Method for calculating characteristic parameters of filter cake

Abstract

The invention relates to the technical field of solid-liquid separation, and particularly provides a method for calculating characteristic parameters of a filter cake. The method comprises the following steps: obtaining filter cloth resistance by using a filter cloth resistance calculation formula; fitting experimental data through a middle hole blockage model to obtain a relational expression that the pressure drop of the filter cake changes along with time; optimizing a filter cake characteristic parameter model by using a genetic algorithm, and performing global search and optimizing filter cake compressibility, an initial permeability coefficient, standardized pressure and an initial solid content parameter by minimizing a mean square error, so that a correlation coefficient is averaged between a calculated value and a measured value; based on the optimized filter cake characteristic parameters, the filtrate volume, the filter cake thickness and the filter cake permeability of the vacuum filtration equipment under specific operation conditions are calculated, the method is based on experimental data and model optimization, the filter cake characteristics are accurately described, the filtering efficiency is improved, and the energy consumption is reduced; and a more accurate process control method can be provided for the solid-liquid separation process in the fields of rare earth resource recovery and the like.

Description

Technical Field

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

[0002] As an important by-product in the rare earth resource recovery process, the filtration and separation process of monazite slag hydrochloric acid leachate faces a series of technical challenges. Since the monazite slag hydrochloric acid leachate contains a large amount of fine particles and suspended matter in the slurry, problems such as rapid accumulation of filter cake and rapid decrease of filtrate flow rate often occur during the filtration process. These factors not only lead to low filtration efficiency, but also increase energy consumption and put great pressure on the equipment load. In addition, the formation and characteristics (thickness and permeability) of the filter cake during the filtration process change over time, making the precise control of the filtration process more complicated. Although some filtration technologies have been used to treat similar slurries, due to the special composition and high-concentration particle characteristics of monazite slag hydrochloric acid leachate, the existing filtration equipment has not yet been able to efficiently process such materials on an industrial scale, and there is a lack of effective methods for real-time monitoring and adjustment of filter cake characteristic parameters.

[0003] Vacuum filtration is a commonly used solid-liquid separation technology and is widely used in slurry filtration and liquid cleaning processes. However, when faced with high-concentration suspensions such as monazite slag hydrochloric acid leaching solution, traditional vacuum filtration equipment often cannot provide stable filtration performance, resulting in low filter cake processing efficiency, high equipment maintenance costs, and a lack of scientific basis for the optimization of the filtration process. Summary of the invention

[0004] In view of this, the present invention provides a method for calculating filter cake characteristic parameters, which is used 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: Step 1, calculate the filter cloth resistance, conduct a gravity filtration experiment with deionized water, measure the liquid column height and filtration time, and use the filter cloth resistance calculation formula to obtain the filter cloth resistance; Step 2, calculating the relationship between the filter cake pressure drop and time, fitting the experimental data through the intermediate pore blockage model, and obtaining the relationship between the filter cake pressure drop and time; Step 3: Use genetic algorithm to optimize the filter cake characteristic parameter model by global search and minimize the mean square error MSE As the goal, the experimental data were fitted to optimize the filter cake compressibility, initial permeability coefficient, normalized pressure and initial solid content parameters so that 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.

[0006] Optionally, the filter cloth resistance calculation formula in step 1 is: ; in, is the filter cloth resistance, in units of ; is the pure water filtration rate of the filter cloth, in m / s; is the density of the liquid in ; is the acceleration due to gravity, take 9.81 ; is the height of the liquid column, in m; is the viscosity of deionized water, in units of .

[0007] Optionally, the expression of the filter cake pressure drop in step 2 is: ; in, is the vacuum degree, the unit is Pa; m , n is the model coefficient; A is the filtration area, in m 2 .

[0008] Optionally, the model coefficients m , n The intermediate pore blocking model is satisfied, and the relationship is: ; in, V is the volume of the filtrate, in m 3 .

[0009] Optionally, the genetic algorithm optimization process in step 3 includes selection, crossover and mutation operations, and the filter cake characteristic parameters are optimized through global search to obtain the best fitting parameters.

[0010] Optionally, the filter cake characteristic parameter model in step 3 is: ; in, u is the flow velocity in m / s; is the filter cake pressure drop, in Pa; is the standardized pressure, in Pa; is the permeability compressibility coefficient; is the filtrate viscosity, in Pa·s; is the initial solid content; is the initial permeability coefficient, in m 2 ; is the solid content of the slurry, t is the filtering time, in seconds.

[0011] Optionally, the calculation model of the filter cake thickness in step 4 is: ; in, L is the filter cake thickness, in m; The calculation model of filter cake permeability is: ; in, k is the permeability, in m 2 .

