Online identification method and system for adsorption kinetics parameters of imidazolium resin

Abstract

The present application relates to the field of adsorption detection technology, and discloses an online identification method and system for imidazolium resin adsorption kinetics parameters, comprising: step 1, synchronously collecting flow, inlet and outlet water concentration, conductivity, temperature and pH, and obtaining apparent ionic strength from conductivity; step 2, performing mass balance based on flow, inlet and outlet water concentration and resin dry base mass to obtain real-time trajectory of average adsorption amount of resin; step 3, constructing counter-ion coupled isotherm driving force and screening quasi-equilibrium section; step 4, solving isotherm coupled parameters by simultaneously solving quasi-equilibrium relationship; step 5, point-by-point calculating overall mass transfer coefficient; step 6, simultaneously solving outer membrane mass transfer proportion coefficient and pore mass transfer coefficient under two flow rates; and step 7, constructing core parameter group and outputting consistency judgment result identifier. The present application realizes online identification and consistency judgment of imidazolium resin adsorption thermodynamic parameters and mass transfer kinetic parameters.

Description

Technical Field

[0001] This invention belongs to the field of adsorption detection technology, specifically relating to an online identification method and system for adsorption kinetic parameters of imidazolium resin. Background Technology

[0002] As an adsorbent material with ionic groups, imidazolium resin's adsorption process is affected not only by operating conditions such as influent and effluent water concentrations and flow rates, but also by changes in the solution's ionic environment, leading to synchronous changes in isothermal affinity and mass transfer processes. In actual adsorption column operation, fluctuations in counterions or ionic strength can easily cause isothermal affinity parameters and mass transfer / diffusion parameters to drift in a coordinated manner, accompanied by a shift in the weighting of external membrane mass transfer and intrapore diffusion. This manifests as kinetic parameters no longer maintaining constant characteristics under different operating conditions.

[0003] In existing technologies, adsorption kinetic parameters are typically obtained through offline isothermal experiments or batch fitting, or the kinetic behavior is simplified to a single rate constant during online modeling, assuming that the parameters are stable within the operating cycle. These approaches are prone to problems such as unidentifiable parameters, multiple solutions, and parameter jumps with varying operating conditions in scenarios with significant changes in the ion environment. This makes it difficult to reliably reuse online analysis results and to establish a consistent data link with online detection data. Summary of the Invention

[0004] This invention provides an online identification method and system for adsorption kinetic parameters of imidazolium resin, which solves the technical problems in related technologies such as the difficulty in synchronously identifying adsorption isothermal parameters and mass transfer parameters under fluctuating ion environment conditions, the instability of online calculation results of kinetic parameters, and the lack of a consistent correlation mechanism between online detection data and parameter models.

[0005] This invention provides a method for online identification of adsorption kinetic parameters of imidazolium resin, comprising the following steps:

[0006] Step 1: Simultaneously collect flow rate, influent concentration, effluent concentration, conductivity, temperature and pH, and obtain apparent ionic strength from conductivity according to preset calibration relationship;

[0007] Step 2: Perform a mass balance calculation based on the flow rate, influent concentration, effluent concentration, and resin dry weight to obtain the real-time trajectory of the average resin adsorption amount.

[0008] Step 3: Construct the anti-ion coupling isothermal driving force based on the maximum adsorption capacity of the resin, the effluent concentration, the apparent ionic strength and the effective affinity coefficient, and screen the quasi-equilibrium section according to the rate of change of the average adsorption capacity of the resin.

[0009] Step 4: For the two quasi-equilibrium sections corresponding to different apparent ionic intensities, obtain the average resin adsorption amount and effluent concentration, and solve the quasi-equilibrium relationship to obtain the isothermal coupling parameters.

[0010] Step 5: Substitute the isothermal coupling parameters into the anti-ion coupling isothermal driving force, and calculate the overall mass transfer coefficient point by point based on the average resin adsorption amount and the anti-ion coupling isothermal driving force according to the linear driving force kinetic framework.

[0011] Step 6: Select the stable section of the counterion state, set two flow rates in sequence within the stable section of the counterion state and obtain the corresponding overall mass transfer coefficients, establish the resistance series equation by combining the preset flow power law exponent, solve the outer membrane mass transfer ratio coefficient and the pore mass transfer coefficient, and obtain the outer membrane mass transfer coefficient.

[0012] Step 7: The isothermal coupling parameters, outer membrane mass transfer ratio coefficient, pore mass transfer coefficient, preset flow power law exponent, and maximum resin adsorption capacity are combined into a core parameter group to reconstruct the effective affinity coefficient, outer membrane mass transfer coefficient, and overall mass transfer coefficient, and output the consistency judgment result identifier.

[0013] This invention also provides an online identification system for adsorption kinetic parameters of imidazolium resin, comprising:

[0014] The data acquisition module is used to simultaneously collect flow rate, influent concentration, effluent concentration, conductivity, temperature and pH, and obtain the apparent ionic strength from conductivity according to the preset calibration relationship;

[0015] The mass balance module is used to perform mass balance based on flow rate, influent concentration, effluent concentration and resin dry basis mass to obtain the real-time trajectory of the average resin adsorption amount.

[0016] The isothermal drive module is used to construct the anti-ion coupling isothermal drive force based on the maximum resin adsorption capacity, effluent concentration, apparent ionic strength and effective affinity coefficient, and to screen the quasi-equilibrium section according to the rate of change of the average resin adsorption capacity.

[0017] The isothermal solution module is used to obtain the average resin adsorption amount and effluent concentration for two quasi-equilibrium sections corresponding to two different apparent ionic intensities, and solve the isothermal coupling parameters by combining the quasi-equilibrium relationship with the quasi-equilibrium relationship.

[0018] The overall mass transfer module is used to substitute the isothermal coupling parameters into the anti-ion coupling isothermal driving force, and calculate the overall mass transfer coefficient point by point based on the average resin adsorption amount and the anti-ion coupling isothermal driving force according to the linear driving force kinetic framework.

[0019] The resistance decoupling module is used to screen the counterion state stable section. Within the counterion state stable section, two flow rates are set sequentially and the corresponding overall mass transfer coefficients are obtained. The resistance series equation is established in combination with the preset flow power law exponent. The outer membrane mass transfer ratio coefficient and the pore mass transfer coefficient are solved, and the outer membrane mass transfer coefficient is obtained.

[0020] The parameter reconstruction module is used to assemble the isothermal coupling parameters, the outer membrane mass transfer ratio coefficient, the pore mass transfer coefficient, the preset flow power law exponent, and the maximum resin adsorption capacity into a core parameter group, reconstruct the effective affinity coefficient, the outer membrane mass transfer coefficient, and the overall mass transfer coefficient, and output a consistency judgment result identifier.

