A method for optimizing temperature and flow of a circulating water system

Abstract

The present application relates to the technical field of energy saving optimization of industrial circulating water system, and particularly relates to a circulating water system temperature and flow optimization design method, which comprises the following steps: obtaining the reference circulating water total flow, the cooling tower inlet and outlet water temperature and the heat exchanger group hot side inlet and outlet temperature; determining the heat load according to the energy conservation, and establishing the temperature boundary of the cooling tower outlet corresponding to the heat exchanger group cold side inlet, the cooling tower inlet corresponding to the heat exchanger group cold side outlet, and calculating the reference logarithmic mean temperature difference; obtaining the allowable water spray density after the transformation, the design wet bulb temperature and the preset threshold value; taking the reference circulating water total flow as the initial value for iteration, using the approximation degree model to calculate the cooling tower outlet water temperature, combining the heat load to calculate the cooling tower inlet water temperature and calculating the target logarithmic mean temperature difference, updating the flow according to the relative deviation until the threshold value is met, and outputting the target circulating water total flow. The present application can obtain a verifiable matching flow under the constraint condition, reduce the trial operation adjustment cost and inhibit the risk of over-limit.

Description

Technical Field

[0001] This invention relates to the field of energy-saving optimization technology for industrial circulating water systems, and specifically to a method for optimizing the temperature and flow rate of a circulating water system. Background Technology

[0002] Circulating water systems are widely used in continuous production scenarios such as power generation, petrochemicals, metallurgy, and large public buildings. Their operational stability directly affects the safety margin of the equipment, product quality, and downtime risk. Circulating water pumps and cooling tower fans are typically the main energy-consuming units in public works projects. Improper configuration of flow and temperature boundaries can lead to persistently high pump consumption, redundant or insufficient cooling capacity, and increased temperature fluctuations at the heat exchange terminals. Especially after the cooling tower packing is modified, the water distribution capacity and heat exchange characteristics change. Traditional methods relying on empirical coefficients, single-point verification, or separate design of the cooling tower and heat exchanger are insufficient to quickly obtain verifiable matching flow rates under given heat loads and ambient wet-bulb conditions. This often requires repeated trial runs and manual corrections, resulting in unclear boundaries, untraceable results, risks of exceeding allowable water spray density, and operational instability. Summary of the Invention

[0003] This invention provides a method for optimizing the temperature and flow rate of a circulating water system, which at least solves the problem of determining the total flow rate of the circulating water under the constraints of heat load and environmental wet-bulb conditions after the cooling tower packing is modified.

[0004] This invention provides a method for optimizing the temperature and flow rate of a circulating water system, the method comprising: Obtain the baseline total circulating water flow rate, cooling tower inlet water temperature, cooling tower outlet water temperature, and heat exchanger group hot side inlet and outlet temperatures; The heat load is determined based on the law of conservation of energy, and the inlet temperature of the cold side of the heat exchanger group is set as the outlet temperature of the cooling tower and the outlet temperature of the cold side of the heat exchanger group is set as the inlet temperature of the cooling tower. The baseline logarithmic mean temperature difference is calculated. Obtain the allowable water spray density, design wet-bulb temperature, and preset threshold after modification; Using the baseline total circulating water flow rate as the initial value of the iterative flow rate, the cooling tower outlet water temperature is determined by the cooling tower approximation model based on the allowable spray density after modification, the design wet-bulb temperature, and the iterative flow rate. The cooling tower inlet water temperature is determined based on the heat load and the iterative flow rate, and the target logarithmic mean temperature difference is calculated. The iterative flow rate is updated according to the relative deviation until the relative deviation is not greater than the preset threshold, and the target total circulating water flow rate is output.

[0005] In one possible implementation, the inlet and outlet temperatures of the heat exchanger group on the hot side include the inlet temperature and the outlet temperature of the heat exchanger group on the hot side. When the heat exchanger group contains multiple heat exchangers, the inlet temperature and outlet temperature of each heat exchanger on the hot side are obtained, the circulating water flow rate of each heat exchanger is obtained, and the inlet temperature of each heat exchanger on the hot side is obtained by weighted averaging based on the circulating water flow rate of each heat exchanger. The outlet temperature of each heat exchanger on the hot side is obtained by weighted averaging based on the outlet temperature of each heat exchanger.

[0006] In one possible implementation, determining the heat load based on energy conservation includes: setting the specific heat capacity of the circulating water as a preset constant; and calculating the heat load based on the reference total circulating water flow rate and the temperature difference between the cooling tower inlet water temperature and the cooling tower outlet water temperature.

[0007] In one possible implementation, calculating the baseline logarithmic mean temperature difference includes: decomposing the inlet and outlet temperatures of the heat exchanger group on the hot side into the inlet temperature and outlet temperature of the heat exchanger group on the hot side; calculating the first end temperature difference as the difference between the inlet temperature and the outlet temperature of the heat exchanger group on the hot side, and calculating the second end temperature difference as the difference between the outlet temperature and the inlet temperature of the heat exchanger group on the hot side; and obtaining the baseline logarithmic mean temperature difference based on the first end temperature difference and the second end temperature difference.

[0008] In one possible implementation, obtaining the allowable water spray density after modification includes: determining the allowable water spray density after modification based on the product parameters of the modified cooling tower packing; or, determining the allowable water spray density after modification based on the correspondence between packing type and allowable water spray density; the allowable water spray density after modification is used to indicate the upper limit of the total circulating water flow allowed to pass through a unit water spray area.

[0009] In one possible implementation, the design wet-bulb temperature is determined by one of the following methods: by measuring with a wet-bulb thermometer; by obtaining the wet-bulb temperature for the corresponding time period from meteorological observation data and averaging it; or by determining the annual average wet-bulb temperature as the design wet-bulb temperature.

[0010] In one possible implementation, the preset threshold is a relative deviation threshold, which is used to limit the maximum allowable value of the relative deviation. The relative deviation represents the proportion of the target logarithmic mean temperature difference that deviates from the reference logarithmic mean temperature difference.

