Intelligent control and energy-saving workover rig integrated system
By collecting and analyzing well repair operation data in real time and adjusting power output dynamically, the problem of friction resistance changes in the existing technology being not identified in time and power adjustment lag is achieved, and efficient and energy-saving well repair operations are achieved.
Patent Information
- Application Number
- CN202510485620.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-17
- Publication Date
- 2025-08-01
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
The existing technology failed to realize multi-dimensional real-time monitoring of well fluid parameters and friction resistance changes in well repair operations, resulting in lag in power regulation, increasing energy consumption and reducing equipment stability, lacking prediction and response to future loads, affecting equipment operation efficiency and life.
By collecting data such as repairing pipe column depth, wellbore temperature, well fluid viscosity and well wall pressure, calculate the friction resistance change trend, dynamically adjust the power output, combine historical data to predict future load changes, optimize power consumption strategies, identify low resistance states and adjust power output.
It realizes accurate capture and prediction of frictional resistance changes, optimizes power adjustment timing, improves operating efficiency, reduces energy consumption, extends equipment life, and enhances the system's adaptability to complex working conditions.
Smart Images

Figure CN120401978A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of intelligent manufacturing equipment, and particularly to an integrated system of intelligent control and energy-saving workover rigs. Background Art
[0002] The technical field of intelligent manufacturing equipment includes intelligent production equipment, automated control systems, digital management platforms, and cyber-physical systems, etc. The core content of this technical field is to achieve intelligent regulation of the production process by integrating sensors, actuators, industrial controllers, and human-machine interaction systems. The overall technical field involves multiple aspects such as computer control, mechanical design, sensing technology, network communication, and industrial software. Among them, computer control is used to manage and optimize the production process, mechanical design ensures the structural stability and functional adaptability of the equipment, sensing technology is used to monitor the equipment status and working parameters in real time, network communication realizes remote monitoring and data transmission, and industrial software supports data analysis and optimized configuration of the production process.
[0003] Among them, the integrated system of intelligent control and energy-saving workover rigs refers to a system that uses intelligent control technology to monitor and dynamically adjust the operating status of workover equipment in real time to reduce energy consumption and improve operation efficiency. This system controls and manages technical matters such as equipment operation parameter acquisition, power distribution optimization, load adjustment, and abnormal state identification during the workover operation process. Specifically, it uses a data acquisition method based on a sensor array to obtain real-time load information, uses an energy management model to dynamically adjust the power output of the hydraulic system, adopts a valve-controlled flow regulation strategy to optimize the response speed of the hydraulic actuator, and combines a state estimation algorithm to identify and warn of abnormal working conditions of the equipment to ensure the stability and safety of the workover operation.
[0004] The existing technology fails to achieve multi-dimensional real-time monitoring in data acquisition, lacks detailed analysis of well fluid parameters and friction resistance changes, resulting in untimely identification of friction resistance trends and affecting the accuracy of power regulation. During the power regulation process, it fails to dynamically adjust the output according to the load change trend, has problems of lag or over-adjustment, increases energy consumption and reduces equipment stability. The utilization of historical data is insufficient, lacking prediction and response to future loads, increasing the risk of sudden abnormalities. Energy consumption management fails to achieve dynamic optimization, has inaccurate identification of low-resistance states, and lags in power output adjustment, resulting in high energy consumption and affecting the operation efficiency and lifespan of the equipment. The above problems limit the improvement of operation efficiency and increase the operation and maintenance difficulty and cost. Summary of the Invention
[0005] The purpose of the present invention is to solve the deficiencies existing in the prior art and to propose an integrated system of intelligent control and energy-saving workover rigs.
[0006] To achieve the above object, the present invention adopts the following technical solutions: An intelligent control and energy-saving integrated system for a workover rig includes:
[0007] The data acquisition module obtains the depth of the workover string, the wellbore temperature and the viscosity of the well fluid, calls the strain device to collect the friction resistance, calls the pressure device to collect the wellbore pressure, and generates a friction resistance monitoring data set based on the depth, resistance, temperature, viscosity, and pressure;
[0008] The friction resistance trend calculation module calls the friction resistance monitoring data set, calculates the change amount of the friction resistance per unit depth according to the continuous data, calls the threshold value to judge whether the change exceeds the benchmark, and calls the calculation of the change amplitude to generate a friction resistance change trend coefficient;
[0009] The power dynamic adjustment module calls the friction resistance change trend coefficient, judges the interval power adjustment requirement based on the change direction of the friction resistance, calculates the additional power requirement according to the current power of the workover rig, compares the additional power with the preset threshold value based on the power compensation threshold value, calls the time parameter to calculate the duration of the power gain, and adjusts the output of the workover rig based on the additional power requirement and the duration to generate a dynamic power output value;
[0010] The feedforward power optimization module calls the dynamic power output value, obtains the historical friction resistance trend data, calls the depth data to judge the future resistance direction, calls the temperature and viscosity data to correct the prediction value, and calls the compensation threshold value to calculate and generate a feedforward power control value.
[0011] As a further solution of the present invention, the friction resistance monitoring data set is specifically the pipe string depth data, the wellbore temperature data, the well fluid viscosity data, the friction resistance data, and the wellbore pressure data. The friction resistance change trend coefficient includes the resistance change rate, the benchmark overrun index, and the amplitude change amount. The dynamic power output value is specifically the additional power requirement value, the power gain duration, and the output adjustment amount. The feedforward power control value specifically refers to the historical trend reference, the future resistance prediction, the corrected prediction index, and the compensation adjustment value.
[0012] As a further solution of the present invention, the data acquisition module includes:
[0013] The depth temperature viscosity acquisition sub-module obtains the depth of the workover string, detects the wellbore temperature and the viscosity of the well fluid, collects the temperature data at various depth positions during workover, analyzes the temperature change trend at multiple depths, calculates the viscosity of the well fluid under different temperature conditions, and matches the viscosity correction value in combination with the depth information to obtain the depth temperature viscosity data;
[0014] The friction resistance acquisition sub-module, based on the depth temperature viscosity data, calls the strain device to collect the friction resistance data, analyzes the distribution characteristics of the friction force at multiple depths, calculates the friction resistance of the pipe string at different depths, and combines the temperature viscosity to correct the friction force calculation value to obtain the friction resistance data;
[0015] The wellbore pressure calculation sub-module calls a pressure device to collect wellbore pressure data, calculates the force on the pipe string based on the friction resistance data, analyzes the change of wellbore pressure in combination with depth information, and uses the formula:
[0016]
[0017] Performs operations to obtain wellbore pressure data and establishes a friction resistance monitoring data set;
[0018] Among them, Pr represents the wellbore pressure, Ffr a represents the friction resistance at the a-th position, Fvf a represents the vertical force of the depth pipe string, η a represents the viscosity of the well fluid, Dia a represents the wellbore diameter at the depth, T inf a represents the depth temperature influence factor, and b represents the total number of measurement points.