[0021] The beneficial effects of this invention are as follows: By converting conductivity online to apparent ionic strength and introducing a kinetic framework of counterion coupling isothermal driving force and linear driving force, this invention achieves stepwise identification of isothermal coupling parameters, overall mass transfer coefficient, and external membrane and pore mass transfer parameters under continuous operation conditions, enabling unified calculation of adsorption thermodynamics and mass transfer characteristics in the same data link. By screening the quasi-equilibrium segment and the counterion stable segment, the parameter solution conditions are limited, improving the stability and repeatability of parameter solutions; by constructing a resistance series equation through two flow rates, mass transfer resistance decomposition is achieved; and by reconstructing the core parameter set and determining consistency, the self-consistency and traceability of online output results are enhanced. Overall, this invention achieves online identification and consistency determination of imidazolium resin adsorption thermodynamic parameters and mass transfer kinetic parameters. Attached Figure Description

[0022] Figure 1 This is a flowchart of the online identification method for adsorption kinetic parameters of imidazolium resin according to the present invention. Detailed Implementation

[0023] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0024] It should be noted that, unless otherwise defined, the technical or scientific terms used in one or more embodiments of the present invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in one or more embodiments of the present invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0025] like Figure 1 As shown, the online identification method for adsorption kinetic parameters of imidazolium resin includes the following steps:

[0026] Step 1: Simultaneously collect flow rate, influent concentration, effluent concentration, conductivity, temperature and pH, and obtain apparent ionic strength from conductivity according to preset calibration relationship;

[0027] Step 2: Perform a mass balance calculation based on the flow rate, influent concentration, effluent concentration, and resin dry weight to obtain the real-time trajectory of the average resin adsorption amount.

[0028] Step 3: Construct the anti-ion coupling isothermal driving force based on the maximum adsorption capacity of the resin, the effluent concentration, the apparent ionic strength and the effective affinity coefficient, and screen the quasi-equilibrium section according to the rate of change of the average adsorption capacity of the resin.

[0029] Step 4: For the two quasi-equilibrium sections corresponding to different apparent ionic intensities, obtain the average resin adsorption amount and effluent concentration, and solve the quasi-equilibrium relationship to obtain the isothermal coupling parameters.

[0030] Step 5: Substitute the isothermal coupling parameters into the anti-ion coupling isothermal driving force, and calculate the overall mass transfer coefficient point by point based on the average resin adsorption amount and the anti-ion coupling isothermal driving force according to the linear driving force kinetic framework.

[0031] Step 6: Select the stable section of the counterion state, set two flow rates in sequence within the stable section of the counterion state and obtain the corresponding overall mass transfer coefficients, establish the resistance series equation by combining the preset flow power law exponent, solve the outer membrane mass transfer ratio coefficient and the pore mass transfer coefficient, and obtain the outer membrane mass transfer coefficient.

[0032] Step 7: The isothermal coupling parameters, outer membrane mass transfer ratio coefficient, pore mass transfer coefficient, preset flow power law exponent, and maximum resin adsorption capacity are combined into a core parameter group to reconstruct the effective affinity coefficient, outer membrane mass transfer coefficient, and overall mass transfer coefficient, and output the consistency judgment result identifier.

[0033] In one embodiment of the present invention, the imidazolium resin is a functionalized polymeric adsorbent material with imidazolium cationic groups introduced on its surface or backbone. The imidazolium groups are typically fixed to the resin backbone via covalent grafting or in-situ polymerization, forming positively charged active sites that can interact with anions or polar molecules in the solution through electrostatic interactions, ion exchange, or coordination. The imidazolium resin exhibits ion-responsive characteristics; its adsorption performance is not only related to the concentration of the target component but also closely related to the ionic strength, counterion species, and pH conditions in the solution. To achieve online identification of the adsorption kinetic parameters of the imidazolium resin, real-time operational data directly related to the adsorption process needs to be obtained first. In this embodiment, online detection units are arranged at the inlet and outlet of the adsorption column, including a flow sensor, a concentration detection unit, a conductivity sensor, a temperature sensor, and a pH detection unit. The flow rate characterizes the volume of solution flowing through the adsorption column per unit time; the influent and effluent concentrations reflect the concentration changes of the target component before and after adsorption; the conductivity characterizes the ion conduction capacity in the solution; and the temperature and pH reflect the physicochemical environment of the system. Simultaneously collect flow rate, influent concentration, effluent concentration, conductivity, temperature, and pH, and derive apparent ionic strength from conductivity according to a preset calibration relationship, including:

[0034] At the same sampling moment, the control system synchronously collects data on flow rate, influent concentration, effluent concentration, conductivity, temperature, and pH, and uses this sampling moment as a unified time identifier to construct an original data frame. The original data frame refers to a structured data unit formed by organizing the above-mentioned detection parameters according to a fixed field order under the same time identifier, used to ensure the consistency of data in the time dimension during subsequent mass balance and kinetic calculations. By using a unified time identifier, data mismatch problems caused by sampling lags from different sensors can be avoided, thereby ensuring the physical consistency of input data during the kinetic parameter identification process.

[0035] In this embodiment, to obtain the ionic strength information involved in the adsorption isotherm, apparent ionic strength is used to characterize the overall concentration level of all conductive ions in the solution. This embodiment utilizes the functional relationship between conductivity and ionic strength to establish a preset calibration relationship. This preset calibration relationship is determined by linear fitting between two preset conductivity calibration points corresponding to known apparent ionic strengths. Specifically, the corresponding conductivity value is measured under known ionic strength conditions, and calibration coefficients are obtained through linear fitting. These calibration coefficients include a proportional term and a bias term. The proportional term describes the sensitivity of conductivity to ionic strength, and the bias term corrects for baseline shift.

[0036] During online operation, the conductivity is read from the original data frame. The conductivity is multiplied by the proportional term in the calibration coefficient to obtain the proportional result. This proportional result is then added to the bias term in the calibration coefficient to obtain the apparent ion intensity. To avoid negative values ​​due to sensor errors or noise, this embodiment compares the calculated apparent ion intensity with zero. When the apparent ion intensity is less than zero, it is set to zero to ensure physical validity. Subsequently, the apparent ion intensity is written into the original data frame, generating an extended data frame containing the apparent ion intensity field. The extended data frame is a data structure with the apparent ion intensity field added to the original data frame.

[0037] Compared with traditional offline detection methods, this embodiment realizes the real-time quantitative expression of changes in the ionic environment of the adsorption system by inverting apparent ionic strength online through conductivity. This allows the adsorption kinetics of imidazolium resin under different ionic environments to be captured online. By calibrating and converting the conductivity, key chemical parameters for constructing the adsorption isotherm model are obtained, thus providing basic data support for the subsequent online identification of kinetic parameters.

[0038] In one embodiment of the present invention, a mass balance is performed based on the flow rate, influent concentration, effluent concentration, and resin dry basis mass to obtain a real-time trajectory of the average resin adsorption amount, including:

[0039] Step 11: Read the flow rate, influent concentration, and effluent concentration from the extended data frame. Obtain the concentration difference by subtracting the influent concentration from the effluent concentration. This concentration difference characterizes the concentration of the target component removed per unit volume of solution during the adsorption column process, directly reflecting the adsorption intensity.

[0040] Step 12: Multiply the flow rate by the concentration difference to obtain the amount removed per unit time. The amount removed per unit time represents the total mass of the target component adsorbed by the resin within a unit time corresponding to the current sampling moment, reflecting the instantaneous adsorption capacity of the adsorption column at that moment. To normalize this removal amount to the resin bulk, this embodiment further reads the dry basis mass of the resin. The dry basis mass of the resin refers to the actual dry resin mass after deducting the influence of moisture in the resin, used to eliminate the influence of moisture content fluctuations on the adsorption amount calculation, thereby ensuring the comparability of the adsorption amount calculation results. The ratio of the amount removed per unit time to the dry basis mass of the resin is calculated to obtain the average adsorption amount change rate of the resin. The average adsorption amount change rate of the resin represents the change in adsorption amount per unit dry basis mass per unit time, and is the core differential component in the adsorption kinetic equation.