[0011] In one possible implementation, the cooling tower approximation model includes the cooling tower water spray area, which is calculated from the length of a single cooling tower, the width of a single cooling tower, and the number of cooling towers. The cooling tower approximation model determines the water spray density based on the iterative flow rate and the cooling tower water spray area. The water spray density is the total flow rate of circulating water passing through a unit cooling tower water spray area. The cooling tower approximation model determines the cooling tower approximation degree based on the relationship between the water spray density and the allowable water spray density after modification, as well as the design wet-bulb temperature. The cooling tower approximation degree is used to indicate the temperature difference between the cooling tower outlet water temperature and the design wet-bulb temperature.

[0012] In one possible implementation, determining the cooling tower inlet water temperature based on heat load and iterative flow rate includes: determining the circulating water temperature rise based on heat load and iterative flow rate; and determining the cooling tower inlet water temperature as the temperature obtained by adding the cooling tower outlet water temperature and the circulating water temperature rise.

[0013] In one possible implementation, updating the iterative flow rate based on the relative deviation includes: proportionally correcting the iterative flow rate based on the relative deviation and the proportional correction coefficient to obtain the updated iterative flow rate; when the water density corresponding to the updated iterative flow rate is greater than the allowable water density after the modification, the updated iterative flow rate is limited to the maximum allowable flow rate corresponding to the allowable water density after the modification.

[0014] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows: By locking the heat load based on energy conservation and establishing the temperature boundary correspondence between the cooling tower and the heat exchanger group, a verifiable operating condition model with consistent input boundaries was achieved. By introducing a cooling tower approximation model constrained by allowable spray density and design wet-bulb temperature, the outlet water temperature under the condition of changing cooling tower capacity after modification can be predicted. By using the relative deviation of logarithmic mean temperature difference as the convergence criterion and iteratively correcting the flow rate, a closed-loop solution and fast convergence of the matching flow rate were achieved. By limiting the updated flow rate with allowable spray density, the flow rate results are kept within limits and are easy to implement in engineering. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the execution flow of the method of the present invention. Detailed Implementation

[0016] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0017] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0018] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0019] In circulating water systems, flow rate and temperature are two fundamental quantities describing the system's "transport capacity" and "heat exchange state," respectively. Flow rate determines the ability of circulating water to carry heat per unit time, directly corresponding to the pump's operating point and the distribution of pipe network resistance. Temperature reflects the heat exchange results between the heat exchanger assembly and the cooling tower, especially since the inlet and outlet temperatures of the cooling tower and the inlet and outlet temperatures of the heat exchanger assembly together constitute the observable temperature boundary. In engineering design and retrofit evaluation, adjusting the flow rate or checking the temperature alone can easily lead to inconsistent boundaries. For example, under the same heat load, changes in flow rate will simultaneously change the cooling tower temperature difference and heat exchange driving force, while changes in the temperature boundary will conversely affect the judgment of whether the flow rate is "appropriate." Therefore, a method is needed to unify the flow rate and temperature boundaries under the same energy constraint, so that, given environmental conditions and equipment load limitations, a temperature-flow rate matching relationship consistent with the actual system can be obtained, and target flow rate parameters that can be directly used for selection and operation settings can be output.

[0020] like Figure 1 As shown, a method for optimizing the temperature and flow rate of a circulating water system is provided, the method comprising: Obtain the baseline total circulating water flow rate, cooling tower inlet water temperature, cooling tower outlet water temperature, and heat exchanger group hot side inlet and outlet temperatures; In one embodiment, baseline data acquisition is first performed. The baseline total circulating water flow rate is obtained using a pipeline electromagnetic flowmeter or ultrasonic flowmeter, with a sampling period set to the second level and continuous acquisition for at least ten minutes. The cooling tower inlet and outlet water temperatures are obtained using platinum resistance temperature sensors, with temperature measuring points arranged on the straight sections of the cooling tower inlet and outlet main pipes, respectively, avoiding bends and valve disturbance areas. The inlet and outlet temperatures of the heat exchanger group on the hot side are obtained using temperature measuring points on the hot side main pipe, located near the inlet and outlet manifolds of the heat exchanger group. The acquisition end records the flow and temperature data with a unified timestamp, forming the baseline total circulating water flow rate, cooling tower inlet temperature, cooling tower outlet temperature, and heat exchanger group hot side inlet and outlet temperatures within the same time window.

[0021] The inlet and outlet temperatures of the heat exchanger group include the inlet temperature and outlet temperature of the heat exchanger group. When the heat exchanger group contains multiple heat exchangers, the inlet temperature and outlet temperature of each heat exchanger are obtained, the circulating water flow rate of each heat exchanger is obtained, and the inlet temperature of each heat exchanger is weighted and averaged based on the circulating water flow rate of each heat exchanger to obtain the inlet temperature of the heat exchanger group. The outlet temperature of each heat exchanger is weighted and averaged to obtain the outlet temperature of the heat exchanger group.

[0022] In one embodiment, to obtain the hot-side inlet and outlet temperatures representing the overall operating condition of a heat exchanger group containing multiple heat exchangers, a calculation method of "weighted averaging based on the circulating water flow rate corresponding to each heat exchanger" is introduced. The significance of this constraint is that the circulating water flow rates allocated to different heat exchangers are usually inconsistent. Directly averaging the temperatures would amplify the measurement fluctuations of smaller flow branches, leading to distortion of the hot-side inlet and outlet temperatures of the heat exchanger group, thus affecting the consistency of subsequent judgments on the heat exchange driving force. The boundary of this constraint is that each heat exchanger must correspond to one available circulating water flow rate data point, and the temperature and flow rate must be within the same sampling time window.

[0023] In practice, first, establish a heat exchanger list and branch mapping relationship, clarifying the correspondence between heat exchanger numbers, hot-side inlet measuring points, hot-side outlet measuring points, and circulating water branch flow measuring points. Then, obtain the hot-side inlet and outlet temperatures of each heat exchanger. Temperature measuring points can be arranged on the straight pipe sections of the hot-side inlet and outlet short pipes of the heat exchanger, with the measuring point sleeves inserted to cover the mainstream area, avoiding wall-mounted temperature measurements. The circulating water flow rate corresponding to each heat exchanger is preferentially obtained directly using branch flow meters. If branch flow meters are unavailable, branch differential pressure transmitters combined with valve opening characteristics or throttling element coefficients can be used to estimate the branch flow rate. During estimation, the sum of the flow rates of each branch is checked against the total flow rate for the same time period, and if necessary, it is proportionally corrected to match the baseline total circulating water flow rate.

