A method for calculating filter cake characteristic parameters

Abstract

This invention relates to the field of solid-liquid separation technology, and in particular provides a method for calculating filter cake characteristic parameters. The method includes: obtaining the filter cloth resistance using a filter cloth resistance calculation formula; fitting experimental data using a central pore blockage model to obtain the relationship between filter cake pressure drop and time; optimizing the filter cake characteristic parameter model using a genetic algorithm, minimizing the mean square error, performing a global search, and optimizing parameters such as filter cake compressibility, initial permeability coefficient, standardized pressure, and initial solid content to ensure that the calculated values ​​have an average correlation coefficient with the measured values; and calculating the filtrate volume, filter cake thickness, and filter cake permeability of a vacuum filtration device under specific operating conditions based on the optimized filter cake characteristic parameters. This method, based on experimental data and model optimization, not only accurately describes the filter cake characteristics and improves filtration efficiency but also reduces energy consumption, and provides a more precise process control method for solid-liquid separation processes in fields such as rare earth resource recovery.

Description

Technical Field

[0001] This invention relates to the field of solid-liquid separation technology, and in particular to a method for calculating filter cake characteristic parameters. Background Technology

[0002] Monazite slag hydrochloric acid leachate is an important byproduct in rare earth resource recovery, and its filtration and separation process faces a series of technical challenges. Due to the high content of fine particles and suspended solids in the slurry of monazite slag hydrochloric acid leachate, problems such as rapid filter cake accumulation and a rapid decrease in filtrate flow often occur during filtration. These factors not only lead to low filtration efficiency but also increase energy consumption and put significant pressure on the equipment. Furthermore, the formation and characteristics of the filter cake (thickness and permeability) change over time during filtration, making precise control of the filtration process more complex. Although some filtration technologies exist for treating similar slurries, the special composition and high particle concentration of monazite slag hydrochloric acid leachate prevents existing filtration equipment from efficiently processing this material on an industrial scale, and effective methods for real-time monitoring and adjustment of filter cake characteristic parameters are lacking.

[0003] Vacuum filtration, a commonly used solid-liquid separation technology, is widely applied in slurry filtration and liquid cleaning processes. However, when dealing with high-concentration suspensions such as monazite solvent residue hydrochloric acid leachate, traditional vacuum filtration equipment often fails to provide stable filtration performance, resulting in low filter cake processing efficiency, high equipment maintenance costs, and a lack of scientific basis for optimizing the filtration process. Summary of the Invention

[0004] In view of this, the present invention provides a method for calculating filter cake characteristic parameters to accurately describe filter cake characteristics, improve filtration efficiency, and reduce energy consumption.

[0005] In a first aspect, the present invention provides a method for calculating filter cake characteristic parameters, the method comprising:

[0006] Step 1: Calculate the filter cloth resistance. Conduct a gravity filtration experiment using deionized water, measure the liquid column height and filtration time, and obtain the filter cloth resistance using the filter cloth resistance calculation formula.

[0007] Step 2: Calculate the relationship between filter cake pressure drop and time. Fit the experimental data using the intermediate hole blockage model to obtain the relationship between filter cake pressure drop and time.

[0008] Step 3: Optimize the filter cake characteristic parameter model using a genetic algorithm, through global search and minimizing the mean square error. MSE To achieve the desired result, the experimental data were fitted, and the parameters of filter cake compressibility, initial permeability coefficient, normalized pressure, and initial solids content were optimized to improve the average correlation coefficient. R2 Greater than or equal to 0.9;

[0009] Step 4: Based on the optimized filter cake characteristic parameters, calculate the filtrate volume, filter cake thickness, and filter cake permeability of the vacuum filtration equipment under specific operating conditions.

[0010] Optionally, the formula for calculating the filter cloth resistance in step 1 is:

[0011] ;

[0012] in, The filter cloth resistance is expressed in units of... ; The pure water filtration rate of the filter cloth is expressed in m / s. The density of the liquid, in units of . ; Let be the acceleration due to gravity, taken as 9.81. ; The height of the liquid column is in meters (m). The viscosity of deionized water is expressed in units of... .

[0013] Optionally, the expression for the filter cake pressure drop in step 2 is:

[0014] ;

[0015] in, Vacuum degree, unit: Pa; m , n These are the model coefficients; A The filter area is expressed in meters (m²). 2 .

