An iterative optimization method for rheological parameters of a yield stress viscous fluid
By using an iterative optimization method, the influence of the slug layer on shear flow was corrected, the range of yield stress values was calculated, the rheological parameter error caused by the slug layer was solved, and high-precision rheological parameter measurement was achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SOUTHEAST UNIV
- Filing Date
- 2023-05-19
- Publication Date
- 2026-06-23
AI Technical Summary
Existing technologies, when measuring viscous fluids with yield stress, suffer from significant errors in calculating shear deformation rate and shear stress due to the presence of slug layers, thus affecting the accuracy of rheological parameters.
An iterative optimization method was adopted, which calculated the upper and lower limits of the yield stress, corrected the shear radius and shear deformation rate, and used the Herschel-Bulkley model to fit the rheological parameters, gradually reducing the error until the preset threshold was reached.
This improves the accuracy and reliability of rheological parameter calculations, reduces errors, and ensures accurate characterization of rheological properties.
Smart Images
Figure CN116822398B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of materials engineering testing technology, specifically relating to an iterative optimization method for the rheological parameters of viscous fluids with yield stress. Background Technology
[0002] Accurate measurement of material rheological parameters and characterization of their rheological properties are of paramount importance for their production, processing, and applications. Coaxial rotating rheometers are commonly used to measure the rheological properties of viscous fluids. When the rotor rotates, it causes shearing of the fluid. Assuming the fluid is completely sheared, the shear deformation rate can be calculated based on the rotor's rotational speed, and the shear stress within the fluid can be calculated based on the torque on the rotor. By applying a suitable rheological model based on the relationship between the fluid's shear deformation rate and shear stress, the fluid's rheological parameters can be fitted.
[0003] Within a fluid, the shear deformation rate is high near the rotor, corresponding to high shear stress; conversely, the shear deformation rate is low further from the rotor, resulting in low shear stress. When the shear stress within the fluid is less than its yield stress, the fluid will not undergo shear deformation, and a static region exists far from the rotor, known as a throttle layer. Figure 2 As shown, the presence of a slug layer causes the actual shear range of the fluid to be smaller than the illusory shear range. Using the current conversion formula, the shear deformation rate directly calculated based on the rotor speed is smaller than the actual shear deformation rate, resulting in errors between the fitted rheological parameters and the true rheological parameters. The larger the slug layer, the greater the error in the above rheological parameters, severely affecting the accurate characterization of fluid rheological properties.
[0004] For viscous fluids with yield stress, based on the measurement results of a coaxial rotating rheometer, we developed an iterative calculation method for rheological parameters. This method considers the influence of the plug layer caused by yield stress on the shear flow within the fluid, accurately calculates the actual shear deformation rate of the fluid, and thus improves the accuracy of the rheological parameter calculation results and the reliability of the rheological performance characterization conclusions. Summary of the Invention
[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide an iterative optimization method for the rheological parameters of viscous fluids with yield stress.
[0006] To achieve the above objectives, the present invention is implemented using the following technical solution:
[0007] This invention provides an iterative optimization method for the rheological parameters of viscous fluids with yield stress, comprising the following steps:
[0008] Step S1: Obtain the shear parameters of the coaxial rotating rheometer, including the sample container radius, rotor radius, rotor speed, and rotor torque;
[0009] Step S2: Calculate the shear stress and shear deformation rate of the fluid on the rotor surface using the shear parameters;
[0010] Step S3: Select the minimum value of the shear stress to calculate the lower limit of the yield stress of the viscous fluid to be tested, and use the shear stress and shear deformation rate to fit the Herschel-Bulkley model to obtain the upper limit of the yield stress of the viscous fluid to be tested.
[0011] Step S4: Take the average of the upper limit of the yield stress and the lower limit of the yield stress as the predicted yield stress of the viscous fluid to be tested, and calculate the shear radius corresponding to each rotor speed.
[0012] Step S5: Recalculate and correct the shear deformation rate of the fluid on the rotor surface at each rotor speed using the shear radius corresponding to each rotor speed;
[0013] Step S6: Refit and correct the yield stress of the viscous fluid under test using shear stress and corrected shear deformation rate, and redetermine the upper limit and lower limit of yield stress based on the relationship between the predicted yield stress and the corrected yield stress.
[0014] Step S7: Repeat steps S4 to S6 until the absolute difference between the predicted yield stress and the corrected yield stress is less than the preset threshold. Then stop the iteration and use the fitting parameters of the final Herschel-Bulkley model as the rheological parameters of the viscous fluid to be tested.