[0024] For data alignment, both flow rate and temperature are synchronized using the same time base. If the sensor sampling frequencies are different, the data are first resampled to a uniform time interval, and then the average value within the same time window is taken as the representative value of that time window. Outlier removal is performed on temperature data, and outlier criteria can be based on two types of rules: "exceeding the upper limit of the rate of change of neighboring sampling points" or "exceeding a reasonable physical range". Zero drift and abrupt changes are checked for flow rate data. When a branch flow rate is found to be zero or has an unreasonable jump, the valve status and instrument status are checked first, and then it is decided whether to replace it with data from an adjacent time period.

[0025] After completing the above preparations, when calculating the hot-side inlet temperature of the heat exchanger group, perform a product operation of "hot-side inlet temperature multiplied by the corresponding circulating water flow rate" for each heat exchanger. Sum all products and then divide by the sum of the circulating water flow rates of all heat exchangers to obtain the hot-side inlet temperature of the heat exchanger group. When calculating the hot-side outlet temperature of the heat exchanger group, the same weighting method is used to process the hot-side outlet temperature of each heat exchanger to obtain the hot-side outlet temperature of the heat exchanger group. To avoid the weighting result being sensitive due to an insufficient total flow rate, when the sum of the circulating water flow rates of the heat exchanger group is lower than a preset lower limit, the update of the hot-side inlet and outlet temperatures of the heat exchanger group is paused and the results of the previous stable period are used.

[0026] To ensure verifiable results, while outputting the hot-side inlet and outlet temperatures of the heat exchanger group, the number of heat exchangers involved in the weighting, the proportion of circulating water flow in each branch, the time window length, and the number of outlier removals are recorded for subsequent verification. If the heat exchanger group is under maintenance bypass or some heat exchangers are out of service, the circulating water flow corresponding to the out-of-service heat exchanger is set to zero and removed from the weighting set to ensure that the hot-side inlet and outlet temperatures of the heat exchanger group only reflect the operating conditions of the heat exchangers actually in operation. Through this method, the hot-side inlet and outlet temperatures of the heat exchanger group can be stably obtained in scenarios with multiple heat exchangers connected in parallel or in series-parallel combinations, providing a consistent input boundary for subsequent heat load calculations and logarithmic mean temperature difference consistency control.

[0027] The heat load is determined based on the law of conservation of energy, and the inlet temperature of the cold side of the heat exchanger group is set as the outlet temperature of the cooling tower and the outlet temperature of the cold side of the heat exchanger group is set as the inlet temperature of the cooling tower. The baseline logarithmic mean temperature difference is calculated. In one embodiment, the heat load is calculated based on energy conservation and serves as a fixed boundary for subsequent temperature and flow optimization. Simultaneously, the cooling tower outlet water temperature is mapped to the cold-side inlet temperature of the heat exchanger group, and the cooling tower inlet water temperature is mapped to the cold-side outlet temperature of the heat exchanger group, ensuring that the cold-side temperature boundary of the heat exchanger group aligns with the circulating water system loop. Subsequently, combining the hot-side inlet and outlet temperatures of the heat exchanger group, a baseline logarithmic mean temperature difference is calculated to characterize the heat exchange driving force under baseline conditions and serves as a comparison benchmark for subsequent iterative decisions.

[0028] Determining the heat load based on energy conservation includes: setting the specific heat capacity of the circulating water as a preset constant; and calculating the heat load based on the reference total circulating water flow rate and the temperature difference between the cooling tower inlet water temperature and the cooling tower outlet water temperature.

[0029] In one embodiment, to ensure the heat load calculation is applicable to feasible engineering operations, the specific heat capacity of the circulating water is first set to a preset constant. This preset constant can be a commonly used engineering value and is fixed in the system configuration file to ensure consistency across different batches of data. Subsequently, the baseline total circulating water flow rate, cooling tower inlet water temperature, and cooling tower outlet water temperature are read within the same time window. It is recommended to use a continuous interval of stable operation for the time window to avoid short-term interference from start-ups, valve switching, and water replenishment fluctuations. The temperature data is validated for reasonableness, requiring the cooling tower inlet water temperature to be higher than the cooling tower outlet water temperature, and the temperature difference to be within the normal operating range of the equipment. If this is not met, the sensor installation location and signal quality are checked first, and then a new stable time window is selected. The flow rate data is checked for zero points and abrupt changes; after removing obvious anomalies, the average value of the time window is used as the calculation input.

[0030] Heat load can be calculated based on the law of conservation of energy using the following formula:

[0031] in, For heat load, The circulating water mass flow rate per unit time. For the specific heat capacity of circulating water, This represents the temperature difference between the cooling tower inlet water temperature and the cooling tower outlet water temperature. The circulating water mass flow rate per unit time is calculated from the reference total circulating water flow rate using either the commonly used density approximation or the on-site calibrated density. When the reference total circulating water flow rate is provided in mass flow rate form, it can be directly used as the circulating water mass flow rate per unit time. After the heat load calculation is completed, the heat load is written into the operating data record. The record items should at least include the start and end times of the time window, the reference total circulating water flow rate, the cooling tower inlet water temperature, the cooling tower outlet water temperature, and the heat load result.

[0032] To ensure reproducibility, the source of the specific heat capacity of the circulating water and the method of approximating its density can also be recorded. When there are significant changes in the quality of the circulating water or obvious changes in salinity, the specific heat capacity value can be revised during maintenance or calibration. After revision, the same preset constant should be used for subsequent data to avoid incomparability of heat loads at different stages of the same project. Through the above steps, the heat load can be directly obtained from measurable flow rate and temperature, resulting in a short calculation chain, on-site execution, and a stable energy boundary for subsequent temperature and flow rate optimization.

[0033] The calculation of the baseline logarithmic mean temperature difference includes: decomposing the inlet and outlet temperatures of the heat exchanger group on the hot side into the inlet temperature and outlet temperature of the heat exchanger group on the hot side; calculating the first end temperature difference as the difference between the inlet temperature and the outlet temperature of the heat exchanger group on the hot side; calculating the second end temperature difference as the difference between the outlet temperature and the inlet temperature of the heat exchanger group on the hot side; and obtaining the baseline logarithmic mean temperature difference based on the first end temperature difference and the second end temperature difference.