[0041] Step 13: After obtaining the rate of change of the average resin adsorption, this embodiment uses a preset sampling time step for discrete integration calculation. The preset sampling time step refers to the time interval between two adjacent sampling moments, which is preset by the system sampling frequency. The product of the rate of change of the average resin adsorption and the preset sampling time step is taken as the increment of the adsorption amount per unit dry basis mass of resin within that time step, and added to the average resin adsorption amount at the previous sampling moment to obtain the average resin adsorption amount at the current sampling moment. By continuously aggregating the average resin adsorption amounts calculated at each sampling moment, a real-time trajectory of the average resin adsorption amount is formed. The real-time trajectory of the average resin adsorption amount reflects the change of the adsorption amount of imidazolium resin over time throughout the entire operating cycle, and is an important basic data for subsequent construction of the anti-ion coupling isothermal driving force, screening of the quasi-equilibrium segment, and solving for isothermal coupling parameters and mass transfer parameters. Compared with the traditional method that relies on intermittent sampling and offline measurement of resin adsorption amount, this embodiment achieves continuous characterization of the resin adsorption state through online mass balance calculation, transforming the adsorption amount from discrete measurement into a time-continuous function form.

[0042] This embodiment constructs the removal amount per unit time by using the difference between flow rate and concentration, and then normalizes it by combining it with the dry basis mass of the resin. This achieves a real-time quantitative expression of the resin adsorption behavior, avoiding the lag and error accumulation problems caused by manual sampling and weighing. By mathematically processing the online collected flow rate and concentration data, the resin adsorption amount parameter, which is difficult to measure directly online, is indirectly obtained. This provides a continuous, stable and physically meaningful state variable input for the online identification of imidazolium resin adsorption kinetic parameters, thereby supporting the subsequent establishment of the kinetic model and the online parameter identification process.

[0043] In one embodiment of the present invention, a counter-ion coupling isothermal driving force is constructed based on the maximum resin adsorption capacity, effluent concentration, apparent ionic strength, and effective affinity coefficient, and a quasi-equilibrium zone is screened according to the rate of change of the average resin adsorption capacity, including:

[0044] Step 21: Read the water concentration and apparent ionic strength from the extended data frame, and read the maximum resin adsorption capacity. The maximum resin adsorption capacity refers to the theoretical maximum adsorption capacity achievable per unit dry basis mass of resin under specific temperature and system conditions. The isothermal coupling parameters include a first coupling coefficient and a first exponential coefficient. The first coupling coefficient describes the baseline affinity of the system under low ionic strength conditions, and the first exponential coefficient describes the degree of attenuation of affinity due to ionic strength. The product of the first exponential coefficient and the apparent ionic strength is negatively taken as the exponent, and an exponential function is obtained by performing an exponential operation with the natural constant as the base. This exponential function value is then multiplied by the first coupling coefficient to obtain the effective affinity coefficient. The effective affinity coefficient characterizes the apparent binding ability between the target component and the active sites of the imidazolium resin. Specifically, the calculation formula is: , This represents the effective affinity coefficient at the k-th sampling time. Represents the first coupling coefficient. Let exp denote the first exponential coefficient, and exp represent the exponential function. The apparent ion intensity is represented at the k-th sampling time. Through the above method, the effective affinity coefficient can be dynamically adjusted with the change of apparent ion intensity, thereby reflecting the influence of anti-ion coupling on adsorption behavior.

[0045] Step 22: After obtaining the effective affinity coefficient, the product of the effective affinity coefficient and the effluent concentration is used as the numerator, and the constant 1 is added to this product as the denominator. The ratio of the numerator to the denominator is calculated, and this ratio is multiplied by the maximum adsorption capacity of the resin to obtain the counter-ion coupling isothermal driving force. The counter-ion coupling isothermal driving force is used to characterize the theoretically achievable equilibrium adsorption capacity of the resin under the current ion environment and effluent concentration conditions, and is the target adsorption capacity in subsequent kinetic calculations. Specifically, the calculation formula is: , This represents the anti-ion coupling isothermal driving force at the k-th sampling time. This indicates the maximum adsorption capacity of the resin. This represents the effluent concentration at the k-th sampling time. By aggregating the counterion coupling isothermal driving forces calculated at each sampling time, a counterion coupling isothermal driving force sequence is formed, providing a time series input for subsequent overall mass transfer coefficient calculation.

[0046] Step 23: Calculate the rate of change of the average resin adsorption amount based on the real-time trajectory of the average resin adsorption amount and the preset sampling time step. Specifically, use the difference in the average resin adsorption amount between adjacent sampling times as the numerator and the preset sampling time step as the denominator to calculate the ratio and obtain the rate of change of the average resin adsorption amount. The rate of change of the average resin adsorption amount is used to characterize the rate of change of adsorption amount per unit time and is an important criterion for determining whether the system is close to equilibrium.

[0047] For each sampling moment, the absolute value of the rate of change of the average resin adsorption is taken and compared with a preset rate of change threshold. When the absolute value is less than the preset rate of change threshold, it indicates that the adsorption change at that moment tends to stabilize, and this moment is recorded as a candidate moment that meets the quasi-equilibrium condition. When the absolute value is not less than the preset rate of change threshold, the corresponding sampling moment is recorded as a non-candidate moment that does not meet the quasi-equilibrium condition, and the timing of consecutive candidate moments is cleared. If the cumulative duration of consecutive candidate moments is not less than a preset quasi-equilibrium duration threshold, the time interval corresponding to the consecutive candidate moments is determined as a quasi-equilibrium segment. The cumulative duration is calculated by multiplying the number of consecutive candidate moments by the preset sampling time step. Finally, the time index set of the quasi-equilibrium segment is output, along with the average resin adsorption amount segment, the average effluent concentration segment, and the average apparent ionic strength segment within the quasi-equilibrium segment.

[0048] Through the above steps, this invention achieves dynamic construction of thermodynamic driving forces and automatic identification of quasi-equilibrium intervals under online operating conditions. Compared with traditional methods that rely on manual judgment of equilibrium states or offline isothermal experiments, this embodiment can extract time intervals reflecting equilibrium characteristics in real time under actual operating conditions, and construct anti-ion coupling isothermal driving forces by combining changes in the ion environment. Through a combination of online measurement and model calculation, it achieves real-time quantitative expression of the thermodynamic and kinetic behavior of imidazolium resin adsorption, providing reliable basic data for subsequent online identification of isothermal coupling parameters and mass transfer parameters.

[0049] In one embodiment of the present invention, for two quasi-equilibrium segments corresponding to different apparent ionic intensities, the average resin adsorption amount and effluent concentration are obtained and a quasi-equilibrium relationship is established, and the isothermal coupling parameters are solved, including:

[0050] Step 31: From the identified set of quasi-equilibrium segments, select two quasi-equilibrium segments with unequal average apparent ion intensity ranges, designating them as the first quasi-equilibrium segment and the second quasi-equilibrium segment, respectively. A quasi-equilibrium segment refers to the time interval within which the average resin adsorption rate of change meets a preset rate of change threshold and the duration reaches a preset quasi-equilibrium duration threshold; its physical meaning is that the adsorption system is close to equilibrium within this time interval. By selecting two quasi-equilibrium segments with unequal average apparent ion intensity ranges, equilibrium adsorption data can be obtained under different ion environment conditions, thus providing independent equation conditions for solving ion coupling-related parameters. Within each quasi-equilibrium segment, calculate the average resin adsorption rate, the average effluent concentration, and the average apparent ion intensity. The average value is a representative value obtained by arithmetically averaging the values ​​at each sampling time within the corresponding quasi-equilibrium segment time interval, used to reduce the impact of instantaneous fluctuations on parameter solving and improve the stability of isothermal parameter identification.

