Method and device for judging fouling cleaning of plate heat exchanger in service based on operation data
By using a fouling cleaning judgment method based on operational data, the changes in fouling thermal resistance of plate heat exchangers can be accurately assessed, solving the problem of determining the timing of cleaning, improving the energy conversion rate and system stability of the heating system, and reducing resource waste and costs.
Patent Information
- Application Number
- CN202411924003.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-25
- Publication Date
- 2025-11-18
- Estimated Expiration
- 2044-12-25
AI Technical Summary
In the existing technology, there is a lack of specific basis for judging when to clean plate heat exchangers, which leads to frequent cleaning, resulting in waste of resources and costs. Furthermore, it is impossible to accurately assess the fouling condition of the heat exchanger, which affects the energy conversion rate and carbon emissions of the heating system.
By collecting operating data from plate heat exchangers, effective datasets for the cleaning period and the current operating season are generated. Steady-state operating conditions are then screened, and the fouling thermal resistance is calculated and compared with the thermal conductivity ratio during the cleaning period to determine whether cleaning is necessary.
It improves the accuracy of judging the fouling condition of plate heat exchangers, ensures timely cleaning, avoids unnecessary cleaning, saves energy consumption, reduces carbon emissions, extends equipment life, and reduces maintenance costs.
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Figure CN119879637B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of plate heat exchangers, and in particular to a method and device for judging dirt cleaning of a plate heat exchanger in service based on operation data. BACKGROUND
[0002] With the acceleration of urbanization, the urban population and the number of buildings continue to grow, leading to the continuous expansion of heating area. As the main way of urban heating, the energy consumption and carbon emission of the central heating system are increasingly prominent.
[0003] The plate heat exchanger plays a crucial role in the central heating system, and its performance directly affects the efficiency of the entire heating system. However, in actual operation, the plate heat exchanger will be affected by calcium, magnesium and other salts and small particles contained in the water. These substances will precipitate and adhere to the surface of the plate heat exchanger after being heated, forming dirt. These dirt not only increases the thermal resistance and reduces the heat exchange efficiency, but also reduces the flow area of the plate heat exchanger channel, leading to reduced flow and increased pump power, resulting in energy waste.
[0004] In order to reduce the adverse effects of dirt on the heat exchange performance of the plate heat exchanger, improve the heating quality and reduce energy consumption, it is necessary to regularly clean the plate heat exchanger. However, since the plate heat exchanger is usually in a sealed state, workers cannot directly observe the accumulation of dirt inside it with their naked eyes. Currently, heating companies generally adopt a fixed cleaning time or decide whether to clean based on the rate of resident complaints. However, this approach lacks specific basis and not all plate heat exchangers need to be cleaned at fixed times. Therefore, too frequent cleaning will cause waste of resources and costs.
[0005] Therefore, how to accurately determine the cleaning time of the plate heat exchanger to improve the energy conversion rate of the heating system, reduce carbon emissions, and reduce unnecessary waste of resources and costs has become a problem to be solved. Based on this problem, the present application finds a method of judging dirt cleaning of a plate heat exchanger in service only relying on operation data. This method can be applied to urban heating, chemical industry, food industry, textile industry and other industries using plate heat exchangers. SUMMARY
[0006] In the embodiments of the present application, by providing a method for judging dirt cleaning of a plate heat exchanger in service based on operation data, the problem of how to accurately determine the cleaning time of the plate heat exchanger to improve the energy conversion rate of the heating system, reduce carbon emissions, and reduce unnecessary waste of resources and costs is solved.
[0007] In a first aspect, embodiments of this application provide a method for judging fouling cleaning of an in-service plate heat exchanger based on operational data. The method includes: acquiring a preset time period for the cleaning period and the current operating season; collecting each set of operational data from the plate heat exchanger at preset intervals within the preset time period; removing abnormal data to form valid datasets for the cleaning period and the current operating season, respectively; each set of operational data from the plate heat exchanger includes the inlet temperature and outlet temperature of the primary and secondary sides, as well as the mass flow rate of the primary side; calculating the heat exchange and logarithmic mean temperature difference of each set of operational data in the valid datasets for the cleaning period and the current operating season, respectively; performing a steady-state operating condition set filtering step on the valid datasets for the cleaning period and the current operating season to obtain steady-state operating condition sets for the cleaning period and the current operating season; the steady-state operating condition set filtering step includes: dividing the heat exchange and logarithmic mean temperature difference data into multiple subsets, calculating the relative standard deviation of each subset, and selecting the subset with the smallest relative standard deviation. The data set is used as the steady-state operating condition set. Within the steady-state operating condition set of the clean period and the current operating season, the set of data with the smallest difference between adjacent data is found. The heat transfer and logarithmic mean temperature difference of this set of data represent the steady-state heat transfer and steady-state logarithmic mean temperature difference of the clean period and the current operating season, and this is taken as the steady-state operating condition. Using the steady-state operating condition data, the heat transfer resistance and the sum of the negative 0.8 power of the flow rates on both sides of the data for the clean period and the current operating season are calculated. After linear fitting, the intercept is the plate heat exchanger... The thermal resistance of the plate heat exchanger is used to calculate the fouling thermal resistance of the plate heat exchanger in the current operating season; it is then determined whether the ratio of the fouling thermal resistance of the plate heat exchanger in the current operating season to the thermal resistance during the cleaning period exceeds a preset threshold; if the ratio exceeds the preset threshold, the plate heat exchanger is cleaned before the start of the next operating season; if the ratio does not exceed the preset threshold, the plate heat exchanger does not need to be cleaned.
[0008] In one possible implementation, the cleaning period is the first operating season when the plate heat exchanger starts operation and is put into use, or the first operating season after the plate heat exchanger has completed cleaning.
[0009] In one possible implementation, before calculating the heat exchange and logarithmic mean temperature difference for each set of operational data in the valid datasets of the clean period and the current operational season, the data for the first month of the operational season and the last month of the operational season are removed from the valid datasets of the clean period and the current operational season.
