A method for designing the number of stages of a cascade adsorption process

Abstract

The present invention discloses a method for designing the number of stages of a cascade adsorption process. The present invention makes the design of the number of stages of the cascade adsorption process forward-looking, and can avoid the waste of equipment and adsorbent usage costs caused by excessive number of stages; the liquid output of the last stage can stably meet the target substance concentration requirement without adding a concentration feedback system; the minimum required number of stages can be obtained through bench-scale tests and calculations, which is convenient and fast.

Description

Technical Field

[0001] The present invention relates to the technical field of cascade adsorption processes, and in particular, to a method for designing the number of stages of a cascade adsorption process. Background Art

[0002] In the cascade adsorption process, the liquid to be treated is introduced into the first column. After a certain amount of the target substance is adsorbed by the adsorbent, the effluent is then introduced into the next stage, and so on in series for multiple stages. This can achieve that the limit value of the concentration of the target substance in the effluent of the last stage is much lower than the concentration limit that can be achieved by other traditional processes such as precipitation. Therefore, it has broad application prospects in the fields of wastewater treatment, hydrometallurgy, etc. In existing cascade adsorption process design projects, the design of the number of stages mostly relies on experience and lacks foresight. To ensure that the concentration of the target substance in the effluent of the last stage meets the requirements, the number of stages is usually overdesigned, resulting in excessive investment in equipment and adsorbent usage and causing waste. And a target substance concentration detection system needs to be adopted at the last stage, and the actual number of stages used is adjusted temporarily through the feedback of the concentration result. Summary of the Invention

[0003] The present invention aims to solve at least one of the technical problems in the related art to some extent.

[0004] For this reason, an embodiment of the present invention proposes a method for designing the number of stages of a cascade adsorption process. The method of the present invention can be used for preparing an engineering solution and provides a basis for making or optimizing an engineering design solution.

[0005] The present invention proposes a method for designing the number of stages of a cascade adsorption process, including the following steps:

[0006] (1) Conduct a single-stage column saturation adsorption test: Start the adsorption test and start timing simultaneously. Samples of the adsorption stock solution and the post-adsorption solution are taken at unit time intervals, and the concentration of the target substance in the post-adsorption solution is analyzed until the concentration of the target substance in the post-adsorption solution is basically unchanged, which is regarded as reaching equilibrium.

[0007] When starting the adsorption test, a certain volume of adsorbent is loaded into the experimental column, and the liquid to be treated is used as the adsorption stock solution and passes through at a selected feed liquid column passing rate. Among them, there is no specific requirement for the volume of the adsorbent, but the height-diameter ratio of the adsorbent is generally similar to that required for the enlarged design. The column passing rate is determined according to the required rate for the enlarged design, and the column passing rate does not exceed 10 BV / h. The adsorption stock solution is the liquid to be treated, and the time interval is 0.5 - 2 h.

[0008] (2) Calculate the amount of target substance adsorbed per unit time and the initial remaining capacity b0 of the adsorbent, and calculate the stable interval average c of the ratio of the amount of target substance adsorbed per unit time to the remaining capacity of the adsorbent after adsorption according to the amount of target substance adsorbed per unit time and the initial remaining capacity b0 of the adsorbent.

[0009] Among them, at a given height-diameter ratio and column passing rate, the adsorption amount of the target substance per unit time is proportional to the adsorbent dosage.

[0010] (3) Select the column change time t by the trial-and-error method m , calculate the total amount of the target substance in the liquid before adsorption, the remaining capacity of the adsorbent in the second-stage column at the initial time, the maximum theoretical adsorption amount, the adsorption amount, the remaining capacity of the adsorbent after adsorption, the total amount of the target substance in the liquid after adsorption, and the total adsorption amount in the second-stage column from 0 to t 2m for each unit time.

[0011] The column change time is obtained by the trial-and-error method, that is, assume a column change time t m value, substitute it to obtain the minimum theoretical number of stages, and check whether the cost required for the adsorbent loading of the obtained number of stages and the matching number of stages is within the budget. If the budget requirement is not met, then trial-and-error another column change time t m value for calculation. The remaining capacity of the adsorbent in the second-stage column at the initial time is b 0(2) , and its value is b0.