[0012] In the technical solution provided by the present invention, the method comprises calculating the filter cloth resistance, performing a gravity filtration experiment with deionized water, measuring the liquid column height and the filtration time, and obtaining the filter cloth resistance using a filter cloth resistance calculation formula; calculating the relationship between the filter cake pressure drop and time, fitting the experimental data with an intermediate pore blockage model, and obtaining a relationship between the filter cake pressure drop and time; optimizing the filter cake characteristic parameter model using a genetic algorithm, and performing a global search and minimizing the mean square error. MSE As the goal, the experimental data were fitted to optimize the filter cake compressibility, initial permeability coefficient, normalized pressure and initial solid content parameters so that 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 filter cake characteristics, improves the filtration efficiency, and reduces energy consumption, but also provides a more accurate process control method for solid-liquid separation processes in the fields of rare earth resource recovery. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0014] Figure 1 A flow chart of a method for calculating filter cake characteristic parameters provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0015] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0016] It should be clear that the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0017] The terms used in the embodiments of the present invention are only for the purpose of describing specific embodiments, and are not intended to limit the present invention. The singular forms "a", "said" and "the" used in the embodiments of the present invention are also intended to include plural forms, unless the context clearly indicates other meanings.

[0018] It should be understood that the term "and / or" used in this article is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0019] The word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)", depending on the context.

[0020] Aiming at the shortcomings of the prior art in the vacuum filtration process of monazite slag hydrochloric acid leaching solution, the present invention proposes a method for calculating filter cake characteristic parameters based on experimental data and model optimization, and combines the least squares method and genetic algorithm optimization technology to determine the filter cake layer parameters and use them for equipment operating condition calculation.

[0021] The present invention firstly establishes a filter cake characteristic parameter model in the vacuum filtration process of monazite slag hydrochloric acid leaching solution, obtains the filter cloth resistance by deionized water filtration calculation, fits the experimental data by the least square method, and optimizes the parameters in the filter cake characteristic parameter model in combination with the genetic algorithm, and obtains the parameters that can describe the filter cake thickness and permeability. The parameters can be used to calculate the filtrate volume and the properties of the filter cake layer at the outlet under the specific operating conditions of a certain equipment.

[0022] Figure 1 A flow chart of a method for calculating filter cake characteristic parameters provided by an embodiment of the present invention, such as Figure 1 As shown, the method includes: Step 1: Calculate the filter cloth resistance. Perform a gravity filtration experiment with deionized water, measure the liquid column height and filtration time, and use the filter cloth resistance calculation formula to obtain the filter cloth resistance.

[0023] In the embodiment of the present invention, the filter cloth resistance calculation formula in step 1 is: ; in, is the filter cloth resistance, in units of ; is the pure water filtration rate of the filter cloth, in m / s; is the density of the liquid in ; is the acceleration due to gravity, take 9.81 ; is the height of the liquid column, in m; is the viscosity of deionized water, in units of .

[0024] Step 2: Calculate the relationship between the filter cake pressure drop and time, fit the experimental data through the intermediate pore blockage model, and obtain the relationship between the filter cake pressure drop and time.

[0025] After adding monazite slag hydrochloric acid leaching slurry, filtration experiments were carried out under different vacuum degrees. The experimental data were fitted with the intermediate pore blockage model using the least squares method, and the model coefficients were calculated. The model coefficients were substituted into the expression of filter cake pressure drop to obtain the relationship between filter cake pressure drop and time.

[0026] In the embodiment of the present invention, the expression of the filter cake pressure drop in step 2 is: ; in, is the vacuum degree, the unit is Pa; m , n is the model coefficient; A is the filtration area, in m 2 .

[0027] In the embodiment of the present invention, the model coefficient m , n The intermediate pore blocking model is satisfied, and the relationship is: ; in, V is the volume of the filtrate, in m 3 .

[0028] Step 3: Use genetic algorithm to optimize the filter cake characteristic parameter model by global search and minimize the mean square error MSE As the goal, the experimental data were fitted to optimize the filter cake compressibility, initial permeability coefficient, normalized pressure and initial solid content parameters so that the average correlation coefficient R 2 Greater than or equal to 0.9.

[0029] In the embodiment of the present invention, the genetic algorithm optimization process in step 3 includes selection, crossover and mutation operations, and the filter cake characteristic parameters are optimized through global search to obtain the best fitting parameters.