[0016] Optionally, model coefficients m , n The intermediate hole blockage model is satisfied, and its relationship is as follows:

[0017] ;

[0018] in, V The volume of the filtrate is in cubic meters (m³). 3 .

[0019] Optionally, the genetic algorithm optimization process in step 3 includes selection, crossover, and mutation operations, and optimizes the filter cake characteristic parameters through global search to obtain the best fitting parameters.

[0020] Optionally, the filter cake characteristic parameter model in step 3 is:

[0021] ;

[0022] in, u The velocity is expressed in m / s. The pressure drop across the filter cake is expressed in Pa. Standardized pressure, unit is Pa; The compressibility coefficient is the permeability coefficient. The viscosity of the filtrate is expressed in Pa·s. This represents the initial solid content; The initial permeability coefficient is expressed in meters. 2 ; This refers to the solids content of the slurry. t The filtering time is expressed in seconds.

[0023] Optionally, the calculation model for the filter cake thickness in step 4 is as follows:

[0024] ;

[0025] in, L The thickness of the filter cake is in meters (m).

[0026] The calculation model for filter cake permeability is as follows:

[0027] ;

[0028] in, k Permeability, in meters (m) 2 .

[0029] The technical solution provided by this invention includes the following steps: 1) Calculating filter cloth resistance: Performing a gravity filtration experiment with deionized water, measuring the liquid column height and filtration time, and obtaining the filter cloth resistance using the filter cloth resistance calculation formula; 2) Calculating the relationship between filter cake pressure drop and time: Fitting experimental data using a central pore blockage model to obtain the relationship between filter cake pressure drop and time; 3) Optimizing the filter cake characteristic parameter model using a genetic algorithm, through global search and minimizing the mean square error. MSE To achieve the desired result, the experimental data were fitted, and the parameters of filter cake compressibility, initial permeability coefficient, normalized pressure, and initial solids content were optimized to improve the average correlation coefficient. R 2 Greater than or equal to 0.9; Based on the optimized filter cake characteristic parameters, the filtrate volume, filter cake thickness and filter cake permeability of the vacuum filtration equipment under specific operating conditions are calculated. This method is based on experimental data and model optimization. By accurately analyzing the changes in the parameter properties of the filter cake, it provides a theoretical basis for the optimization of the vacuum filtration process. It not only accurately describes the characteristics of the filter cake, improves the filtration efficiency and reduces energy consumption, but also provides a more accurate process control method for solid-liquid separation processes in rare earth resource recovery and other fields. Attached Figure Description

[0030] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 A flowchart illustrating the method for calculating filter cake characteristic parameters provided in an embodiment of the present invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] It should be understood that the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0034] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” used in the embodiments of this invention are also intended to include the plural forms unless the context clearly indicates otherwise.

[0035] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0036] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0037] This invention addresses the shortcomings of existing technologies in the vacuum filtration process of hydrochloric acid leachate from monazite slag. It proposes a method for calculating filter cake characteristic parameters based on experimental data and model optimization, and combines least squares method and genetic algorithm optimization techniques to determine filter cake layer parameters for use in equipment operating condition calculations.

[0038] This invention first establishes a filter cake characteristic parameter model for the vacuum filtration process of hydrochloric acid leachate from monazite slag. The filter cloth resistance is calculated by deionized water filtration. The experimental data is fitted by the least squares method, and the parameters in the filter cake characteristic parameter model are optimized by combining a genetic algorithm. Parameters that can describe the filter cake thickness and permeability are obtained. Using these parameters, the filtrate volume and the properties of the filter cake layer at the outlet can be calculated under specific operating conditions of a certain device.

[0039] Figure 1 A flowchart of the method for calculating filter cake characteristic parameters provided in the embodiments of the present invention is shown below. Figure 1 As shown, the method includes:

[0040] Step 1: Calculate the filter cloth resistance. Conduct a gravity filtration experiment using deionized water, measure the liquid column height and filtration time, and obtain the filter cloth resistance using the filter cloth resistance calculation formula.

[0041] In this embodiment of the invention, the formula for calculating the filter cloth resistance in step 1 is:

[0042] ;

[0043] in, The filter cloth resistance is expressed in units of... ; The pure water filtration rate of the filter cloth is expressed in m / s. The density of the liquid, in units of . ; Let be the acceleration due to gravity, taken as 9.81. ; The height of the liquid column is in meters (m). The viscosity of deionized water is expressed in units of... .