[0051] Step 32: Read the maximum adsorption capacity of the resin, and calculate the corresponding effective affinity coefficients based on the average apparent ionic strength values ​​of the first and second quasi-equilibrium segments, respectively, using the aforementioned method for constructing effective affinity coefficients. Specifically, the product of the first exponential coefficient and the average apparent ionic strength value is negatively multiplied and then exponentially calculated, multiplied by the first coupling coefficient to obtain the effective affinity coefficient. The product of the effective affinity coefficient and the average effluent concentration value is then used as the numerator, and the constant 1 is added to this product as the denominator. The ratio of the numerator to the denominator is calculated and multiplied by the maximum adsorption capacity of the resin to obtain the quasi-equilibrium relationships corresponding to the first and second quasi-equilibrium segments, respectively. These quasi-equilibrium relationships represent the theoretical equilibrium adsorption capacity expression of the resin under specific ionic environment and effluent concentration conditions, and are a discrete form of the isothermal model.

[0052] Step 33: Combine the average resin adsorption capacity of the first quasi-equilibrium segment with the corresponding quasi-equilibrium equation for the first quasi-equilibrium segment, and combine the average resin adsorption capacity of the second quasi-equilibrium segment with the corresponding quasi-equilibrium equation for the second quasi-equilibrium segment to form two equations concerning the first coupling coefficient and the first exponential coefficient. Specifically, the two equations are as follows: , , and These represent the average resin adsorption amounts in the first and second quasi-equilibrium sections, respectively. and These represent the average apparent ionic strength values ​​for the first and second quasi-equilibrium segments, respectively. and These represent the average effluent concentration ranges of the first and second quasi-equilibrium sections, respectively. By solving the system of equations simultaneously, the specific values ​​of the first coupling coefficient and the first exponential coefficient are obtained. The obtained first coupling coefficient and first exponential coefficient are then written into the isothermal coupling parameters for subsequent reconstruction of the isothermal driving force of the counterion coupling and calculation of the overall mass transfer coefficient.

[0053] Using the above method, this invention achieves online solution of isothermal coupling parameters under actual operating conditions by utilizing quasi-equilibrium data from different ionic strength environments. Compared with traditional methods that rely on offline batch isothermal experiments to obtain isothermal constants, this embodiment can identify counterion coupling-related parameters under continuous operating conditions without interrupting the adsorption process. By solving simultaneous equations based on the online collected concentration, ionic strength, and adsorption amount data, real-time characterization of the adsorption thermodynamic behavior of imidazolium resin in complex ionic environments is achieved.

[0054] In one embodiment of the present invention, isothermal coupling parameters are substituted into the counterion coupling isothermal driving force, and the overall mass transfer coefficient is calculated point-by-point from the average resin adsorption amount and the counterion coupling isothermal driving force based on a linear driving force kinetic framework. This linear driving force kinetic framework is an adsorption kinetic expression framework used to represent the process of the resin's actual adsorption state approaching the equilibrium adsorption state. Under this kinetic expression framework, the rate of change of the average resin adsorption amount is linearly proportional to the difference between the current equilibrium adsorption state and the actual adsorption state, where the current equilibrium adsorption state is represented by the counterion coupling isothermal driving force, and the proportionality coefficient in the linear relationship represents the overall mass transfer intensity. By introducing the linear driving force kinetic framework, a unified correlation can be established between the online detected change in adsorption state and the thermodynamic driving force, enabling the isothermal coupling parameter solution results to be further used for online identification of the overall mass transfer parameters, thereby achieving continuous calculation and unified representation of adsorption thermodynamic parameters and mass transfer kinetic parameters under the same data link.

[0055] Specifically, in step 41, the isothermal coupling parameters are read, and the apparent ionic strength and effluent concentration are read from the extended data frame, while the maximum adsorption capacity of the resin is also read. The isothermal coupling parameters include a first coupling coefficient and a first exponential coefficient, which are used to characterize the baseline affinity and the degree of affinity attenuation due to ionic strength, respectively. Using the apparent ionic strength as input, the effective affinity coefficient is obtained according to the aforementioned method for calculating the effective affinity coefficient, that is, based on the exponential response of the first coupling coefficient and the first exponential coefficient to the apparent ionic strength, the affinity characterization quantity as a function of the ionic environment is obtained. Through this back-substitution process, the effective affinity coefficient is calculated from the same set of predetermined isothermal coupling parameters at each sampling time, thereby ensuring the consistency of parameters in the subsequent driving force calculation.

[0056] Step 42: After obtaining the effective affinity coefficient, the effective affinity coefficient, effluent concentration, and maximum resin adsorption capacity are used as inputs to calculate the counterion coupling isothermal driving force according to the aforementioned calculation method. Then, the average resin adsorption capacity is read, and the driving force difference is determined by the difference between the counterion coupling isothermal driving force and the average resin adsorption capacity. This driving force difference measures the deviation between the current adsorption state and the theoretical equilibrium adsorption state and is the driving force term in the linear driving force kinetics framework.

[0057] Step 43: Read the average resin adsorption amount at adjacent sampling times and the preset sampling time step, and obtain the average resin adsorption amount change rate according to the calculation method of the average resin adsorption amount change rate. The average resin adsorption amount change rate is used to characterize the instantaneous rate of change of adsorption amount over time and is the state change term in the kinetic equation. Based on this, the average resin adsorption amount change rate is used as the numerator, and the driving force difference is used as the denominator. The ratio of the numerator to the denominator is calculated to obtain the overall mass transfer coefficient. This calculation reflects the linear relationship described by the linear driving force kinetic framework, that is, the rate of change of adsorption amount is proportional to the driving force difference, and the proportionality coefficient is the overall mass transfer coefficient. To avoid numerical instability or abnormal amplification caused by the driving force difference being too small, this embodiment compares the absolute value of the driving force difference with a preset difference threshold; when the absolute value of the driving force difference is less than the preset difference threshold, the calculation of the overall mass transfer coefficient at the corresponding sampling time is skipped, thereby ensuring the numerical validity and usability of the overall mass transfer coefficient sequence. Finally, the overall mass transfer coefficients calculated at each sampling time are collected to form an overall mass transfer coefficient sequence, which serves as the input for the subsequent resistance series model to decouple the mass transfer parameters between the outer membrane and the pore.

[0058] Through the above steps, this invention achieves online point-by-point identification of the overall mass transfer coefficient without introducing additional offline experiments. This embodiment utilizes the online measurable effluent concentration, apparent ionic strength, and real-time trajectory of the average resin adsorption amount obtained from mass balance, combined with the kinetic framework of anti-ion coupling isothermal driving force and linear driving force, to continuously output the overall mass transfer coefficient sequence during operation. By converting the measurable data into driving forces and state change terms that can be used for kinetic identification, real-time characterization of the mass transfer characteristics of the imidazolium resin adsorption process is achieved.

