Trans.Tianjin Univ.201 1.1 7:051—056 DOI 1 O.1 OO7/sl 2209—01 1—1 489—4 Determination of Diffusion Coefficient and Analysis of Diffusion Factors ofCr(I/1)Ion in Clay Soil YANG Qinglei(杨清雷) ,ZHANG Jinli(张金利) ,YANG Qing(杨庆) , TANG Xiaowei(唐小微) ,YU Yongxian(于永鲜)3 YANG Gang(杨钏) (1.State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology,Dalian 1 1 6024,China; 2.Institute of Geotechnical Engineering,School of Civil and Hydraulic Engineering, Dalian University of Technology,Dalian 1 1 6024,China; 3.School ofChemical Engineering,Dalian University ofTechnology,Dalian 1 16024,China) ◎Tianjin University and Springer—Verlag Berlin Heidelberg 20 1 1 Abstract: Some laboratory diffusion tests were conducted with diflusion device to determine the diflusion coefi—f cient of Cr(VI)ion passing through Dalian red clay samples.The concentrations of Cr(VI)at different places of the samples were then measured spectrophotometrically after a standing time Of 1 000 d.A one-dimensiona1 solute trans・ port equation was used to simulate the transport 0f Cr(Ⅵ)through clay samples.Back.calculation 0f dif sion coeffi— cient of Cr(VI)was made with finite difference method.Parametric analysis was conducted to simulate variations in soil dry density.temperature.pH and standing time.The results show that the method used in this paper is simple and effective.The diffusion coeficifent ofCr(Ⅵ)in Dalian red clay varies from 1.50x10 cm /s to 2.08×10 cm /s.Atier 1 000 d diffusion.the concentration of the source solution drops down to 1-27 mg/L from 62.5 mg/L,and the diffusion distance is only 3.5 cm.U『nder the assumption that diflusion coeficifent is constant,the diffusion effect becomes more obvious with lower density.1ower temperature,higher pH value,and much more time. Keywords:landfill;Cr(Ⅵ)ion;transport;clay soil;diffusion coefficient be confirmed properly.In Due to the limit of economic condition,the main heavy metals onto clay must places,such as sewage oxidation disposal method of solid—waste is still burying.Leachate many waste disposalfrom solid—waste landfills has been found to contain a pond.water head difference between the inside and out— de of the pond is smal1.and the water flow is not obvi— number of harmful substances including heavy metals. siThese heavy metals may enter the aquifer underlying the OUS.In these conditions diffusion becomes the main con— factor for contaminant migration through soilI .Ow— 1andfill and thereby pose a potential threat to human trolexity of difhlsion characterjstics of con— health【lj.To prevent the groundwater resource from being ing to the complicient fpolluted.1andfills are usually lined with clay liners.The taminant ions and the importance of diffusion coefcal research and barrier system designl .re. main purpose of liner system is to minimize permeation in theoretifusion characteristic of leachate through the liner.Although the permeability searches on testing method of dif-coeficifent of liner system is less than 1×1 0 cm/s,many deserve attention as there is little standard reference. heavy metals can still pollute the groundwater by diffu— However,most studies focus primarily on dispersion and sion through a block 1iner【 . adsorption[ 一引and laboratory models of determining dis— ..y column tests ¨Studies The migration of contaminants through soil includes persion coe cient are mostlfour fcli'ins:advection,dispersion,diffusion and adsorp— on diffusion are relatively few.Xi et al did some labora— ne the difillsion coefficient of Cl and tion.In order to effectively predict the migration process tory tests to determin clay samples .However.the peri— of heavy metals in landfill clay liner.parameters such as low valent cations iy short.and studies on seepage velocity,diffusion coeficifent,and adsorption of ods of 1aboratory tests are usuallAccepted date:2010-06・21. *Supported by National Natural Science Foundation ofChina(No 50679015) YANG Qinglei,born in 1 98 1,male,doctorate student. Co ̄espondence to YANG Qinglei,E-mail:qingleiyang@yahoo.com.cn. Transactions ofTianjin University Vo1.1 7No.j 2011 ,J∞自 莒∞0 the diffusion coeficifents of heavy metal anions and dif-from the Maoyingzi zone in Dalian city.The soil speci— fusion influencing factors are quite rare. men had no history of exposure to Cr(VI).The chemical 69%Of SiO2,23.80%0f The obiectives of this study were to measure the composition of the clay was 60.03%of Na20,0.23%of CaP, concentrations of Cr(Ⅵ)at different places of soil sam— A12O3,4.03%of K20,2.05%of TiP2.The pies with diffusion test device after a long standing time, 0.30%of Fe203,0.08%of MgO and 0.cs of the soil samples are given in Tab.1.The thereby to determine the migration rule of Cr(VI)ion characteristiain size distribution of the natural clay is shown in simply under the effect of diffusion,and to analyze the greffects of dry density,temperature,pH value and time on Fig.1.Potassium dichromate solution was used as a diffusion to provide reterence for theoretical study and source of Cr(VI)in the diflusion tests.Chromium was landfill design. selected as the test metal because of its commonness and high toxicity in landfil1leachates. 