[0034] In one embodiment, to obtain a reference logarithmic mean temperature difference that represents the heat exchange driving force under baseline operating conditions, the inlet and outlet temperatures of the heat exchanger group on the hot side are first explicitly separated into the inlet temperature and outlet temperature of the heat exchanger group on the hot side, avoiding the mixing of the hot side boundaries in subsequent calculations. Then, a correspondence between the cold side temperatures is established according to the temperature boundaries of the circulating water loop, using the cooling tower outlet temperature as the inlet temperature of the heat exchanger group on the cold side and the cooling tower inlet temperature as the outlet temperature of the heat exchanger group on the cold side. After completing the temperature correspondence, the temperature differences at both ends are calculated: the first temperature difference is the difference between the inlet temperature and the outlet temperature of the heat exchanger group on the hot side, and the second temperature difference is the difference between the outlet temperature and the inlet temperature of the heat exchanger group on the hot side. Both temperature differences should be positive simultaneously and should not be close to zero; if an anomaly occurs, priority should be given to checking whether the temperature measuring point is located in an insufficiently mixed zone or whether there is bypass flow causing the cold side temperature boundary to not represent the actual heat exchanger inlet and outlet.

[0035] The baseline logarithmic mean temperature difference is calculated using a common method for counter-current heat transfer, as shown in the following formula:

[0036] in, The baseline logarithmic mean temperature difference For the first temperature difference, This represents the temperature difference at the second end. To avoid numerical instability, when the temperature difference at the first end is very close to that at the second end, a lower limit for the difference can be set in the implementation. When the difference is below the lower limit, the average value of the temperature differences at both ends is used to approximate the baseline logarithmic average temperature difference, and this situation is recorded as an approximate calculation event for subsequent verification.

[0037] After the baseline logarithmic mean temperature difference is calculated, it is archived along with the corresponding temperature inputs. The records must include at least the heat exchanger group's hot-side inlet temperature, heat exchanger group's hot-side outlet temperature, cooling tower outlet water temperature, cooling tower inlet water temperature, first-end temperature difference, second-end temperature difference, and the baseline logarithmic mean temperature difference. If the heat exchanger group consists of multiple heat exchangers, and the hot-side inlet and outlet temperatures are obtained using a weighted method, the number of heat exchangers involved in the calculation and the source of the weighted flow rate should also be recorded to ensure that the baseline logarithmic mean temperature difference can be recalculated. Through the above processing, the baseline logarithmic mean temperature difference is obtained from clearly defined hot-side and cold-side boundaries, with a clear temperature correspondence and verifiable calculation inputs. This provides a reliable benchmark for subsequent flow rate iterations aimed at achieving consistency in the logarithmic mean temperature difference.

[0038] Obtain the allowable water spray density, design wet-bulb temperature, and preset threshold after modification; In one embodiment, after calculating the baseline logarithmic mean temperature difference, the process proceeds to the parameter acquisition stage, which defines the feasible flow range and iteration stopping conditions after the modification. Parameters include the allowable spray density after modification, the design wet-bulb temperature, and a preset threshold. The acquisition unit writes these three types of parameters into the same project configuration file, recording the source, applicable time period, and unit. To avoid misuse, the calculation methods for the number of cooling towers, single tower dimensions, and spray area are first verified, then the statistical methods for the temperature data are verified, and finally, the applicability of the preset threshold is verified as a relative deviation. After verification, the three types of parameters are bound to the baseline logarithmic mean temperature difference and stored as the input boundary for subsequent iterative calculations.

[0039] Obtaining the allowable water spray density after modification includes: determining the allowable water spray density after modification based on the product parameters of the cooling tower packing after modification; or, determining the allowable water spray density after modification based on the correspondence between packing type and allowable water spray density; the allowable water spray density after modification is used to indicate the upper limit of the total circulating water flow allowed to pass through a unit water spray area.

[0040] In one embodiment, to ensure that the iterative flow rate does not exceed the cooling tower's post-modification capacity, the allowable spray density is first determined. The allowable spray density represents the upper limit of the total circulating water flow allowed per unit spray area, used to constrain the uniformity of water distribution in the cooling tower and the hydraulic load on the packing channels. The allowable spray density is preferentially obtained using the product parameter method: based on the model and batch of the modified cooling tower packing, the recommended operating range in the supply technical documents is read, and an allowable spray density value matching the on-site design airflow and spraying method is selected, with the corresponding test conditions and units recorded.

[0041] If the product parameters do not provide direct numerical values, a correspondence method is used: A correspondence table is established between packing type and allowable spray density. Packing types should be categorized into at least two types: membrane packing and drip packing, further classified using sheet spacing, wave height, specific surface area, or channel width as classification keys. After entering the structural parameters of the modified packing, the allowable spray density is retrieved from the correspondence table. To avoid retrieval errors due to incorrect parameter input, structural parameters are jointly confirmed by construction acceptance records and physical sampling inspections. Sampling inspections include sheet spacing measurement and packing block dimensional measurement.

[0042] The water spray area is calculated based on the effective water spray area diameter, according to the effective length and width of the water distribution area of ​​a single tower, excluding areas such as maintenance passages and areas blocked by baffles that do not participate in water distribution. When the cooling tower is operating in a segmented manner, the water spray area is calculated based on the actual number of operating segments. For scenarios with multiple cooling towers connected in parallel, the allowable water spray density remains consistent, and the water spray area is calculated by summing the effective water spray area of ​​a single tower and the number of cooling towers. The modified allowable water spray density and water spray area are used together for subsequent limit judgment. After the values ​​are obtained, a consistency check is performed: the baseline water spray density is obtained by dividing the baseline total circulating water flow rate by the water spray area.