[0059] In one embodiment of the present invention, after obtaining the overall mass transfer coefficient sequence, in order to further achieve online identification of the adsorption kinetic parameters of imidazolium resin, it is necessary to decompose the overall mass transfer process into two parts, external membrane mass transfer and pore mass transfer, without introducing additional offline experiments, and obtain the relevant parameters of external membrane mass transfer and pore mass transfer, respectively. Considering that the change of counterion state will cause a coupling change in the isothermal driving force and mass transfer behavior, this embodiment first screens the stable counterion state segment to ensure that the decoupling of mass transfer parameters is carried out in a relatively consistent ionic environment; then, two flow rates are set sequentially in the stable counterion state segment and the corresponding overall mass transfer coefficients are obtained; finally, a resistance series equation is established by combining the preset flow rate power law exponent, and the external membrane mass transfer ratio coefficient and the pore mass transfer coefficient are solved simultaneously, and the external membrane mass transfer coefficient is calculated accordingly. The specific process includes:

[0060] Step 51: Read the apparent ion intensity sequence from the extended data frame. Within the sliding time window of continuous sampling times, determine the maximum and minimum values ​​of the apparent ion intensity, and define the difference between the maximum and minimum values ​​as the fluctuation amplitude. The fluctuation amplitude is used to quantify the degree of change in the ion environment within the sliding time window. Compare the fluctuation amplitude with a preset apparent ion intensity fluctuation threshold. When the fluctuation amplitude is not greater than the preset apparent ion intensity fluctuation threshold and the cumulative duration is not less than a preset stable duration threshold, the corresponding time interval is defined as the counterion state stable segment, and a time index set of the counterion state stable segment is output. The counterion state stable segment refers to the time interval within which the apparent ion intensity remains relatively stable within a certain time range, characterizing the operating stage where the ion environment of the adsorption system does not change significantly. Using the time index set, subsequent flow rate settings and overall mass transfer coefficient statistics can be limited to this stable segment, avoiding parameter inconsistencies caused by the mixing of different counterion states.

[0061] Step 52: After obtaining the stable counterion state range, a first flow rate and a second flow rate are sequentially set within this range. These two flow rates refer to applying two different flow rate settings successively within the same stable counterion state range and maintaining them for a certain period of time to form a stable flow rate holding interval. Subsequently, the overall mass transfer coefficient is obtained within the first and second flow rate holding intervals, respectively. The arithmetic mean of the overall mass transfer coefficients within the first flow rate holding interval is taken to obtain the first overall mass transfer coefficient, and the arithmetic mean of the overall mass transfer coefficients within the second flow rate holding interval is taken to obtain the second overall mass transfer coefficient. The arithmetic mean is used to compress the fluctuations of the overall mass transfer coefficient within the intervals into a single representative value, thereby forming paired data of the first flow rate and the first overall mass transfer coefficient, and paired data of the second flow rate and the second overall mass transfer coefficient, which serve as the observation input for subsequent simultaneous equation solving.

[0062] Step 53: Read the preset flow power law exponent and define the outer membrane mass transfer coefficient as a power law function relationship between the outer membrane mass transfer ratio coefficient and the flow rate, so that the outer membrane mass transfer coefficient can change with the flow rate. The flow power law exponent describes the power function relationship between the outer membrane mass transfer coefficient and the flow rate; the outer membrane mass transfer ratio coefficient quantifies the scale of the outer membrane mass transfer coefficient; and the pore mass transfer coefficient quantifies the diffusion and transfer capacity of the solute within the resin particles. Simultaneously, the reciprocal of the overall mass transfer coefficient is expressed as the sum of the reciprocals of the outer membrane mass transfer coefficient and the pore mass transfer coefficient, thus establishing a resistance series relationship. Then, substitute the paired data of the first flow rate and the first overall mass transfer coefficient, and the paired data of the second flow rate and the second overall mass transfer coefficient, into the above power law function and reciprocal sum relationship to form two equations regarding the outer membrane mass transfer ratio coefficient and the pore mass transfer coefficient. Solve the two equations simultaneously to obtain the outer membrane mass transfer ratio coefficient and the pore mass transfer coefficient. Finally, the first and second flow rates were substituted into the power law function to calculate the outer membrane mass transfer coefficient, so that the outer membrane mass transfer coefficient corresponds one-to-one with the corresponding flow rate setting, providing a definite input for the subsequent construction of the core parameter set and the reconstruction of the outer membrane mass transfer coefficient.

[0063] Through the above steps, this invention achieves decoupled identification of the overall mass transfer coefficient into two types of mass transfer parameters: the outer membrane and the pores, under online operating conditions. In this embodiment, the stable segment of the counterion state is screened and two flow rate pairs are used to construct a set of equations, so that the mass transfer ratio coefficient of the outer membrane and the mass transfer coefficient of the pores can be obtained by solving them simultaneously under the same ionic environment conditions. This reduces the interference of changes in the ionic environment on the identification of mass transfer parameters. By organizing and calculating the available data such as apparent ionic strength, flow rate, and overall mass transfer coefficient, the mass transfer parameters of the outer membrane and the pores, which are difficult to measure directly online, are obtained, realizing the online analysis and output of the mass transfer mechanism parameters of the imidazolium resin adsorption process.

[0064] In one embodiment of the present invention, the isothermal coupling parameters, the outer membrane mass transfer ratio coefficient, the pore mass transfer coefficient, the preset flow power law exponent, and the maximum resin adsorption capacity are used to form a core parameter set. This reconstructs the effective affinity coefficient, the outer membrane mass transfer coefficient, and the overall mass transfer coefficient, and outputs a consistency judgment result identifier, including:

[0065] Step 61: Read the isothermal coupling parameters, including the outer membrane mass transfer ratio coefficient, the pore mass transfer coefficient, the preset flow power law exponent, and the maximum resin adsorption capacity. Assemble the first coupling coefficient, the first exponent coefficient, the outer membrane mass transfer ratio coefficient, the pore mass transfer coefficient, the preset flow power law exponent, and the maximum resin adsorption capacity into a core parameter group according to a fixed field order. This fixed field order means that the above parameters are stored sequentially in predefined field positions within the data structure, enabling the system to read the corresponding parameters in a deterministic manner during system calls, avoiding calculation errors caused by parameter misalignment.

[0066] Step 62: At each sampling moment, read the apparent ion intensity and flow rate from the extended data frame, and read the first coupling coefficient, first exponential coefficient, outer membrane mass transfer ratio coefficient, pore mass transfer coefficient, and preset flow rate power law exponent from the core parameter set. Using the apparent ion intensity as input, the effective affinity coefficient is obtained according to the aforementioned calculation method, so that the effective affinity coefficient can be dynamically reconstructed as the apparent ion intensity changes; using the outer membrane mass transfer ratio coefficient, preset flow rate power law exponent, and flow rate as input, the outer membrane mass transfer coefficient is obtained according to the aforementioned calculation method, so that the outer membrane mass transfer coefficient corresponds one-to-one with the real-time flow rate; further, using the outer membrane mass transfer coefficient and pore mass transfer coefficient as input, the overall mass transfer coefficient is obtained according to the aforementioned reciprocal sum relationship of the overall mass transfer coefficient, so that at any sampling moment, the effective affinity coefficient, outer membrane mass transfer coefficient, and overall mass transfer coefficient can be consistently reconstructed from the core parameter set, forming a continuously updated parameter sequence output.

[0067] Step 63: Within the same counterion stable state segment, following the simultaneous solution process described in Step 63 above, perform a preset number of simultaneous solutions on the external membrane mass transfer ratio coefficient and the pore mass transfer coefficient. In each simultaneous solution, the same preset flow rate power law exponent and paired data of the first flow rate and the first overall mass transfer coefficient, and the second flow rate and the second overall mass transfer coefficient within the same counterion stable state segment are used. The paired data is obtained by the arithmetic mean of the overall mass transfer coefficients within the two flow rate holding intervals, and is used to compress the continuous sequence into representative overall mass transfer coefficients under the corresponding flow rate conditions. The pore mass transfer coefficients obtained from each simultaneous solution are sequentially written into the repeated solution result set of the pore mass transfer coefficients in the solution order. The repeated solution result set refers to the aggregated storage result of the pore mass transfer coefficients obtained by repeatedly performing simultaneous solutions under the same input conditions within the same counterion stable state segment, serving as the basic data object for subsequent statistical analysis.