[0010] In one possible implementation, the definition criteria for abnormal data are as follows: if the primary side inlet temperature, primary side outlet temperature, secondary side inlet temperature, secondary side outlet temperature, or primary side mass flow rate in any set of operating data is zero or negative, the set of data is considered abnormal data; if the calculated result of the logarithmic mean temperature difference is negative, the set of data is considered abnormal data; if the temperature or primary side mass flow rate of two or more adjacent sets of data is the same, the set of data is considered abnormal data.
[0011] In one possible implementation, the heat exchange is calculated as follows: calculate the temperature difference between the primary side inlet temperature and the primary side outlet temperature in the effective data set during the clean period and the current operating season; multiply the temperature difference by the mass flow rate of the primary side in the effective data set during the clean period and the current operating season to obtain an intermediate value; multiply this intermediate value by the specific heat capacity of the fluid to obtain the heat exchange of the effective data set during the clean period and the current operating season.
[0012] In one possible implementation, the logarithmic mean temperature difference is calculated as follows: For the valid datasets of the cleaning period and the current operating season, two sets of temperature differences are calculated respectively; wherein, the first temperature difference is the temperature from the primary side inlet temperature to the secondary side inlet temperature, and the second temperature difference is the temperature from the primary side outlet temperature to the secondary side outlet temperature; the ratio of the first temperature difference to the second temperature difference is calculated, and the ratio is used as the base of the logarithm for logarithmic operation to obtain the logarithmic value; using the logarithmic value as the denominator and the difference between the first temperature difference and the second temperature difference as the numerator, a division operation is performed to obtain the logarithmic mean temperature difference of the valid datasets of the cleaning period and the current operating season.
[0013] In one possible implementation, the relative standard deviation of each subset is calculated as follows: sum the values of each heat exchange or logarithmic mean temperature difference in the subset to obtain a sum, divide the sum by the total number of data points to obtain the mean; calculate the difference between the value of the heat exchange or logarithmic mean temperature difference in the subset and the mean; and obtain the squared difference; sum all the squared differences to obtain a sum of squared differences, divide the sum of squared differences by the total number of data points in each subset, and take the square root to calculate the standard deviation; divide the standard deviation by the mean to obtain the relative standard deviation.
[0014] In one possible implementation, the heat transfer resistance of the plate heat exchanger is calculated using steady-state operating data for both the clean period and the current operating season, along with the sum of the negative 0.8 powers of the flow rates on both sides. This is then linearly fitted, and the intercept is taken as the thermal resistance of the plate heat exchanger. This is used to calculate the fouling resistance of the plate heat exchanger, including: calculating the corresponding heat transfer capacity UA for both the clean period and the current operating season, UA = Φ / LMTD; where the heat transfer capacity UA is the product of the total heat transfer coefficient and the heat transfer area of the plate heat exchanger, Φ is the heat transfer capacity, and LMTD is the logarithmic mean temperature difference; when UA is calculated using the thermal resistance of the plate heat exchanger, the clean period... Current operating season Where h1 and h2 are the convective heat transfer coefficients of the primary and secondary sides of the plate heat exchanger, A1 and A2 are the heat transfer areas of the primary and secondary sides of the plate heat exchanger, rw is the thermal resistance coefficient of the plate of the plate heat exchanger, rf is the fouling thermal resistance coefficient, A0 is the heat transfer area of the plate of the plate heat exchanger, and Ai is the heat transfer area of the fouling. Nu = cRe n Pr m Where Re is the Reynolds number, Pr is the Prandtl number, n is 0.8, and m is 0.3-0.4. Where ρ is density, u is flow velocity, l is characteristic length, and μ is dynamic viscosity; the formula for calculating UA is simplified to obtain Furthermore, h is proportional to the 0.8 power of the flow velocity u, and h is also proportional to the 0.8 power of the flow rate G. Simplifying the calculation formula for UA, the total heat transfer thermal resistance... in G2 = G1(T1-T2) / (T3-T4), where G1 and G2 are the primary and secondary flow rates, respectively. Expressed as a function, y = kx + b, where y = 1 / UA, x = (G1 -0.8 +G2 -0.8 ), and perform linear fitting, with a goodness-of-fit R. 2 Not less than 0.8; After obtaining the fitted curves of the cleaning period and the current period, the intercept b is the thermal resistance of the plate heat exchanger. By comparing the intercepts b of the two periods, the fouling thermal resistance of the heat exchanger in the current operating season can be obtained. ratio of dirt thermal resistance to clean-period thermal resistance bu is the intercept for the current period, and bc is the intercept for the clean period.
[0015] Secondly, this application provides a fouling cleaning judgment device for an in-service plate heat exchanger based on operational data. The device includes: an acquisition module for acquiring a preset time period for the cleaning period and the current operating season; collecting each set of operational data from the plate heat exchanger at preset intervals within the preset time period; removing abnormal data to form valid datasets for the cleaning period and the current operating season; each set of operational data from the plate heat exchanger includes the inlet temperature and outlet temperature of the primary and secondary sides, as well as the mass flow rate of the primary side; an unknown quantity calculation module for calculating the heat exchange and logarithmic mean temperature difference of each set of operational data in the valid datasets for the cleaning period and the current operating season; and a screening step module for performing a steady-state operating condition set screening step on the valid datasets for the cleaning period and the current operating season to obtain a steady-state operating condition set for the cleaning period and the current operating season; the steady-state operating condition set screening step includes: dividing the heat exchange and logarithmic mean temperature difference data into multiple subsets, calculating the relative standard deviation of each subset, and selecting the subset with the smallest relative standard deviation as the steady-state set. The system includes several modules: a steady-state operating condition set and a steady-state operating condition module. The steady-state operating condition set is obtained by calculating the differences between adjacent data points within the clean period and the current operating season. The heat transfer and logarithmic mean temperature difference of this set of data represent the steady-state heat transfer and logarithmic mean temperature difference for both the clean period and the current operating season, and this is taken as the steady-state operating condition. A plate heat exchanger fouling thermal resistance calculation module is used to calculate the heat transfer thermal resistance of the plate heat exchanger from the clean period and the current operating season, as well as the sum of the negative 0.8 powers of the flow rates on both sides, using the steady-state operating condition data. This data is then linearly fitted. The intercept is the thermal resistance of the plate heat exchanger, used to calculate the fouling thermal resistance of the plate heat exchanger in the current operating season; the judgment module is used to determine whether the ratio of the fouling thermal resistance of the plate heat exchanger in the current operating season to the thermal resistance during the cleaning period exceeds a preset threshold; if the ratio of the fouling thermal resistance of the plate heat exchanger in the current operating season to the thermal resistance during the cleaning period exceeds the preset threshold, the plate heat exchanger is cleaned before the start of the next operating season; if the ratio of the fouling thermal resistance of the plate heat exchanger in the current operating season to the thermal resistance during the cleaning period does not exceed the preset threshold, the plate heat exchanger does not need to be cleaned.