[0015] Further, iterative calculations are performed, including the following steps: determining whether the absolute difference between the predicted yield stress and the corrected yield stress is greater than a preset threshold.
[0016] 1) If the absolute difference is greater than the preset threshold, further determine the relationship between the predicted yield stress and the corrected yield stress:
[0017] When the predicted yield stress is greater than the corrected yield stress, the upper limit of the yield stress of the viscous fluid under test is updated to the predicted yield stress.
[0018] When the predicted yield stress is not greater than the corrected yield stress, the lower limit of the yield stress value of the viscous fluid to be tested is updated to the predicted yield stress.
[0019] 2) If the absolute difference between the predicted yield stress and the corrected yield stress is less than the preset threshold, the iteration stops.
[0020] Furthermore, the formula for calculating the shear stress is expressed as follows:
[0021]
[0022] In the formula, τ is the shear stress on the outer surface of the rotor (Pa), T[i] is the rotor torque acting on the rotor (N·m), where i represents the i-th measurement data, R1 is the rotor radius (m), and H is the height of the effective shear portion of the rotor (m);
[0023] Furthermore, in step S2, assuming the viscous fluid is in a state of complete shear, i.e., the radius of the sample container is taken as the shear radius of the viscous fluid in a state of complete shear, the formula for calculating the shear deformation rate is expressed as:
[0024]
[0025] In the formula, The shear deformation rate (s) of the fluid on the outer surface of the rotor -1 R2 is the radius (m) of the sample container of the rheometer, and ω[i] is the rotor speed.
[0026] Furthermore, the minimum value of the shear stress is selected to calculate the lower limit of the yield stress of the viscous fluid under test, expressed by the following formula:
[0027]
[0028] In the formula, τ 0，1 τ is the lower limit of the yield stress value. min [i] represents the minimum value in the calculated shear stress array;
[0029] The shear stress τ[i] and shear deformation rate are obtained using the above calculations. The upper limit τ of the yield stress of the fluid under test is obtained based on the fitting of rheological model parameters. 0,2 .
[0030] Furthermore, the shear radius corresponding to each rotor speed is calculated using the predicted yield stress, and the calculation formula is expressed as follows:
[0031]
[0032] In the formula, R s [i] is the shear radius, and τ[i] is the shear stress;
[0033] Considering the influence of the slug layer on shear flow, using the shear radius R s [i] Calculate the shear deformation rate of the fluid on the rotor surface corresponding to each corrected rotor speed. The calculation formula is expressed as:
[0034]
[0035] Furthermore, the preset threshold value ranges from 0 to 0.001.
[0036] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:
[0037] The iterative optimization method for rheological parameters of viscous fluids with yield stress provided by this invention fully considers the influence of the slug layer caused by the fluid yield stress on the fluid shear flow during the measurement of fluid rheological properties using a coaxial rotating rheometer. It uses an iterative calculation method to continuously correct rheological parameters such as the shear radius range and the fluid shear deformation rate of the viscous fluid, which can improve the accuracy and reliability of rheological parameter calculation. Moreover, the method has low requirements for equipment and materials, is easy to operate, and has strong versatility. It is of great significance for accurately characterizing and evaluating the rheological properties of fluids. Attached Figure Description
[0038] Figure 1 A flowchart illustrating the iterative optimization method for yield stress viscous fluid rheological parameters provided in an embodiment of the present invention;
[0039] Figure 2 This is a schematic diagram of fluid shearing in a coaxial rotating rheometer.
[0040] Figure 3 This is an example of setting the rotor speed during the rheological testing process in a specific embodiment;
[0041] Figure 4 This is a comparison chart of the fluid shear range calculated based on ideal assumptions and the present invention in a specific embodiment;
[0042] Figure 5 This is a comparison chart of rheological curves calculated based on ideal assumptions and the present invention in a specific embodiment. Detailed Implementation
[0043] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.
