Testing system and method for measuring specific heat capacity of fluid under high-temperature and high-pressure conditions

Abstract

The invention discloses a testing system and method for measuring the specific heat capacity of fluid under high-temperature and high-pressure conditions, and belongs to the technical field of petroleum engineering. The test system comprises a water loss meter, a test assembly and a specific heat data processing system, the testing assembly comprises a slurry cup body, an upper cover, a bottom cover, a bidirectional binding post and a pressurizing interface which are arranged on the upper cover, a probe assembly which is arranged at the top of the slurry cup body and extends into the slurry cup body, and a thermocouple arranged on the bottom cover; the pressurization interface is communicated with an air delivery valve rod of the water loss instrument, an outer binding post and an inner binding post of the bidirectional binding post are electrically connected with the specific heat data processing system and the probe assembly respectively, and an outer coupling interface of the water loss instrument is electrically connected with the thermocouple and the specific heat data processing system respectively. According to the specific heat capacity testing method based on the secondary testing system, time correction is introduced, so that accurate measurement of thermophysical parameters of high-temperature and high-pressure fluid can be achieved, meanwhile, a shaft-stratum transient heat transfer model is established, and the accuracy of measured specific heat capacity data is verified.

Description

Technical Field

[0001] The present invention relates to the technical field of petroleum engineering, and in particular to a testing system and method for measuring the specific heat capacity of a fluid under high temperature and high pressure conditions. Background Art

[0002] As oil and gas exploration advances to deeper levels, the number of deep and ultra-deep wells continues to grow, and the temperature and pressure inside the wellbore increase significantly. This extreme high temperature and high pressure environment not only poses severe challenges to drilling, completion and production processes, but also affects the physical and thermodynamic properties of wellbore fluids, thereby posing a potential threat to the safety of downhole operations and the accuracy of wellbore temperature field predictions.

[0003] Accurately predicting the wellbore temperature field is crucial for multiple key engineering processes, including drilling fluid rheology control, cement slurry optimization, wellbore stability assessment, and thermodynamic research in high-temperature and high-pressure reservoirs. Due to the high complexity of the downhole environment, existing temperature field prediction methods primarily rely on experimentally measured fluid thermophysical parameters, such as thermal conductivity, specific heat capacity, and thermal diffusivity. However, under high-temperature and high-pressure conditions, these parameters can change significantly, and existing experimental equipment is mostly limited to normal temperature and pressure or a single high-temperature environment, making it difficult to truly represent actual downhole conditions. These limitations in experimental conditions can lead to large deviations between experimental data and actual downhole conditions, thereby reducing the prediction accuracy of the wellbore temperature field evolution model and further affecting the safety assessment of downhole operations.

[0004] For example, under high temperature and high pressure, the thermal conductivity characteristics of drilling and completion fluids can change significantly. Lack of accurate thermophysical parameters can lead to inaccurate assessments of the drilling fluid's cooling performance, impacting wellbore stability and even causing downhole accidents such as well collapses and blowouts. Specific heat capacity, a key thermophysical parameter that measures a fluid's ability to absorb and release heat, is particularly affected by temperature and pressure.

[0005] However, existing experimental equipment is primarily based on measurements at room temperature and pressure, and the data obtained cannot accurately reflect the actual downhole thermodynamic behavior, thus limiting the accuracy of wellbore temperature predictions and adversely affecting safety assessments in high-temperature and high-pressure environments. Furthermore, with the accelerated development of unconventional oil and gas resources, the scientific value of accurately measuring downhole fluid thermophysical parameters is becoming increasingly prominent for improving oil and gas recovery, optimizing wellbore thermal prediction, and improving completion design. Summary of the Invention

[0006] The purpose of the present invention is to provide a test system and method for measuring the specific heat capacity of fluids under high temperature and high pressure conditions, so as to solve the problem that the existing specific heat capacity measurement experimental device is based on normal temperature and pressure measurement, and the data obtained is difficult to accurately reflect the actual thermodynamic behavior downhole, thereby limiting the accuracy of wellbore temperature prediction.