[0068] After obtaining the repeated solution set of the in-orifice mass transfer coefficients, the mean and standard deviation of the repeated solution set are calculated. The mean characterizes the central tendency of the repeated solution results and is calculated as the ratio of the sum of all in-orifice mass transfer coefficients in the repeated solution set to the number of elements in the repeated solution set. The standard deviation characterizes the dispersion of the repeated solution results relative to the mean and is calculated as the square root of the ratio of the sum of the squares of the differences between each in-orifice mass transfer coefficient and the mean in the repeated solution set to the number of elements in the repeated solution set. Both the mean and standard deviation use the repeated solution set as input and are normalized using the number of elements to ensure that the calculation rules are determined and reproducible when the preset number of iterations is fixed.

[0069] The ratio of the standard deviation to the mean is defined as the coefficient of variation. This coefficient of variation characterizes the relative dispersion of repeated solutions to the mass transfer coefficient within the borehole. It is a dimensionless relative fluctuation index, avoiding inconsistencies in the judgment scale caused by the magnitude of parameters when using only the standard deviation. The coefficient of variation is then compared to a preset threshold. If the coefficient of variation is not greater than the preset threshold, the consistency of mass transfer within the borehole is determined to be passed; if the coefficient of variation is greater than the preset threshold, the consistency of mass transfer within the borehole is determined to be failed. The preset threshold is a pre-set judgment threshold used by the system to map the dispersion of repeated solutions to a deterministic pass or fail output.

[0070] On the other hand, this embodiment reads the apparent ion strength and effective affinity coefficient within the stable segment of the same counterion state, and verifies the response relationship that the effective affinity coefficient does not increase when the apparent ion strength increases, thus obtaining a response consistency judgment. This response relationship reflects the exponential decay law limited by the isothermal coupling parameter, that is, the effective affinity coefficient should remain non-increasing when the ion strength increases, thereby verifying whether the isothermal coupling parameter and the online reconstruction process are consistent within the stable segment. Finally, when the in-pore mass transfer consistency judgment is passed and the response consistency judgment is passed, the consistency judgment result is output as passed; otherwise, the consistency judgment result is output as failed. The consistency judgment result identifier is a deterministic status flag output by the system, used to indicate whether the current core parameter set and the reconstruction result meet the preset consistency conditions.

[0071] Through the above steps, this invention solidifies the isothermal coupling parameters and mass transfer parameters into a core parameter set, and reconstructs the effective affinity coefficient, outer membrane mass transfer coefficient, and overall mass transfer coefficient using a unified parameter source during online operation. This enables continuous and traceable calculation of key parameters in the adsorption process, and allows for dual constraint verification of the dispersion of repeated solutions to the pore mass transfer coefficient and the response law of the effective affinity coefficient to the apparent ion intensity within the same counterion stable state. This provides the invention with a parameter set and consistency identifier output that can be directly called by the detection and analysis system.

[0072] In one embodiment of the present invention, an online identification system for adsorption kinetic parameters of imidazolium resin is also provided, comprising:

[0073] The data acquisition module is used to simultaneously collect flow rate, influent concentration, effluent concentration, conductivity, temperature and pH, and obtain the apparent ionic strength from conductivity according to the preset calibration relationship;

[0074] The mass balance module is used to perform mass balance based on flow rate, influent concentration, effluent concentration and resin dry basis mass to obtain the real-time trajectory of the average resin adsorption amount.

[0075] The isothermal drive module is used to construct the anti-ion coupling isothermal drive force based on the maximum resin adsorption capacity, effluent concentration, apparent ionic strength and effective affinity coefficient, and to screen the quasi-equilibrium section according to the rate of change of the average resin adsorption capacity.

[0076] The isothermal solution module is used to obtain the average resin adsorption amount and effluent concentration for two quasi-equilibrium sections corresponding to two different apparent ionic intensities, and solve the isothermal coupling parameters by combining the quasi-equilibrium relationship with the quasi-equilibrium relationship.

[0077] The overall mass transfer module is used to substitute the isothermal coupling parameters into the anti-ion coupling isothermal driving force, and calculate the overall mass transfer coefficient point by point based on the average resin adsorption amount and the anti-ion coupling isothermal driving force according to the linear driving force kinetic framework.

[0078] The resistance decoupling module is used to screen the counterion state stable section. Within the counterion state stable section, two flow rates are set sequentially and the corresponding overall mass transfer coefficients are obtained. The resistance series equation is established in combination with the preset flow power law exponent. The outer membrane mass transfer ratio coefficient and the pore mass transfer coefficient are solved, and the outer membrane mass transfer coefficient is obtained.

[0079] The parameter reconstruction module is used to assemble the isothermal coupling parameters, the outer membrane mass transfer ratio coefficient, the pore mass transfer coefficient, the preset flow power law exponent, and the maximum resin adsorption capacity into a core parameter group, reconstruct the effective affinity coefficient, the outer membrane mass transfer coefficient, and the overall mass transfer coefficient, and output a consistency judgment result identifier.

[0080] It should be noted that the range and threshold size are set for ease of comparison. The size of the threshold depends on the amount of sample data and the number of bases set by those skilled in the art for each set of sample data, as long as it does not affect the ratio between the parameter and the quantized value.

[0081] The embodiments of the present invention have been described above, but the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of the present embodiments, all of which are within the protection scope of the present embodiments.

Claims

1. A method for on-line identification of adsorption kinetic parameters of imidazolium resins, characterized in that, Includes the following steps: Step 1: Simultaneously collect flow rate, influent concentration, effluent concentration, conductivity, temperature, and pH, and derive the apparent ionic strength from conductivity according to a preset calibration relationship, including: At the same sampling time, flow rate, influent concentration, effluent concentration, conductivity, temperature and pH are acquired, and the original data frame is generated using the sampling time as a unified time identifier; Apparent ion intensity is obtained from conductivity based on a preset calibration relationship. The calibration coefficients of the preset calibration relationship are determined by linear fitting of conductivity calibration points corresponding to two preset known apparent ion intensities. The calibration coefficients include a proportional term and a bias term. Conductivity is read from the original data frame, and the conductivity is multiplied by the proportional term in the calibration coefficient to obtain a proportional result. The proportional result is added to the bias term in the calibration coefficient to obtain the apparent ion intensity. The apparent ion intensity is compared with zero. When the apparent ion intensity is less than zero, the apparent ion intensity is set to zero. The apparent ion intensity is written into the original data frame to obtain an extended data frame. Step 2: Perform a mass balance calculation based on flow rate, influent concentration, effluent concentration, and resin dry weight to obtain the real-time trajectory of the average resin adsorption capacity, including: Step 11: Read the flow rate, influent concentration, and effluent concentration from the extended data frame, and determine the difference between the influent concentration and the effluent concentration as the concentration difference. Step 12: The product of the flow rate and the concentration difference is determined as the amount removed per unit time. The dry weight of the resin is read, and the ratio of the amount removed per unit time to the dry weight of the resin is determined as the rate of change of the average adsorption amount of the resin. Step 13: Call the preset sampling time step, add the product of the average resin adsorption change rate and the preset sampling time step to the average resin adsorption at the previous sampling time to obtain the average resin adsorption at the current sampling time, and collect the average resin adsorption at each sampling time into a real-time trajectory of the average resin adsorption. Step 3: Construct the anti-ion coupling isothermal driving force based on the maximum adsorption capacity of the resin, the effluent concentration, the apparent ionic strength and the effective affinity coefficient, and screen the quasi-equilibrium section according to the rate of change of the average adsorption capacity of the resin. Step 4: For the two quasi-equilibrium sections corresponding to different apparent ionic intensities, obtain the average resin adsorption amount and effluent concentration, and solve the quasi-equilibrium relationship to obtain the isothermal coupling parameters. Step 5: Substitute the isothermal coupling parameters into the anti-ion coupling isothermal driving force, and calculate the overall mass transfer coefficient point by point based on the average resin adsorption amount and the anti-ion coupling isothermal driving force according to the linear driving force kinetic framework. Step 6: Select the stable section of the counterion state, set two flow rates in sequence within the stable section of the counterion state and obtain the corresponding overall mass transfer coefficients, establish the resistance series equation by combining the preset flow power law exponent, solve the outer membrane mass transfer ratio coefficient and the pore mass transfer coefficient, and obtain the outer membrane mass transfer coefficient. Step 7: The isothermal coupling parameters, outer membrane mass transfer ratio coefficient, pore mass transfer coefficient, preset flow power law exponent, and maximum resin adsorption capacity are combined into a core parameter group to reconstruct the effective affinity coefficient, outer membrane mass transfer coefficient, and overall mass transfer coefficient, and output the consistency judgment result identifier.

