Blowout preventer group full life cycle evaluation method based on RFID

Abstract

The invention discloses an RFID-based blowout preventer group full life cycle evaluation method, which belongs to the field of petroleum well safety monitoring, and comprises the following steps: installing an RFID tag on a blowout preventer, monitoring functional data such as pressure, flow, temperature and sulfur content parameters in a blowout preventer group cavity, and establishing a blowout preventer group simulation model; further establishing a blowout preventer group full information storage database; correcting and predicting the simulation model; carrying out full life cycle monitoring on the blowout preventer group according to the RFID tag; according to the simulation model and the prediction model, performing safety prediction on a blowout preventer group flashboard, a blowout preventer group rubber core and a blowout preventer group flange connection seal of the blowout preventer assembly; and S6, the blowout preventer assembly is maintained according to the safety prediction result, based on the RFID technology, the pressure, the temperature, the sulfur content, the flow and other environmental parameters in a blowout preventer cavity under the blowout working condition can be more truly sensed, and more reliable data are provided for safety prediction of the blowout preventer assembly.

Description

Technical Field

[0001] The invention relates to the field of oil well safety monitoring, and in particular to a blowout preventer group full life cycle assessment method based on RFID. Background Art

[0002] During oil exploration and oilfield development, the BOP group is the last barrier to ensure the safety of oil wells. Under extreme blowout conditions such as high temperature, high pressure, and high sulfur content, the sealing components of the BOP group may fail due to erosion by the high-speed fluid in the well, causing deformation or leakage of key components of the BOP group. If a component of the BOP group fails, it will lead to the inability to successfully shut down the well, which will lead to uncontrolled blowout, causing serious consequences such as environmental pollution and casualties.

[0003] The BOP group is a fully sealed device. It is impossible to directly observe the inside of its cavity to determine whether key components are deformed or failed. It is very costly to dismantle the BOP for a comprehensive inspection. However, the current flaw detection equipment has poor detection effect on the cavity of the BOP group. It is crucial to obtain more realistic information about the BOP group under blowout conditions while ensuring safety, more accurately evaluate the safety performance of each component of the BOP group, and solve the technical problems of difficulty for on-site maintenance personnel. Summary of the invention

[0004] In view of the above problems, the present invention provides an RFID-based blowout preventer group full life cycle assessment method, which can accurately evaluate the safety performance of each component of the blowout preventer group and provide accurate guidance for on-site maintenance.

[0005] The technical solution of the present invention is:

[0006] A method for evaluating the life cycle of a blowout preventer group based on RFID includes the following steps:

[0007] S1. Install RFID tags on the BOP to monitor the pressure, flow, temperature, sulfur content and other functional data in the BOP group cavity, and establish a simulation model of the BOP group;

[0008] S2. Establish a full information storage database of the BOP group based on the acquired functional data;

[0009] S3, modifying and predicting the simulation model;

[0010] S4. Monitor the BOP group throughout its life cycle based on RFID tags;

[0011] S5. Bring the RFID tag data obtained in step S4 into the simulation model and the prediction model to perform safety prediction on the blowout preventer group gate, the blowout preventer group rubber core, and the blowout preventer group flange connection seal of the blowout preventer assembly;

[0012] S6. Maintain the BOP components based on the safety prediction results.

[0013] In step S1, a simulation model of a blowout preventer group is established through geometric parameters and physical parameters of the blowout preventer group, and a position of the blowout preventer to be installed with an RFID tag is determined.

[0014] In step S2, the functional parameters include: basic information of the BOP group and tag installation simulation data, various test data of BOP group materials, monitoring data of special RFID safety monitoring tags, maintenance and operation knowledge of the BOP group, and safety prediction data of the BOP group, wherein the safety prediction data of the BOP group includes: operation mechanics simulation data of the BOP group, erosion prediction data of sealing components, remaining life prediction data, and fatigue prediction data.

[0015] In step S3, fatigue, corrosion resistance, erosion resistance and other tests are conducted on the materials used to manufacture the BOP assembly, and the simulation model is corrected and predicted based on the test results.

[0016] In step S4, the data recorded by the RFID tag is transmitted to a full information storage database.