[0007] The technical solution of the present invention to solve the above technical problems is as follows:

[0008] A test system for measuring the specific heat capacity of a fluid under high-temperature and high-pressure conditions, comprising: a water loss meter, a test assembly located inside the water loss meter, and a specific heat data processing system; the test assembly comprising a slurry cup, an upper cover and a bottom cover respectively disposed at the top and bottom ends of the slurry cup, a two-way terminal disposed on the upper cover, a pressurization interface disposed on the upper cover, a probe assembly disposed on the top of the slurry cup and extending into the interior of the slurry cup, and a thermocouple disposed on the bottom cover for measuring the temperature of the fluid inside the slurry cup;

[0009] The pressurizing interface is connected to the gas valve stem of the water loss meter, the outer terminal and the inner terminal of the two-way terminal are electrically connected to the specific heat data processing system and the probe assembly respectively, and the outer couple interface of the water loss meter is electrically connected to the thermocouple and the specific heat data processing system respectively.

[0010] Furthermore, the upper cover and the pulp cup body, the upper cover and the two-way terminal, and the bottom cover and the pulp cup body are all sealed.

[0011] Furthermore, the probe assembly includes a clip and a probe, the clip is connected to the upper cover, and the probe is connected to the clip, so that the probe is clamped in the middle of the clip.

[0012] Furthermore, the inner terminal of the bidirectional terminal is made of stainless steel, and the outer terminal of the bidirectional terminal is made of copper or copper alloy.

[0013] A specific heat capacity testing method based on the above-mentioned testing system for measuring the specific heat capacity of fluids under high temperature and high pressure conditions comprises the following steps:

[0014] S1: Inject the cement slurry sample into the slurry cup. The injection height should be enough to submerge the detection part of the probe.

[0015] S2: Connect the upper cover to the slurry cup, ensuring that the detection part of the probe extends into the cement slurry sample;

[0016] S3: electrically connecting the specific heat data processing system to the external couple interface of the water loss meter and the external terminal of the two-way terminal, and connecting the pressurizing interface to the gas transmission valve stem of the water loss meter;

[0017] S4: Start the water loss meter, adjust the heating temperature of the water loss meter according to the set annular space temperature T, simulate the high-temperature environment downhole, and pressurize the slurry cup through the water loss meter to simulate the high-pressure environment downhole;

[0018] S5: The thermal conductivity of the cement slurry sample is obtained through the probe, and the temperature data is obtained through the thermocouple. The specific heat data processing system obtains the specific heat capacity of the cement slurry sample by introducing time correction based on the obtained thermal conductivity and temperature data;

[0019] S6: Establish a wellbore-formation transient heat transfer model to determine the accuracy of the specific heat capacity of the cement slurry sample.

[0020] Furthermore, in the above step S5, the specific heat capacity of the cement slurry sample is calculated as follows:

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] in: is the specific heat capacity of the cement paste sample; is the thermal conductivity of the cement paste sample; is the thermal diffusivity of the cement paste sample; is the density of the cement paste sample; is the radius of the outermost ring of the probe; Measure time for features; is the time variable; For time; For time correction; is a function of time; is the number of concentric ring sources; is the time interval from the initial moment to the current moment; is the wave number in the radial direction; is the wave number in the axial direction; is the Bessel function; For time Temperature changes at all times; is the output power of the probe.

[0027] Furthermore, the above time correction Not more than 0.5% of the total measurement time.

[0028] Furthermore, the above step S6 includes the following sub-steps:

[0029] S61: Substitute the specific heat capacity of the cement slurry sample into the wellbore-formation transient heat transfer model to obtain the calculated annular temperature;

[0030] S62: Compare the set annular temperature with the calculated annular temperature; if the error is ≤3%, the specific heat capacity measurement of the cement slurry sample is accurate; if the error is >3%, the specific heat capacity measurement of the cement slurry sample is inaccurate.

[0031] Furthermore, the wellbore-formation transient heat transfer model includes a pipe temperature distribution model, a drill string wall temperature distribution model, and an annulus temperature distribution model;

[0032] The expression of the temperature distribution model inside the tube is:

[0033] ;

[0034] The expression of the drill string wall temperature distribution model is:

[0035] ;

[0036] The expression of the annular temperature distribution model is:

[0037] ;

[0038] in: is the drilling fluid density; is the specific heat capacity of drilling fluid; is the displacement; is the depth step; is the inner radius of the drill string; is the convective heat transfer coefficient of the drill string inner wall; is the time step; Generate heat for complex heat source terms; is the radius of the drill string wall; is the thermal conductivity of the drill string wall; is the depth step at node j-0.5; is the depth step at node j+0.5; is the convective heat transfer coefficient of the drill string outer wall; is the wellbore radius; is the well wall convection heat transfer coefficient; is the fluid temperature in the drill string at the well depth j-1 and time n+1; is the fluid temperature in the drill string at the well depth j and time n+1; is the drill string wall temperature at depth j and time n+1; is the fluid temperature in the drill string at a well depth of j and a time of n; is the drill string wall temperature at depth j-1 and time n+1; is the drill string wall temperature at depth j+1 and time n+1; is the annular temperature at well depth j and time n+1; is the drill string wall temperature at depth j and time n; is the annular temperature at well depth j+1 and time n+1; is the annular temperature at well depth j and time n.