[0012] (4) t 2m is denoted as the second column change time, and so on. For each increase of t m is denoted as the next column change time. Compare the total adsorption amount values of each stage until they are basically unchanged, which is regarded as reaching equilibrium. When reaching equilibrium, round up the quotient of the difference between the total column passing time minus the time corresponding to the first time when the total amount of the target substance in the liquid before adsorption is greater than zero and the selected column change time to obtain the minimum number of stages required for the design.

[0013] Taking the pth-stage column reaching equilibrium as an example, the total column passing time is denoted as t pm , find the time t n(p-1) corresponding to the first time when the total amount of the target substance d n in the liquid before adsorption is greater than zero, and calculate X = (t pm -t n ) / t m . Round up X to obtain the integer value X*, and X* is the minimum number of stages required for the design. On the basis of obtaining the minimum number of stages required for the design, an insurance increment y = 0-2 stages can also be selected, and X* + y is used as the design value of the number of stages of the cascade adsorption process to ensure that the target substance concentration in the effluent of the last stage meets the design requirements.

[0014] It can be understood that calculate the maximum theoretical adsorption amount, adsorption amount, remaining capacity of the adsorbent after adsorption, total amount of the target substance in the liquid after adsorption, and total adsorption amount values in each unit time of the next-stage column according to the method of calculating the parameters of the second-stage column, and compare the total adsorption amount of each stage. When the total adsorption amount value is basically unchanged, it is regarded as reaching equilibrium.

[0015] In some embodiments, the remaining capacities of the adsorbent after adsorption from the first unit time, the second unit time to the xth unit time are b1, b2 to bx , and b x =b x-1 -a x , x≥1.

[0016] In some embodiments, the ratios of the target substance adsorption amount to the remaining capacity of the adsorbent after adsorption in the unit time from the first unit time, the second unit time to the x-th unit time are a1 / b1, a2 / b2, to a x / b x , x≥1.

[0017] In some embodiments, with the ratio of the target substance adsorption amount to the remaining capacity of the adsorbent after adsorption in the unit time as the ordinate and the column passing time as the abscissa, a graph is plotted, and the average value of the ordinates corresponding to the straight-line segments with a linear fitting equation slope ≤ 0.01 is obtained as the stable interval average c.

[0018] In some embodiments, in the second-stage column, from 0 to t m The total amount of the target substance in the liquid before adsorption in each unit time is the total amount of the target substance in the liquid after adsorption in the first-stage column in each unit time from 0 to t m , which are respectively denoted as d 1(1) , d 2(1) to d m(1) ; in the second-stage column, from t m to t 2m The total amount of the target substance in the liquid before adsorption in each unit time is calculated according to the concentration of the target substance in the original adsorption liquid and the selected column passing rate, and are respectively denoted as d m+1(1) , d m+2(1) to d 2m(1) .

[0019] In some embodiments, the maximum theoretical adsorption amount e 1(2) =b 0(2)* c in the first unit time of the second-stage column, and the maximum theoretical adsorption amounts e 2(2) to e 2m(2) in the second unit time to the 2m-th unit time of the second-stage column are calculated in sequence, where b 0(2) is the remaining capacity of the adsorbent at the initial time of the second-stage column.

[0020] In some embodiments, the adsorption amount f 1(2) =Min[d 1(1) , e 1(2) in the first unit time of the second-stage column, and the adsorption amounts f 2(2) to f 2m(2) in the second unit time to the 2m-th unit time of the second-stage column are calculated in sequence, where e 1(2) is the maximum theoretical adsorption in the first unit time of the second-stage column, and d 1(1)is the total amount of the target substance in the pre-adsorption liquid in the second-stage column within the first unit time.

[0021] In some embodiments, the remaining capacity b of the adsorbent after adsorption in the second-stage column within the first unit time 1(2) = b 0(2) - f 1(2) , and successively calculate the remaining capacity b of the adsorbent after adsorption in the second-stage column from the 2nd unit time to the 2m-th unit time 2(2) to b 2m(2) where f 1(2) is the adsorption amount within the first unit time in the second-stage column, and b 0(2) is the initial remaining capacity of the adsorbent in the second-stage column.