[0016] One or more technical solutions provided in the embodiments of this application have at least the following technical effects:
[0017] This application provides a method for judging fouling cleaning of in-service plate heat exchangers based on operational data. By collecting multiple sets of operational data from the plate heat exchanger during the cleaning period and the current operating season, and removing abnormal data to form valid datasets for the cleaning period and the current operating season, the method further ensures the accuracy and representativeness of the data used to calculate fouling thermal resistance and the ratio of fouling thermal resistance in the current operating season to the thermal conductivity thermal resistance in the cleaning period through steps such as steady-state condition filtering. This significantly improves the accuracy of judging the fouling condition of the plate heat exchanger. The ratio of fouling thermal resistance in the current operating season to the thermal conductivity thermal resistance in the cleaning period, calculated based on steady-state conditions, allows for an objective assessment of the plate heat exchanger's performance changes. Cleaning is only performed when the ratio of fouling thermal resistance in the current operating season to the thermal conductivity thermal resistance in the cleaning period exceeds a preset threshold. This ensures timely cleaning while avoiding unnecessary cleaning and cost waste. Timely cleaning of the plate heat exchanger effectively removes fouling, reduces thermal resistance, and improves heat exchange efficiency, thereby saving energy consumption. This is of great significance for improving the overall energy efficiency of centralized heating systems and reducing carbon emissions. Regular cleaning of plate heat exchangers can reduce the impact of fouling on the flow area of the plate heat exchanger channels, avoiding problems such as reduced flow rate and increased pump power, thereby enhancing the stability and reliability of the operating system. It also avoids frequent cleaning operations, reducing maintenance costs. Furthermore, accurate timing of cleaning ensures optimal results each time, extending the service life of the plate heat exchanger. This solves the problem of accurately determining the cleaning time of plate heat exchangers to improve the energy conversion rate of the heating system, reduce carbon emissions, and minimize unnecessary waste of resources and costs. Attached Figure Description
[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments of this application or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0019] Figure 1 A flowchart illustrating a method for determining fouling in an in-service plate heat exchanger based on operational data, provided in this application embodiment;
[0020] Figure 2 This is a schematic diagram of steady-state operating condition screening provided in an embodiment of this application;
[0021] Figure 3 A schematic diagram illustrating the linear relationship provided in the embodiments of this application;
[0022] Figure 4 A schematic diagram of a fouling cleaning judgment device for an in-service plate heat exchanger based on operating data, provided in an embodiment of this application;
[0023] Figure 5 This is a schematic diagram of a fouling cleaning judgment server for an in-service plate heat exchanger based on operating data, provided in an embodiment of this application. Detailed Implementation
[0024] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.
[0025] The following description of some technologies involved in the embodiments of this application is provided to aid understanding and should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, some descriptions of well-known functions and structures are omitted in the following description.
[0026] This application provides a method for determining fouling cleanliness in in-service plate heat exchangers based on operational data, such as... Figure 1 As shown, the method includes steps S101 to S108. Wherein, Figure 1 This is merely one execution order shown in the embodiments of this application, and does not represent the only execution order for a fouling cleaning judgment method for in-service plate heat exchangers based on operating data. Where the final result can be achieved... Figure 1 The steps shown can be performed in parallel or in reverse order.
[0027] S101: Obtain preset time periods for the cleaning period and the current operating season. Within these preset time periods, collect each set of operating data from the plate heat exchanger at preset intervals, and remove abnormal data to form valid datasets for the cleaning period and the current operating season, respectively. Each set of operating data for the plate heat exchanger includes the inlet and outlet temperatures of the primary and secondary sides, as well as the mass flow rate of the primary side.
[0028] The cleaning period is either the first operating season after the plate heat exchanger starts operation or the first operating season after the plate heat exchanger has been cleaned.
[0029] Specifically, the effective dataset for the clean period includes all operational data within the clean period, serving as a benchmark for evaluating the performance of the current operating season. The effective dataset for the current operating season includes all operational data within the current operating season, used for comparison with the data from the clean period to assess performance changes in the plate heat exchanger.
[0030] Furthermore, the preset time period can be set to one day, meaning we are focusing on the plate heat exchanger's operational data throughout the day. To gain a comprehensive and detailed understanding of the plate heat exchanger's performance, data can be collected every hour. Specifically, from the beginning of the day (e.g., midnight) to the end (i.e., 24 hours later), data will be collected at every hour on the hour (e.g., 1 AM, 2 AM, ..., 11 PM). In the datasets for the cleaning period and the current operating season, data acquisition is performed in chronological order, meaning the data collected earlier is listed first, and the data collected later is listed later. This data arrangement facilitates subsequent data analysis and processing.
[0031] The definition of abnormal data is as follows: If any set of operating data contains zero or negative values for the primary side inlet temperature, primary side outlet temperature, secondary side inlet temperature, secondary side outlet temperature, or primary side mass flow rate, that set of data is considered abnormal. This is because in actual physical processes, temperature and flow rate are rarely zero or negative; such values are usually caused by data recording errors or sensor malfunctions. If the calculated logarithmic mean temperature difference is negative, that set of data is considered abnormal. The logarithmic mean temperature difference is an important parameter for measuring the efficiency of plate heat exchangers, and its value should be positive. A negative value usually indicates data errors or measurement conditions that do not conform to physical laws. If two or more adjacent sets of data have the same temperature or primary side mass flow rate, that set of data is considered abnormal. In normal data recordings, data from adjacent time points usually exhibit some fluctuation or variation. If the data are completely identical, it may be due to data recording errors or data duplication.