[0019] As a further solution of the present invention, the friction resistance trend calculation module includes:
[0020] The friction resistance monitoring data processing sub-module calls the friction resistance monitoring data set, extracts the data of the change of friction resistance with depth, rearranges the friction resistance data sequence according to the depth interval, compares adjacent data points, screens out missing and abnormal values, calculates the depth increment of adjacent data points, and obtains the friction resistance depth change data sequence;
[0021] The unit-depth friction resistance calculation sub-module calculates the standard deviation of the friction resistance within the depth interval based on the friction resistance depth change data sequence and normalizes it to the unit depth, using the formula:
[0022]
[0023] Calculates the standard deviation of the unit-depth friction resistance and obtains the change amount of the unit-depth friction resistance;
[0024] Among them, ΔRsd represents the standard deviation of the unit-depth friction resistance, M c represents the friction resistance value at the c-th place, M represents the average friction resistance value, d represents the total number of monitoring data points, and Dep represents the total depth;
[0025] The trend change analysis sub-module calculates the change amplitude by calling a set threshold according to the change amount of the unit-depth friction resistance, determines whether it exceeds the reference value, and calculates and obtains the friction resistance change trend coefficient.
[0026] As a further solution of the present invention, the power dynamic adjustment module includes:
[0027] The power adjustment requirement judgment sub-module calls the friction resistance change trend coefficient, judges the power adjustment requirement within the interval based on the change direction of the friction resistance, calculates the positive and negative of the change direction of the friction resistance, and determines the amplitude of the power adjustment of the workover rig according to the power adjustment requirement, and obtains the power adjustment demand quantity;
[0028] The additional power calculation sub-module calculates the additional power requirement according to the power adjustment demand quantity, combines it with the current power of the workover rig, calls the power compensation threshold, compares the additional power requirement with the preset threshold, and uses the formula:
[0029]
[0030] Calculates the additional power requirement and makes a judgment on the power compensation threshold to obtain the power adjustment parameter of the workover rig;
[0031] Among them, Pwr represents the newly calculated additional power requirement, W current represents the current power, ΔP represents the additional power calculated from the power adjustment demand quantity, Tadj represents the efficiency adjustment time, Rtr represents the friction resistance change trend coefficient, T norm represents the normalized time parameter;
[0032] The dynamic power output sub-module calls the power adjustment parameter of the workover rig, calculates the power gain duration by calling the time parameter, and adjusts the output of the workover rig according to the additional power requirement and the duration to obtain the dynamic power output value.
[0033] As a further solution of the present invention, the feedforward power optimization module includes:
[0034] The dynamic power data processing sub-module calls the dynamic power output value, obtains the corresponding time series, extracts the output value corresponding to the time point, calculates the instantaneous change rate according to the time interval, screens out abnormal data and eliminates missing values, and at the same time calls the past friction resistance trend data, matches the data in the corresponding time interval, calculates the average power output, and obtains the time series matching data set;
[0035] The future resistance trend calculation sub-module calls the depth data based on the time series matching data set, calculates the depth change rate, and at the same time calculates the friction resistance increase and decrease rate according to the past trend data, and uses the formula:
[0036]
[0037] Obtains the future resistance trend value;
[0038] Among them, Rf represents the future resistance trend value, V e represents the velocity difference at the e-th time, H e represents the depth difference at the e-th time, f represents the total number of velocity change data points, g represents the total number of depth data points, Hh represents the depth value;
[0039] The feed-forward power adjustment sub-module calls the temperature and viscosity data according to the future resistance trend value, calculates the temperature and viscosity influence factors, and at the same time calls the compensation threshold, adjusts the power parameters based on the trend value, calculates the compensated power output, and obtains the feed-forward power regulation value.
[0040] As a further solution of the present invention, the system further includes:
[0041] The energy consumption regulation module calls the feed-forward power regulation value, obtains the power consumption data of the workover rig, calls the energy-saving mode parameters to judge the low-resistance state, calls the power strategy to adjust the consumption, and generates the energy consumption optimization value;
[0042] The energy consumption optimization value includes the power consumption monitoring index, the low-resistance state determination value, and the strategy adjustment effect.
[0043] As a further solution of the present invention, the energy consumption regulation module includes:
[0044] The power consumption data acquisition sub-module calls the feed-forward power regulation value, obtains the power consumption data during the operation of the workover rig, sorts the power consumption data based on the time series, screens out the abnormal points and missing values, calculates the average power within multiple time intervals, and obtains the average power consumption data;
[0045] The low-resistance state determination sub-module calls the energy-saving mode parameters based on the power consumption data of the workover rig, calculates the power fluctuation range within the target time period, and at the same time determines the low-resistance state according to the fluctuation amplitude, calls the set low-resistance threshold, and calculates the power fluctuation deviation value according to the time series to obtain the low-resistance state determination result;
[0046] The energy consumption optimization analysis sub-module calls the power strategy adjustment parameters according to the low-resistance state determination result and uses the formula:
[0047]
[0048] Calculate to obtain the energy consumption optimization value;
[0049] where, E opt represents the energy consumption optimization value, P max represents the maximum power consumption value within the monitoring period, P min represents the minimum power consumption value within the monitoring period, P avg represents the average power consumption value within the monitoring period, P tot represents the total power consumption value within the monitoring period, T int i represents the time interval at the i-th moment, j represents the number of time periods, and k represents the total number of monitoring data points.