[0043] When the baseline spray density is higher than the allowable spray density after modification, it is marked as exceeding the limit risk, and the upper limit of the target total circulating water flow rate in subsequent calculations is limited to the product of the allowable spray density after modification and the spray area. When the baseline spray density is lower than the allowable spray density after modification, the iterative flow rate is allowed to be adjusted within the above upper limit. To account for the long-term operational impacts such as scaling and clogging, a safety margin can be introduced on the allowable spray density after modification. The safety margin is given as a fixed proportion and recorded separately in the parameter list. When the values ​​given in the product document are inconsistent with the results in the corresponding relationship table, the product document shall be used first, and the reasons for the difference and the basis for selection shall be recorded. Finally, the allowable spray density after modification, packing type, data source, effective spray area, sampling records and verification conclusions shall be written into the parameter list for use in subsequent steps.

[0044] The design wet-bulb temperature is determined by one of the following methods: by measuring with a wet-bulb thermometer; by obtaining the wet-bulb temperature for the corresponding period from meteorological observation data and averaging it; or by determining the annual average wet-bulb temperature as the design wet-bulb temperature.

[0045] In one embodiment, to ensure a clear source of input for the cooling tower approximation model, the design wet-bulb temperature is determined. The design wet-bulb temperature represents the ambient humidity level under the target operating conditions and serves as the environmental boundary for predicting the cooling tower outlet water temperature. Three pathways are available for obtaining the design wet-bulb temperature, and projects can choose one based on their data conditions.

[0046] The first approach involves on-site measurement: Dry-bulb and wet-bulb thermometers or integrated temperature and humidity measuring devices are placed on the air inlet side of the cooling tower. The measuring points are avoided from heat sources and direct sunlight, and the measurement height is close to the center height of the air inlet louvers. The measurement period is selected within a continuous interval of stable system operation, lasting no less than thirty minutes, with sampling intervals on the order of minutes. To reduce the impact of random fluctuations, the measured wet-bulb temperatures are filtered by median, and then the average is taken as the design wet-bulb temperature. Simultaneously, the measurement date, time of day, wind speed, and instrument calibration information are recorded.

[0047] The second approach involves obtaining basic data on wet-bulb temperature or equivalent wet-bulb temperature from local weather stations or authoritative meteorological data services, selecting records that match the project location, altitude, and season. When meteorological data is provided in hourly values, missing and outlier values ​​are first removed, and then the average is calculated based on the design period. When meteorological data is provided in multi-year statistical values, the representative value corresponding to the period with the highest cooling load is used.

[0048] The third approach is to use the annual average value: when on-site measurement conditions are limited and meteorological data is difficult to obtain, the annual average wet-bulb temperature is used as the design wet-bulb temperature for scheme comparison and preliminary design. To ensure that the results of the three approaches are comparable, the parameter list records the data source type and the value caliber, such as peak value, average value, or seasonal value. When the design wet-bulb temperature is used for post-modification verification, a verification step can be added: select a high-temperature and high-humidity day for on-site re-measurement, compare the re-measurement results with the established design wet-bulb temperature, and if the difference exceeds the preset range, update the parameter list and re-evaluate the subsequent calculation results.

[0049] When meteorological data only provides dry-bulb temperature and relative humidity instead of wet-bulb temperature, a standard wet-air calculation method is used for conversion. The conversion algorithm can employ the industry-standard psychometric wetness chart lookup method or equivalent numerical calculation method. The calculation process is implemented by a software module, which retains input and output records. To avoid unit confusion, Celsius temperature is used uniformly. Unit conversion and result range verification are performed before wet-bulb temperature conversion. Consistency checks are also conducted along the on-site measurement path: two adjacent measurement points are set up for parallel measurements. If the difference in wet-bulb temperature between the two points consistently exceeds one degree, the ventilation conditions and the wetting status of the wet gauze are checked. If necessary, the wet gauze is replaced and the measurement is repeated. When the cooling tower has multiple air inlets, measurements can be taken at each air inlet, and the weighted average is taken as the design wet-bulb temperature. The weighting factor is determined based on the effective air inlet area of ​​each air inlet.

[0050] The preset threshold is the relative deviation threshold, which is used to limit the maximum allowable value of the relative deviation. The relative deviation represents the proportion of the target logarithmic mean temperature difference that deviates from the reference logarithmic mean temperature difference.

[0051] In one embodiment, to provide an executable stopping condition for the iterative calculation, a preset threshold is set and defined as a relative deviation threshold. The relative deviation describes the proportion of the target logarithmic mean temperature difference deviating from the reference logarithmic mean temperature difference. The iterative process uses whether the relative deviation is not greater than the relative deviation threshold as a convergence criterion. The value of the relative deviation threshold is determined based on engineering accuracy requirements and data noise levels, and is typically configured as a percentage and written into the parameter list.

[0052] When temperature measurement points are stable, flow measurement points have high accuracy, and a more stringent flow matching result is desired, a smaller relative deviation threshold is used. When system fluctuations are large or sensor noise is significant, a larger relative deviation threshold is used to avoid repeated oscillations within the noise range during iteration. To prevent the threshold from being too small and causing the iteration to fail to stop, a minimum achievable threshold lower limit is set, which is obtained by evaluating the relative deviation fluctuation amplitude of historical operating data. In implementation, after each round of calculating the target logarithmic mean temperature difference, the iteration module first calculates the relative deviation and then compares it with the relative deviation threshold. When the conditions are met, the target total circulating water flow rate is output, and the final relative deviation and iteration number are recorded.

[0053] If the conditions are not met, the iterative flow rate continues to be updated. A maximum iteration count protection is introduced; if the conditions are still not met after the maximum iteration count is reached, the current iterative flow rate is output as a temporary result, and a non-convergence flag is given. The non-convergence flag triggers a review process: checking the reference values ​​for the allowable spray density and design wet-bulb temperature after the modification, checking for abnormal jumps in the cooling tower inlet and outlet temperatures, and checking whether the inlet and outlet temperatures on the hot side of the heat exchanger group are within a stable range. When the review confirms that the data source is correct, a two-step strategy can be used to adjust the threshold: first, moderately relax the relative deviation threshold, and then re-execute the iteration; if convergence still fails after relaxation, keep the threshold unchanged and adjust the step size coefficient of the iterative flow rate update to make the iteration step smaller, thereby improving stability.

