression for calculation. This method allows for more accurate determination of the gas compressibility factor at different depths, improving the accuracy of annular pressure calculations. The gas compressibility factor significantly affects the gas's volume and pressure properties; an accurate gas compressibility factor value more accurately reflects the gas's state within the annulus when calculating annular pressure. For example, when the gas compressibility factor is large, the volume occupied by the same amount of gas in the annulus will decrease, resulting in an increase in annular pressure. By accurately calculating the gas compressibility factor, changes in annular pressure can be better assessed, providing strong support for optimizing cementing processes and improving the gas channeling prevention capability of cement slurry.

[0042] Example Five

[0043] Based on the above embodiments, the number of axial nodes and the number of time nodes are determined based on the length of the cement grout sealing section, the preset time, and the preset step size.

[0044] When discretizing the seepage equation, it is necessary to determine a reasonable number of axial nodes and time nodes to ensure the accuracy and efficiency of the calculation. Related technologies lack scientific methods for determining the number of nodes, leading to inaccurate calculation results or low computational efficiency. In this embodiment, the number of axial nodes and time nodes is determined based on the length of the cement slurry sealing section, a preset time, and a preset step size. In some implementations, the number of axial grids is determined by dividing the length of the cement slurry sealing section by the axial step size, and the number of time grids is determined by dividing the total time by the time step size. This embodiment clarifies the method for determining the number of nodes, namely, based on the length of the cement slurry sealing section, the preset time, and the preset step size. This allows for a more scientific division of the computational region, improving the accuracy and efficiency of the calculation. This method enables the determination of a reasonable number of axial nodes and time nodes, improving the accuracy and efficiency of annular pressure calculation. In the oil drilling cementing process, a reasonable number of nodes can better reflect the temperature changes and gas property parameters at different depths of the cement slurry, thereby more accurately calculating the annular pressure value. For example, if the number of nodes is too small, changes in cement slurry temperature and gas properties may not be accurately captured, leading to inaccurate calculation results; while if the number of nodes is too large, it will increase the computational load and reduce computational efficiency. By scientifically determining the number of nodes, computational efficiency can be improved while ensuring calculation accuracy, providing strong support for real-time monitoring and decision-making in cementing engineering.

[0045] Example Six

[0046] Based on the above embodiments, the step of iteratively calculating the discrete seepage equation to obtain the annular pressure value includes: obtaining a gas migration model to the wellhead based on the discrete seepage equation; and solving the gas migration model to obtain the annular pressure.

[0047] In calculating annular pressure, it is necessary to establish an effective gas migration model to the wellhead and solve this model to obtain accurate annular pressure values. Existing technologies have shortcomings in model establishment and solution, leading to inaccurate annular pressure calculation results. In this embodiment, a gas migration model to the wellhead is obtained based on discrete seepage equations. In some implementations, by considering the influence of temperature at different depths of the cement slurry on annular gas properties, and combining the real gas state equation and gas seepage rate calculation equation, a mathematical model for gas migration to the wellhead is established. This embodiment clarifies the process of processing the discrete seepage equations to obtain the gas migration model to the wellhead. Then, the gas migration model is solved to obtain the annular pressure. During the solution process, iterative methods and other numerical calculation methods can be used to improve computational efficiency and convergence. By establishing and solving an effective gas migration model to the wellhead, the annular pressure value can be accurately obtained, improving the accuracy of annular pressure calculation. In oil drilling cementing, accurate annular pressure values ​​are crucial for evaluating the gas migration prevention capability and cementing quality of the cement slurry. For example, by solving the gas migration model at the wellhead, we can better understand the gas seepage process and annular pressure changes within the cement slurry matrix, providing a scientific basis for optimizing the cement slurry system and cementing process. Simultaneously, employing efficient solution methods allows for rapid acquisition of calculation results, providing timely support for real-time monitoring and decision-making in cementing engineering.

[0048] Example Seven

[0049] Figure 2 This is a schematic diagram of the structure of an annular pressure calculation device provided in an embodiment of this application, as shown below. Figure 2 As shown in the technical solution of this embodiment, an annular pressure calculation device is provided. The device includes: a temperature acquisition module for acquiring the temperature at different depths of cement slurry; a property acquisition module for determining the gas property parameters at different depths based on the temperature at different depths of cement slurry using gas property expressions; a model construction module for discretizing the seepage equation based on preset axial nodes and time nodes; and a pressure calculation module for iteratively calculating the discrete seepage equation using preset axial nodes as the outer circulation condition and preset time nodes as the inner circulation condition to obtain the annular pressure value.