[0017] The safety prediction method of the blowout preventer gate is as follows:

[0018] The BOP operation data monitored by the tag is imported into the constructed 3D gate simulation model. Based on the three-dimensional transient temperature field control equation, a set of linear differential equations with time t as the independent variable is obtained:

[0019]

[0020] Where C is the heat capacity matrix; is the array of derivatives of nodal temperature with respect to time t; K is the heat transfer matrix; φ is the array of nodal temperatures; P is the array of temperature loads; the matrices C, K, and P are integrated through the corresponding matrix elements of the elements as follows:

[0021]

[0022]

[0023]

[0024] Using the above equations, the partial differential equation problem in the time domain and space domain is transformed into a temperature differential equation φ with N nodes in the space domain i The initial value problem of (t); the calculation equation using thermal structural analysis is as follows:

[0025]

[0026] Where M is the mass matrix; u and T are displacement and temperature loads respectively; C is the structural damping matrix; C t is the specific heat matrix; K is the structural stiffness matrix; K t is the heat transfer matrix; F is the total equivalent nodal force matrix; Q is the total equivalent nodal heat flux vector.

[0027] The safety prediction of the BOP rubber core is as follows:

[0028] The operation information monitored by the tag and the rubber core data stored in the full information storage database are imported into the constructed 3D rubber core simulation model, and the rubber core constitutive model is constructed based on the Mooney-Rivlin model. The original model is expanded to obtain the following strain energy function model:

[0029]

[0030] Where, d k is the compressibility coefficient of the material, J is the ratio of the volume after deformation to the volume before deformation, and N is the polynomial order;

[0031] Based on Miner damage mechanism, Fe-safe is used to calculate the fatigue of the rubber core. The maximum fatigue damage value is set to x (x < 1), and the calculation formula is:

[0032]

[0033] Where Ni is Δσ i Fatigue life under cyclic loading of stress; ni is the fatigue life under Δσ i The number of times the stress is cyclically loaded;

[0034] Based on the variable conversion algorithm, the aging performance change and life of the rubber core are predicted. The corrected relationship between the rubber core performance P, time t and temperature T is:

[0035]

[0036] P(T0,t0)=P(T,t)

[0037]

[0038] ρ1 and ρ2 are the core densities at T1 and T2; T0 is the reference temperature; α T It is only related to T0; b is the point slope slope after the improvement of Dakin life estimation method. The relationship between performance and time at different temperatures is obtained, so as to predict the aging performance change and life of the rubber core at different temperatures;

[0039] Based on the Oka model, the rubber core erosion rate is predicted as follows:

[0040] ε(θ)=f(θ)ε(r)

[0041]

[0042] Where ε(θ) and ε(r) are the erosion rates at and angle r, respectively, in mg / kg; n1 and n2 are coefficients related to the Vickers hardness (Hv) of the material. f(θ) is the erosion angle function.

[0043] The method for predicting the safety of the flange connection seal of the BOP group is as follows:

[0044] Import the tag monitoring data and the full information storage database data into the constructed flange connection and metal sealing ring 3D model to perform mechanical performance analysis and determine the maximum stress area and flange sealing connection strength;

[0045] Erosion prediction is performed based on the recognized semi-empirical erosion model. The DES model is used for the continuous phase, and the k-ε model is used for boundary calculation. The random walk model is used for the discrete phase to calculate the effect of turbulent diffusion on particles. The erosion model relationship is as follows:

[0046]

[0047]

[0048] Where ER is the erosion rate. When the solid particles are spherical, the sharpness factor of the Fs particles is 0.2. When the solid particles are sharp, the sharpness factor of the Fs particles is 1. p is the particle impact velocity (m / s); na is the velocity index;

[0049] At the same time, the installation process of the metal sealing ring is simulated to obtain the compressed metal sealing ring model, and the thermal stress simulation is performed on it to determine the thermal stress distribution of the metal sealing ring. Finally, the fatigue life simulation prediction is performed based on the Conffin-Masson fatigue model. The relationship between the fatigue model and the life prediction is as follows:

[0050]

[0051]

[0052] In the formula, ε a is the total deformation; ε ea is the elastic deformation component; ε pa is the plastic deformation component; E is the elastic modulus; σ' f is the fatigue strength coefficient; b is the fatigue strength index; ε' f is the fatigue ductility coefficient; C is the fatigue ductility index; N is the number of life cycles; ΔT is the temperature difference; K is the Boltzmann constant; f is the cycle frequency; T maxis the highest temperature; δ, β1, β2, E a is the coefficient to be determined.