[0044] Example
[0045] like Figure 1 As shown in the figure, an iterative optimization method for the rheological parameters of a viscous fluid with yield stress is provided in this embodiment of the invention. The operation steps are detailed below:
[0046] Step 1: Set the rotor speed of the coaxial rotary rheometer and use the rheometer to measure the rheological properties of the fluid to be tested according to the predetermined rotation process;
[0047] Step 2: Extract the results measured by the rheometer to obtain the rotor speed ω[i] and the torque T[i] acting on the rotor;
[0048] Step 3: Calculate the shear stress in the fluid on the rotor surface based on the torque acting on the rotor;
[0049] Step 4: Assuming the fluid is completely sheared, calculate the shear deformation rate of the fluid on the rotor surface;
[0050] Step 5: Use the calculated shear stress τ[i] and shear deformation rate This case study uses the Herschel-Bulkley model, a commonly used rheological model, to fit the rheological parameters, obtaining the upper limit τ of the yield stress of the fluid under test. 0,2 ;
[0051] Step 6: Select the minimum value τ from the shear stress array obtained in step S3. min The lower limit τ of the estimated yield stress of the fluid to be tested. 0,1 ;
[0052] Step 7: Take the average of the upper and lower limits of the yield stress value. As the predicted yield stress of the fluid under test;
[0053] Step 8: Based on the calculated predicted yield stress, calculate the shear radius R corresponding to each rotational speed. s ;
[0054] Step 9: Based on the shear radius corresponding to each rotational speed calculated in step S8, and considering the influence of the plug layer on the shear flow, recalculate the shear deformation rate of the rotor surface fluid corresponding to each rotational speed.
[0055] Step 10: Use the shear stress τ[i] and the corrected shear deformation rate Refit and correct the yield stress τ0 of the fluid under test;
[0056] Step 11: Compare the corrected yield stress τ0 with the predicted yield stress. The upper or lower limit of the yield stress is updated based on the corrected yield stress, thus narrowing the range of yield stress values.
[0057] Step 12: Repeat steps 7 through 11 until the corrected yield stress τ0 and the predicted yield stress are found. The absolute difference between them falls within the allowed preset threshold range;
[0058] Step 13: The fitting parameters of the Herschel-Bulkley model are used as the rheological parameters of the viscous fluid to be tested.
[0059] The working principle of the iterative optimization method for yield stress viscous fluid rheological parameters of the present invention will be described below in conjunction with the usage of specific embodiments.
[0060] Freshly mixed cement paste was prepared as a viscous fluid to be tested, exhibiting yield stress.
[0061] Pour the prepared fresh cement paste into the sample container of the rheometer, such as... Figure 2 As shown. Specifically, the sample container used has a diameter of 10cm, and a cross-shaped paddle rotor is selected. The diameter of the rotor used is 3cm, and the height of the effective shearing cylindrical part is 6cm.
[0062] The rheometer performs rheological performance tests according to a predetermined rotational procedure. The preset rotational procedure uses a speed control mode, such as... Figure 3 The process is divided into three stages: the pre-shearing stage, the static stage, and the step deceleration stage.
[0063] Specifically, during the pre-shearing stage, the rotor accelerates from a standstill to 100 rpm in 10 seconds, and then decelerates from 100 rpm to a stop in another 10 seconds. After the cement paste is left to stand for 25 seconds, it enters the stepped acceleration and deceleration stage.
[0064] The step-by-step process sets six speeds: 40 rpm, 30 rpm, 20 rpm, 15 rpm, 10 rpm, and 5 rpm, with each step lasting 10 seconds.
[0065] The rheometer records the rotor speed and torque at each deceleration stage. The shear stress on the rotor surface is calculated using the following formula:
[0066]
[0067] In the formula: τ is the shear stress on the outer surface of the rotor (Pa), T is the torque on the rotor (N·m), and g is the acceleration due to gravity (m / s²). 2 R1 is the rotor radius (m), and H is the height of the cylindrical part of the rotor (m).
[0068] The experimental data of rotational speed, torque, and shear stress obtained by the rheometer are shown in Table 1 below.
[0069] Table 1
[0070]
[0071] Assuming the viscous fluid is completely sheared, the shear deformation rate of the fluid on the rotor surface is calculated using the following formula;
[0072]
[0073] In the formula: The shear deformation rate (s) of the fluid on the outer surface of the rotor -1 R2 is the radius (m) of the sample container of the rheometer.
[0074] The shear stress τ[i] and shear deformation rate are obtained using the above calculations. The upper limit τ of the yield stress of the fluid under test was obtained by fitting the parameters of the Herschel-Bulkley model. 0,2 .
[0075] It should be noted that the upper limit τ for calculating the yield stress of the fluid under test is... 0,2 When the influence of the slug layer on the actual shear range is ignored, the shear deformation rate calculated based on the ideal assumptions is less than the actual shear deformation rate at low-speed shear. The yield stress obtained by fitting is greater than the actual yield stress. The corresponding yield stress is used as the upper limit of the fluid yield stress.
[0076] At the same time, the minimum value τ in the calculated shear stress array is selected. min The lower limit τ of the yield stress of the fluid to be tested can be estimated by the following formula. 0,1 ;
[0077]
[0078] The lower limit τ for calculating the yield stress of the fluid under test is as follows. 0,1 When the rotor torque is at its minimum, the fluid is just in a state of complete shearing. In all subsequent measurements, the fluid is in a state of complete shearing, which meets the rational assumption. The yield stress corresponding to this point is taken as the lower limit of the fluid yield stress.