[0054] The relative deviation is calculated using the baseline logarithmic mean temperature difference as the denominator. The difference between the target logarithmic mean temperature difference and the baseline logarithmic mean temperature difference is normalized using the absolute value of the baseline logarithmic mean temperature difference to obtain a dimensionless proportion. The absolute value is then used for comparison with the relative deviation threshold. When the baseline logarithmic mean temperature difference approaches zero, causing instability in normalization, the relative deviation criterion is discontinued, and the absolute difference threshold of the logarithmic mean temperature difference is used instead as the stopping condition. Both the relative deviation threshold and the absolute difference threshold are stored in the parameter list for automatic switching by the software. To ensure consistency between reading and implementation, the relative deviation threshold is explicitly marked as a dimensionless proportion in the configuration interface, and the threshold value and its corresponding percentage representation are given in the exported report. All adjustments are recorded in the parameter list with version numbers and reasons for adjustment to ensure traceability across different calculation batches within the same project.

[0055] Using the baseline total circulating water flow rate as the initial value of the iterative flow rate, the cooling tower outlet water temperature is determined by the cooling tower approximation model based on the allowable spray density after modification, the design wet-bulb temperature, and the iterative flow rate. The cooling tower inlet water temperature is determined based on the heat load and the iterative flow rate, and the target logarithmic mean temperature difference is calculated. The iterative flow rate is updated according to the relative deviation until the relative deviation is not greater than the preset threshold, and the target total circulating water flow rate is output.

[0056] In one embodiment, an iterative solution phase is entered to determine the target total circulating water flow rate under the constraints after modification. The initial value of the iterative flow rate is taken as the baseline total circulating water flow rate. In each iteration, the cooling tower outlet water temperature is obtained first using the cooling tower approximation model based on the allowable spray density after modification, the design wet-bulb temperature, and the current iterative flow rate. Then, the cooling tower inlet water temperature is obtained by using the heat load as a fixed boundary and combining it with the current iterative flow rate, and the target logarithmic mean temperature difference is obtained accordingly. The target logarithmic mean temperature difference is compared with the baseline logarithmic mean temperature difference to obtain the relative deviation, and the iterative flow rate is corrected according to the update rule. This process is repeated until the relative deviation is no greater than a preset threshold, at which point the target total circulating water flow rate is output, and the iteration number, the final relative deviation, and the limit trigger status are recorded.

[0057] The cooling tower approximation model includes the cooling tower water spray area, which is calculated from the length, width, and number of individual cooling towers. The cooling tower approximation model determines the water spray density based on the iterative flow rate and the cooling tower water spray area. The water spray density is the total flow rate of circulating water passing through a unit cooling tower water spray area. The cooling tower approximation model determines the cooling tower approximation degree based on the relationship between the water spray density and the allowable water spray density after modification, as well as the design wet-bulb temperature. The cooling tower approximation degree is used to indicate the temperature difference between the cooling tower outlet water temperature and the design wet-bulb temperature.

[0058] In one embodiment, to base the prediction of cooling tower outlet water temperature on measurable and verifiable structural parameters, a cooling tower approximation model incorporating the cooling tower's water distribution area is introduced. The added constraint is that the calculation of the cooling tower outlet water temperature must explicitly depend on the combination of the cooling tower's water distribution area and the iterative flow rate. This ensures that the impact of flow rate changes on the outlet water temperature has a clear physical boundary, avoiding result drift caused by directly correcting based solely on empirical temperature differences. The cooling tower water distribution area adopts the effective water distribution area commonly used in engineering, calculated from the length of a single cooling tower, the width of a single cooling tower, and the number of cooling towers. When the cooling tower operates in sections or is partially shut down, the number of cooling towers is counted according to the actual number of units in operation, and the length and width of a single cooling tower are counted according to the effective dimensions of the water distribution area of ​​the operating unit. The calculation scope is written into the parameter list to ensure consistency across different batches.

[0059] In terms of model input construction, the iterative flow rate is first combined with the cooling tower's spray area to obtain the spray density. The spray density represents the total flow rate of circulating water passing through a unit cooling tower spray area, used to characterize the water distribution load level. Then, a relationship is established between the spray density and the allowable spray density after modification. This relationship is expressed with the core concept of "the degree of closeness of the current spray density to the allowable upper limit," which can be achieved using piecewise functions or lookup tables to avoid introducing complex formulas. In the piecewise function approach, the ratio of the spray density to the allowable spray density is divided into multiple intervals, each corresponding to a correction coefficient range for the cooling tower's approximation degree. In the lookup table approach, a mapping table of "ratio interval - cooling tower approximation degree increment" is pre-established, and the cooling tower approximation degree increment is retrieved based on the current ratio during implementation. Regardless of whether a piecewise function or lookup table approach is used, it is necessary to ensure that the cooling tower approximation degree does not exhibit a non-physical reverse jump as the spray density increases, and a monotonicity check is performed using historical operating data during the parameter verification phase.

[0060] The cooling tower approximation model also incorporates the design wet-bulb temperature as an environmental boundary. The model output is the cooling tower approximation, which indicates the temperature difference between the cooling tower outlet water temperature and the design wet-bulb temperature. Specifically, the cooling tower outlet water temperature is defined as the sum of the design wet-bulb temperature and the cooling tower approximation, with reasonable constraints imposed on it. The outlet water temperature is required to be no lower than the design wet-bulb temperature and no higher than a reasonable upper limit range of the cooling tower inlet water temperature. If the calculated cooling tower outlet water temperature violates these constraints, the consistency of the cooling tower spray area diameter, iterative flow rate unit, and allowable spray density unit is checked first, followed by checking the interval configuration of the mapping table or piecewise function. To improve feasibility, the model module outputs the spray density, the ratio of the spray density to the allowable spray density, and the hit interval number or table entry number simultaneously for on-site verification and software debugging.

[0061] In terms of engineering implementation, the length and width of a single cooling tower can be obtained from construction drawings or as-built drawings, and the number of cooling towers can be obtained from the operation log. If the effective water distribution area is reduced due to packing replacement, the non-water-distribution area should be deducted from the cooling tower's water distribution area, and the basis for this deduction should be recorded as a water distribution area revision item. Through this constraint, the input-output chain of the cooling tower approximation model is clear, the parameter sources are explicit, and it can be reused in different projects, meeting the requirements of those skilled in the art to implement it according to the instructions.