[0032] S102: Calculate the heat exchange and logarithmic mean temperature difference for each set of operating data in the valid datasets for the clean period and the current operating season, respectively.
[0033] The heat exchange is calculated as follows: Calculate the temperature difference between the primary side inlet temperature and the primary side outlet temperature in the effective data set during the clean period and the current operating season. Multiply this temperature difference by the primary side mass flow rate in the effective data set during the clean period and the current operating season to obtain an intermediate value. Multiply this intermediate value by the specific heat capacity of the fluid to obtain the heat exchange of the effective data set during the clean period and the current operating season.
[0034] Specifically, the formula for calculating the heat exchange of the effective dataset during the clean period is: Φ i1 =C p ·G·(T1-T2). Wherein, Φ i1 The heat exchange in the effective dataset during the clean period refers to the heat transferred by the fluid during the heat exchange process described in this dataset. T1 is the primary side inlet temperature in the effective dataset during the clean period, T2 is the primary side outlet temperature in the effective dataset during the clean period, G is the primary side mass flow rate in the effective dataset during the clean period, and C...p The specific heat capacity of the fluid. In this application, the unit of temperature is °C, the unit of mass flow rate is kg / s, and the specific heat capacity of the fluid is the specific heat capacity of water, with the unit of kJ / (kg·°C), which is taken as 4.2 kJ / (kg·°C).
[0035] Specifically, the formula for calculating the heat exchange of the effective dataset in the current operating season is: Φ i2 =C p ·g·(t1-t2). Where, Φ i2 The heat exchange in the valid dataset for the current operating season refers to the heat transferred by the fluid during the heat exchange process described in this dataset. t1 is the primary-side inlet temperature in the valid dataset for the current operating season, t2 is the primary-side outlet temperature in the valid dataset for the current operating season, g is the primary-side mass flow rate in the valid dataset for the current operating season, and C is the heat transfer rate. p The specific heat capacity of the fluid. In this application, the unit of temperature is °C, the unit of mass flow rate is kg / s, and the specific heat capacity of the fluid is the specific heat capacity of water, with the unit of kJ / (kg·°C), which is taken as 4.2 kJ / (kg·°C).
[0036] The logarithmic mean temperature difference is calculated as follows: For the valid datasets of the cleaning period and the current operating season, two sets of temperature differences are calculated separately. The first temperature difference is the temperature difference from the primary side inlet temperature to the secondary side inlet temperature, and the second temperature difference is the temperature difference from the primary side outlet temperature to the secondary side outlet temperature. The ratio of the first temperature difference to the second temperature difference is calculated, and this ratio is used as the base of the logarithm for logarithmic calculation to obtain the logarithmic value. Using the logarithmic value as the denominator and the difference between the first and second temperature differences as the numerator, a division operation is performed to obtain the logarithmic mean temperature difference for the valid datasets of the cleaning period and the current operating season.
[0037] Specifically, the formula for calculating the average temperature difference of the effective dataset during the cleaning period is: Among them, LMTD i1 T1 is the average temperature difference of the effective dataset during the cleaning period, T3 is the primary side inlet temperature of the effective dataset during the cleaning period, T2 is the primary side outlet temperature of the effective dataset during the cleaning period, T4 is the secondary side outlet temperature of the effective dataset during the cleaning period, and ln is the natural logarithm, i.e., the logarithm to the base e.
[0038] Specifically, the formula for calculating the average temperature difference of the valid dataset for the current operating season is: Among them, LMTD i2t1 is the average temperature difference of the valid dataset in the current operating season, t2 is the primary inlet temperature of the valid dataset in the current operating season, t3 is the secondary inlet temperature of the valid dataset in the current operating season, t4 is the primary outlet temperature of the valid dataset in the current operating season, and ln is the natural logarithm, i.e., the logarithm to the base e.
[0039] Before calculating the heat exchange and logarithmic mean temperature difference for each set of operational data in the valid datasets of the clean period and the current operational season, the data for the first month of the operational season and the last month of the operational season are removed from the valid datasets of the clean period and the current operational season.
[0040] Specifically, during the initial period of operation, the operating data of plate heat exchangers may be unstable and subject to significant fluctuations due to factors such as system startup, debugging, and changes in user heating habits. This data cannot accurately reflect the long-term operating performance of the plate heat exchanger and therefore needs to be removed when calculating heat exchange and logarithmic mean temperature difference. In the heating industry, the operating data of plate heat exchangers may also be affected during the last month of the heating season as temperatures gradually rise and heating demand decreases. Furthermore, the performance of plate heat exchangers may decline during this period due to equipment aging and insufficient maintenance. Therefore, this data also needs to be removed to avoid interfering with the calculation results. Other industries can process their data effectively according to their specific industry characteristics.
[0041] S103: Perform a steady-state condition set filtering step on the valid datasets for the cleaning period and the current operating season respectively to obtain the steady-state condition sets for the cleaning period and the current operating season.
[0042] The steady-state operating condition set selection steps include: dividing the heat exchange and logarithmic mean temperature difference data into multiple subsets, calculating the relative standard deviation of each subset, and selecting the subset with the smallest relative standard deviation as the steady-state operating condition set.
[0043] Specifically, the heat exchange and logarithmic mean temperature difference data are divided into multiple subsets based on certain criteria (such as time, operating conditions, etc.). Each subset contains multiple data points for heat exchange and logarithmic mean temperature difference, representing the operating conditions of the plate heat exchanger under different conditions. For each subset, the relative standard deviation of the heat exchange data and the logarithmic mean temperature difference is calculated. The relative standard deviation is an indicator of the dispersion of a dataset; a smaller relative standard deviation indicates that the data points in the dataset are more concentrated, i.e., the data is more stable. After calculating the relative standard deviation of each subset, the subset with the smallest relative standard deviation is selected as the steady-state operating condition set. The data points in this steady-state operating condition set have high stability and representativeness, and can better reflect the operating conditions of the plate heat exchanger under steady-state conditions.