[0050] In annular pressure detection during oil drilling cementing, the accurate calculation of annular pressure values ​​is a challenge. Existing technologies struggle to accurately account for the influence of cement slurry temperatures at different depths on gas properties, leading to inaccurate annular pressure calculations. This embodiment addresses this issue by first acquiring the temperatures of the cement slurry at different depths, achieved through wellbore structure design and on-site measurements. Then, based on these temperatures, gas properties at different depths are determined using the gas property expressions described later, including gas viscosity and compressibility factor. Next, the flow equation is discretized based on preset axial and time nodes. The number of time and axial grids is determined, simplifying the transient process into a quasi-steady-state process for solution. Finally, using preset axial nodes as the outer circulation condition and preset time nodes as the inner circulation condition, the discrete flow equation is iteratively calculated to obtain the annular pressure value. This approach fully considers the influence of cement slurry temperatures at different depths on gas properties, making the simulation process more closely resemble actual conditions. Discretization and iterative calculation of the seepage equation improve computational efficiency and enable rapid acquisition of annular pressure values. For example, in practical cementing projects, accurate calculation of annular pressure values ​​allows for better evaluation of the cement slurry's ability to prevent gas channeling, providing an important basis for optimizing the cement slurry system.

[0051] Other technical features and beneficial effects of this embodiment correspond to those of the above embodiments, and will not be repeated here.

[0052] Example Eight

[0053] In the technical solution of this embodiment, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, it performs the steps of the annular pressure calculation method of any of the above embodiments.

[0054] In the technical solution of this embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of the annular pressure calculation method of any of the above embodiments.

[0055] In the technical solution of this embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps of the annular pressure calculation method of any of the above embodiments.

[0056] The processor may include, but is not limited to, one or more processors or microprocessors. Each processor may be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Digital Signal Processing Device (DSPD), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic component, for executing the methods described in the above embodiments.

[0057] Example Nine

[0058] Based on the above embodiments, this embodiment provides an application example.

[0059] Cementing is characterized by high investment, high risk, short operation time, one-time operation, and strong systemic nature. The main purpose of cementing is to effectively isolate layers, consolidate drilling achievements, and ensure the safe extraction of oil and gas resources. However, in the early stages of cement slurry solidification, the pore pressure decreases due to weight loss. Under the influence of pressure differential, gas can penetrate the cement slurry matrix and then enter the annulus, causing annular pressure and adversely affecting the safe extraction of oil and gas wells. Therefore, the anti-gas channeling capability of cement slurry during the solidification period is an important factor affecting the evaluation of cement in oil and gas wells. The technical problem of how to calculate annular pressure exists in this field.

[0060] When cement slurry is in a period of risk of gas intrusion, gas is highly likely to penetrate into the cement slurry matrix under the influence of the pressure difference between the upper and lower layers, and gradually migrate towards the low-pressure layer. After the gas penetrates the cement slurry matrix, it is very likely to reach the wellhead due to the buoyancy of the liquid cement slurry. However, considering that the cement slurry sealing section is relatively long during tailpipe cementing, and that the temperature difference between the bottom and top of the cement slurry column is significant, and that the annular gas viscosity, compressibility factor, and other physical properties are very sensitive to temperature, this application cannot simply regard the process of gas reaching the wellhead as a steady-state process. It is necessary to consider the impact of temperature differences at different depths on the performance of the cement slurry and the annular gas, and obtain the annular pressure value formed by gas reaching the wellhead under actual operating conditions in order to truly and accurately evaluate the gas channeling prevention capability of the cement slurry.

[0061] Currently, there is limited research on the impact of cement slurry temperature at different depths on the annular pressure at the wellhead. Existing studies mainly focus on the influence of cement slurry properties during the cementing process on the annular pressure at the wellhead. Some techniques have established mathematical models for the leakage to the wellhead and conducted sensitivity factor analyses on these models. However, due to the long annular cement slurry sealing section and the significant temperature difference between the bottom and top of the slurry column, the annular gas properties change. These techniques approximate these parameters as constants, making the model difficult to apply accurately and effectively in practice.

[0062] The technical solution of this invention rigorously establishes a mathematical model of gas migration to the wellhead during the cement slurry setting period, and determines the boundary conditions and initial conditions of the model. It also estimates the annular pressure value of gas migration to the wellhead in the early stage of cement slurry setting, which can accurately judge the gas migration prevention capability of cement slurry.

[0063] This invention belongs to the field of cementing in oil extraction, specifically relating to a method for calculating gas leakage to the wellhead considering the temperature at different depths of the cement slurry.