[0039] Furthermore, in the above step S61, the specific heat capacity of the cement slurry sample Replace drilling fluid specific heat capacity , the calculated annular temperature is the annular temperature at a well depth of j and a time of n. .

[0040] The present invention has the following beneficial effects:

[0041] (1) The test system for measuring the specific heat capacity of fluids under high-temperature and high-pressure conditions of the present invention can simulate downhole high-temperature and high-pressure working conditions in an experimental environment, enabling traditional specific heat capacity measurement probes to accurately measure the thermophysical parameters of high-temperature and high-pressure fluids under controlled conditions, thereby obtaining experimental data with greater engineering adaptability. At the same time, the system can be widely used in the study of the thermophysical properties of different types of downhole fluids, not only making up for the limitations of current experimental technology, but also providing experimental support for wellbore temperature field prediction, downhole operation safety assessment, and high-temperature and high-pressure fluid dynamics research, laying an important technical foundation for the efficient and safe development of deep and ultra-deep wells.

[0042] (2) Due to the hardware and software delays of the equipment when testing data, the test time is longer than the actual time when the sensor is at full power output. Therefore, the present invention introduces time correction when measuring specific heat capacity to obtain the actual measurement time, so that the measured specific heat capacity data is more accurate.

[0043] (3) Based on the principle of conservation of energy and combined with the heat transfer mechanism of each control area of the wellbore-formation, the present invention establishes a wellbore-formation transient heat transfer model, substitutes the measured specific heat capacity data into the model, and verifies the accuracy of the measured specific heat capacity data by comparing the set annular space temperature with the calculated annular space temperature. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of the structure of the test assembly of the present invention.

[0045] In the figure: 10 - pulp cup; 20 - upper cover; 21 - two-way terminal; 22 - probe assembly; 23 - clip; 24 - probe; 30 - bottom cover. DETAILED DESCRIPTION

[0046] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0047] This embodiment provides a testing system for measuring the specific heat capacity of a fluid under high-temperature and high-pressure conditions, comprising a dehydration meter, a test assembly located within the dehydration meter, and a specific heat data processing system. The dehydration meter is a conventional high-temperature and high-pressure dehydration meter, configured to simulate a high-temperature environment externally and a high-pressure environment internally. The test assembly is configured to obtain thermal conductivity and temperature data of a cement slurry sample. The specific heat data processing system is a conventional specific heat data processing system, configured to obtain the specific heat capacity of the cement slurry sample after obtaining the thermal conductivity and temperature data of the cement slurry sample.

[0048] The present invention's test system for measuring the specific heat capacity of fluids under high-temperature, high-pressure conditions can simulate downhole high-temperature, high-pressure conditions in an experimental environment, enabling traditional specific heat capacity measurement probes to accurately measure the thermophysical properties of high-temperature, high-pressure fluids under controlled conditions, thereby obtaining experimental data with greater engineering adaptability. Furthermore, the system can be widely applied to the study of the thermophysical properties of various types of downhole fluids, not only addressing the limitations of current experimental techniques but also providing experimental support for wellbore temperature field prediction, downhole operation safety assessment, and high-temperature, high-pressure fluid dynamics research, laying an important technical foundation for the efficient and safe development of deep and ultra-deep wells.