[0044] The relative standard deviation of each subset is calculated as follows: Sum the values of each heat exchange or logarithmic mean temperature difference in the subset, divide the sum by the total number of data points to obtain the mean. Calculate the difference between the heat exchange or logarithmic mean temperature difference in each subset and the mean, obtaining the squared difference. Sum all squared differences to obtain the sum of squared differences, divide the sum of squared differences by the total number of data points in each subset, and take the square root to calculate the standard deviation. Divide the standard deviation by the mean to obtain the relative standard deviation.
[0045] Specifically, the formula for calculating the relative standard deviation is: Where, x i For each individual measurement, which can be the heat exchange or the logarithmic mean temperature difference, n is the total number of data points in the subset. 1 is the mean, SD is the standard deviation, and RSD is the relative standard deviation.
[0046] S104: In the steady-state operating condition set of the clean period and the current operating season, by calculating the difference between adjacent data, find the set of data with the smallest difference. The heat exchange and logarithmic mean temperature difference of this set of data are the steady-state heat exchange and steady-state logarithmic mean temperature difference of the clean period and the current operating season, and take it as the steady-state operating condition.
[0047] Specifically, for the data points in the steady-state condition set, pairwise differences are calculated in chronological order: the difference between the first and second data points, the difference between the second and third data points, and so on. These differences reflect the degree of variation between the data points. The two data points (a set of data) with the smallest differences are selected as the steady-state points. This steady-state point represents the most stable data point in the steady-state condition set, and its corresponding heat transfer and logarithmic mean temperature difference will be used as the steady-state condition for subsequent calculations.
[0048] S105: Calculate the heat exchange thermal resistance of the plate heat exchanger during the cleaning period and the current operating season using steady-state operating data, as well as the sum of the flow rates on both sides to the power of -0.8. After linear fitting, the intercept is the thermal resistance of the plate heat exchanger, in order to calculate the fouling thermal resistance of the plate heat exchanger during the current operating season.
[0049] For the cleaning period and the current operating season, calculate the corresponding heat exchange capacity UA, where UA = Φ / LMTD. Here, UA is the product of the total heat transfer coefficient and the heat transfer area of the plate heat exchanger, Φ is the heat transfer capacity, and LMTD is the logarithmic mean temperature difference.
[0050] When the heat exchange capacity UA is calculated using the thermal resistance of the heat exchanger, the cleaning period Current operating season Where h1 and h2 are the convective heat transfer coefficients of the primary and secondary sides of the plate heat exchanger, A1 and A2 are the heat transfer areas of the primary and secondary sides of the plate heat exchanger, rw is the thermal resistance coefficient of the plate of the plate heat exchanger, rf is the fouling thermal resistance coefficient, A0 is the heat transfer area of the plate of the plate heat exchanger, and Ai is the heat transfer area of the fouling. Nu = cRe n Pr m Where Re is the Reynolds number, Pr is the Prandtl number, n is 0.8, and m is 0.3-0.4. Where ρ is density, u is flow velocity, l is characteristic length, and μ is dynamic viscosity.
[0051] For cleaning fouling in heat exchangers, highly accurate calculations are unnecessary, and it is assumed that the heat exchange areas on both sides of the plate heat exchanger are the same. Therefore, the calculation formula for UA is simplified to obtain... Furthermore, h is proportional to the 0.8 power of the flow velocity u. Since the structural parameters remain constant for the same plate heat exchanger, h is also proportional to the 0.8 power of the flow rate G. The convective heat transfer coefficients on both sides are not significantly different, so only the flow rate G is retained. The calculation formula for UA is further simplified, and the heat transfer resistance... in G2 = G1(T1-T2) / (T3-T4), where G1 and G2 are the primary and secondary flow rates, respectively.
[0052] During the cleaning period, the plate heat exchanger did not accumulate scale; only the thermal resistance of the plates remained. Furthermore, the plate thermal resistance remained unchanged before and after cleaning. However, due to different flow rates in different operating seasons, [the following is unclear and likely refers to a different process]. Expressed as a function, y = kx + b, where y = 1 / UA and x = G1 -0.8 +G2 -0.8After obtaining the fitted curves for the cleaning period and the current period, the intercept b between the two periods is compared. Intercept b represents the thermal resistance of the plate heat exchanger, thus yielding its fouling thermal resistance. ratio of dirt thermal resistance to clean-period thermal resistance bu is the intercept for the current period, and bc is the intercept for the clean period.
[0053] S106: Determine whether the ratio of the fouling thermal resistance to the thermal conductivity during the cleaning period of the plate heat exchanger in the current operating season exceeds the preset threshold.
[0054] If the ratio of the fouling thermal resistance to the thermal conductivity during the cleaning period of the plate heat exchanger in the current operating season exceeds the preset threshold, the judgment result is yes, and S107 is executed: the plate heat exchanger is cleaned before the start of the next operating season.
[0055] Specifically, if the ratio of the fouling thermal resistance to the thermal conductivity during the cleaning period of the plate heat exchanger exceeds a preset threshold during the current operating season, the plate heat exchanger needs to be cleaned before the start of the next operating season.
[0056] If the ratio of the fouling thermal resistance to the thermal conductivity during the cleaning period of the plate heat exchanger does not exceed the preset threshold, the result is negative, and S108 is executed: no cleaning of the plate heat exchanger is required.
[0057] Specifically, if the ratio of fouling thermal resistance to thermal conductivity thermal resistance during the current operating season does not exceed a preset threshold, it indicates that the fouling level of the plate heat exchanger is within an acceptable range and immediate cleaning is unnecessary. However, it is recommended to continue monitoring the increase in thermal conductivity thermal resistance of the plate heat exchanger so that timely measures can be taken if necessary.
[0058] The following case study illustrates this application by showing a heating company using real data to evaluate the performance of a plate heat exchanger.