[0022] In some embodiments, the total amount d of the target substance in the liquid after adsorption in the second-stage column within the first unit time 1(2) = d 1(1) - f 1(2) , and successively calculate the total amount d of the target substance in the liquid after adsorption in the second-stage column from the 2nd unit time to the 2m-th unit time 2(2) to d 2m(2) where d 1(1) is the total amount of the target substance in the pre-adsorption liquid in the second-stage column within the first unit time, and f 1(2) is the adsorption amount within the first unit time in the second-stage column.

[0023] In some embodiments, the total adsorption amount of the second-stage column is obtained by summing the values of the adsorption amounts f 1(2) to f 2m(2) in the second-stage column from the 1st unit time to the 2m-th unit time.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] The method for designing the number of stages of the cascade adsorption process of the present invention makes the design of the number of stages of the cascade adsorption process forward-looking, and can avoid the waste of equipment and adsorbent usage costs caused by excessive number of stages; the liquid discharged from the last stage can stably meet the target substance concentration requirement without adding a concentration feedback system; the minimum required number of stages can be obtained through small-scale experiments and calculations, which is convenient and fast. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The above and / or additional aspects and advantages of the present invention will become apparent and be readily understood from the following description of the embodiments in conjunction with the drawings, wherein:

[0027] Figure 1 is a flowchart of the method for designing the number of stages of the cascade adsorption process of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0028] Embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where like or similar reference numerals denote like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the present invention, and should not be construed as limiting the present invention.

[0029] The following describes a method for designing the number of stages of a cascade adsorption process according to an embodiment of the present invention.

[0030] For a design project of a cascade adsorption process for a liquid to be treated, the main components of the liquid to be treated are shown in Table 1 below. Design the number of cascade adsorption stages to ensure that Ni ≤ 0.5 mg / L in the effluent of the last stage.

[0031] Table 1. Main metal content (g / L) of the liquid to be treated.

[0032] Ni Mg Mn 0.25 5.25 1.87

[0033] 1. Conduct a single-stage column saturation adsorption test: Load 122 ml of nickel-extracting resin into the experimental column, and pass the liquid to be treated at a column passing rate of 10 BV / h while starting to time; sample the adsorption stock solution and the post-liquid every 1 h to analyze the Ni concentration in the post-liquid. The results are shown in Table 2 below.

[0034] Table 2. Ni concentration (mg / L) and post-liquid volume (mL) in the post-liquid after adsorption.

[0035]

[0036]

[0037] 2. Calculate the Ni adsorption amount per unit time in the single-stage saturation adsorption test as shown in Table 3 below. Calculate the cumulative adsorption amount of the target substance after equilibrium according to Table 3, and record the remaining capacity of Ni in the adsorbent at the initial time as b0 = 3645 mg.

[0038] Table 3. Hourly Ni adsorption amount (mg) in the single-stage saturation adsorption test.

[0039]

[0040]

[0041] 3. Calculate b1 = b0 - a1, b2 = b1 - a2, etc., and successively obtain the values of b1, b2 to b x as shown in Table 4 below, which are respectively recorded as the remaining capacity of the adsorbent after adsorption in the 1st unit time, the 2nd unit time to the xth unit time.

[0042] Table 4. Remaining Ni capacity (mg) after adsorption per hour.

[0043]

[0044] 4. Calculate the values of a1 / b1, a2 / b2 to a x / b x as shown in Table 5 below.

[0045] Table 5. Ratio of Ni adsorption amount per hour to remaining capacity of adsorbent.

[0046] Column passing time / h Ni Column passing time / h Ni Column passing time / h Ni 1 0.09092 20 0.09908 39 0.13882 2 0.10096 21 0.10889 40 0.14876 3 0.10968 22 0.11452 41 0.15668 4 0.10719 23 0.12052 42 0.15880 5 0.10477 24 0.11460 43 0.05315 6 0.09959 25 0.06946 44 0.21601 7 0.10010 26 0.10078 45 0.18427 8 0.09792 27 0.09900 46 0.16104 9 0.10039 28 0.11768 47 0.31099 10 0.10290 29 0.11560 48 0.03949 11 0.10075 30 0.13157 49 -0.07009 12 0.09978 31 0.12763 50 0.09665 13 0.09992 32 0.12446 51 0.50965 14 0.09850 33 0.14033 52 0.69592 15 0.09951 34 0.13740 53 0.62124 16 0.10143 35 0.11392 54 -0.08419 17 0.10667 36 0.11663 55 1.44954 18 0.10496 37 0.11496 56 11619.04762 19 0.09804 38 0.05850

[0047] 5. Plot the data in Table 5 against the column passing time. It can be seen from the graph that there is a quasi-linear segment from 0 h to ~20 h, and its linear fitting slope is 9.955565E-4. The average value of the data in the table corresponding to 0 - 20 h is 0.101152, that is, c = 0.101152.