[0050] Compared with the prior art, the advantages and positive effects of the present invention are as follows:
[0051] In the present invention, by collecting real-time data such as the depth of the pipe string, wellbore temperature, well fluid viscosity, friction resistance, and wellbore pressure during workover operations, the change in friction resistance is accurately captured, abnormal trends are identified in advance, and the timing of power adjustment is optimized. Based on the trend of friction resistance change, the power output is dynamically adjusted to ensure a rapid response when the load changes, improve the operation efficiency, and avoid energy waste. The future load change is predicted using historical data, and the predicted value is corrected by combining temperature and viscosity parameters to enhance the adaptability to complex working conditions and reduce the impact of unexpected situations. By optimizing the power consumption strategy, the low-resistance state is identified and the power output is adjusted to reduce energy consumption and extend the equipment life. This processing method improves the energy utilization rate, reduces the operation and maintenance cost, enhances the adaptability of the system to complex working environments, optimizes the operation process, and ensures the stability and economy of the operation. BRIEF DESCRIPTION OF THE DRAWINGS
[0052] Figure 1 is the system flow chart of the present invention;
[0053] Figure 2 is the flow chart of the data acquisition module of the present invention;
[0054] Figure 3 is the flow chart of the friction resistance trend calculation module of the present invention;
[0055] Figure 4 is the flow chart of the power dynamic adjustment module of the present invention;
[0056] Figure 5 is the flow chart of the feedforward power optimization module of the present invention;
[0057] Figure 6 is the flow chart of the energy consumption regulation module of the present invention. DETAILED DESCRIPTION OF THE INVENTION
[0058] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.
[0059] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by terms such as "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention. In addition, in the description of the present invention, the meaning of "a plurality of" is two or more, unless otherwise specifically defined.
[0060] Embodiment 1
[0061] Please refer to Figure 1 , an integrated system of intelligent control and energy-saving workover rig includes:
[0062] The data acquisition module obtains the depth of the workover string, the wellbore temperature and the viscosity of the well fluid, calls the strain device to collect the frictional resistance, calls the pressure device to collect the wellbore pressure, and generates a frictional resistance monitoring data set based on the depth, resistance, temperature, viscosity, and pressure;
[0063] The frictional resistance trend calculation module calls the frictional resistance monitoring data set, calculates the change amount of the frictional resistance per unit depth according to the continuous data, calls the threshold value to judge whether the change exceeds the benchmark, and calls the calculation of the change amplitude to generate a frictional resistance change trend coefficient;
[0064] The power dynamic adjustment module calls the frictional resistance change trend coefficient, judges the interval power adjustment requirement based on the change direction of the frictional resistance, calculates the additional power requirement according to the current power of the workover rig, compares the additional power with the preset threshold value based on the power compensation threshold value, calls the time parameter to calculate the duration of the power gain, and adjusts the output of the workover rig based on the additional power requirement and the duration to generate a dynamic power output value;
[0065] The feedforward power optimization module calls the dynamic power output value, obtains the past frictional resistance trend data, calls the depth data to judge the future resistance direction, calls the temperature and viscosity data to correct the predicted value, and calls the compensation threshold value to calculate and generate a feedforward power regulation value;
[0066] The energy consumption regulation module calls the feedforward power regulation value, obtains the power consumption data of the workover rig, calls the energy-saving mode parameter to judge the low-resistance state, calls the power strategy to adjust the consumption, and generates an energy consumption optimization value.
[0067] The friction monitoring dataset specifically includes pipe string depth data, wellbore temperature data, well fluid viscosity data, friction resistance data, and wellbore wall pressure data. The friction change trend coefficients include the resistance change rate, the reference tolerance index, and the amplitude change amount. The dynamic power output value specifically refers to the additional power demand value, the power gain duration, and the output adjustment amount. The feedforward power regulation value specifically refers to the historical trend reference, the future resistance prediction, the correction prediction index, and the compensation adjustment value. The energy consumption optimization value includes the power consumption monitoring index, the low-resistance state determination value, and the strategy adjustment effect.
[0068] Please refer to Figure 2 , and the data acquisition module includes:
[0069] The depth-temperature-viscosity acquisition sub-module obtains the depth of the workover pipe string, detects the wellbore temperature and the well fluid viscosity, collects the temperature data at various depth positions during workover, analyzes the temperature change trend at multiple depths, calculates the viscosity of the well fluid under different temperature conditions, matches the viscosity correction value with the depth information, and obtains the depth-temperature-viscosity data;
[0070] In the specific execution process, first, call the depth measurement device, such as a magnetic depth sounder or an electronic depth sounder, to obtain the current depth information of the pipe string in the well, and record the sounding time point to establish a time-depth data pair. Secondly, use a thermocouple or a fiber optic temperature sensor to detect the wellbore temperature at multiple depth positions, with each measurement point spacing set to 2m, to obtain the temperature change trend along the wellbore depth direction. Further, use an on-line viscosity measurement device, such as a capillary rheometer or a rotational viscometer, to measure the well fluid viscosity. Among them, the viscosity measurement is based on the shear rate response of the well fluid at different temperatures. When measuring, select the viscosity values at three shear rates, and use linear interpolation to calculate the well fluid viscosity at the corresponding temperature points, complete the matching of the temperature-viscosity data, and then combine the depth information to calculate the corrected viscosity value of the well fluid under this depth condition, and correct it using the temperature-viscosity empirical model. The model parameters are taken from historical test data or laboratory calibration values, and finally obtain the depth-temperature-viscosity data. The data record is shown in Table 1 below:
[0071] Table 1 Depth-Temperature-Viscosity Data Table
[0072] Depth (m) Wellbore Temperature (°C) Well Fluid Viscosity (mPa·s) 500 50 10.5 1000 80 7.8 1500 110 5.2
[0073] As shown in Table 1, at depths of 500m, 1000m, and 1500m, the temperatures are 50°C, 80°C, and 110°C respectively, and the corresponding well fluid viscosities are 10.5mPa·s, 7.8mPa·s, and 5.2mPa·s respectively, indicating that the well fluid viscosity decreases with the increase of depth. This data can be used for subsequent friction resistance calculation.