[0064] The purpose of this invention is to provide a method for calculating gas migration to the wellhead considering the temperature at different depths of cement slurry. This method obtains the temperature distribution at different depths of the cement slurry sealing section based on cementing design parameters such as wellbore structural design parameters and geological design parameters. Considering the influence of different depth temperatures on annular gas properties (e.g., gas viscosity, gas compressibility factor), and combining cement slurry characteristics and static gel strength transition time data, a gas migration model to the wellhead is constructed to obtain the annular pressure distribution characteristics during the cement slurry setting period. This research result helps to obtain annular pressure under actual working conditions, and has important theoretical significance for judging the gas migration prevention capability of cement slurry and optimizing the cement slurry system, with broad market prospects.

[0065] To achieve the above-mentioned technical objectives, the present invention adopts the following technical solution.

[0066] The basic performance parameters of cement slurry during the curing period, the actual wellbore structural dimensions, and the physical properties of the gas in the wellbore are obtained. Considering the influence of temperature at different depths of the cement slurry sealing section on the physical properties of the annular gas, a mathematical model for gas migration to the wellhead is established by combining the real gas state equation and the gas seepage rate calculation equation. Considering the temperature difference at different depths, the seepage equation is discretized to obtain the annular pressure value under actual conditions.

[0067] Symbol table:

[0068] Δh is the axial step size;

[0069] Δt is the time step;

[0070] It represents the increase in the amount of gas at the wellhead at time n, or the amount of gas that has leaked into the wellhead.

[0071] Let n be the increase in the volume of gas at the wellhead at time n;

[0072] Let be the volume of drilling fluid compressed at time n;

[0073] Let n be the volume of drilling fluid compressed at time n-1;

[0074] A α , where is the flow area;

[0075] C is the correction factor;

[0076] c m , where is the drilling fluid compressibility coefficient;

[0077] j represents the number of grid cells along the axis;

[0078] k is the cement slurry permeability;

[0079] k n , where is the cement slurry permeability at time n;

[0080] L c , where is the length of the sealed section;

[0081] M g , where is the molar mass;

[0082] n is the number of time grids;

[0083] Let n be the amount of gas at the wellhead at time n-1.

[0084] p c , is the pressure at the top of the cement slurry;

[0085] p g , which is the gas layer pressure;

[0086] The pore pressure of the cement paste matrix at position j at time n-1; The annular pressure at time n-1;

[0087] Let be the pore pressure of the cement paste matrix at position j at time n;

[0088] Let n be the annular pressure at time n;

[0089] p r This is to contrast the pressure.

[0090] p sc , is the gas pressure under standard conditions;

[0091] q c , where is the gas permeation rate within the cement paste matrix;

[0092] Let n be the gas seepage rate at time n;

[0093] R is a universal gas constant;

[0094] T c , where is the temperature of the cement slurry;

[0095] T r , is the apparent contrast temperature;

[0096] T sc , where is the gas temperature under standard conditions;

[0097] T wh , where is the wellhead temperature;

[0098] Let be the volume of gas at the wellhead at time n-1;

[0099] Let n be the volume of drilling fluid compressed at time n-1;

[0100] Z is the gas compressibility factor;

[0101] Z j , is the gas compressibility factor at position j;

[0102] μ is the gas viscosity;

[0103] μ j , where is the gas viscosity at position j;

[0104] ρ is the gas density;

[0105] ρ r , which represents the apparent contrast density.

[0106] A calculation method considering gas migration to the wellhead under the heat of hydration includes the following steps:

[0107] Initial condition assignment: Based on the actual wellbore structure and casing size, input the wellbore size, casing size, and cemented section depth for each well opening; at the same time, 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; in addition, provide the downhole temperature, wellhead temperature, formation pressure, and thermophysical parameters of each component.

[0108] (1) Based on the wellbore structure design and field measurement data, the temperature T at different depths of the cement slurry (sealing section) was obtained. c ;

[0109] (2) Based on the preset axial step length (Δh) and the preset time step length (Δt), the number of axial grids j is determined by dividing the length of the cement grout sealing section by the axial step length Δh, and the number of time grids n is determined by dividing the total time by the time step length Δt. Based on this, the number of axial grids and the number of time grids are j and n, respectively.

[0110] (3) Determine the gas physical property parameters (including gas viscosity μ and gas compressibility factor Z) at different depths of the annulus based on the cement slurry temperature and gas physical property expression, and then discretize them:

[0111] The expression for the gas viscosity μ is:

[0112]

[0113] Among them, M g Where ρ is the molar mass, ρ is the gas density, and T is the gas density. c This refers to the temperature of the cement slurry.