[0059] The data comes from a data acquisition system installed by a heating company. This system collects data hourly for a total of 120 days. Due to the large volume of data, only one day's data is used as an example. Table 1 shows the hourly data collected by a heat exchange station provided in this embodiment of the application, with only a portion selected for illustration. This includes the primary side inlet temperature, primary side outlet temperature, secondary side inlet temperature, secondary side outlet temperature, and primary side mass flow rate. This data forms the basis for evaluating the performance of the plate heat exchanger. This data will be used to calculate key parameters such as the heat transfer capacity and logarithmic mean temperature difference of the plate heat exchanger, thereby evaluating its performance. Since the performance evaluation of the plate heat exchanger needs to be conducted under steady-state conditions, the raw data needs to be processed for steady-state operation. Here, 5 hours of data are grouped together, and steady-state processing calculations are performed sequentially. The purpose of steady-state processing is to eliminate fluctuations and noise in the data, obtaining more accurate and stable performance parameters. Figure 2After steady-state processing, the data corresponding to 13:00 was selected as representative of the steady-state operating condition. This means that around 13:00, the plate heat exchanger's operating state is relatively stable and can be used for subsequent performance evaluation.
[0060] Table 1
[0061] Time Φ / kW Time Φ / kW 0:00 835.98 12:00 844.80 1:00 832.04 13:00 844.80 2:00 880.50 14:00 844.80 3:00 825.16 15:00 844.80 4:00 853.75 16:00 849.71 5:00 834.98 17:00 873.83 6:00 840.93 18:00 849.71 7:00 827.12 19:00 873.83 8:00 837.95 20:00 862.86 9:00 830.07 21:00 890.16 10:00 840.93 22:00 846.32 11:00 835.98 23:00 847.52
[0062] This application, through calculation and analysis of 120 days of data from a heating company (one day's data has been given as an example above), obtained detailed data on the heat exchange capacity Φ during the clean period and the current heating season, as well as the heat exchange capacity UA of the plate heat exchanger. Table 2 shows the G1 values for the clean period and the current heating season provided in the embodiments of this application. -0.8 +G2 -0.8 The data is compared with 1 / UA. To better understand these data, they were plotted on a graph, and a linear relationship was obtained by linearly fitting the data of the clean period and the current heating season. Figure 3 A schematic diagram of the linear relationship provided for embodiments of this application, such as... Figure 3 As shown, the fitted linear functions for both periods were obtained simultaneously. Figure 2 The cleaning period is the cleaning period, and the current period is the current heating season. Cleaning period: yc = 0.06536x + 0.00127. Current heating season: yu = 0.19059x + 0.000172.
[0063] Table 2
[0064]
[0065] The intercept b for the clean period is 0.01376, and the intercept b for the current period is 0.04419. The fouling thermal resistance of the plate heat exchanger in the current operating season is calculated to be 0.03043℃ / W. The ratio of the fouling thermal resistance in the current operating season to the thermal conductivity thermal resistance in the clean period is... This is far above the company's maximum acceptable threshold of 1, based on economic cost considerations. Therefore, the plate heat exchanger needs to be cleaned before the start of the next heating season.
[0066] Meanwhile, an analysis of multiple plate heat exchangers was also conducted. As shown in Table 3, the ratio of fouling thermal resistance to thermal conductivity during the cleaning period differs for each plate heat exchanger during the current operating season. Plate heat exchangers No. 1, 2, 3, and 5 have exceeded the set threshold and meet the cleaning requirements. Plate heat exchangers No. 4 and No. 6 have not exceeded the set threshold and do not require cleaning at present.
[0067] Table 3
[0068]
[0069] This application embodiment also provides a fouling cleaning judgment device 400 for an in-service plate heat exchanger based on operating data, such as... Figure 4 As shown, the device includes: an acquisition module 401, an unknown quantity calculation module 402, an execution screening step module 403, an acquisition steady-state condition module 404, a plate heat exchanger fouling thermal resistance calculation module 405, and a judgment module 406.
[0070] The acquisition module 401 is used to acquire preset time periods for the cleaning period and the current operating season. Within the preset time period, it collects each set of operating data from the plate heat exchanger at preset intervals, removes abnormal data, and forms valid datasets for the cleaning period and the current operating season, respectively. Each set of operating data from the plate heat exchanger includes the inlet temperature and outlet temperature of the primary and secondary sides, as well as the mass flow rate of the primary side.
[0071] The unknown quantity calculation module 402 is used to calculate the heat exchange and logarithmic mean temperature difference of each set of operating data in the effective dataset of the clean period and the current operating season, respectively.
[0072] The execution filtering module 403 is used to perform a steady-state operating condition set filtering step on the valid datasets for the clean period and the current operating season, respectively, to obtain the steady-state operating condition sets for the clean period and the current operating season. The steady-state operating condition set filtering step includes: dividing the heat exchange and logarithmic mean temperature difference data into multiple subsets, calculating the relative standard deviation of each subset, and selecting the subset with the smallest relative standard deviation as the steady-state operating condition set.
[0073] The steady-state operating condition acquisition module 404 is used to find the set of data with the smallest difference between adjacent data in the steady-state operating condition set during the clean period and the current operating season by calculating the difference between adjacent data. The heat exchange and logarithmic mean temperature difference of this set of data are the steady-state heat exchange and steady-state logarithmic mean temperature difference during the clean period and the current operating season, and this is taken as the steady-state operating condition.
[0074] The fouling thermal resistance calculation module 405 for plate heat exchangers is used to calculate the heat transfer thermal resistance of the clean period and the current operating season data, as well as the sum of the flow rates on both sides to the power of -0.8, using steady-state operating data. After linear fitting, the intercept is the thermal conductivity thermal resistance of the plate heat exchanger, so as to calculate the fouling thermal resistance of the plate heat exchanger in the current operating season.
[0075] The judgment module 406 is used to determine whether the ratio of the fouling thermal resistance to the thermal conductivity during the cleaning period of the plate heat exchanger in the current operating season exceeds a preset threshold. If the ratio exceeds the preset threshold, the plate heat exchanger will be cleaned before the start of the next operating season. If the ratio does not exceed the preset threshold, the plate heat exchanger does not need to be cleaned.