[0049] Please refer to Figure 1 The test assembly includes a slurry cup body 10, an upper cover 20, a bottom cover 30, a bidirectional terminal 21, a probe assembly 22 and a thermocouple 30. The slurry cup body 10 is used to inject cement slurry samples. The upper cover 20 and the bottom cover 30 are respectively connected to the top and bottom ends of the slurry cup body 10 by threads, and a high-temperature O-ring is provided at the connection for sealing. The bidirectional terminal 21 passes through the upper cover 20, and its outer terminal extends to the outside of the upper cover 20, and its inner terminal extends to the inside of the upper cover 20. A high-temperature O-ring is also provided between the bidirectional terminal 21 and the upper cover 20 for sealing. The probe assembly 22 is connected to the top of the slurry cup body 10 and extends only to the inside of the slurry cup body 10, and is used to obtain the thermal conductivity of the cement slurry sample. The thermocouple 30 extends from the bottom cover 30 into the slurry cup body 10 to obtain temperature data of the cement slurry sample. The thermocouple 30 adopts an E-type thermocouple, which is threadedly matched with the bottom cover 30, and a high-temperature O-ring is also provided between the thermocouple 30 and the bottom cover 30 for sealing.

[0050] In this embodiment, a pressurized interface is provided on the upper cover 20, which is connected to the interior of the slurry cup body 10 and the gas valve stem of the water loss meter, and is used to provide high-pressure gas to the interior of the slurry cup body 10, preferably high-pressure nitrogen, to simulate a high-pressure environment; the external terminal and the internal terminal of the two-way terminal 21 are electrically connected to the specific heat data processing system and the probe assembly 22, respectively, and the external couple interface of the water loss meter is electrically connected to the thermocouple 30 and the specific heat data processing system, respectively.

[0051] Probe assembly 22 includes a two-piece clip 23 and a probe 24. Clip 23 is a two-piece design that clamps the top of probe 24. A flange is provided on the top of clip 23, which mates with a step on the inner wall of the paddle cup 10 and is connected via a screw. In this embodiment, the top wall of clip 23 contacts the bottom wall of upper cover 20.

[0052] In this embodiment, in order to adapt to the high temperature and high pressure environment inside the pulp cup body 10, the inner terminal of the two-way terminal 21 is made of stainless steel, while the outer terminal of the two-way terminal 21 is made of copper or copper alloy.

[0053] This embodiment further provides a specific heat capacity testing method based on the above-mentioned testing system for measuring the specific heat capacity of a fluid under high temperature and high pressure conditions, comprising the following steps:

[0054] S1: inject the cement slurry sample into the slurry cup 10, and the injection height is sufficient to submerge the detection part of the probe 24;

[0055] S2: Connect the upper cover 20 to the slurry cup 10, ensuring that the detection portion of the probe 24 extends into the cement slurry sample;

[0056] S3: The specific heat data processing system is electrically connected to the external couple interface of the water loss meter and the external terminal of the two-way terminal 21, and the pressurizing interface is connected to the gas valve stem of the water loss meter;

[0057] S4: Start the dehydration meter, adjust the heating temperature of the dehydration meter according to the set annular space temperature T, simulate the underground high temperature environment, and pressurize the slurry cup (10) through the gas valve stem of the dehydration meter to simulate the underground high pressure environment;

[0058] S5: The thermal conductivity of the cement slurry sample is obtained through the probe 24, and the temperature data is obtained through the thermocouple. The specific heat data processing system obtains the specific heat capacity of the cement slurry sample by using the obtained thermal conductivity and temperature data and introducing time correction;

[0059] S6: Establish a wellbore-formation transient heat transfer model to determine the accuracy of the specific heat capacity of the cement slurry sample.

[0060] In step S5, the specific heat capacity of the cement slurry sample is calculated as follows:

[0061] ;

[0062] ;

[0063] ;

[0064] ;

[0065] ;

[0066] in: is the specific heat capacity of the cement paste sample; is the thermal conductivity of the cement paste sample; is the thermal diffusivity of the cement paste sample; is the density of the cement paste sample; is the radius of the outermost ring of the probe; Measure time for features; is the time variable; For time; For time correction; is a function of time; is the number of concentric ring sources; is the time interval from the initial moment to the current moment; is the wave number in the radial direction; is the wave number in the axial direction; is the Bessel function; For time Temperature changes at all times; is the output power of the probe.

[0067] In this embodiment, the time correction Not more than 0.5% of the total measurement time.

[0068] Since the test data is delayed by the hardware and software of the equipment, the test time is longer than the actual time when the sensor is at full power output. Therefore, the present invention introduces time correction when measuring the specific heat capacity to obtain the actual measurement time, so that the measured specific heat capacity data is more accurate.