[0053] The beneficial effects of the present invention are:

[0054] 1. RFID-based technology can more realistically sense environmental parameters such as pressure, temperature, sulfur content, flow rate, etc. in the blowout preventer cavity under blowout conditions, providing more reliable data for safety prediction of blowout preventer components;

[0055] 2. Safety prediction calculations were performed on the gate, flange connection seal and rubber core of the BOP group, fully considering various factors affecting the sealing performance of the BOP group, and improving the reliability and accuracy of safety monitoring of the BOP group throughout its life cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a method flow chart of a method for evaluating the entire life cycle of a blowout preventer group based on RFID according to an embodiment of the present invention;

[0057] Figure 2 is a schematic diagram of a blowout preventer group simulation model of a blowout preventer group full life cycle assessment method based on RFID according to an embodiment of the present invention;

[0058] Figure 3 is a schematic diagram of an RFID tag of a blowout preventer group full life cycle assessment method based on RFID according to an embodiment of the present invention;

[0059] Figure 4 It is a schematic diagram of a full information storage database of a blowout preventer group full life cycle assessment method based on RFID according to an embodiment of the present invention;

[0060] Figure 5 It is a schematic diagram of a material performance test of a blowout preventer group according to an RFID-based blowout preventer group full life cycle assessment method described in an embodiment of the present invention;

[0061] Figure 6 It is a schematic diagram of a safety prediction model of each component of a blowout preventer group in a blowout preventer group full life cycle assessment method based on RFID according to an embodiment of the present invention;

[0062] Figure 7 It is a schematic diagram of a blowout preventer group maintenance and replacement guidance model of a blowout preventer group full life cycle assessment method based on RFID according to an embodiment of the present invention;

[0063] Figure 8 It is a schematic diagram of the integration of historical maintenance information and virtual guidance scheme of a blowout preventer group full life cycle assessment method based on RFID according to an embodiment of the present invention;

[0064] Fig. 9It is a schematic diagram of information interaction of an RFID-based blowout preventer group full life cycle assessment method described in an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The embodiments of the present invention will be further described below in conjunction with the accompanying drawings.

[0066] Example:

[0067] like Figure 1-Figure 5 As shown, a method for evaluating the entire life cycle of a blowout preventer group based on RFID includes the following steps:

[0068] S1. Install RFID tags on the BOP to monitor the pressure, flow, temperature, sulfur content and other functional data in the BOP group cavity, and establish a simulation model of the BOP group;

[0069] The simulation model of the BOP group is established through the geometric parameters and physical parameters of the BOP group, and the position of the RFID tag to be installed on the BOP group is determined.

[0070] S2. Establish a full information storage database of the BOP group based on the acquired functional data;

[0071] Functional parameters include: basic information of BOP group and tag installation simulation data, various test data of BOP group materials, monitoring data of special RFID safety monitoring tags, maintenance and operation knowledge of BOP group and safety prediction data of BOP group, among which the safety prediction data of BOP group includes: operation mechanics simulation data of BOP group, erosion prediction data of sealing components, remaining life prediction data and fatigue prediction data.

[0072] S3, modifying and predicting the simulation model;

[0073] The materials used to manufacture the BOP group are tested for fatigue, corrosion resistance, erosion resistance, etc., and the simulation model is corrected and predicted based on the test results.

[0074] S4. Monitor the BOP group throughout its life cycle based on RFID tags;

[0075] The data recorded by the RFID tag is transmitted to the full information storage database.