[0048] 6. Select the column changing time t m = 9 h. Denote the adsorption amounts of the target substances a1, a2 to a m within the time period from 0 to 9 h in the single-stage column passing saturation adsorption experiment as the Ni hourly adsorption amounts in the 1st column from 0 to 9 h, as shown in Table 6 below.

[0049] Table 6. Ni hourly adsorption amounts (mg) in the 1st column from 0 to 9 h.

[0050] Column passing time / h Ni 1 303.7359 2 306.359 3 299.918 4 264.726 5 234.2214 6 202.4672 7 184.9943 8 164.822 9 153.5655

[0051] 7. Based on the results of the single-stage column passing saturation adsorption experiment, calculate the total amounts d m of the target substances in the liquid after adsorption by the 1st column for each unit time from 0 to t 1(1) 、d 2(1) to d m(1) as shown in Table 7 below.

[0052] Table 7. Total amounts of Ni (mg) in the liquid after adsorption in the 1st column from 0 to 9 h.

[0053] Column passing time / h Ni 1 0.0798 2 1.4225 3 5.9102 4 31.04 5 55.25 6 77.86 7 91.71 8 106.04 9 124.93

[0054] 8. Taking the 2nd column as an example, the total amounts of the target substances in the liquid before adsorption per hour from 0 to 18 h are as shown in Table 8 below;

[0055] Table 8. Total amounts of Ni (mg) in the liquid before adsorption in the 2nd column from 0 to 18 h.

[0056] Column passing time / h Ni 1 0.0798 2 1.4225 3 5.9102 4 31.04 5 55.25 6 77.86 7 91.71 8 106.04 9 124.93 10 305 11 305 12 305 13 305 14 305 15 305 16 305 17 305 18 305

[0057] 9. Denote the remaining capacity of the adsorbent at the initial time of the 2nd column as b 0(2) , and its value is 3645 mg.

[0058] 10. Calculate e 1(2)= b 0(2) * c is recorded as the maximum theoretical adsorption capacity of the 2nd - stage column in the first 1 h, which is 368.64 mg.

[0059] 11. Take f 1(2) = Min[d 1(1) , e 1(2) , which is recorded as the adsorption capacity of the 2nd - stage column in the first 1 h, 0.0798 mg.

[0060] 12. Calculate b 1(2) = b 0(2) - f 1(2) which is recorded as the remaining capacity of the adsorbent after adsorption in the first 1 h of the 2nd - stage column, 3644.44 mg.

[0061] 13. Calculate d 1(2) = d 1(1) - f 1(2) which is recorded as the total amount of Ni in the liquid after adsorption in the first 1 h of the 2nd - stage column, 0 mg.

[0062] 14. Calculate successively according to the method in step 10 to obtain the values of e 2(2) to e 2m(2) , which are respectively recorded as the maximum theoretical adsorption capacities in the 2nd to 18th h as shown in Table 9 below.

[0063] Table 9. Maximum theoretical adsorption capacities of the 2nd - stage column in the 2nd to 18th h (mg).

[0064] Column passing time / h Ni 2 368.50 3 367.90 4 364.76 5 359.17 6 351.30 7 342.02 8 331.29 9 318.66 10 289.38 11 262.80 12 238.66 13 216.74 14 196.83 15 178.75 16 162.33 17 147.42 18 133.87

[0065] 15. Calculate successively according to the method in step 11 to obtain the values of f 2(2) to f 2m(2) , which are respectively recorded as the Ni adsorption amounts of the 2nd - stage column in the 2nd to 18th h as shown in Table 10 below.

[0066] Table 10. Ni adsorption amounts of the 2nd - stage column in the 2nd to 18th h (mg).

[0067]

[0068]

[0069] 16. Calculate successively according to the method in step 12 to obtain the values of b 2(2) to b 2m(2) , which are respectively recorded as the remaining capacities of the adsorbent after adsorption in the 2nd to 18th h of the 2nd - stage column as shown in Table 11 below.