[0044] Step 2: Calculate the relationship between filter cake pressure drop and time. Fit the experimental data using the intermediate hole blockage model to obtain the relationship between filter cake pressure drop and time.

[0045] After adding monazite slag and leaching the slurry with hydrochloric acid, filtration experiments were conducted under different vacuum levels. The experimental data were fitted with a pore blockage model using the least squares method, and the model coefficients were calculated. Substituting the model coefficients into the expression for filter cake pressure drop, the relationship between filter cake pressure drop and time was obtained.

[0046] In this embodiment of the invention, the expression for the filter cake pressure drop in step 2 is:

[0047] ;

[0048] in, Vacuum degree, unit: Pa; m , n These are the model coefficients; A The filter area is expressed in meters (m²). 2 .

[0049] In this embodiment of the invention, the model coefficients m , n The intermediate hole blockage model is satisfied, and its relationship is as follows:

[0050] ;

[0051] in, V The volume of the filtrate is in cubic meters (m³). 3 .

[0052] Step 3: Optimize the filter cake characteristic parameter model using a genetic algorithm, through global search and minimizing the mean square error. MSE To achieve the desired result, the experimental data were fitted, and the parameters of filter cake compressibility, initial permeability coefficient, normalized pressure, and initial solids content were optimized to improve the average correlation coefficient. R 2 Greater than or equal to 0.9.

[0053] In this embodiment of the invention, the genetic algorithm optimization process in step 3 includes selection, crossover, and mutation operations, and optimizes the filter cake characteristic parameters through global search to obtain the best fitting parameters.

[0054] Substituting the relationship between filter cake pressure drop and time from step 2 into the filter cake characteristic parameter model, and optimizing it using a genetic algorithm, including selection, crossover, and mutation operations, the filter cake characteristic parameter model undergoes global search and multi-generation iterative optimization to achieve mean squared error. MSE The goal is to minimize the parameter set and select the optimal combination. If the output parameters do not meet the requirements... R 2 If the value is greater than or equal to 0.9, the genetic algorithm optimization is performed again to obtain the permeability compressibility coefficient. Initial permeability coefficient Standardized pressure Initial solid content .

[0055] In this embodiment of the invention, the filter cake characteristic parameter model in step 3 is as follows:

[0056] ;

[0057] in, u The velocity is expressed in m / s. The pressure drop across the filter cake is expressed in Pa. Standardized pressure, unit is Pa; The compressibility coefficient is the permeability coefficient. The viscosity of the filtrate is expressed in Pa·s. This represents the initial solid content; The initial permeability coefficient is expressed in meters. 2 ; This refers to the solids content of the slurry. t The filtering time is expressed in seconds.

[0058] Step 4: Based on the optimized filter cake characteristic parameters, calculate the filtrate volume, filter cake thickness, and filter cake permeability of the vacuum filtration equipment under specific operating conditions.

[0059] In this embodiment of the invention, the operating conditions of the device are calculated based on specific properties.

[0060] Calculate the filtration time in a filtration cycle of a vacuum filtration device. T Filter area A Vacuum degree, filter cloth mesh size, select the corresponding filter cake characteristic parameter model, and establish the relationship between flow rate and time; calculate the filtrate volume in one filtration cycle, the expression of which is:

[0061] ;

[0062] in, V The volume of the filtrate is in cubic meters (m³). 3 .

[0063] In this embodiment of the invention, the calculation model for the filter cake thickness in step 4 is as follows:

[0064] ;

[0065] in, L The thickness of the filter cake is in meters (m).

[0066] The calculation model for filter cake permeability is as follows:

[0067] ;

[0068] in, k Permeability, in meters (m) 2 .

[0069] Example 1

[0070] Taking monazite slurry from a rare earth resource recycling plant as an example, this study investigated the changes in filtrate volume and filter cake properties when filtering monazite slurry slurry using a 400-mesh PTFE filter cloth under different vacuum conditions. The filtrate viscosity at 25℃ is known to be 0.00157 Pa·s, and the slurry solid content is 0.0849%. The 400-mesh PTFE filter cloth was soaked in deionized water for 2 hours at an ambient temperature of 25℃. 25 mL of deionized water was filtered under gravity, and the required filtration time was recorded. 25 mL of monazite slurry was leached with hydrochloric acid at an ambient temperature of 25℃, and filtration experiments were conducted by adjusting the vacuum degree (20 kPa, 30 kPa, 40 kPa, 50 kPa, 60 kPa, 70 kPa, 80 kPa). The filtrate volume and filtration time were measured, and the results are shown in Table 1.