[0114] The expression for the gas compressibility factor Z is:

[0115]

[0116] Where, p r To contrast the pressure, T r For the apparent contrast temperature, ρ r For apparent contrast density.

[0117] (4) Construct a calculation model for gas infiltration velocity, and calculate the gas infiltration rate q in the cement paste matrix. c The expression is:

[0118]

[0119] In the formula, C is the correction coefficient, k is the cement slurry permeability, and p g p is the gas layer pressure. c T represents the pressure at the top of the cement grout. sc Let A be the gas temperature under standard conditions. a Where L is the flow area, μ is the gas viscosity, Z is the gas compressibility factor, and L is the flow area. c p is the length of the sealed section. sc This represents the gas pressure under standard conditions.

[0120] (5) Considering the influence of temperature at different depths of cement slurry on gas viscosity μ, the gas seepage velocity calculation model is discretized, divided into n time steps and j spatial steps, simplifying the transient process into a quasi-steady-state process for solution:

[0121]

[0122] in, Let k be the gas seepage rate at time n. n Let n be the cement slurry permeability at time n. Let be the pore pressure of the cement paste matrix at position j at time n. Let μ be the pore pressure of the cement paste matrix at position j-1 at time n. j Let Z be the gas viscosity at position j. j Let be the gas compressibility factor at position j.

[0123] (6) The real gas state equation for the annular top column within n time steps of the time grid is expressed as:

[0124]

[0125] in, Let n be the amount of gas at the wellhead at time n-1. Let R be the increase in the amount of gas at the wellhead at time n, R be the universal gas constant, and T be the amount of gas at the wellhead. wh The wellhead temperature, Let n be the annular pressure. Let n be the volume of gas at the wellhead at time n-1. Let n be the increase in the gas volume at the wellhead at time n.

[0126] (7) Drilling fluid compression within n time steps of the number of time grids Represented as:

[0127]

[0128] in, Let c be the volume of drilling fluid compressed at time n. m The drilling fluid compressibility coefficient. Let n be the volume of drilling fluid compressed at time n-1. Let n be the annular pressure at time n-1.

[0129] (8) The amount of gas that has leaked into the wellhead can be obtained using the above method. Represented as:

[0130]

[0131] (9) Combining the above expressions, we can obtain a mathematical model for the leakage of cement slurry to the wellhead considering the temperature at different depths:

[0132]

[0133] in, Let n be the annular pressure at time n.

[0134] Compared with the prior art, the present invention has the following significant advantages:

[0135] (1) The present invention fully considers the influence of temperature at different depths of cement slurry on gas physical parameters, and uses this as the calculation condition to make the simulation process closer to the actual conditions and the simulation results have better feasibility.

[0136] (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 quickly obtain the annular pressure value.

[0137] 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.

[0138] Figure 3 This is a flowchart illustrating a method for calculating gas leakage to the wellhead, taking into account the temperature at different depths of cement slurry, as provided in an embodiment of this disclosure. Figure 4 This is a schematic diagram illustrating gas leakage to the wellhead, provided as part of a disclosed embodiment. Figure 3 and Figure 4 As shown, a method for calculating gas leakage to the wellhead based on the temperature at different depths of cement slurry includes the following steps:

[0139] (1) Based on the cementing design parameters and geological design parameters, the properties of cement slurry and annular working fluid, surface temperature, formation temperature, and wellbore structure were obtained. The well depth is 4007m, and the drilling fluid density is 2.3g / cm³. 3 The drilling fluid compressibility coefficient is 1.0e. -6 / psi, cement paste density is 2.35g / cm³ 3 The formation pressure and temperature were 85 MPa and 108℃, respectively. The wellhead and top cement slurry column temperatures were 23.4℃ and 97℃, respectively. The wellbore diameter was 0.1524 m, the casing diameter was 0.1197 m, the casing wall thickness was 12.7 mm, the drilling depth was 4003 m, the cemented section was 3610 m to 4007 m, and the length of the cemented section was 397 m.

[0140] (2) Determine the axial direction and time step, with an axial step of 20m and a time step of 60s;

[0141] (3) Based on the temperatures at different depths of the cement slurry obtained above, calculate the viscosity and compressibility factor of the annular gas at different depths. Figure 5 This is a schematic diagram of the gas compressibility factor at different depths of cement slurry, provided in an embodiment of the present invention. Figure 6 This is a schematic diagram of gas viscosity at different depths of cement slurry, provided as an embodiment of the present invention.