[0079] The average of the upper and lower limits of the yield stress is taken as the predicted yield stress of the fluid under test. Based on the predicted yield stress Calculate the shear radius R corresponding to each rotor speed using the following formula. s The formula is expressed as follows.
[0080]
[0081] Based on the shear radius R calculated above s Meanwhile, considering the influence of the slug layer on the shear flow, the shear deformation rate of the rotor surface fluid corresponding to each rotor speed is recalculated according to the following formula, which is expressed as follows.
[0082]
[0083] Using shear stress τ[i] and the corrected shear deformation rate again The Herschel-Bulkley model was re-parameterized to correct the yield stress τ0 of the fluid under test. Simultaneously, the corrected yield stress τ0 was compared with the predicted yield stress. The upper or lower limit of the yield stress value is updated by replacing the upper limit or lower limit of the yield stress value with the corrected yield stress, so as to narrow the range of yield stress values.
[0084] The update replacement principle is as follows: determine whether the absolute difference between the predicted yield stress and the corrected yield stress is greater than a preset threshold.
[0085] 1) If the absolute difference is greater than the preset threshold, further determine the relationship between the predicted yield stress and the corrected yield stress:
[0086] When the predicted yield stress is greater than the corrected yield stress, the upper limit of the yield stress of the viscous fluid under test is updated to the predicted yield stress.
[0087] When the predicted yield stress is not greater than the corrected yield stress, the lower limit of the yield stress value of the viscous fluid to be tested is updated to the predicted yield stress.
[0088] 2) If the absolute difference between the predicted yield stress and the corrected yield stress is less than the preset threshold, the iteration stops.
[0089] As shown in Table 2 below, the above iterative calculations for correcting the shear radius and yield stress are repeated, gradually narrowing the range of yield stress values until the corrected yield stress τ0 and the predicted yield stress are reached. The absolute difference between them is less than 0.001.
[0090] Table 2
[0091]
[0092] At this point, the fitting parameters of the final Herschel-Bulkley model are used as the rheological parameters of the viscous fluid to be measured.
[0093] In this embodiment, assuming the freshly mixed cement paste is completely sheared, the shear radius under ideal conditions is 50 mm. The technical solution in this embodiment employs an iterative optimization method for the yield stress viscous fluid rheological parameters.
[0094] In this embodiment, the actual shear radius of the sample was also measured, and the calculated shear radius, the ideal shear radius, and the actual shear radius were compared. Figure 4 As shown.
[0095] The data in the figure shows that the lower the shear rate, the greater the slug layer thickness, and the smaller the actual shear radius of the sample. The results calculated by this method are consistent with the actual measurement patterns. Using the method of this invention, the slug phenomenon during the testing of the rheological properties of the sample can be reflected, and the approximate actual shear radius of the sample after the influence of slug flow can be obtained.
[0096] This embodiment calculates the actual shear deformation rate of freshly mixed cement paste at various rotational speeds based on the corrected shear radius, obtaining a rheological curve that considers the influence of the plug layer. A comparison is made between the rheological curve obtained using the optimization method of this invention and a rheological curve based on ideal assumptions and actual measurements. Figure 5 As shown.
[0097] Currently, existing technologies often employ rheological curves based on ideal conditions, which show significant differences from actual rheological curves at lower shear strain rates. As the shear rate decreases, the slug layer thickens, the shear radius of the sample decreases, and the influence of the slug layer on the calculated shear deformation rate increases. Ignoring the influence of the slug layer will lead to an underestimation of the calculated shear deformation rate at the same rotational speed, causing the rheological curve based on ideal conditions to shift towards lower shear deformation. The rheological curve obtained by the proposed method almost coincides with the actual rheological curve.
[0098] Based on the Herschel-Bulkley model, the rheological curves of cement paste were fitted using existing ideal conditions, the calculation method proposed in this invention, and experimental results, respectively. The fitting parameters are shown in Table 3 below.
[0099] Table 3
[0100]
[0101] Since ideal assumptions are difficult to guarantee in actual experiments, there is a significant error between the rheological parameters obtained based on these assumptions and the actual rheological parameters. As shown in the table above, the error between the rheological parameters fitted based on the ideal assumptions and the measured rheological parameters reaches a maximum of 111.4%, while the error between the rheological parameters fitted by this invention and the measured rheological parameters is only 20.6%. To a large extent, using the calculation method proposed in this invention can significantly improve the accuracy of rheological parameters.