[0076] Some modules in the apparatus described in this application can be described in the general context of computer-executable instructions that are executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, classes, etc., that perform a specific task or implement a specific abstract data type. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.
[0077] The apparatus or module described in the above embodiments can be implemented by a computer chip or physical entity, or by a product with a certain function. For ease of description, the above apparatus is described by dividing it into various modules according to their functions. When implementing the embodiments of this application, the functions of each module can be implemented in one or more software and / or hardware. Of course, a module that implements a certain function can also be implemented by combining multiple sub-modules or sub-units.
[0078] The methods, apparatus, or modules described in this application can be implemented in a computer-readable program code manner. The controller can be implemented in any suitable manner, such as a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers. Examples of controllers include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicon Labs C8051F320. A memory controller can also be implemented as part of the control logic of a memory. Those skilled in the art will also recognize that, in addition to implementing the controller in purely computer-readable program code manner, the same functionality can be achieved by logically programming the method steps to make the controller take the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the means included within it for implementing various functions can also be considered as structures within the hardware component. Alternatively, the device used to implement various functions can be viewed as either a software module that implements the method or a structure within a hardware component.
[0079] like Figure 5As shown in the figure, this application embodiment also provides a fouling cleaning judgment server for an in-service plate heat exchanger based on operating data, including a memory 501 and a processor 502; the memory 501 is used to store computer-executable instructions; the processor 502 is used to execute computer-executable instructions to implement the fouling cleaning judgment method for an in-service plate heat exchanger based on operating data described above in this application embodiment.
[0080] This application also provides a computer-readable storage medium storing executable instructions. When a computer executes the executable instructions, it can implement the cleaning judgment method for in-service plate heat exchangers for heating based on operating data as described above in this application.
[0081] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary hardware. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product, or it can be embodied in the process of data migration. The computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, mobile terminal, server, or network device, etc.) to execute the methods described in the embodiments of this application.
[0082] The various embodiments described in this specification are presented in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. All or part of this application can be used in numerous general-purpose or special-purpose computer system environments or configurations.
[0083] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of this application.
Claims
1. A method for judging fouling cleaning in an in-service plate heat exchanger based on operational data, characterized in that, include: The system acquires preset time periods for the cleaning period and the current operating season. Within these preset time periods, it collects each set of operating data from the plate heat exchanger at preset intervals and removes abnormal data to form valid datasets for the cleaning period and the current operating season. Each set of operating data from the plate heat exchanger includes the inlet temperature and outlet temperature of the primary and secondary sides, as well as the mass flow rate of the primary side. Calculate the heat exchange and logarithmic mean temperature difference for each set of operational data in the valid datasets for the cleaning period and the current operating season, respectively. Perform a steady-state operating condition set filtering step on the valid datasets of the cleaning period and the current operating season respectively to obtain the steady-state operating condition sets of the cleaning period and the current operating season; The steady-state operating condition set screening step includes: dividing the heat exchange and logarithmic mean temperature difference data into multiple subsets, calculating the relative standard deviation of each subset, and selecting the subset with the smallest relative standard deviation as the steady-state operating condition set. In the steady-state operating condition set of the clean period and the current operating season, by calculating the difference between adjacent data, the set of data with the smallest difference is found. The heat exchange and logarithmic mean temperature difference of this set of data are the steady-state heat exchange and steady-state logarithmic mean temperature difference of the clean period and the current operating season, and it is taken as the steady-state operating condition. The heat exchange thermal resistance of the plate heat exchanger during the cleaning period and the current operating season is calculated using steady-state operating data, as well as the sum of the negative 0.8 power of the flow rates on both sides. After linear fitting, the intercept is the thermal resistance of the plate heat exchanger, so as to calculate the fouling thermal resistance of the plate heat exchanger during the current operating season. Determine whether the ratio of fouling thermal resistance to thermal conductivity during the cleaning period of the plate heat exchanger in the current operating season exceeds a preset threshold. If the ratio of the fouling thermal resistance to the thermal conductivity during the cleaning period of the plate heat exchanger exceeds the preset threshold during the current operating season, the plate heat exchanger shall be cleaned before the start of the next operating season. If the ratio of the fouling thermal resistance to the thermal conductivity during the cleaning period does not exceed the preset threshold, there is no need to clean the plate heat exchanger.
2. The method for judging fouling cleaning in an in-service plate heat exchanger based on operational data according to claim 1, characterized in that, The cleaning period is either the first operating season after the plate heat exchanger starts operation or the first operating season after the plate heat exchanger has been cleaned.
3. The method for judging fouling cleaning in an in-service plate heat exchanger based on operational data according to claim 1, characterized in that, Before calculating the heat exchange and logarithmic mean temperature difference for each set of operational data in the valid datasets of the clean period and the current operating season, the data from the period before the start of the operating season in the valid datasets of the clean period and the current operating season that has not yet reached a stable operating period is also removed.
4. The method for judging fouling cleaning of in-service plate heat exchangers based on operational data according to claim 1, characterized in that, The definition standard for abnormal data is as follows: if the primary side inlet temperature, primary side outlet temperature, secondary side inlet temperature, secondary side outlet temperature, or primary side mass flow rate in any set of operating data is zero or negative, the set of data is considered abnormal data. If the calculated logarithmic mean temperature difference is negative, the data set is considered outlier. If two or more adjacent sets of data have the same temperature or primary mass flow rate, the data set is considered abnormal.
5. The method for judging fouling cleaning in an in-service plate heat exchanger based on operational data according to claim 1, characterized in that, The calculation method for heat exchange is as follows: Calculate the temperature difference between the primary side inlet temperature and the primary side outlet temperature in the effective data of the cleaning period and the current operating season; Multiply the temperature difference by the mass flow rate of the primary side of the effective data set for the cleaning period and the current operating season to obtain the intermediate value; Multiply this intermediate value by the specific heat capacity of the fluid to obtain the heat exchange rate of the effective dataset for the clean period and the current operating season.