[0076] S5. Bring the RFID tag data obtained in step S4 into the simulation model and the prediction model to perform safety prediction on the blowout preventer group gate, the blowout preventer group rubber core, and the blowout preventer group flange connection seal of the blowout preventer assembly;

[0077] The safety prediction method of the blowout preventer gate is as follows:

[0078] The BOP operation data monitored by the tag is imported into the constructed 3D gate simulation model. Based on the three-dimensional transient temperature field control equation, a set of linear differential equations with time t as the independent variable is obtained:

[0079]

[0080] Where C is the heat capacity matrix; is the array of derivatives of nodal temperature with respect to time t; K is the heat transfer matrix; φ is the array of nodal temperatures; P is the array of temperature loads; the matrices C, K, and P are integrated through the corresponding matrix elements of the elements as follows:

[0081]

[0082]

[0083]

[0084] Using the above equations, the partial differential equation problem in the time domain and space domain is transformed into a temperature differential equation φ with N nodes in the space domain i The initial value problem of (t); the calculation equation using thermal structural analysis is as follows:

[0085]

[0086] Where M is the mass matrix; u and T are displacement and temperature loads respectively; C is the structural damping matrix; C t is the specific heat matrix; K is the structural stiffness matrix; K t is the heat transfer matrix; F is the total equivalent nodal force matrix; Q is the total equivalent nodal heat flux vector.

[0087] The safety prediction of the BOP rubber core is as follows:

[0088] The operation information monitored by the tag and the rubber core data stored in the full information storage database are imported into the constructed 3D rubber core simulation model, and the rubber core constitutive model is constructed based on the Mooney-Rivlin model. The original model is expanded to obtain the following strain energy function model:

[0089]

[0090] Where, d k is the compressibility coefficient of the material, J is the ratio of the volume after deformation to the volume before deformation, and N is the polynomial order;

[0091] Based on Miner damage mechanism, Fe-safe is used to calculate the fatigue of the rubber core. The maximum fatigue damage value is set to x (x < 1), and the calculation formula is:

[0092]

[0093] Where Ni is Δσ i Fatigue life under cyclic loading of stress; ni is the fatigue life under Δσ i The number of times the stress is cyclically loaded;

[0094] Based on the variable conversion algorithm, the aging performance change and life of the rubber core are predicted. The corrected relationship between the rubber core performance P, time t and temperature T is:

[0095]

[0096] P(T0,t0)=P(T,t)

[0097]

[0098] ρ1 and ρ2 are the core densities at T1 and T2; T0 is the reference temperature; α T It is only related to T0; b is the point slope slope after the improvement of Dakin life estimation method. The relationship between performance and time at different temperatures is obtained, so as to predict the aging performance change and life of the rubber core at different temperatures;

[0099] Based on the Oka model, the rubber core erosion rate is predicted as follows:

[0100] ε(θ)=f(θ)ε(r)

[0101]

[0102] Where ε(θ) and ε(r) are the erosion rates at and angle r, respectively, in mg / kg; n1 and n2 are coefficients related to the Vickers hardness (Hv) of the material. f(θ) is the erosion angle function.

[0103] The method for predicting the safety of the flange connection seal of the BOP group is as follows:

[0104] Import the tag monitoring data and the full information storage database data into the constructed flange connection and metal sealing ring 3D model to perform mechanical performance analysis and determine the maximum stress area and flange sealing connection strength;

[0105] Erosion prediction is performed based on the recognized semi-empirical erosion model. The DES model is used for the continuous phase, and the k-ε model is used for boundary calculation. The random walk model is used for the discrete phase to calculate the effect of turbulent diffusion on particles. The erosion model relationship is as follows:

[0106]

[0107]

[0108] Where ER is the erosion rate. When the solid particles are spherical, the sharpness factor of the Fs particles is 0.2. When the solid particles are sharp, the sharpness factor of the Fs particles is 1. p is the particle impact velocity (m / s); na is the velocity index;

[0109] At the same time, the installation process of the metal sealing ring is simulated to obtain the compressed metal sealing ring model, and the thermal stress simulation is performed on it to determine the thermal stress distribution of the metal sealing ring. Finally, the fatigue life simulation prediction is performed based on the Conffin-Masson fatigue model. The relationship between the fatigue model and the life prediction is as follows:

[0110]

[0111]

[0112] In the formula, ε a is the total deformation; ε ea is the elastic deformation component; ε pa is the plastic deformation component; E is the elastic modulus; σ' f is the fatigue strength coefficient; b is the fatigue strength index; ε' f is the fatigue ductility coefficient; C is the fatigue ductility index; N is the number of life cycles; ΔT is the temperature difference; K is the Boltzmann constant; f is the cycle frequency; T max is the highest temperature; δ, β1, β2, E a is the coefficient to be determined.