[0030] Substitute the relationship between the filter cake pressure drop and time in step 2 into the filter cake characteristic parameter model, and optimize it through genetic algorithm, including selection, crossover and mutation operations, to perform global search and multi-generation iterative optimization on the filter cake characteristic parameter model. MSE Minimization is the goal, and the optimal parameter combination is selected. If the output parameters do not meet R 2 If it is greater than or equal to 0.9, the genetic algorithm optimization is performed again; the permeability compressibility coefficient is obtained , initial permeability coefficient , Standardized pressure , initial solid content .

[0031] In the embodiment of the present invention, the filter cake characteristic parameter model in step 3 is: ; in, u is the flow velocity in m / s; is the filter cake pressure drop, in Pa; is the standardized pressure, in Pa; is the permeability compressibility coefficient; is the filtrate viscosity, in Pa·s; is the initial solid content; is the initial permeability coefficient, in m 2 ; is the solid content of the slurry, t is the filtering time, in seconds.

[0032] 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.

[0033] In an embodiment of the present invention, the device operating condition is calculated based on the specific property.

[0034] Calculation of vacuum filtration equipment, based on the filtration time in a filtration cycle in a certain equipment T , filtration area A , vacuum degree, filter cloth mesh number, select the corresponding filter cake characteristic parameter model, establish the relationship between flow rate and time; calculate the filtrate volume in a filtration cycle, the expression is: ; in, V is the volume of the filtrate, in m 3 .

[0035] In the embodiment of the present invention, the calculation model of the filter cake thickness in step 4 is: ; in, L is the filter cake thickness, in m; The calculation model of filter cake permeability is: ; in, k is the permeability, in m 2 .

[0036] Example 1 Taking the monazite slag from a rare earth resource recovery plant as an example, the changes in the filtrate volume and filter cake properties when using a 400-mesh PTFE filter cloth to filter the monazite slag slurry under different vacuum conditions were investigated. It is known that the filtrate viscosity at 25°C is 0.00157 Pa·s and the solid content of the slurry is 0.0849. The 400-mesh PTFE filter cloth was soaked in deionized water for 2 hours and then used for standby use. The ambient temperature was 25°C. 25 mL of deionized water was filtered under gravity conditions, and the required filtration time was recorded. 25 mL of monazite slag hydrochloric acid leaching slurry was taken, the ambient temperature was 25°C, and the vacuum degree (20 kPa, 30 kPa, 40 kPa, 50 kPa, 60 kPa, 70 kPa, 80 kPa) was adjusted to perform a filtration experiment, and the filtrate volume and filtration time were measured. The results are shown in Table 1.

[0037] The time required to filter 25 mL of deionized water under gravity conditions is 81 seconds, and the average liquid level is 7 cm. The resistance of the 400-mesh PTFE filter cloth can be calculated using the filter cloth resistance model. .

[0038] Table 1 Relationship between filtrate volume and required filtration time under different vacuum degrees

[0039] The least square method was used to fit the experimental data to the intermediate pore blockage model, and the fitting results were substituted into the relationship between the filter cake pressure drop and time, as shown in Table 2.

[0040] Table 2 Relationship between filter cake pressure drop and time under different vacuum degrees

[0041] According to the relationship between filter cake pressure drop and time under different vacuum degrees in Table 2, the filter cake parameter model was substituted and optimized by genetic algorithm in MATLAB environment, and the average correlation coefficient of the output parameter calculation was R 2 Greater than or equal to 0.9, the filter cake property parameters are calculated as shown in Table 3.

[0042] Table 3 Filter cake property parameters

[0043] Example 2 For the horizontal belt vacuum filter involved in patent CN118179125A, the filter cloth precision is 400 mesh, the filtration area 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. The device is used to filter the monazite slag slurry in Example 1, and the following operating conditions can be calculated: According to the filter cake characteristic parameter model calculation in Example 1, it can be obtained: ; Time of one filtration cycle t 1 =660 s, effective filtration area A =2.31 m 2 ; The volume of filtrate obtained in one filtration cycle is: ; The filter cake thickness at the outlet is: ; The filter cake permeability at the outlet is: .

[0044] Example 3 For ZLG25 / 24-N rotary table vacuum filter, the filtration area is 25 m 2, the number of filter discs is 24, the angle of the filter area is 120°, the vacuum degree of filtration is 60 kPa, and the thickness of the filter cake is not less than 10 mm when leaving the filter area. The device is used to filter the monazite slag slurry in Example 1, and the maximum disc speed can be calculated as: According to the filter cake characteristic parameters in Example 1, the shortest residence time of a filter disc in the filtration zone is t 2 , when the filter cake thickness at the outlet is 10 mm, that is: ; The calculation can be obtained: t 2 =2741 s; Then the maximum rotation speed of the disc is: r = 0.0073 r / min.