[0074] The friction resistance acquisition sub-module collects friction resistance data by calling a strain device based on depth temperature viscosity data, analyzes the distribution characteristics of friction forces at multiple depths, calculates the friction resistance of the pipe string at different depths, and combines temperature viscosity to correct the calculated friction force value to obtain friction resistance data;
[0075] During the specific execution process, first, axial strain at each depth position of the pipe string is detected by installing strain gauges on the surface of the pipe string. The axial load is calculated based on the measured strain value in combination with the material elastic modulus and cross-sectional area. The formula F = σ·A is used, where σ is the stress and A is the cross-sectional area of the pipe string. The friction resistance of the pipe string is calculated at each depth. Secondly, the influence of well fluid viscosity on friction force calculation is considered, and the corrected friction coefficient μ c = μ0·η a / η ref is adopted, where μ0 is the reference friction coefficient, η a is the viscosity at the current depth, and η ref is the viscosity at the reference temperature. By calculating the friction forces at different depths and plotting the friction resistance distribution curve, the change trend of friction force can be intuitively analyzed. The calculation results are as follows:
[0076] Table 2 Friction Resistance Data Table
[0077] Depth (m) Axial Load (kN) Friction Force (kN) 500 12.5 3.1 1000 9.2 2.6 1500 7.5 2.1
[0078] Table 2 lists the calculation results of friction resistance. The friction force is the largest at a depth of 500m, and the friction force shows a downward trend as the depth increases. This result indicates that depth temperature viscosity has a significant impact on friction force, which can be used for wellbore pressure calculation in the future.
[0079] The wellbore pressure calculation sub-module calls a pressure device to collect wellbore pressure data, calculates the force condition of the pipe string based on the friction resistance data, analyzes the change of wellbore pressure in combination with depth information, and uses the formula:
[0080]
[0081] to calculate and obtain wellbore pressure data and establish a friction resistance monitoring data set;
[0082] where Pr represents the wellbore pressure, Ffr a represents the friction resistance at the a-th position, Fvf a represents the vertical force of the pipe string at the depth, η a represents the well fluid viscosity, Dia a represents the wellbore diameter at the depth, Tinf a represents the depth temperature influence factor, and b represents the total number of measurement points.
[0083] During the specific implementation process, first, call the downhole pressure sensor to measure the pressure values at each depth position and record them in the database. Secondly, combine the friction resistance data to calculate the stress state of the pipe string at different depths, using the formula:
[0084]
[0085] Wherein, The term represents the sum of squares of the temperature influence factors. Calculate by combining the obtained data. Take the friction resistance Ffr a and the vertical acting force Fvf a at depths of 500m, 1000m, and 1500m. Based on the friction force data in Table 2, η a Take the well fluid viscosity in Table 1, and set the wellbore diameter Dia a to 0.3m, and assume the temperature influence factor Tinf a to be Calculate, and set the reference temperature T ref to 25°C, and perform numerical calculations as follows:
[0086]
[0087]
[0088] Finally, the calculated wellbore pressure is 836.87 kPa. This result shows that the wellbore pressure is affected by multiple factors such as depth, friction resistance, and well fluid viscosity, and can be further used to establish a friction resistance monitoring dataset to optimize the workover construction parameters
[0089] Please refer to Figure 3 , the friction resistance trend calculation module includes:
[0090] The friction resistance monitoring data processing sub-module calls the friction resistance monitoring dataset, extracts the data of the change of friction resistance with depth, rearranges the friction resistance data sequence according to the depth interval, compares adjacent data points, screens out missing and abnormal values, calculates the depth increment of adjacent data points, and obtains the friction resistance depth change data sequence;
[0091] Specifically, first read all the monitoring data and sort them in ascending order of the monitoring depth to ensure the orderliness of the data. After the sorting is completed, compare the friction resistance values of adjacent data points to identify possible abnormal values. When the sudden increase or decrease of the friction resistance change exceeds the set threshold, it is determined as an abnormal value. The threshold is set based on statistical analysis, such as determining the abnormal range based on the mean μ and the standard deviation σ. The specific threshold can be set to μ ± 3σ, that is, the value exceeding three times the standard deviation will be excluded to ensure the stability of the data. For missing data, linear interpolation is used to fill it to ensure the continuity of the data. After that, calculate the depth increment of adjacent data points. Assume the depth points {D1, D2,..., D n}, and the corresponding frictional resistances {M1, M2,..., M n} are used to calculate the depth increment ΔD i = D i+1 - D i . After obtaining the data sequence of frictional resistance depth changes, this data is used for subsequent calculations of the frictional resistance per unit depth.
[0092] Based on the data sequence of frictional resistance depth changes, the unit depth frictional resistance calculation sub-module calculates the standard deviation of the frictional resistance within the depth interval and normalizes it to the unit depth, using the formula:
[0093]
[0094] Calculate the standard deviation of the frictional resistance per unit depth to obtain the change amount of the frictional resistance per unit depth;
[0095] where ΔRsd represents the standard deviation of the frictional resistance per unit depth, M c represents the frictional resistance value at the c-th position, represents the average frictional resistance value, d represents the total number of monitoring data points, and Dep represents the total depth;
[0096] First, for each depth interval, calculate the mean value of all frictional resistance values within this interval Then calculate the standard deviation σ, and the standard deviation formula is:
[0097]
[0098] Next, calculate the standard deviation of the frictional resistance per unit depth, using the normalization formula:
[0099]
[0100] where Dep represents the total depth, d is the number of data points. Suppose within a certain drilling depth interval, the frictional resistance values are as follows:
[0101] Table 3 Example of frictional resistance values
[0102] Depth (m) Friction Resistance Value (N) 10 1200 15 1250 20 1190 25 1300 30 1220
[0103] As shown in Table 3, calculate the mean value for this interval
[0104]
[0105] Then calculate the standard deviation:
[0106]
[0107]
[0108] Renormalize to unit depth, and set the total depth Dep = 30m:
[0109]
[0110] This result shows that the standard deviation of the friction resistance per unit depth is low, indicating that the change in friction resistance within this drilling depth range is relatively uniform, without obvious mutations or anomalies. This value is used for subsequent trend analysis to further determine whether there are significant anomalies in the trend of friction resistance change.
[0111] The trend change analysis sub-module calculates the change amplitude according to the change in friction resistance per unit depth, calls the set threshold to judge whether it exceeds the reference value, and calculates and obtains the friction resistance change trend coefficient.