2. The method according to claim 1, wherein the imidazolium resin adsorption kinetics parameters are identified on-line. A counter-ion coupling isothermal driving force was constructed based on the resin's maximum adsorption capacity, effluent concentration, apparent ionic strength, and effective affinity coefficient. A quasi-equilibrium zone was then selected based on the rate of change in the resin's average adsorption capacity, including: Step 21: Read the water concentration and apparent ionic strength from the extended data frame, and read the maximum adsorption capacity of the resin; the isothermal coupling parameters include the first coupling coefficient and the first exponential coefficient. The product of the first exponential coefficient and the apparent ionic strength is negative and used as the exponent. The exponential calculation result with the natural constant as the base is calculated. The exponential calculation result is multiplied by the first coupling coefficient to obtain the effective affinity coefficient. Step 22: The product of the effective affinity coefficient and the effluent concentration is used as the numerator, and the result of adding the constant 1 to the product is used as the denominator. The ratio of the numerator to the denominator is multiplied by the maximum adsorption capacity of the resin to obtain the anti-ion coupling isothermal driving force. The anti-ion coupling isothermal driving forces at each sampling time are collected to form an anti-ion coupling isothermal driving force sequence. Step 23: Calculate the rate of change of average resin adsorption based on the real-time trajectory of average resin adsorption and the preset sampling time step. The difference in average resin adsorption at adjacent sampling times is used as the numerator, and the preset sampling time step is used as the denominator. The ratio of the numerator to the denominator is used to obtain the rate of change of average resin adsorption. For each sampling moment, the absolute value of the change rate of the average resin adsorption is taken. When the absolute value is less than a preset change rate threshold, the corresponding sampling moment is recorded as a candidate moment that meets the quasi-equilibrium condition. When the absolute value is not less than the preset change rate threshold, the timing of consecutive candidate moments is cleared and the corresponding sampling moment is recorded as a non-candidate moment that does not meet the quasi-equilibrium condition. When the cumulative duration of consecutive candidate moments is not less than a preset quasi-equilibrium duration threshold, the time interval corresponding to the consecutive candidate moments is determined as a quasi-equilibrium segment, and the time index set of the quasi-equilibrium segment, as well as the average resin adsorption amount segment, the average effluent concentration segment, and the average apparent ionic strength segment within the quasi-equilibrium segment are output. The cumulative duration is calculated by multiplying the number of consecutive candidate moments by the preset sampling time step.

3. The method according to claim 2, wherein the method is characterized by, For two quasi-equilibrium sections corresponding to two different apparent ionic intensities, the average resin adsorption capacity and effluent concentration are obtained and their quasi-equilibrium relationship is established. The isothermal coupling parameters are then solved, including: Step 31: Select two quasi-equilibrium segments with unequal average apparent ion intensity from the quasi-equilibrium segment set, and determine them as the first quasi-equilibrium segment and the second quasi-equilibrium segment respectively. Obtain the average resin adsorption amount, average effluent concentration and average apparent ion intensity of the first quasi-equilibrium segment and the second quasi-equilibrium segment respectively. Step 32: Read the maximum adsorption capacity of the resin. Calculate the effective affinity coefficients of the first and second quasi-equilibrium sections according to the method in Step 21, based on the average apparent ionic strength values ​​of the first and second quasi-equilibrium sections respectively. Take the product of the effective affinity coefficient and the average effluent concentration value as the numerator, add the constant 1 to the product as the denominator, and multiply the ratio of the numerator to the denominator by the maximum adsorption capacity of the resin to obtain the quasi-equilibrium relationship corresponding to the first and second quasi-equilibrium sections respectively. Step 33: Combine the average resin adsorption amount of the first quasi-equilibrium segment with the corresponding quasi-equilibrium relation of the first quasi-equilibrium segment, and combine the average resin adsorption amount of the second quasi-equilibrium segment with the corresponding quasi-equilibrium relation of the second quasi-equilibrium segment to form two equations about the first coupling coefficient and the first exponential coefficient. Solve the equations to obtain the first coupling coefficient and the first exponential coefficient, and write the first coupling coefficient and the first exponential coefficient into the isothermal coupling parameters.

4. The method according to claim 3, wherein the method is characterized by, The isothermal coupling parameters are substituted into the isothermal driving force of the counterion coupling, and the overall mass transfer coefficient is calculated point by point based on the average resin adsorption amount and the isothermal driving force of the counterion coupling, according to the linear driving force kinetic framework. This includes: Step 41: Read the isothermal coupling parameters, read the apparent ionic strength and effluent concentration from the extended data frame, and read the maximum adsorption capacity of the resin; use the apparent ionic strength as input and calculate the effective affinity coefficient in the manner of step 21. Step 42: Using the effective affinity coefficient, effluent concentration and maximum resin adsorption capacity as inputs, calculate the counterion coupling isothermal driving force in the manner of Step 22; read the average resin adsorption capacity, and determine the driving force difference by the difference between the counterion coupling isothermal driving force and the average resin adsorption capacity. Step 43: Read the average resin adsorption amount and preset sampling time step of adjacent sampling times, and obtain the average resin adsorption amount change rate according to the calculation method of the average resin adsorption amount change rate in step 23; use the average resin adsorption amount change rate as the numerator and the driving force difference as the denominator, and calculate the ratio of the numerator to the denominator to obtain the overall mass transfer coefficient; when the absolute value of the driving force difference is less than the preset difference threshold, skip the calculation of the overall mass transfer coefficient of the corresponding sampling time, and collect the overall mass transfer coefficients of each sampling time to form an overall mass transfer coefficient sequence.