[0070] Table 11. Remaining capacities of the adsorbent after adsorption in the 2nd to 18th h of the 2nd - stage column (mg).

[0071] Column passing time / h Ni 2 3643.02 3 3637.11 4 3606.07 5 3550.82 6 3472.96 7 3381.25 8 3275.21 9 3150.28 10 2860.89 11 2598.09 12 2359.43 13 2142.69 14 1945.86 15 1767.12 16 1604.79 17 1457.37 18 1323.50

[0072] 17. Calculate d successively according to the method in step 13 2(2) to d 2m(2) values, which are respectively recorded as the total amount of Ni in the liquid after adsorption in the 2nd to 18th hour of the 2nd - stage column, and also the total amount of Ni in the liquid before adsorption in the next - stage column, as shown in Table 12 below.

[0073] Table 12. Total amount of Ni in the liquid after adsorption in the 2nd - stage column from 2nd to 18th hour (mg).

[0074]

[0075]

[0076] 18. Calculate the total amount of Ni adsorbed by the 2nd - stage column g (2) = 2321.02mg.

[0077] 19. Record 18h as the time of the 2nd column change, and so on. Every time 9h is increased, it is recorded as the time of the next column change. According to the methods in steps 8 to 18, calculate the values of all b, d, e, f, and g in each unit time of the next - stage column successively, and compare the g values of each stage. When it reaches the 23rd stage, g approaches 2745mg, which is regarded as reaching equilibrium.

[0078] 20. The time when the total amount of Ni in the liquid before adsorption in the 23rd stage is greater than zero for the first time is 190h, and the total column - passing time is 207h. Calculate X = 1.89, and round up to get the integer value 2, which is recorded as the minimum number of required stages for design.

[0079] 21. Select the insurance increment y = 1 stage, and design the number of stages of the cascade adsorption process as 3.

[0080] 22. Taking 3 as the designed number of stages, after actual operation, the Ni concentration in the effluent of the last stage is as shown in Table 13 below, which can meet the requirement of Ni ≤ 0.5mg / L.

[0081] Table 13. Ni concentration in the effluent of the last stage of 3 - stage series actual operation adsorption (mg / L).

[0082] Column passing time / h Ni 9 0.00 18 0.00 27 0.06 36 0.06 45 0.07 54 0.02 63 0.09 72 0.15 81 0.22 90 0.11 99 0.17 108 0.08 117 0.30 126 0.08 135 0.22 144 0.08

[0083] The present invention makes the design of the number of stages of the cascade adsorption process forward - looking, which can avoid the waste of equipment and adsorbent usage costs caused by excessive number of stages; the effluent of the last stage can stably reach the target substance concentration requirement without adding a concentration feedback system; the minimum required number of stages for design can be obtained through small - scale tests and calculations, which is convenient and fast.

[0084] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms may be directed to different embodiments or examples. Moreover, the specific features, structures, materials, or characteristics described may be combined in a suitable manner in any one or more embodiments or examples. In addition, without contradiction, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0085] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of such feature. In the description of the present invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise specifically and clearly defined.

[0086] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the claims and their equivalents.