[0112] Call the set threshold to calculate the change amplitude, judge whether it exceeds the reference value, and calculate the friction resistance change trend coefficient. The set threshold is θ = 1.5. If ΔRsd exceeds this threshold, it is determined that the friction resistance change is significant. As calculated in the above example, ΔRsd = 1.32, which is lower than the threshold of 1.5. Therefore, it is not determined as an abnormal trend of friction resistance. Further, calculate the friction resistance change trend coefficient:
[0113] [[ID=1——6]]
[0114] This result shows that the friction resistance change in the current depth section is still within the normal range and there is no need to adjust the drilling parameters. The calculation of the trend coefficient K is used for further analysis of the smoothness of the friction resistance change. When K is close to 1 or greater than 1, it indicates that the friction resistance change reaches the set threshold and the drilling strategy may need to be adjusted. The current calculation result K = 0.88 indicates that the friction resistance change trend is relatively stable and does not exceed the preset threshold. Therefore, the current drilling state can continue to be maintained without additional intervention.
[0115] [[ID=——1]]Please refer to Figure 4 , the power dynamic adjustment module includes:
[0116] The power adjustment demand judgment sub-module calls the friction resistance change trend coefficient, judges the power adjustment demand within the interval based on the direction of friction resistance change, calculates the positive and negative of the friction resistance change direction, and determines the amplitude of the workover rig power adjustment according to the power adjustment demand to obtain the power adjustment demand quantity;
[0117] The friction resistance change trend coefficient Rtr is calculated from the historical friction resistance change data. Based on time series analysis, the friction resistance change rate at adjacent times is compared, and the friction resistance growth rate ΔF friction and the time interval Δt are used to calculate the friction resistance change trend coefficient. The formula is as follows:
[0118]
[0119] Among them, ΔFfriction Obtained from the friction resistance data measured by the sensor. For example, the friction resistance is 2000N at time t1 and 2200N at time t2, and the time interval is 5s, then:
[0120]
[0121] A positive value indicates an increase in friction resistance, and a negative value indicates a decrease. If the growth rate of the friction resistance exceeds the set threshold Rtr threshold (such as 30N / s), it is determined that the power needs to be increased, otherwise the power is decreased, and the adjustment amplitude is determined by the empirical weight coefficient K adj Calculate:
[0122] ΔP = K adj ×Rtr;
[0123] Let K adj = 1.2, then:
[0124] ΔP = 1.2×40 = 48W;
[0125] This result indicates that the current change trend of the friction resistance is significant, and the growth rate of the friction resistance has exceeded the set threshold. Therefore, an additional power of 48W is required to compensate for the additional load caused by the increase in the friction resistance and improve the operation stability of the workover rig.
[0126] The additional power calculation sub-module calculates the additional power demand according to the power adjustment demand, combines it with the current power of the workover rig, calculates the additional power demand, calls the power compensation threshold, compares the additional power demand with the preset threshold, and uses the formula:
[0127]
[0128] Calculate the additional power demand, make a judgment on the power compensation threshold, and obtain the power adjustment parameters of the workover rig;
[0129] Among them, Pwr represents the newly calculated additional power demand, W current represents the current power, ΔP represents the additional power calculated from the power adjustment demand, Tadj represents the efficiency adjustment time, Rtr represents the friction resistance change trend coefficient, T norm represents the normalized time parameter;
[0130] Formula:
[0131]
[0132] Among them: W currentRepresents the current power of the workover rig, assuming its current value is 5000 W; ΔP is obtained from the aforementioned calculation and is 48 W; Tadj represents the efficiency adjustment time, assuming a value of 2 s; Tnorm is the normalized time parameter, taking 5 s; Rtr represents the friction resistance change trend coefficient, and the aforementioned calculation is 40 N / s; ΔRtr represents the change in the current friction resistance change trend compared to the previous cycle. Assuming Rtr = 35 N / s in the previous cycle, then:
[0133] ΔRtr = 40 - 35 = 5 N / s;
[0134] Substitute into the calculation:
[0135]
[0136] e -1 ≈0.3679;
[0137]
[0138] This result indicates that under the current friction resistance change trend, the final power adjustment target calculated for the additional power requirement is 3725 W. If this value is higher than the set power compensation threshold P threshold (assuming 3700 W), then power compensation needs to be performed, otherwise the existing power output is maintained.
[0139] The dynamic power output sub-module calculates the power gain duration based on the workover rig power adjustment parameters and the time parameters, and adjusts the workover rig output according to the additional power requirement and the duration to obtain the dynamic power output value.
[0140] The power gain duration T of the workover rig gain is calculated from the adjustment amplitude ΔP and the adjustment rate R adj Calculate:
[0141]
[0142] Assume the adjustment rate R adj = 10 W / s, then:
[0143]
[0144] The power output adjustment process adopts a linear increasing method and gradually adjusts the power within the time T gain at a rate of increasing by:
[0145]
[0146] The power of the workover rig increases at a rate of 10 W / s within 4.8 s and finally stabilizes at 3725 W.
[0147] Table 4 Summary of calculation results
[0148]
[0149] As shown in Table 4, the power adjustment demand, additional power demand, and power gain duration calculated from each parameter can be used to dynamically adjust the power output of the workover rig to match the current change in frictional resistance.
[0150] The results show that under the set adjustment rate condition, the workover rig will complete the power adjustment within 4.8 seconds, gradually increase the power output at a rate of 10 W / s, and finally reach 3725 W to adapt to the current change trend of frictional resistance, ensure that the workover rig operates within a reasonable load range, and avoid system instability caused by sudden power changes.