[0142] (4) Discretize the gas seepage equation in the cement slurry matrix by taking the axial node j as the external circulation condition and the time node n as the internal circulation condition.

[0143] (5) The flow equation of the discretized gas in the cement slurry matrix is ​​iteratively calculated to obtain the gas flow rate entering the annulus at time node n, and then the annulus pressure at time node n is obtained. As the annulus pressure increases, the circulation stops when the sum of the annulus pressure and the drilling fluid hydrostatic pressure is greater than the gas layer pressure.

[0144] (6) Obtain the annular pressure value of gas reaching the wellhead.

[0145] This method was used to obtain the annular pressure at different depths of the cement slurry considering gas leakage to the wellhead, and a sensitivity analysis of the gas leakage annular pressure was performed. For example... Figure 7 As shown, comparing the annular pressure of high-permeability cement slurry with that of low-permeability cement slurry in this scheme, it can be seen that the high-permeability cement slurry has a higher annular pressure at the wellhead within the same gas channeling time; as Figure 8 As shown, a comparison of annular pressure at different gas intrusion times in this scheme reveals that delaying the gas intrusion time before the gas channeling danger time (780 min) has a relatively small impact on annular pressure.

[0146] In summary, this invention considers the influence of the temperature at different depths of cement slurry during the curing period on gas seepage, establishes a gas migration model to the wellhead, determines the boundary conditions of the model, and obtains the annular pressure zone for gas migration to the wellhead.

[0147] In the embodiments provided by this invention, it should be understood that the disclosed apparatus and methods can also be implemented in other ways. The apparatus embodiments described above are merely illustrative; for example, the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0148] It should be noted that, in this invention, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element limited by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0149] While the embodiments disclosed in this invention are as described above, the above content is merely for the purpose of facilitating understanding of this invention and is not intended to limit the invention. Any person skilled in the art to which this invention pertains may make any modifications and changes in form and detail of the implementation without departing from the spirit and scope disclosed in this invention; however, the scope of patent protection of this invention shall still be determined by the scope defined in the appended claims.

Claims

1. A method for calculating annular pressure, characterized in that, The method includes: Obtain the temperature at different depths of the cement slurry; Based on the temperature at different depths of cement slurry, the gas physical property parameters at different depths are determined by the gas physical property expression. The seepage equation is discretized based on preset axial nodes and time nodes; Using preset axial nodes as the outer circulation condition and preset time nodes as the inner circulation condition, the discrete seepage equation is iteratively calculated to obtain the annular pressure value.

2. The annular pressure calculation method according to claim 1, characterized in that, The method further includes: The iteration stops when the sum of the annular zone pressure calculated iteratively and the hydrostatic pressure of the drilling fluid exceeds the gas layer pressure.

3. The annular pressure calculation method according to claim 1, characterized in that, The gas physical properties include: gas viscosity; The method of determining gas property parameters at different depths based on the temperature of cement slurry at different depths using gas property expressions includes: Based on the cement slurry temperature, gas density, and molar mass, the gas viscosity at different depths is obtained using a gas viscosity expression.

4. The annular pressure calculation method according to claim 1, characterized in that, The gas physical properties include: gas compressibility factor; The method of determining gas property parameters at different depths based on the temperature of cement slurry at different depths using gas property expressions includes: Based on apparent contrast temperature, apparent contrast density, and apparent contrast pressure, the gas compressibility factor at different depth points is obtained through the gas compressibility factor expression.

5. The annular pressure calculation method according to claim 1, characterized in that, Based on the length of the cement grout sealing section, the preset time, and the preset step size, the number of axial nodes and the number of time nodes are determined.

6. The annular pressure calculation method according to claim 2, characterized in that, The step of iteratively calculating the discrete seepage equations to obtain the annular pressure value includes: Based on the discrete seepage equations, a gas migration model to the wellhead is obtained; The annular pressure was obtained by solving the gas leakage model at the wellhead.

7. A pressure calculation device for annular space, characterized in that, The device includes: Temperature acquisition module is used to acquire the temperature of cement slurry at different depths; The property acquisition module is used to determine the gas property parameters at different depths based on the temperature of the cement slurry at different depths by using gas property expressions. The model building module is used to discretize the seepage equation based on preset axial nodes and time nodes; The pressure calculation module is used to iteratively calculate the discrete seepage equation using a preset axial node as the outer circulation condition and a preset time node as the inner circulation condition, in order to obtain the annular pressure value.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it represents the steps of the annular pressure calculation method as described in any one of claims 1 to 6.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the annular pressure calculation method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the annular pressure calculation method as described in any one of claims 1 to 6.

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