[0045] The above method can be used to obtain the filtrate volume, filter cake thickness at the outlet and filter cake permeability of monazite slag hydrochloric acid leaching slurry in a filtration cycle when vacuum filtration is performed on a certain device. The present 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 important industrial application value.

[0046] The present invention is applicable to rare earth resource recovery, slurry treatment and other industrial fields involving filtration processes, and is particularly widely used in optimizing filtration processes, improving filtration efficiency, reducing energy consumption and increasing resource recovery rates.

[0047] The present invention experimentally determines the physicochemical properties of the leachate and the filtrate volume at different filtration time points, fits the experimental data using the least squares method, and optimizes the filter cake characteristic parameters using a genetic algorithm, the filter cake characteristic parameters include specific resistance, permeability compressibility coefficient, initial solid content, etc., to obtain characteristic parameters that can describe the filter cake layer, and these parameters can accurately predict the changes in filter cake thickness and permeability over time. By applying the model parameters to the vacuum filtration equipment, performance indicators such as filtrate flow rate and filter cake thickness in the filtration process can be analyzed and adjusted. This method helps to improve filtration efficiency and reduce energy consumption, breaks through the limitations of traditional vacuum constant pressure measurement technology, and provides an accurate basis for the design and operation of filtration equipment. In addition, the application of the present invention in the field of solid-liquid separation such as rare earth resource recovery helps to achieve more accurate process control, improve resource recovery rate, and thus improve overall process performance.

[0048] In the technical solution provided by the present invention, the method comprises calculating the filter cloth resistance, performing a gravity filtration experiment with deionized water, measuring the liquid column height and the filtration time, and obtaining the filter cloth resistance using the filter cloth resistance calculation formula; calculating the relationship between the filter cake pressure drop and time, fitting the experimental data with the intermediate pore blockage model, and obtaining the relationship between the filter cake pressure drop and time; using a genetic algorithm to optimize the filter cake characteristic parameter model, and by minimizing the mean square error MSE , conduct global search and optimize the filter cake compressibility, initial permeability coefficient, normalized pressure and initial solid content parameters to make the calculated value have an average correlation coefficient with the measured value; 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. 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 filter cake characteristics, improves filtration efficiency, and reduces energy consumption, but also provides a more accurate process control method for solid-liquid separation processes in fields such as rare earth resource recovery.

[0049] 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 in the scope of protection of the present invention.

Claims

1. A method for calculating filter cake characteristic parameters, characterized in that: The method comprises: Step 1, calculate the filter cloth resistance, conduct a gravity filtration experiment with deionized water, measure the liquid column height and filtration time, and use the filter cloth resistance calculation formula to obtain the filter cloth resistance; Step 2, calculating the relationship between the filter cake pressure drop and time, fitting the experimental data through the intermediate pore blockage model, and obtaining the relationship between the filter cake pressure drop and time; Step 3: Use genetic algorithm to optimize the filter cake characteristic parameter model by global search and minimize the mean square error MSE As the goal, the experimental data were fitted to optimize the filter cake compressibility, initial permeability coefficient, normalized pressure and initial solid content parameters so that 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.

2. The method according to claim 1, characterized in that The calculation formula of the filter cloth resistance in step 1 is: ； in, is the filter cloth resistance, in units of ; is the pure water filtration rate of the filter cloth, in m / s; is the density of the liquid in ; is the acceleration due to gravity, take 9.81 ; is the height of the liquid column, in m; is the viscosity of deionized water, in units of .

3. The method according to claim 1, characterized in that The expression of the filter cake pressure drop in step 2 is: ； in, is the vacuum degree, the unit is Pa; m , n is the model coefficient; A is the filtration area, in m 2 .

4. The method according to claim 3, characterized in that Model coefficients m , n The intermediate pore blocking model is satisfied, and the relationship is: ； in, V is the volume of the filtrate, in m 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, and the filter cake characteristic parameters are optimized through global search to obtain the best fitting parameters.

6. The method according to claim 1, characterized in that The filter cake characteristic parameter model in step 3 is: ； in, u is the flow velocity in m / s; is the filter cake pressure drop, in Pa; is the standardized pressure, in Pa; is the permeability compressibility coefficient; is the filtrate viscosity, in Pa·s; is the initial solid content; is the initial permeability coefficient, in m 2 ; is the solid content of the slurry, t is the filtering time, in seconds.

7. The method according to claim 1, characterized in that The calculation model of the filter cake thickness in step 4 is: ； in, L is the filter cake thickness, in m; The calculation model of filter cake permeability is: ； in, k is the permeability, in m 2 .

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