5. The method according to claim 2, wherein the method is characterized by, The stable counterion state range is selected, and two flow rates are sequentially set within this range to obtain the corresponding overall mass transfer coefficients. A resistance series equation is established using the preset flow rate power law exponent. The external membrane mass transfer ratio and the pore mass transfer coefficient are solved to obtain the external membrane mass transfer coefficient, including: Step 51: Read the apparent ion intensity in the extended data frame, determine the maximum and minimum values ​​of the apparent ion intensity within the sliding time window of the continuous sampling time, and determine the difference between the maximum and minimum values ​​as the fluctuation amplitude; compare the fluctuation amplitude with the preset apparent ion intensity fluctuation threshold, and when the fluctuation amplitude is not greater than the preset apparent ion intensity fluctuation threshold and the cumulative duration is not less than the preset stable duration threshold, determine the corresponding time interval as the counterion state stable segment and output the time index set of the counterion state stable segment; Step 52: Set the first flow rate and the second flow rate sequentially within the counterion state stable section, and obtain the overall mass transfer coefficient within the first flow rate holding interval and the second flow rate holding interval respectively; take the arithmetic mean of the overall mass transfer coefficient within the first flow rate holding interval to obtain the first overall mass transfer coefficient, and take the arithmetic mean of the overall mass transfer coefficient within the second flow rate holding interval to obtain the second overall mass transfer coefficient, thus forming paired data of the first flow rate and the first overall mass transfer coefficient, and paired data of the second flow rate and the second overall mass transfer coefficient. Step 53: Read the preset flow power law exponent, define the outer membrane mass transfer coefficient as a power law function of the outer membrane mass transfer ratio coefficient and the flow rate, and express the reciprocal of the overall mass transfer coefficient as the sum of the reciprocal of the outer membrane mass transfer coefficient and the reciprocal of the pore mass transfer coefficient; substitute the paired data of the first flow rate and the first overall mass transfer coefficient and the paired data of the second flow rate and the second overall mass transfer coefficient into the power law function and the sum of the reciprocals to form two equations about the outer membrane mass transfer ratio coefficient and the pore mass transfer coefficient, solve them simultaneously to obtain the outer membrane mass transfer ratio coefficient and the pore mass transfer coefficient, and calculate the outer membrane mass transfer coefficient by substituting the first flow rate and the second flow rate into the power law function.

6. The method according to claim 5, wherein the method is characterized by, The isothermal coupling parameters, outer membrane mass transfer ratio coefficient, pore mass transfer coefficient, preset flow power law exponent, and maximum resin adsorption capacity are used to form a core parameter set. This reconstructs the effective affinity coefficient, outer membrane mass transfer coefficient, and overall mass transfer coefficient, and outputs a consistency judgment result identifier, including: Step 61: Read the isothermal coupling parameters, including the outer membrane mass transfer ratio coefficient, the pore mass transfer coefficient, the preset flow power law exponent, and the maximum resin adsorption capacity. Then, arrange the first coupling coefficient, the first exponent coefficient, the outer membrane mass transfer ratio coefficient, the pore mass transfer coefficient, the preset flow power law exponent, and the maximum resin adsorption capacity into a core parameter group in a fixed field order. Step 62: At each sampling time, read the apparent ion intensity and flow rate from the extended data frame, and read the first coupling coefficient, the first exponential coefficient, the outer membrane mass transfer ratio coefficient, the pore mass transfer coefficient, and the preset flow rate power law exponent from the core parameter group; using the apparent ion intensity as input, calculate the effective affinity coefficient according to the method in step 21; using the outer membrane mass transfer ratio coefficient, the preset flow rate power law exponent, and the flow rate as input, obtain the outer membrane mass transfer coefficient according to the calculation method of the outer membrane mass transfer coefficient in step 53; using the outer membrane mass transfer coefficient and the pore mass transfer coefficient as input, obtain the overall mass transfer coefficient according to the reciprocal sum relationship of the overall mass transfer coefficient in step 53. Step 63: Read the set of repeated solutions for the mass transfer coefficient within the pore within the stable counterion state, calculate the coefficient of variation of the repeated solution set and compare it with the preset coefficient of variation threshold to obtain the consistency judgment of mass transfer within the pore; read the apparent ion intensity and effective affinity coefficient within the same stable counterion state, and verify the response relationship that the effective affinity coefficient does not increase when the apparent ion intensity increases point by point to obtain the consistency judgment of response; when the consistency judgment of mass transfer within the pore is passed and the consistency judgment of response is passed, output the consistency judgment result as passed, otherwise output the consistency judgment result as failed.

7. The method according to claim 6, wherein the method is characterized by, The determination of mass transfer consistency within the orifice includes: Step 71: Within the same counterion state stable segment, following the simultaneous solution process in Step 53, perform a preset number of simultaneous solutions on the external membrane mass transfer ratio coefficient and the pore mass transfer coefficient; wherein, each simultaneous solution uses the same preset flow power law exponent and the paired data of the first flow rate and the first overall mass transfer coefficient and the second flow rate and the second overall mass transfer coefficient within the same counterion state stable segment, and the pore mass transfer coefficient obtained from each simultaneous solution is sequentially written into the repeated solution result set of the pore mass transfer coefficient; Step 72: Calculate the mean and standard deviation of the repeated solution results set of the mass transfer coefficient in the pores. The mean is the ratio of the sum of all mass transfer coefficients in the repeated solution results set of the mass transfer coefficient in the pores to the number of elements in the repeated solution results set of the mass transfer coefficient in the pores. The standard deviation is the square root of the ratio of the sum of the squares of the differences between each mass transfer coefficient in the pores and the mean in the repeated solution results set of the mass transfer coefficient in the pores to the number of elements in the repeated solution results set of the mass transfer coefficient in the pores. Step 73: Determine the ratio of standard deviation to mean as coefficient of variation, and compare the coefficient of variation with a preset coefficient of variation threshold; when the coefficient of variation is not greater than the preset coefficient of variation threshold, determine that the mass transfer consistency in the orifice is passed; when the coefficient of variation is greater than the preset coefficient of variation threshold, determine that the mass transfer consistency in the orifice is failed.

8. An on-line system for identifying adsorption kinetic parameters of imidazolium resins, characterized in that it comprises: The online identification method for adsorption kinetic parameters of imidazolium resin as described in any one of claims 1-7 includes: The data acquisition module is used to simultaneously collect flow rate, influent concentration, effluent concentration, conductivity, temperature and pH, and obtain the apparent ionic strength from conductivity according to the preset calibration relationship; The mass balance module is used to perform mass balance based on flow rate, influent concentration, effluent concentration and resin dry basis mass to obtain the real-time trajectory of the average resin adsorption amount. The isothermal drive module is used to construct the anti-ion coupling isothermal drive force based on the maximum resin adsorption capacity, effluent concentration, apparent ionic strength and effective affinity coefficient, and to screen the quasi-equilibrium section according to the rate of change of the average resin adsorption capacity. The isothermal solution module is used to obtain the average resin adsorption amount and effluent concentration for two quasi-equilibrium sections corresponding to two different apparent ionic intensities, and solve the isothermal coupling parameters by combining the quasi-equilibrium relationship with the quasi-equilibrium relationship. The overall mass transfer module is used to substitute the isothermal coupling parameters into the anti-ion coupling isothermal driving force, and calculate the overall mass transfer coefficient point by point based on the average resin adsorption amount and the anti-ion coupling isothermal driving force according to the linear driving force kinetic framework. The resistance decoupling module is used to screen the counterion state stable section. Within the counterion state stable section, two flow rates are set sequentially and the corresponding overall mass transfer coefficients are obtained. The resistance series equation is established in combination with the preset flow power law exponent. The outer membrane mass transfer ratio coefficient and the pore mass transfer coefficient are solved, and the outer membrane mass transfer coefficient is obtained. The parameter reconstruction module is used to assemble the isothermal coupling parameters, the outer membrane mass transfer ratio coefficient, the pore mass transfer coefficient, the preset flow power law exponent, and the maximum resin adsorption capacity into a core parameter group, reconstruct the effective affinity coefficient, the outer membrane mass transfer coefficient, and the overall mass transfer coefficient, and output a consistency judgment result identifier.

Images