[0151] Please refer to Figure 5 , the feedforward power optimization module includes:
[0152] The dynamic power data processing sub-module calls the dynamic power output value, obtains the corresponding time series, extracts the output value corresponding to the time point, calculates the instantaneous change rate according to the time interval, filters out abnormal data and eliminates missing values. At the same time, it calls the historical frictional resistance trend data, matches the data in the corresponding time interval, calculates the average power output, and obtains the time series matching data set;
[0153] First, call the timestamp indexing function to extract the power data points from the stored data set and sort them in chronological order to ensure data continuity. When extracting the output value corresponding to the time point, perform index matching according to the data storage format. If the data storage format is an array form, directly obtain it through the index. If it is a key-value pair format, traverse and match the timestamps to extract the data. For calculating the instantaneous change rate of the time interval, set the time step Δt to 1 second, and the calculation formula is:
[0154]
[0155] where, P t is the power value at time t, P t+1 is the power value at the next time step. When the calculated change rate is abnormal, data screening is required. Set the change rate threshold θ to 0.2, that is, when |ΔP|>θ, the data is determined to be abnormal and eliminated. The missing value processing uses linear interpolation, that is, for any missing point P [[ID=X]] miss , according to:
[0156]
[0157] to interpolate and complete. When calling the historical frictional resistance trend data, it is necessary to match the data in the corresponding time interval. Set the backtracking time window T history to 30 seconds, that is, search for data 30 seconds forward from the current time point, and calculate the average power output within this time window:
[0158]
[0159] Among them, n is the number of data points within the time window. When obtaining the time series matching data set, with the current time point as the center, the historical data set of the same time window is selected and normalized so that its numerical range is mapped to [0, 1] to ensure data comparability. After such processing, the time series matching data set can be used for subsequent trend calculations.
[0160] Table 5 Example of power data processing
[0161] Time (s) Power (W) Rate of Change (W / s) Power after Processing (W) 0 1500 - 1500 1 1520 20 1520 2 1400 -120 Interpolation 1460 3 1450 -10 1450 4 1480 30 1480
[0162] The result shows that through the screening and interpolation processing of power data, the abnormally fluctuating data are eliminated and the missing values are supplemented, making the change trend of the data smoother in the time series, ensuring the integrity and reliability of the data during power calculation. At the same time, the normalized time series data can be used for trend matching to improve the accuracy of subsequent trend calculations.
[0163] The future resistance trend calculation sub-module is based on the time series matching data set, calls the depth data, calculates the depth change rate, and at the same time calculates the friction resistance increase and decrease rate according to the past trend data, using the formula:
[0164]
[0165] Obtain the future resistance trend value;
[0166] Among them, Rf represents the future resistance trend value, V e represents the velocity difference at the e-th time, H e represents the depth difference at the e-th time, f represents the total number of velocity change data points, g represents the total number of depth data points, and H [[ID=3l]] h represents the depth value;
[0167] First, call the depth data, which is collected by the underwater depth sensor and aligned with the time series to ensure that the depth values used in the calculation process correspond to the same time point. When calculating the depth change rate, the time interval is set as Δt = 1 s, and the depth change rate calculation formula is as follows:
[0168]
[0169] Among them, H t represents the depth value at time t, and H t+1 represents the depth value at the next time step.
[0170] Table 6 Depth, velocity, and friction resistance data
[0171] Time (s) Velocity (m / s) Depth (m) Friction Resistance (N) 0 2.1 50 10 1 2.3 51 10.2 2 2.2 53 10.4 3 2.5 55 10.7 4 2.4 58 11.0
[0172] Calculate the future resistance trend:
[0173]
[0174] R f = 0.0285;
[0175] This result indicates that the resistance trend value R f represents the change trend of underwater friction resistance. The larger the value, the more obvious the increase in friction resistance. The subsequent power adjustment module needs to adjust the power according to this trend to offset the influence of the resistance.
[0176] The feedforward power adjustment sub-module calls the temperature and viscosity data according to the future resistance trend value, calculates the temperature and viscosity influence factors, and at the same time calls the compensation threshold, adjusts the power parameters based on the trend value, calculates the compensated power output, and obtains the feedforward power control value.
[0177] Call the temperature and viscosity data to calculate the temperature and viscosity influence factors:
[0178] η = 0.0012 × 20 + 0.8 = 0.824;
[0179] Calculate the compensated power output:
[0180] P comp = 1500 + 500 × 0.0285 × 0.824;
[0181] P comp = 1511.75W;
[0182] This result indicates that the calculated feedforward power control value P comp = 1511.75W, which means that compared with the reference power of 1500W, the system needs to increase 11.75W of power to compensate for the possible increase in underwater friction resistance in the future. This power adjustment amount is jointly determined by the future resistance trend R f and the temperature and viscosity influence factors. The numerical result reflects the dynamic power adjustment demand under the current environmental conditions to maintain the stable operation of the underwater equipment.
[0183] Please refer to Figure 6 , the energy consumption control module includes:
[0184] The power consumption data acquisition sub-module calls the feedforward power control value, obtains the power consumption data during the operation of the workover rig, sorts the power consumption data based on the time series, screens out the abnormal points and missing values, calculates the average power within multiple time intervals, and obtains the average power consumption data;
[0185] First, the feedforward power regulation value needs to be called, which can be obtained from the historical operation data of the workover rig or through real-time calculation. For example, the average power consumption value is extracted from the operation data in the past 24 hours as the feedforward input. When obtaining the power consumption data during the operation of the workover rig, data collection can be carried out through power sensors installed on various key components of the workover rig. These sensors are usually installed at the motor input end, hydraulic system, and auxiliary system. The data is recorded at a sampling interval of 1 second to form a time series data set. For the collected power consumption data, it is necessary to sort it in chronological order to ensure the continuity and comparability of the data. On this basis, anomaly detection methods are used to screen out abnormal points. For example, data with a power consumption fluctuation exceeding a set threshold (such as exceeding ±20% of the average value) compared to the previous and subsequent moments at a certain moment is excluded. For the missing value part, interpolation or historical data filling methods can be used to complete it. Furthermore, the average power within multiple time intervals is calculated. Assuming a 10-minute time interval, the calculation formula is:
[0186]
[0187] where P avg,i is the average power of the i-th 10-minute time period, N is the number of sampling points within this time period, and P k is the power value of the k-th sampling point. For example, within a 10-minute time interval, a total of 600 sampling points (1 time per second) are recorded. If the power data of these points are [50, 52, 48, 49, …, 51] kW respectively, then its average power is:
[0188]
[0189] Finally, the power consumption data of the workover rig is obtained to form a complete time series data table. This result indicates that the power consumption characteristics of the workover rig during operation have been effectively recorded by the system, and the accuracy of the data is ensured by screening out abnormal values and filling in missing values. These data can be used for subsequent low-resistance state determination and energy consumption optimization calculations to ensure that subsequent calculations are based on real and reasonable data inputs.