[0062] Determining the cooling tower inlet water temperature based on heat load and iterative flow rate includes: determining the circulating water temperature rise based on heat load and iterative flow rate; and determining the cooling tower inlet water temperature as the temperature obtained by adding the cooling tower outlet water temperature and the circulating water temperature rise.

[0063] In one embodiment, to directly obtain the cooling tower inlet water temperature using heat load and iterative flow rate, a "circulating water temperature rise" is introduced as an intermediate quantity. The added constraint at this limiting point is that the determination of the cooling tower inlet water temperature does not rely on external empirical corrections, but is derived from the energy balance between the heat load and the current iterative flow rate, thereby ensuring that the temperature boundary and flow rate changes remain consistent during the iteration process. The circulating water temperature rise refers to the temperature increase of the circulating water after absorbing heat in the heat exchanger assembly; numerically, it is positively correlated with the heat load and negatively correlated with the iterative flow rate.

[0064] In practical implementation, after obtaining the heat load and iterative flow rate, the iterative module first performs unit consistency processing on the iterative flow rate to ensure it matches the calculation scope of the heat load. If the heat load is given in the form of heat per unit time, the iterative flow rate must correspond to the circulating water mass flow rate per unit time; if the iterative flow rate is the volumetric flow rate, it is converted to mass flow rate through density approximation or on-site calibrated density. Subsequently, the circulating water temperature rise is obtained based on the energy conservation relationship. This relationship has been given in the previous heat load calculation, and the formula will not be repeated hereafter, only maintaining the same specific heat capacity and density scope in the implementation. To avoid the circulating water temperature rise calculation being sensitive to noise, the input heat load and iterative flow rate for the circulating water temperature rise both use the average value of the same time window, and a lower limit is set for the iterative flow rate. When it is below the lower limit, the update is paused, and the circulating water temperature rise result of the previous stable period is used.

[0065] After obtaining the circulating water temperature rise, the cooling tower inlet water temperature is defined as the sum of the cooling tower outlet water temperature and the circulating water temperature rise. This temperature corresponds to the temperature boundary of the circulating water as it enters the heat exchanger group from the cooling tower outlet, absorbs heat, and returns to the cooling tower inlet water. To ensure a reasonable temperature boundary, a consistency check is set: the cooling tower inlet water temperature should be higher than the cooling tower outlet water temperature, and the difference between the two should be consistent with the circulating water temperature rise. If the cooling tower inlet water temperature is lower than the cooling tower outlet water temperature, the following checks are performed first: whether the heat load is positive; whether the temperature measuring points are interchanged; and whether there are unit errors in the iterative flow conversion.

[0066] In engineering applications, the cooling tower outlet water temperature is derived from the cooling tower approximation model, while the circulating water temperature rise is derived from energy balance calculations. Both can be implemented as independent functions in the software, facilitating modular testing. When outputting the cooling tower inlet water temperature, the circulating water temperature rise, iterative flow rate, density caliber, and specific heat capacity values ​​are also recorded, making it easier to pinpoint the source of error during the commissioning phase. Through this constraint, the path to obtain the cooling tower inlet water temperature is short, verifiable, and strictly consistent with the heat load, providing a stable input for subsequent calculations of the target logarithmic mean temperature difference.

[0067] The updated iterative flow rate based on relative deviation includes: proportionally correcting the iterative flow rate based on the relative deviation and the proportional correction coefficient to obtain the updated iterative flow rate; when the water density corresponding to the updated iterative flow rate is greater than the allowable water density after the modification, the updated iterative flow rate is limited to the maximum allowable flow rate corresponding to the allowable water density after the modification.

[0068] In one embodiment, to ensure stable convergence of the iterative process without exceeding the cooling tower's capacity, an iterative flow rate update rule based on "proportional correction with amplitude limiting based on relative deviation" is introduced. The added constraint at this limiting point is that the update amplitude of the iterative flow rate is proportional to the relative deviation; the larger the deviation, the more pronounced the update. Simultaneously, when the update result causes the water spray density to exceed the allowable water spray density after modification, the update result is forcibly limited to the maximum allowable flow rate range to prevent unenforceable flow rate commands. The proportional correction coefficient is used to control the step size of each update, avoiding oscillations caused by excessively large step sizes and slow convergence caused by excessively small step sizes.

[0069] In implementation, after obtaining the target logarithmic mean temperature difference in each iteration, the relative deviation is calculated, and its sign and magnitude are determined. A positive relative deviation indicates that the target logarithmic mean temperature difference is higher than the baseline logarithmic mean temperature difference, requiring adjustment of the iteration flow to change the temperature boundary; a negative relative deviation indicates the opposite. The update module generates an update iteration flow based on the relative deviation and a proportional correction coefficient. To ensure readability and feasibility, the update process uses textual rules: the current iteration flow is increased or decreased proportionally by multiplying the proportional correction coefficient by the relative deviation to obtain the update iteration flow. A minimum change is set for the update iteration flow; if the change is below the minimum, the iteration flow remains unchanged, and the process directly enters the threshold judgment, avoiding meaningless fluctuations caused by minor noise.

[0070] After completing the proportional correction, a limit judgment is executed. The limit judgment relies on the comparison between the water spray density and the allowable water spray density after the modification. The water spray density is calculated from the updated flow rate and the cooling tower water spray area. The cooling tower water spray area has been established in the cooling tower approximation model and uses the same diameter. If the water spray density corresponding to the updated flow rate is greater than the allowable water spray density after the modification, the updated flow rate is limited to the maximum allowable flow rate. The maximum allowable flow rate is obtained by multiplying the allowable water spray density after the modification by the cooling tower water spray area, and a limit trigger event is recorded. If the limit is triggered multiple times consecutively and the relative deviation still does not meet the preset threshold, a review process is triggered to check whether the allowable water spray density after the modification is too low, whether the diameter of the cooling tower water spray area is too small, whether the design wet-bulb temperature is too high, and whether the logarithmic mean temperature difference calculation input is stable.