[0113] S6. Maintain the BOP components based on the safety prediction results.

[0114] Transmit the sorted data to the full information storage database and information interaction module;

[0115] The data sorting and comparison unit compares the temperature field load P0 of the blowout preventer gate; the remaining fatigue life N1 of the blowout preventer group rubber core, the rubber core performance P1, the erosion function f(θ); the remaining fatigue life N2 of the flange connection metal sealing ring, the erosion rate ER. When the safety boundary conditions set in advance are not met, the fatigue, erosion, and life prediction alarm unit of the information interaction module will issue an alarm;

[0116] Figure 7As shown, repair and replacement of damaged or high-position components are guided, wherein: a maintenance guidance platform is established according to the technical manual for maintenance guidance of failure forms of the blowout preventer group, and then a 3D model of the blowout preventer group is established, and then a maintenance standard schematic diagram is established, and finally a blowout preventer group maintenance guidance animation is formed, and the blowout preventer group failure analysis and information matching unit first identifies and classifies the prediction results, classifies the failure model identification, and then establishes a blowout preventer group failure form database, and then establishes a blowout preventer group failure ID identification number, and finally matches the best maintenance solution for the blowout preventer group failure;

[0117] Figure 8 As shown, the best maintenance solution matched in S6 and the historical maintenance information are fused virtual and real by combining failure feature registration and manual identification registration, and a maintenance guidance solution for the failure parts of the blowout preventer group is generated and transmitted to a visual portable device to guide maintenance personnel to perform failure maintenance of the blowout preventer group;

[0118] Fig. 9 As shown, the historical maintenance information includes RFID tag positioning coordinates, blowout preventer component failure identification, maintenance 3D scene reconstruction, blowout preventer component failure part life and failure form, etc.

[0119] This technology uses special RFID safety monitoring tags to sense the environmental data information inside the blowout preventer group cavity under blowout conditions. While monitoring the operation of the blowout preventer, it provides accurate data support for its safety prediction. It can take real-time consideration of changes in operating conditions and ensure the safety performance of the blowout preventer group throughout its life cycle.

[0120] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for evaluating the life cycle of a blowout preventer group based on RFID, characterized in that: The steps include: S1. Install RFID tags on the BOP to monitor the pressure, flow, temperature, sulfur content and other functional data in the BOP group cavity, and establish a simulation model of the BOP group; S2. Establish a full information storage database of the BOP group based on the acquired functional data; S3, modifying and predicting the simulation model; S4. Monitor the BOP group throughout its life cycle based on RFID tags; S5. Bring the RFID tag data obtained in step S4 into the simulation model and the prediction model to perform safety prediction on the blowout preventer group gate, the blowout preventer group rubber core, and the blowout preventer group flange connection seal of the blowout preventer assembly; S6. Maintain the BOP components based on the safety prediction results.

2. The RFID-based BOP group life cycle assessment method according to claim 1, characterized in that: In step S1, a simulation model of a blowout preventer group is established through geometric parameters and physical parameters of the blowout preventer group, and a position of the blowout preventer to be installed with an RFID tag is determined.

3. The RFID-based BOP group life cycle assessment method according to claim 1, characterized in that: In step S2, the functional parameters include: basic information of the BOP group and tag installation simulation data, various test data of BOP group materials, monitoring data of special RFID safety monitoring tags, maintenance and operation knowledge of the BOP group, and safety prediction data of the BOP group, wherein the safety prediction data of the BOP group includes: operation mechanics simulation data of the BOP group, erosion prediction data of sealing components, remaining life prediction data, and fatigue prediction data.

4. The RFID-based BOP group life cycle assessment method according to claim 1, characterized in that: In step S3, fatigue, corrosion resistance, erosion resistance and other tests are conducted on the materials used to manufacture the BOP assembly, and the simulation model is corrected and predicted based on the test results.

5. The RFID-based BOP group life cycle assessment method according to claim 1, characterized in that: In step S4, the data recorded by the RFID tag is transmitted to a full information storage database.