[0102] It should be noted that the Herschel-Bulkley model, which is more suitable for fresh cement paste, was selected in this case. The method of this invention is also applicable to other rheological models, such as the Bingham model and the Modified Bingham model, which can significantly reduce the calculation error of rheological parameters.
[0103] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. An iterative optimization method for rheological parameters of a viscous fluid with yield stress, characterized in that, Includes the following steps: Step S1: Obtain the shear parameters of the coaxial rotating rheometer, including the sample container radius, rotor radius, rotor speed, and rotor torque; Step S2: Calculate the shear stress and shear deformation rate of the fluid on the rotor surface using the shear parameters; Step S3: Select the minimum value of the shear stress to calculate the lower limit of the yield stress of the viscous fluid to be tested. Use the shear stress and shear deformation rate to fit the rheological model to obtain the upper limit of the yield stress of the viscous fluid to be tested. Step S4: Take the average of the upper limit and lower limit of the yield stress as the predicted yield stress of the viscous fluid to be tested, and calculate the shear radius corresponding to each rotor speed. Step S5: Recalculate and correct the shear deformation rate of the fluid on the rotor surface at each rotor speed using the shear radius corresponding to each rotor speed; Step S6: Refit and correct the yield stress of the viscous fluid under test using shear stress and corrected shear deformation rate, and redetermine the upper limit and lower limit of yield stress based on the relationship between the predicted yield stress and the corrected yield stress. Step S7: Repeat steps S4 to S6 until the absolute difference between the predicted yield stress and the corrected yield stress is less than the preset threshold. Then stop the iteration and use the final fitted parameters as the rheological parameters of the viscous fluid to be tested.
2. The iterative optimization method for yield stress viscous fluid rheological parameters according to claim 1, characterized in that, The iterative calculation includes the following steps: determining whether the absolute difference between the predicted yield stress and the corrected yield stress is greater than a preset threshold. 1) If the absolute difference is greater than the preset threshold, further determine the relationship between the predicted yield stress and the corrected yield stress: When the predicted yield stress is greater than the corrected yield stress, the upper limit of the yield stress of the viscous fluid under test is updated to the predicted yield stress. When the predicted yield stress is not greater than the corrected yield stress, the lower limit of the yield stress value of the viscous fluid to be tested is updated to the predicted yield stress. 2) If the absolute difference between the predicted yield stress and the corrected yield stress is less than the preset threshold, the iteration stops.
3. The iterative optimization method for yield stress viscous fluid rheological parameters according to claim 2, characterized in that, The formula for calculating the shear stress is as follows: In the formula, τ is the shear stress (Pa) on the outer surface of the rotor, T[i] is the rotor torque (N·m) acting on the rotor, where i represents the i-th measurement data, R1 is the rotor radius (m), and H is the height of the effective shear portion of the rotor (m).
4. The iterative optimization method for yield stress viscous fluid rheological parameters according to claim 3, characterized in that, In step S2, assuming the viscous fluid is in a state of complete shear, i.e., the radius of the sample container is taken as the shear radius under the complete shear state of the viscous fluid, the formula for calculating the shear deformation rate is expressed as: In the formula, The shear deformation rate (s) of the fluid on the outer surface of the rotor -1 R2 is the radius (m) of the sample container of the rheometer, and ω[i] is the rotor speed.
5. The iterative optimization method for yield stress viscous fluid rheological parameters according to claim 4, characterized in that, The minimum value of the shear stress is selected to calculate the lower limit of the yield stress of the viscous fluid under test, and the calculation formula is expressed as follows: In the formula, τ 0，1 τ is the lower limit of the yield stress value. min [i] represents the minimum value in the calculated shear stress array; The shear stress τ[i] and shear deformation rate are obtained using the above calculations. The upper limit τ of the yield stress of the fluid under test is obtained based on the fitting of rheological model parameters. 0,2 .
6. The iterative optimization method for yield stress viscous fluid rheological parameters according to claim 5, characterized in that, The shear radius corresponding to each rotor speed is calculated using the predicted yield stress, and the calculation formula is expressed as follows: In the formula, R s [i] is the shear radius, and τ[i] is the shear stress; Considering the influence of the slug layer on shear flow, using the shear radius R s [i] Calculate the shear deformation rate of the fluid on the rotor surface corresponding to each corrected rotor speed. The calculation formula is expressed as:
7. The iterative optimization method for yield stress viscous fluid rheological parameters according to claim 1, characterized in that, The preset threshold value ranges from 0 to 0.001.