6. The method for judging fouling cleaning of in-service plate heat exchangers based on operational data according to claim 1, characterized in that, The logarithmic mean temperature difference is calculated as follows: For the valid datasets of the cleaning period and the current operating season, two sets of temperature differences are calculated respectively; where the first temperature difference is the temperature from the primary side inlet temperature to the secondary side inlet temperature, and the second temperature difference is the temperature from the primary side outlet temperature to the secondary side outlet temperature. Calculate the ratio of the first temperature difference to the second temperature difference, and use this ratio as the base of the logarithm to perform a logarithmic operation to obtain the logarithmic value; Using the logarithmic value as the denominator and the difference between the first and second temperature differences as the numerator, a division operation is performed to obtain the logarithmic mean temperature difference of the effective dataset for the cleaning period and the current operating season.
7. The method for judging fouling cleaning in an in-service plate heat exchanger based on operational data according to claim 1, characterized in that, The relative standard deviation of each subset of data is calculated as follows: Add up the values of each heat exchange or logarithmic mean temperature difference in the subset of data to get the sum, and divide the sum by the total number of data points to get the average value; Calculate the difference between the heat exchange or logarithmic mean temperature difference in the subset of data and the mean value; And obtain the squared difference; Sum all the squared differences to get the total of the squared differences. Divide the total of the squared differences by the total number of data in each subset and take the square root to calculate the standard deviation. The relative standard deviation is obtained by dividing the standard deviation by the mean.
8. The method for judging fouling cleaning of an in-service plate heat exchanger based on operating data according to claim 1, characterized in that, The heat transfer resistance during the clean period and the current operating season, along with the sum of the negative 0.8 power of the flow rates on both sides, are calculated using steady-state operating data. A linear fit is then performed, and the intercept is taken as the thermal resistance of the plate heat exchanger. This is used to calculate the fouling resistance of the plate heat exchanger, including: For the cleaning period and the current operating season, calculate the corresponding heat exchange capacity UA, UA=Φ / LMTD; where, the heat exchange capacity UA is the product of the total heat transfer coefficient of the plate heat exchanger and the heat transfer area, Φ is the heat transfer, and LMTD is the logarithmic mean temperature difference; When UA uses the thermal resistance of a plate heat exchanger for calculation, the clean period Current operating season Where h1 and h2 are the convective heat transfer coefficients of the primary and secondary sides of the plate heat exchanger, A1 and A2 are the heat transfer areas of the primary and secondary sides of the plate heat exchanger, rw is the thermal resistance coefficient of the plate of the plate heat exchanger, rf is the fouling thermal resistance coefficient, A0 is the heat transfer area of the plate of the plate heat exchanger, and Ai is the heat transfer area of the fouling. Nu = cRe n Pr m Where Re is the Reynolds number, Pr is the Prandtl number, n is 0.8, and m is 0.3-0.
4. Where ρ is density, u is flow velocity, l is characteristic length, and μ is dynamic viscosity; The formula for calculating UA is simplified to obtain: Furthermore, h is proportional to the 0.8 power of the flow velocity u, and h is also proportional to the 0.8 power of the flow rate G. Simplifying the calculation formula for UA, the total heat transfer thermal resistance... in G2 = G1(T1-T2) / (T3-T4), where G1 and G2 are the primary and secondary flow rates, respectively. Will Expressed as a function, y = kx + b, where y = 1 / UA, x = (G1 -0.8 +G2 -0.8 ), and perform linear fitting, with a goodness-of-fit R. 2 Not less than 0.8; After obtaining the fitted curves for the cleaning period and the current period, the intercept b is the thermal resistance of the plate heat exchanger. By comparing the intercepts b of the two periods, the fouling thermal resistance of the heat exchanger in the current operating season can be obtained. ratio of dirt thermal resistance to clean-period thermal conductivity bu is the intercept for the current period, and bc is the intercept for the clean period.
9. A fouling cleaning judgment device for an in-service plate heat exchanger based on operational data, characterized in that, include: The acquisition module is used to acquire preset time periods for the cleaning period and the current operating season. Within the preset time period, it collects each set of operating data of the plate heat exchanger at preset intervals and removes abnormal data to form valid datasets for the cleaning period and the current operating season, respectively. Each set of operating data of the plate heat exchanger includes the inlet temperature and outlet temperature of the primary and secondary sides, as well as the mass flow rate of the primary side. The unknown quantity calculation module is used to calculate the heat exchange and logarithmic mean temperature difference for each set of operational data in the effective dataset of the cleaning period and the current operating season, respectively. The module for performing the filtering steps is used to perform the steady-state operating condition set filtering steps on the valid datasets of the cleaning period and the current operating season respectively, so as to obtain the steady-state operating condition sets of the cleaning period and the current operating season. The steady-state operating condition set screening step includes: dividing the heat exchange and logarithmic mean temperature difference data into multiple subsets, calculating the relative standard deviation of each subset, and selecting the subset with the smallest relative standard deviation as the steady-state operating condition set. The steady-state operating condition module is used to find the set of data with the smallest difference between adjacent data in the steady-state operating condition set during the clean period and the current operating season by calculating the difference between adjacent data. The heat exchange and logarithmic mean temperature difference of this set of data are the steady-state heat exchange and steady-state logarithmic mean temperature difference during the clean period and the current operating season, and this is taken as the steady-state operating condition. The module for calculating the fouling thermal resistance of a plate heat exchanger is used to calculate the heat transfer thermal resistance of the clean period and the current operating season using steady-state operating data, as well as the sum of the negative 0.8 power of the flow rates on both sides. After linear fitting, the intercept is the thermal conductivity thermal resistance of the plate heat exchanger, so as to calculate the fouling thermal resistance of the plate heat exchanger in the current operating season. The judgment module is used to determine whether the ratio of the fouling thermal resistance to the thermal conductivity during the cleaning period of the plate heat exchanger in the current operating season exceeds a preset threshold. If the ratio exceeds the preset threshold, the plate heat exchanger will be cleaned before the start of the next operating season. If the ratio does not exceed the preset threshold, the plate heat exchanger does not need to be cleaned.
Citation Information
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