Claims

1. A method for designing the number of stages of a cascade adsorption process, characterized in that, It includes the following steps: Perform a single-stage column passing saturation adsorption test: Start the adsorption test and start timing simultaneously. Samples of the original adsorption solution and the post-adsorption solution are taken at unit time intervals to analyze the concentration of the target substance in the post-adsorption solution until the concentration of the target substance in the post-adsorption solution remains unchanged, which is regarded as reaching equilibrium. Calculate the adsorption amount of the target substance per unit time and the remaining capacity b0 of the adsorbent at the initial time. Calculate the average value c of the stable interval of the ratio of the adsorption amount of the target substance per unit time to the remaining capacity b0 of the adsorbent after adsorption according to the adsorption amount of the target substance per unit time and the remaining capacity b0 of the adsorbent at the initial time. Select the column change time t by the trial-and-error method m , calculate the values from 0 to t for the second-stage column 2m For each unit time, calculate the total amount of the target substance in the liquid before adsorption, the remaining capacity of the adsorbent at the initial stage of the second-stage column, the maximum theoretical adsorption capacity, the adsorption amount, the remaining capacity of the adsorbent after adsorption, the total amount of the target substance in the liquid after adsorption, and the total adsorption amount. The column change time is obtained by the trial-and-error method, that is, assume a column change time t m value, substitute it to obtain the minimum theoretical number of stages, and check whether the cost required for the adsorbent loading of the obtained number of stages and the supporting number of stages is within the budget. If the budget requirement is not met, then try another column change time t m value for calculation; t 2m It is recorded as the second column replacement time, and so on. For each increase of t m It is recorded as the next column replacement time. Compare the total adsorption amount values of each stage until they remain unchanged, which is regarded as reaching equilibrium. When reaching equilibrium, take the quotient of the difference obtained by subtracting the time corresponding to the first time when the total amount of the target substance in the liquid before adsorption is greater than zero from the total column passing time and the selected column replacement time, and round up to obtain the minimum number of stages required for the design. Among them, in the second - stage column, from 0 to t m The total amount of the target substance in the pre - adsorption liquid per unit time is from 0 to t m The total amount of the target substance in the post - adsorption liquid of the first - stage column per unit time, which are respectively denoted as d 1（1） 、d 2（1） to d m（1） ; In the second - stage column, from t m to t 2m The total amount of the target substance in the pre - adsorption liquid per unit time is calculated according to the concentration of the target substance in the original adsorption liquid and the selected column - passing rate, which are respectively denoted as d m+1（1） 、d m+2（1） to d 2m（1） , The maximum theoretical adsorption amount e within the first unit time in the second-stage column 1（2） =b 0（2） *c, and successively calculate the maximum theoretical adsorption amounts e 2（2） to e 2m（2） values within the second unit time to the 2m-th unit time in the second-stage column, where b 0（2） is the remaining capacity of the adsorbent at the initial stage of the second-stage column The adsorption amount f within the first unit time in the second-stage column 1（2） = Min[d 1（1） , e 1（2） , and calculate the adsorption amounts f 2（2） to f 2m（2） within the second unit time to the 2m-th unit time in the second-stage column in sequence, where e 1（2） is the maximum theoretical adsorption within the first unit time in the second-stage column, and d 1（1） is the total amount of the target substance in the pre-adsorption liquid within the first unit time in the second-stage column. The remaining capacity b of the adsorbent after adsorption in the first unit time in the second-stage column 1（2） =b 0（2） -f 1（2） , and successively calculate the remaining capacity b of the adsorbent after adsorption in the second unit time to the 2m-th unit time in the second-stage column 2（2） to b 2m（2） . Among them, f 1（2） is the adsorption amount in the first unit time in the second-stage column, and b 0（2） is the remaining capacity of the adsorbent at the initial time of the second-stage column The total amount d of the target substance in the liquid after adsorption in the first unit time in the second-stage column 1（2） =d 1（1） -f 1（2）， And successively calculate the total amount d of the target substance in the liquid after adsorption in the second-stage column from the second unit time to the 2m-th unit time 2（2） to d 2m（2） The value of, where d 1（1） is the total amount of the target substance in the liquid before adsorption in the first unit time in the second-stage column, and f 1（2） is the adsorption amount in the first unit time in the second-stage column. By summing the adsorption amounts f 1（2） to f 2m（2） in the second-stage column from the first unit time to the 2m-th unit time, the total adsorption amount of the second-stage column is obtained.

2. The method according to claim 1, characterized in that, The remaining capacities of the adsorbent after adsorption from the first unit time, the second unit time to the x-th unit time are b1, b2 to bx in sequence x , and bx x = bx x-1 - a x , x ≥ 1, where a x is the amount of the target substance adsorbed within the unit time of the x-th unit time.

3. The method according to claim 2, characterized in that, The ratios of the adsorbed amount of the target substance to the remaining capacity of the adsorbent after adsorption within the unit time from the first unit time, the second unit time to the x-th unit time are a1 / b1, a2 / b2, to a x / b x , where x ≥ 1.

4. The method according to claim 3, wherein Taking the ratio of the adsorption amount of the target substance per unit time to the remaining capacity of the adsorbent after adsorption as the ordinate and the column passing time as the abscissa to plot a graph, and calculate the average value of the ordinates corresponding to the straight-line segments with a slope of the linear fitting equation ≤ 0.01 to obtain the average value c of the stable interval.

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