[0190] The low-resistance state determination sub-module, based on the power consumption data of the workover rig, calls the energy-saving mode parameters, calculates the power fluctuation range within the target time period, and at the same time determines the low-resistance state according to the fluctuation amplitude. It calls the set low-resistance threshold, calculates the power fluctuation deviation value based on the time series, and obtains the low-resistance state determination result;
[0191] First, based on the power consumption data of the workover rig, call the energy-saving mode parameters, which include the power change rate threshold and the low-resistance state determination threshold. For example, if the set energy-saving mode parameters for a certain device are a power fluctuation range of ±5% and a low-resistance determination threshold of 3 kW, then within the target time period, calculate its power fluctuation range. The method is as follows:
[0192] P Δ =P max -P min ;
[0193] where P max is the maximum power within the target time period, and P min is the minimum power. Assuming that the power data for a certain time period are [48, 52, 50, 51, 49] kW respectively, then:
[0194] P Δ =52 - 48 = 4 kW;
[0195] Next, determine the low-resistance state based on the fluctuation amplitude. If the fluctuation amplitude is lower than the set low-resistance determination threshold (3 kW), then it is determined to be in the low-resistance state; otherwise, it does not belong to the low-resistance state. In this example, since 4 > 3 kW, it does not meet the low-resistance state determination standard. Finally, call the set low-resistance threshold and calculate the power fluctuation deviation value based on the time series. The calculation method is as follows:
[0196]
[0197] Assume that at 5 time points (j = 5), the powers are [48, 52, 50, 51, 49] kW respectively, and its average power is:
[0198]
[0199] Then calculate the deviation:
[0200]
[0201] Finally, based on the calculation results, obtain the low-resistance state determination result. If the deviation is lower than the set threshold (for example, 1 kW), then it is determined to be in the low-resistance state; otherwise, it does not belong to the low-resistance state. In this example, 1.2 > 1 kW, so the device is not in the low-resistance state. This result indicates that the power fluctuation of the workover rig during this time period exceeds the determination standard of the low-resistance state, indicating that there is still a large power fluctuation during its operation and it does not meet the low-power operation mode, so it cannot enter the energy consumption optimization stage.
[0202] The energy consumption optimization analysis sub-module calls the power strategy adjustment parameters according to the low-resistance state determination result and uses the formula:
[0203]
[0204] The energy consumption optimization value is calculated;
[0205] Among them, E opt represents the energy consumption optimization value, and P max represents the maximum power consumption value within the monitoring period,
[0206] P min represents the minimum power consumption value within the monitoring period, and P avg represents the average power consumption value within the monitoring period,
[0207] P tot represents the total power consumption value within the monitoring period, Tint i represents the time interval at the i-th moment, j represents the number of time periods, and k represents the total number of monitoring data points.
[0208] First, according to the low-resistance state determination result, if it is determined to be in the low-resistance state, then the power strategy adjustment parameters are called. These parameters usually include the adjusted target power range and the load optimization strategy. For example, the adjusted target power range is 48 - 52 kW, and the energy consumption optimization value is calculated using the following formula:
[0209]
[0210] Among them: P max = 52 kW, P min = 48 kW, so P max - P min = 4 kW. Set Tint i = 10 min, then (5 time periods), set k = 600 (a total of 600 data points are sampled), P avg = 50 kW - P tot = P avg × j = 50 × 5 = 250 kW
[0211] Substitute into the formula for calculation:
[0212]
[0213] Finally, the calculated energy consumption optimization value is 0.0817. This result indicates that the current energy consumption optimization potential of the workover rig is relatively low, indicating that there are still power fluctuations in the current equipment operation state, and it does not fully meet the low-resistance energy-saving mode. Therefore, it is impossible to directly enter the power strategy adjustment stage. It is necessary to further optimize the power control parameters to reduce the fluctuation amplitude and evaluate the optimized effect in the subsequent monitoring period, and then adjust the operating power to achieve the energy-saving goal.
[0214] The above are only the preferred embodiments of the present invention, and do not limit the present invention in other forms. Any person skilled in the relevant art may use the technical content disclosed above to make changes or modifications into equivalent embodiments with equivalent changes and apply them to other fields. However, as long as it does not depart from the technical solution content of the present invention, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims
1. An intelligent control and energy-saving integrated system for workover rigs, characterized in that, The system includes: The data acquisition module obtains the workover string depth, wellbore temperature, and well fluid viscosity, calls the strain device to collect the friction resistance, calls the pressure device to collect the wellbore pressure, and generates a friction resistance monitoring data set based on the depth, resistance, temperature, viscosity, and pressure. The friction resistance trend calculation module calls the friction resistance monitoring data set, calculates the change amount of the friction resistance per unit depth according to the continuous data, calls the threshold to judge whether the change exceeds the benchmark, and calls the calculation of the change amplitude to generate a friction resistance change trend coefficient. The power dynamic adjustment module calls the friction resistance change trend coefficient, judges the interval power adjustment requirement based on the change direction of the friction resistance, calculates the additional power requirement according to the current power of the workover rig, compares the additional power with the preset threshold based on the power compensation threshold, calls the time parameter to calculate the duration of the power gain, and adjusts the output of the workover rig based on the additional power requirement and the duration to generate a dynamic power output value. The feedforward power optimization module calls the dynamic power output value, obtains the past friction resistance trend data, calls the depth data to judge the future resistance direction, calls the temperature and viscosity data to correct the prediction value, and calls the compensation threshold to calculate and generate a feedforward power control value.
2. The integrated system of intelligent control and energy-saving workover rig according to claim 1, wherein, The friction resistance monitoring data set is specifically the pipe string depth data, wellbore temperature data, well fluid viscosity data, friction resistance data, and wellbore pressure data. The friction resistance change trend coefficient includes the resistance change rate, benchmark overrun index, and amplitude change amount. The dynamic power output value is specifically the additional power requirement value, power gain duration, and output adjustment amount. The feedforward power control value specifically refers to the historical trend reference, future resistance prediction, corrected prediction index, and compensation adjustment value.