[0071] To improve convergence stability, an adaptive adjustment strategy for the proportional correction coefficient can be set: when the sign of the relative deviation reverses in two adjacent iterations, overshoot is detected, and the proportional correction coefficient is decreased; when the relative deviation has the same sign for several consecutive iterations and decreases slowly, convergence is considered too slow, and the proportional correction coefficient is appropriately increased. The adaptive adjustment strategy uses upper and lower bound constraints to prevent the proportional correction coefficient from getting out of control. All changes to the proportional correction coefficient are recorded in the iteration log, including the triggering reason, the values ​​before and after the change, and the relative deviation at that time.

[0072] Regarding termination conditions, immediately after updating the iterative flow rate, a new relative deviation is calculated to determine whether a preset threshold is met. If met, the target total circulating water flow rate is output, along with the corresponding cooling tower inlet water temperature, cooling tower outlet water temperature, water spray density, and whether a limit has been triggered, for project delivery and operational verification. Through this constraint point, the iterative update rule can effectively correct deviations while ensuring that the flow rate does not exceed the allowable water spray density constraint after the modification. The process boundaries are clear, and the process is implementable on-site.

[0073] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects.

[0074] The above are merely embodiments of the present invention and are not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for optimizing the temperature and flow rate of a circulating water system, characterized in that, The method includes: Obtain the baseline total circulating water flow rate, cooling tower inlet water temperature, cooling tower outlet water temperature, and heat exchanger group hot side inlet and outlet temperatures; The heat load is determined based on the law of conservation of energy, and the cold side inlet temperature of the heat exchanger group is set as the outlet temperature of the cooling tower and the cold side outlet temperature of the heat exchanger group is set as the inlet temperature of the cooling tower. The baseline logarithmic mean temperature difference is calculated. Obtain the allowable water spray density, design wet-bulb temperature, and preset threshold after modification; Using the baseline total circulating water flow rate as the initial value of the iterative flow rate, and based on the allowable spray density after modification, the design wet-bulb temperature, and the iterative flow rate, the cooling tower outlet water temperature is determined through the cooling tower approximation model. The cooling tower inlet water temperature is determined based on the heat load and the iterative flow rate, and the target logarithmic mean temperature difference is calculated. The iterative flow rate is updated according to the relative deviation until the relative deviation is not greater than the preset threshold, and the target total circulating water flow rate is output.

2. The method according to claim 1, characterized in that, The inlet and outlet temperatures of the heat exchanger assembly include the inlet temperature and the outlet temperature on the hot side of the heat exchanger assembly. When the heat exchanger group includes multiple heat exchangers, the hot-side inlet temperature and hot-side outlet temperature of each heat exchanger are obtained, the circulating water flow rate corresponding to each heat exchanger is obtained, and the hot-side inlet temperature of each heat exchanger is weighted and averaged based on the circulating water flow rate corresponding to each heat exchanger to obtain the hot-side inlet temperature of the heat exchanger group, and the hot-side outlet temperature of each heat exchanger is weighted and averaged to obtain the hot-side outlet temperature of the heat exchanger group.

3. The method according to claim 1, characterized in that, Determining the heat load based on energy conservation includes: Set the specific heat capacity of the circulating water to a preset constant. The heat load is calculated based on the total reference circulating water flow rate and the temperature difference between the cooling tower inlet water temperature and the cooling tower outlet water temperature.

4. The method according to claim 1, characterized in that, The calculated baseline logarithmic mean temperature difference includes: The inlet and outlet temperatures of the heat exchanger group on the hot side are decomposed into the inlet temperature of the heat exchanger group on the hot side and the outlet temperature of the heat exchanger group on the hot side. The first end temperature difference is calculated as the difference between the hot side inlet temperature of the heat exchanger group and the cold side outlet temperature of the heat exchanger group. The second end temperature difference is calculated as the difference between the hot side outlet temperature of the heat exchanger group and the cold side inlet temperature of the heat exchanger group. The reference logarithmic average temperature difference is calculated based on the temperature difference at the first end and the temperature difference at the second end.

5. The method according to claim 1, characterized in that, The process of obtaining the permissible water spray density after modification includes: The allowable water spray density after the modification is determined based on the product parameters of the modified cooling tower packing. Alternatively, the allowable water spray density after modification can be determined based on the correspondence between the type of filler and the allowable water spray density. The modified allowable water spray density is used to indicate the upper limit of the total circulating water flow allowed to pass through a unit water spray area.

6. The method according to claim 1, characterized in that, The design wet-bulb temperature is determined by one of the following methods: The temperature was obtained using a wet-bulb and dry-bulb thermometer. The wet-bulb temperature for the corresponding time period is obtained from meteorological observation data and then averaged. The annual average wet-bulb temperature is determined as the design wet-bulb temperature.

7. The method according to claim 1, characterized in that, The preset threshold is a relative deviation threshold, which is used to limit the maximum allowable value of the relative deviation. The relative deviation represents the proportion of the deviation of the target logarithmic mean temperature difference from the reference logarithmic mean temperature difference.

8. The method according to claim 1, characterized in that, The cooling tower approximation model includes the cooling tower water spray area, which is calculated from the length of a single cooling tower, the width of a single cooling tower, and the number of cooling towers. The cooling tower approximation model determines the water spray density based on the iterative flow rate and the cooling tower spray area. The water spray density is the total flow rate of circulating water passing through a unit of the cooling tower spray area. The cooling tower approximation model determines the cooling tower approximation based on the relationship between the water spray density and the allowable water spray density after modification, as well as the design wet-bulb temperature. The cooling tower approximation is used to indicate the temperature difference between the cooling tower outlet water temperature and the design wet-bulb temperature.

9. The method according to claim 1, characterized in that, Determining the cooling tower inlet water temperature based on the heat load and the iterative flow rate includes: The circulating water temperature rise is determined based on the heat load and the iterative flow rate. The inlet water temperature of the cooling tower is determined as the temperature obtained by adding the outlet water temperature of the cooling tower to the temperature rise of the circulating water.

10. The method according to claim 1, characterized in that, The method of updating the iterative flow based on the relative deviation includes: The iterative flow is proportionally corrected based on the relative deviation and the proportional correction coefficient to obtain the updated iterative flow; If the water density corresponding to the updated flow rate is greater than the allowable water density after modification, the updated flow rate is limited to the maximum allowable flow rate corresponding to the allowable water density after modification.

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