[0069] Step S6 includes the following sub-steps:

[0070] S61: Substitute the specific heat capacity of the cement slurry sample into the wellbore-formation transient heat transfer model to obtain the calculated annular temperature;

[0071] S62: Compare the set annular temperature with the calculated annular temperature; if the error is ≤3%, the specific heat capacity measurement of the cement slurry sample is accurate; if the error is >3%, the specific heat capacity measurement of the cement slurry sample is inaccurate.

[0072] In S61, the wellbore-formation transient heat transfer model includes the pipe temperature distribution model, the drill string wall temperature distribution model, and the annulus temperature distribution model;

[0073] The expression of the temperature distribution model inside the tube is:

[0074] ;

[0075] The expression of the drill string wall temperature distribution model is:

[0076] ;

[0077] The expression of the annular temperature distribution model is:

[0078] ;

[0079] in: is the drilling fluid density; is the specific heat capacity of drilling fluid; is the displacement; is the depth step; is the inner radius of the drill string; is the convective heat transfer coefficient of the drill string inner wall; is the time step; Generate heat for complex heat source terms; is the radius of the drill string wall; is the thermal conductivity of the drill string wall; is the depth step at node j-0.5; is the depth step at node j+0.5; is the convective heat transfer coefficient of the drill string outer wall; is the wellbore radius; is the well wall convection heat transfer coefficient; is the fluid temperature in the drill string at the well depth j-1 and time n+1; is the fluid temperature in the drill string at the well depth j and time n+1; is the drill string wall temperature at depth j and time n+1; is the fluid temperature in the drill string at a well depth of j and a time of n; is the drill string wall temperature at depth j-1 and time n+1; is the drill string wall temperature at depth j+1 and time n+1; is the annular temperature at well depth j and time n+1; is the drill string wall temperature at depth j and time n; is the annular temperature at well depth j+1 and time n+1; is the annular temperature at well depth j and time n.

[0080] In step S62, the specific comparison process is:

[0081] The specific heat capacity c of the cement slurry sample measured in step S5 is used to replace the specific heat capacity of the drilling fluid in the wellbore-formation transient heat transfer model. , calculate the annular temperature at well depth j and time n , set the annular temperature T and the annular temperature at well depth j and time n Compare; if the error is ≤3%, the specific heat capacity measurement of the cement slurry sample is accurate; if the error is >3%, the specific heat capacity measurement of the cement slurry sample is inaccurate.

[0082] in, .

[0083] This embodiment is based on the principle of conservation of energy and combines the heat transfer mechanisms of each wellbore-formation control area to establish a wellbore-formation transient heat transfer model. The measured specific heat capacity data is substituted into the model, and the accuracy of the measured specific heat capacity data is verified by comparing the set annular space temperature with the calculated annular space temperature.

[0084] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A test system for measuring the specific heat capacity of fluids under high temperature and high pressure conditions, characterized in that: include: A water loss meter, a test assembly located inside the water loss meter, and a specific heat data processing system; the test assembly includes a pulp cup body (10), an upper cover (20) and a bottom cover (30) respectively arranged at the top and bottom ends of the pulp cup body (10), a two-way terminal (21) arranged on the upper cover (20), a pressurizing interface arranged on the upper cover (20), a probe assembly (22) arranged at the top of the pulp cup body (10) and extending into the interior of the pulp cup body (10), and a thermocouple (30) arranged on the bottom cover (30) and used to measure the temperature of the fluid inside the pulp cup body (10); The pressurizing interface is connected to the gas delivery valve stem of the water loss meter, the outer terminal and the inner terminal of the two-way terminal (21) are electrically connected to the specific heat data processing system and the probe assembly (22) respectively, and the outer couple interface of the water loss meter is electrically connected to the thermocouple (30) and the specific heat data processing system respectively.

2. The test system for measuring the specific heat capacity of fluids under high temperature and high pressure conditions according to claim 1, characterized in that: The upper cover (20) and the pulp cup body (10), the upper cover (20) and the bidirectional terminal (21), and the bottom cover (30) and the pulp cup body (10) are all sealed.

3. The test system for measuring the specific heat capacity of fluids under high temperature and high pressure conditions according to claim 1, characterized in that: The probe assembly (22) includes a clip (23) and a probe (24), wherein the clip (23) is connected to the upper cover (20), and the probe (24) is connected to the clip (23), so that the probe (24) is clamped in the middle of the clip (23).