3. The integrated system of intelligent control and energy-saving workover rig according to claim 2, wherein The data acquisition module includes: The depth temperature viscosity acquisition sub-module obtains the depth of the workover string, detects the wellbore temperature and well fluid viscosity, collects the temperature data at various depth positions during workover, analyzes the temperature change trend at multiple depths, calculates the viscosity of the well fluid under different temperature conditions, and matches the viscosity correction value in combination with the depth information to obtain the depth temperature viscosity data. The friction resistance acquisition sub-module, based on the depth temperature viscosity data, calls the strain device to collect the friction resistance data, analyzes the distribution characteristics of the friction force at multiple depths, calculates the friction resistance of the pipe string at different depths, and combines the temperature viscosity to correct the friction force calculation value to obtain the friction resistance data. The wellbore pressure calculation sub-module calls the pressure device to collect the wellbore pressure data, calculates the force condition of the pipe string based on the friction resistance data, analyzes the change of the wellbore pressure in combination with the depth information, and uses the formula: Performs operations to obtain the wellbore pressure data and establishes a friction resistance monitoring data set. Among them, Pr represents the wellbore pressure, Ffr a represents the frictional resistance at the a-th position, Fvf a represents the vertical force of the depth string, η a represents the well fluid viscosity, Dia a represents the wellbore diameter at depth, T inf a represents the depth temperature influence factor, and b represents the total number of measurement points.
4. The intelligent control and energy-saving integrated workover rig system according to claim 3, wherein The friction resistance trend calculation module includes: The friction resistance monitoring data processing sub-module calls the friction resistance monitoring data set, extracts the data of the friction resistance change with depth, rearranges the friction resistance data sequence according to the depth interval, compares adjacent data points, screens out missing and abnormal values, calculates the depth increment of adjacent data points, and obtains the friction resistance depth change data sequence. The unit depth friction resistance calculation sub-module, based on the friction resistance depth change data sequence, calculates the standard deviation of the friction resistance within the depth interval and normalizes it to the unit depth. Using the formula: Calculate the standard deviation of the frictional resistance per unit depth and obtain the change amount of the frictional resistance per unit depth; Among them, ΔRsd represents the standard deviation of the frictional resistance per unit depth, M c represents the frictional resistance value at the c-th location, M represents the average frictional resistance value, d represents the total number of monitoring data points, and Dep represents the total depth; The trend change analysis sub-module calls a set threshold to calculate the change amplitude according to the change amount of the frictional resistance per unit depth, determines whether it exceeds the reference value, and calculates and obtains the frictional resistance change trend coefficient.
5. The integrated system of intelligent control and energy-saving workover rig according to claim 4, wherein The power dynamic adjustment module includes: The power adjustment demand judgment sub-module calls the frictional resistance change trend coefficient, judges the power adjustment demand within the interval based on the change direction of the frictional resistance, calculates the positive and negative of the change direction of the frictional resistance, and determines the amplitude of the workover rig power adjustment according to the power adjustment demand to obtain the power adjustment demand quantity; The additional power calculation sub-module calculates the additional power demand according to the power adjustment demand quantity, combines it with the current power of the workover rig, calls the power compensation threshold, compares the additional power demand with the preset threshold, and uses the formula: Calculate the additional power demand and perform power compensation threshold determination to obtain the workover rig power adjustment parameter; Wherein, Pwr represents the newly calculated additional power requirement, in W current represents the current power, ΔP represents the additional power calculated from the power adjustment demand, Tadj represents the efficiency adjustment time, Rtr represents the friction resistance change trend coefficient, T norm represents the normalized time parameter; The dynamic power output sub-module calls the time parameter to calculate the power gain duration based on the workover rig power adjustment parameter, and adjusts the output of the workover rig according to the additional power demand and the duration to obtain the dynamic power output value.
6. The integrated intelligent control and energy-saving workover rig system according to claim 5, characterized in that, The feedforward power optimization module includes: The dynamic power data processing sub-module calls the dynamic power output value to obtain the corresponding time series, extracts the output value corresponding to the time point, calculates the instantaneous change rate according to the time interval, screens out abnormal data and eliminates missing values, and at the same time calls the previous frictional resistance trend data, matches the data in the corresponding time interval, calculates the power output mean value, and obtains the time series matching data set; The future resistance trend calculation sub-module calls the depth data based on the time series matching data set to calculate the depth change rate, and at the same time calculates the frictional resistance increase and decrease rate according to the previous trend data, and uses the formula: Obtain the future resistance trend value; Among them, Rf represents the future resistance trend value, V e represents the velocity difference at the e-th time, H e represents the depth difference at the e-th time, f represents the total number of velocity change data points, g represents the total number of depth data points, H h represents the depth value; The feedforward power adjustment sub-module calls the temperature and viscosity data according to the future resistance trend value to calculate the temperature and viscosity influence factors, and at the same time calls the compensation threshold, adjusts the power parameter based on the trend value, calculates the compensated power output, and obtains the feedforward power control value.
7. The integrated system of intelligent control and energy-saving workover rig according to claim 6, wherein The system further includes: The energy consumption regulation module calls the feedforward power control value to obtain the workover rig power consumption data, calls the energy-saving mode parameter to judge the low-resistance state, calls the power strategy to adjust the consumption, and generates the energy consumption optimization value; The energy consumption optimization value includes power consumption monitoring indicators, low-resistance state determination values, and strategy adjustment effects.
8. The integrated system of intelligent control and energy-saving workover rig according to claim 7, characterized in that The energy consumption regulation module includes: The power consumption data acquisition sub-module calls the feedforward power control value to obtain the power consumption data during the operation of the workover rig, sorts the power consumption data based on the time series, screens out abnormal points and missing values, calculates the average power within multiple time intervals, and obtains the average power consumption data; The low-resistance state determination sub-module calls the energy-saving mode parameter based on the workover rig power consumption data to calculate the power fluctuation range within the target time period, and at the same time determines the low-resistance state according to the fluctuation amplitude, calls the set low-resistance threshold, and calculates the power fluctuation deviation value according to the time series to obtain the low-resistance state determination result; Based on the low-resistance state determination result, the energy consumption optimization analysis sub-module calls the power policy adjustment parameters and uses the formula: Calculate the energy consumption optimization value; Among them, E opt represents the energy consumption optimization value, P max represents the maximum power consumption value during the monitoring period, P min represents the minimum power consumption value during the monitoring period, P avg represents the average power consumption value during the monitoring period, P tot represents the total power consumption value during the monitoring period, T int i represents the time interval at the i-th moment, j represents the number of time periods, and k represents the total number of monitoring data points.