6. The RFID-based BOP group life cycle assessment method according to claim 1, characterized in that: In step S5, the method for predicting the safety of the blowout preventer gate is as follows: The BOP operation data monitored by the tag is imported into the constructed 3D gate simulation model. Based on the three-dimensional transient temperature field control equation, a set of linear differential equations with time t as the independent variable is obtained: Where C is the heat capacity matrix; is the array of derivatives of nodal temperature with respect to time t; K is the heat transfer matrix; φ is the array of nodal temperatures; P is the array of temperature loads; the matrices C, K, and P are integrated through the corresponding matrix elements of the elements as follows: Using the above equations, the partial differential equation problem in the time domain and space domain is transformed into a temperature differential equation φ with N nodes in the space domain i The initial value problem of (t); the calculation equation using thermal structural analysis is as follows: Where M is the mass matrix; u and T are displacement and temperature loads respectively; C is the structural damping matrix; C t is the specific heat matrix; K is the structural stiffness matrix; K t is the heat transfer matrix; F is the total equivalent nodal force matrix; Q is the total equivalent nodal heat flux vector.

7. The RFID-based BOP group life cycle assessment method according to claim 1, characterized in that: In step S5, the safety prediction of the rubber core of the BOP assembly is as follows: The operation information monitored by the tag and the rubber core data stored in the full information storage database are imported into the constructed 3D rubber core simulation model, and the rubber core constitutive model is constructed based on the Mooney-Rivlin model. The original model is expanded to obtain the following strain energy function model: Where, d k is the compressibility coefficient of the material, J is the ratio of the volume after deformation to the volume before deformation, and N is the polynomial order; Based on Miner damage mechanism, Fe-safe is used to calculate the fatigue of the rubber core. The maximum fatigue damage value is set to x (x < 1), and the calculation formula is: Where Ni is Δσ i Fatigue life under cyclic loading of stress; ni is the fatigue life under Δσ i The number of times the stress is cyclically loaded; Based on the variable conversion algorithm, the aging performance change and life of the rubber core are predicted. The corrected relationship between the rubber core performance P, time t and temperature T is: P(T0,t0)=P(T,t) ρ1 and ρ2 are the core densities at T1 and T2; T0 is the reference temperature; α T It is only related to T0; b is the point slope slope after the improvement of Dakin life estimation method. The relationship between performance and time at different temperatures is obtained, so as to predict the aging performance change and life of the rubber core at different temperatures; Based on the Oka model, the rubber core erosion rate is predicted as follows: ε(θ)=f(θ)ε(r) Where ε(θ) and ε(r) are the erosion rates at and angle r, respectively, in mg / kg; n1 and n2 are coefficients related to the Vickers hardness (Hv) of the material. f(θ) is the erosion angle function.

8. The RFID-based BOP group life cycle assessment method according to claim 1, characterized in that: In step S5, the method for predicting the safety of the flange connection seal of the blowout preventer group is as follows: Import the tag monitoring data and the full information storage database data into the constructed flange connection and metal sealing ring 3D model to perform mechanical performance analysis and determine the maximum stress area and flange sealing connection strength; Erosion prediction is performed based on the recognized semi-empirical erosion model. The DES model is used for the continuous phase, and the k-ε model is used for boundary calculation. The random walk model is used for the discrete phase to calculate the effect of turbulent diffusion on particles. The erosion model relationship is as follows: Where ER is the erosion rate. When the solid particles are spherical, the sharpness factor of the Fs particles is 0.

2. When the solid particles are sharp, the sharpness factor of the Fs particles is 1. p is the particle impact velocity (m / s); na is the velocity index; At the same time, the installation process of the metal sealing ring is simulated to obtain the compressed metal sealing ring model, and the thermal stress simulation is performed on it to determine the thermal stress distribution of the metal sealing ring. Finally, the fatigue life simulation prediction is performed based on the Conffin-Masson fatigue model. The relationship between the fatigue model and the life prediction is as follows: In the formula, ε a is the total deformation; ε ea is the elastic deformation component; ε pa is the plastic deformation component; E is the elastic modulus; σ′ f is the fatigue strength coefficient; b is the fatigue strength index; ε′ f is the fatigue ductility coefficient; C is the fatigue ductility index; N is the number of life cycles; ΔT is the temperature difference; K is the Boltzmann constant; f is the cycle frequency; T max is the highest temperature; δ, β1, β2, E a is the coefficient to be determined.

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