[0071] The time required to filter 25 mL of deionized water under gravity is 81 s, with an average liquid level of 7 cm. The resistance of the 400-mesh PTFE filter cloth, calculated using a filter cloth resistance model, is... .

[0072] Table 1. Relationship between filtrate volume and required filtration time under different vacuum levels.

[0073]

[0074] The experimental data were fitted using the least squares method to the intermediate pore blockage model, and the fitting results were then substituted to obtain the relationship between filter cake pressure drop and time, as shown in Table 2.

[0075] Table 2 Relationship between filter cake pressure drop and time under different vacuum levels

[0076]

[0077] Based on the relationship between filter cake pressure drop and time under different vacuum levels in Table 2, the filter cake parameter model was substituted into the model and optimized using a genetic algorithm in the MATLAB environment. The average correlation coefficient of the output parameters was calculated. R 2 If the value is greater than or equal to 0.9, the filter cake property parameters are calculated and shown in Table 3.

[0078] Table 3 Filter cake properties

[0079]

[0080] Example 2

[0081] For the horizontal belt vacuum filter involved in patent CN118179125A, the filter cloth precision is 400 mesh, the filtration zone is 3.3 m long and 0.7 m wide, the filter cloth travel speed is 0.005 m / s, and the filtration vacuum degree is 80 kPa. Using this device to filter the monazite dissolution slurry in Example 1, the following operating conditions can be calculated:

[0082] Based on the filter cake characteristic parameter model in Example 1, the following can be calculated:

[0083] ;

[0084] Time of one filtering cycle t 1 = 660 s, effective filtration area A =2.31 m 2 ;

[0085] The volume of filtrate obtained in one filtration cycle is:

[0086] ;

[0087] The filter cake thickness at the outlet is:

[0088] ;

[0089] The filter cake permeability at the outlet is:

[0090] .

[0091] Example 3

[0092] The ZLG25 / 24-N rotary vacuum filter has a filtration area of ​​25 m². 2 With 24 filter discs, a filtration zone angle of 120°, and a filtration vacuum of 60 kPa, the filter cake thickness should be no less than 10 mm when exiting the filtration zone. Using this device to filter the monazite dissolution slurry from Example 1, the maximum disc rotation speed can be calculated as follows:

[0093] Based on the filter cake characteristic parameters in Example 1, let the shortest residence time of a filter disc in the filtration zone be... t 2. When the filter cake thickness at the outlet is 10 mm, that is:

[0094] ;

[0095] Calculation yields: t 2 = 2741 s;

[0096] The maximum rotational speed of the disk is: r = 0.0073 r / min.

[0097] The above methods can be used to determine the filtrate volume, filter cake thickness at the outlet, and filter cake permeability of monazite superior solvent residue hydrochloric acid leaching slurry during one filtration cycle in a certain equipment. This invention can better adapt to changes in different equipment and operating conditions, thereby achieving performance improvement and cost reduction in the filtration process, and has significant industrial application value.

[0098] This invention is applicable to rare earth resource recovery, slurry treatment and other industrial fields involving filtration processes, especially in optimizing filtration processes, improving filtration efficiency, reducing energy consumption and increasing resource recovery rates.

[0099] This invention experimentally determines the physicochemical properties of the leachate and the filtrate volume at different filtration time points. The experimental data are fitted using the least squares method, and a genetic algorithm is employed to optimize the filter cake characteristic parameters, including specific resistance, permeability compressibility coefficient, and initial solid content, to obtain parameters that describe the filter cake layer. These parameters can accurately predict changes in filter cake thickness and permeability over time. By applying the model parameters to vacuum filtration equipment, performance indicators during the filtration process, such as filtrate flow rate and filter cake thickness, can be analyzed and adjusted. This method helps improve filtration efficiency, reduce energy consumption, and overcomes the limitations of traditional vacuum constant pressure measurement techniques, providing a precise basis for the design and operation of filtration equipment. Furthermore, the application of this invention in solid-liquid separation fields such as rare earth resource recovery helps achieve more precise process control, improve resource recovery rates, and thus enhance overall process performance.