4. The test system for measuring the specific heat capacity of fluids under high temperature and high pressure conditions according to claim 1, characterized in that: The material of the inner terminal of the bidirectional terminal (21) is stainless steel, and the material of the outer terminal of the bidirectional terminal (21) is copper or copper alloy.

5. A specific heat capacity testing method based on the test system for measuring the specific heat capacity of fluid under high temperature and high pressure conditions according to any one of claims 1 to 4, characterized in that: The following steps are involved: S1: injecting the cement slurry sample into the slurry cup (10), with the injection height being such as to submerge the detection part of the probe (24); S2: Connect the upper cover (20) to the slurry cup (10), ensuring that the detection portion of the probe (24) extends into the cement slurry sample; S3: electrically connecting the specific heat data processing system to the external couple interface of the water loss meter and the external terminal of the two-way terminal (21), and connecting the pressurizing interface to the gas valve stem of the water loss meter; S4: Start the dehydration meter, adjust the heating temperature of the dehydration meter according to the set annular space temperature T, simulate the high temperature environment downhole, and pressurize the slurry cup (10) through the dehydration meter to simulate the high pressure environment downhole; S5: obtaining thermal conductivity of the cement slurry sample through the probe (24), obtaining temperature data through the thermocouple, and obtaining the specific heat capacity of the cement slurry sample through the specific heat data processing system by introducing time correction through the obtained thermal conductivity and temperature data; S6: Establish a wellbore-formation transient heat transfer model to determine the accuracy of the specific heat capacity of the cement slurry sample.

6. The specific heat capacity testing method according to claim 5, characterized in that: In step S5, the specific heat capacity of the cement slurry sample is calculated as follows: ； ； ； ； ； in: is the specific heat capacity of the cement paste sample; is the thermal conductivity of the cement paste sample; is the thermal diffusivity of the cement paste sample; is the density of the cement paste sample; is the radius of the outermost ring of the probe; Measure time for features; is the time variable; For time; For time correction; is a function of time; is the number of concentric ring sources; is the time interval from the initial moment to the current moment; is the wave number in the radial direction; is the wave number in the axial direction; is the Bessel function; For time Temperature changes at all times; is the output power of the probe.

7. The specific heat capacity testing method according to claim 6, characterized in that: Time Correction Not more than 0.5% of the total measurement time.

8. The specific heat capacity testing method according to claim 6, characterized in that: Step S6 includes the following sub-steps: S61: Substitute the specific heat capacity of the cement slurry sample into the wellbore-formation transient heat transfer model to obtain the calculated annular temperature; S62: Compare the set annular temperature with the calculated annular temperature; if the error is ≤3%, the specific heat capacity measurement of the cement slurry sample is accurate; if the error is >3%, the specific heat capacity measurement of the cement slurry sample is inaccurate.

9. The specific heat capacity testing method according to claim 8, characterized in that: The wellbore-formation transient heat transfer model includes the pipe temperature distribution model, the drill string wall temperature distribution model and the annulus temperature distribution model; The expression of the temperature distribution model inside the tube is: ； The expression of the drill string wall temperature distribution model is: ； The expression of the annular temperature distribution model is: ； in: is the drilling fluid density; is the specific heat capacity of drilling fluid; is the displacement; is the depth step; is the inner radius of the drill string; is the convective heat transfer coefficient of the drill string inner wall; is the time step; Generate heat for complex heat source terms; is the radius of the drill string wall; is the thermal conductivity of the drill string wall; is the depth step at node j-0.5; is the depth step at node j+0.5; is the convective heat transfer coefficient of the drill string outer wall; is the wellbore radius; is the well wall convection heat transfer coefficient; is the fluid temperature in the drill string at the well depth j-1 and time n+1; is the fluid temperature in the drill string at the well depth j and time n+1; is the drill string wall temperature at depth j and time n+1; is the fluid temperature in the drill string at a well depth of j and a time of n; is the drill string wall temperature at depth j-1 and time n+1; is the drill string wall temperature at depth j+1 and time n+1; is the annular temperature at well depth j and time n+1; is the drill string wall temperature at depth j and time n; is the annular temperature at well depth j+1 and time n+1; is the annular temperature at well depth j and time n.

10. The specific heat capacity testing method according to claim 9, characterized in that: In step S61, the specific heat capacity of the cement slurry sample Replace drilling fluid specific heat capacity , the calculated annular temperature is the annular temperature at a well depth of j and a time of n. .

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