[0100] The technical solution provided by this invention includes the following steps: 1) Calculating filter cloth resistance: Performing a gravity filtration experiment with deionized water, measuring the liquid column height and filtration time, and obtaining the filter cloth resistance using the filter cloth resistance calculation formula; 2) Calculating the relationship between filter cake pressure drop and time: Fitting experimental data using a central pore blockage model to obtain the relationship between filter cake pressure drop and time; 3) Optimizing the filter cake characteristic parameter model using a genetic algorithm, by minimizing the mean square error. MSE This method performs a global search and optimizes parameters such as filter cake compressibility, initial permeability coefficient, standardized pressure, and initial solid content to ensure that the calculated and measured values ​​have an average correlation coefficient. Based on the optimized filter cake characteristic parameters, the method calculates the filtrate volume, filter cake thickness, and filter cake permeability of the vacuum filtration equipment under specific operating conditions. This method, based on experimental data and model optimization, provides a theoretical basis for optimizing the vacuum filtration process by accurately analyzing the changes in the parameter properties of the filter cake. It not only accurately describes the characteristics of the filter cake, improves filtration efficiency, and reduces energy consumption, but also provides a more precise process control method for solid-liquid separation processes in fields such as rare earth resource recovery.

[0101] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating filter cake characteristic parameters, characterized in that, The method includes: Step 1: Calculate the filter cloth resistance. Conduct a gravity filtration experiment using deionized water, measure the liquid column height and filtration time, and obtain the filter cloth resistance using the filter cloth resistance calculation formula. Step 2: Calculate the relationship between filter cake pressure drop and time. Fit the experimental data using the intermediate hole blockage model to obtain the relationship between filter cake pressure drop and time. Step 3: Optimize the filter cake characteristic parameter model using a genetic algorithm, through global search and minimizing the mean square error. MSE To achieve the desired result, the experimental data were fitted, and the parameters of filter cake compressibility, initial permeability coefficient, normalized pressure, and initial solids content were optimized to improve the average correlation coefficient. R 2 Greater than or equal to 0.9; Step 4: Based on the optimized filter cake characteristic parameters, calculate the filtrate volume, filter cake thickness, and filter cake permeability of the vacuum filtration equipment under specific operating conditions; The filter cake characteristic parameter model in step 3 is as follows: ； The calculation model for the filter cake thickness in step 4 is as follows: ； The calculation model for filter cake permeability is as follows: ； in, u The velocity is expressed in m / s. The pressure drop across the filter cake is expressed in Pa. Standardized pressure, unit is Pa; The compressibility coefficient is the permeability coefficient. The viscosity of the filtrate is expressed in Pa·s. This represents the initial solid content; The initial permeability coefficient is expressed in meters. 2 ; This refers to the solids content of the slurry. t The filtering time is expressed in seconds. L The thickness of the filter cake is in meters (m). k Permeability, in meters (m) 2 .

2. The method according to claim 1, characterized in that, The formula for calculating the filter cloth resistance in step 1 is: ； in, The filter cloth resistance is expressed in units of... ; The pure water filtration rate of the filter cloth is expressed in m / s. The density of the liquid, in units of . ; Let be the acceleration due to gravity, taken as 9.

81. ; The height of the liquid column is in meters (m). The viscosity of deionized water is expressed in units of... .

3. The method according to claim 1, characterized in that, The expression for the filter cake pressure drop in step 2 is: ； in, Vacuum degree, unit: Pa; m , n These are the model coefficients; A The filter area is in meters (m²). 2 ; The filter cloth resistance is expressed in units of... ; The viscosity of the filtrate is expressed in Pa·s. t The filtering time is expressed in seconds (s).

4. The method according to claim 3, characterized in that Model coefficients m , n The intermediate hole blockage model is satisfied, and its relationship is as follows: ； in, V The volume of the filtrate is in cubic meters (m³). 3 .

5. The method according to claim 1, characterized in that, The genetic algorithm optimization process in step 3 includes selection, crossover, and mutation operations. It optimizes the filter cake characteristic parameters through global search to obtain the best fitting parameters.

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