1 Testing materials and methods 1.1 Testing materials In order to determine the diffusion coeficient of fcontaminant in soil,a simple laboratory test device (Fig.2)was designed to simulate one dimensional con. on The natural clay used in this study was obtained taminant migration through a clay medium by diffusiTab.1 Characteristics of the soil samples used in the tests only.This device is a rectangle box made uD of porous contaminant at different places of soil samples were polyethylene plastic plates which is 1 cm thick.The de— measured to determine the diffusion coeficient D.The fvice is divided into three parts by two polyethylene po— sizes of the test device are as follows:W=10 cm.H=10 rous plates.The soi1 sample is located in the middle part cm,L1=10 cm L,:5 cm,L3=l0 cm. and source of contaminant and distilled water in the other 1.2 Testing method two parts respectively.The top of the device was sealed. Potassium dichromate solution was used as a source Aftcr a standing time of 1 000 d.the concentrations of of Cr(VI)in the diffusion tests.The initial concentration of the source solution was 62.5 mgm.The initial pH value of our test solution was adjusted to approximately 7.0 with dilute HNO and NaOH,and the test was con— ducted in a constant temperature room of 295 K.The test procedures were as follows.Firstly.soi1 was dried by air and sieved through a 2 mm sieve.Secondly,the soil pre- pared was put in the middle part of the device,rammed gradationally,and the dry density of soil P and soil poros— Grain diameter/mm ity n were measured(see Tab.1).Distilled water was added in the other two parts of the device,so that the soil Fig.1 Grain size distribution of natural clay adsorbed water slowly and the air in pores of the soil was \・— — \ — removed.Thirdly.after the soiI sample in devices was saturated.the stock solution of Cr(Ⅵ)and distilled water were added jn these two parts of the device respectively. The water 1evels in these two parts should be Of the same value in order to avoid advective flow.After a standing time of 1 000 d.the soil sample was sliced into l 5 sublayers using a stainless steel thread.The pore water was extracted from the slices under 1 0 kPa pressure for Fig.2 Diffusion test device 1 2 h.Aflerwards.the slurry was centrifuged at a speed of 一52一 YANGQinglei et口, Determination ofDiffusionCoefifcientandAnalysis ofDiffusionFactors ofCr( IoninClaySoil 1 0 000 r/min for 30 min to obtain the supernatant.The spectrophotometer was then used to determine the Cr(VI)concentration at different places of the soil sam— ples. Batch tests were conducted to investigate the ad— [ + 备 。 a2C oc (4) D in Eq.(4)can be expressed as D=Dm+D , is longitudinal dispersivity,whose value is gen— at different temperatures and where Dm is a mechanicalsorption behavior of Cr(VI) diffusion coeficient,Dm= fpH values.Dry soil samples 2—12.5 g and 25 mL aque— aLv, OHS solutions of different concentrations of Cr(VI)were erally given as the average particle size;D’is a diffusion mixed in each flask.The sample flasks were then put into coeficient.If fthe hydraulic gradient is zero,the seepage a temperature—controlled shaking box which was rotated velocity equals zero.Eq.(4)can be simpliifed as at 1 60 r/min.After different adsorption time.the slurry was centrifuged at a speed of 5 000 r/min for 5 min to 02C。 。obtain the supematant.The concentration of Cr(Ⅵ)in the supernatant solution was then measured spectropho— 1 Ot (+6c) J Ox (5) The test device in this paper is a test device for dif_ tometrically.The concentration 0f Cr(VI)adsorbed onto the soil solids was calculated from the mass balance. fusion only,the initial and boundary conditions are = Co- C, (1) C(x>0:t=0)=0 C =0; =0)一C (6a) (6b) where is the amount of Cr(VI)adsorbed onto the soi1 samples at time f;Co the initial concentration of Cr(VI); C = :,>0)=0 (6c) Eq.(6a)means that the soil sample is free of con— C,aqueous phase concentration of Cr(VI)at time V the taminant at the initia】time(,=0):Eq.(6b)means that volume of the aqueous phase;and M the mass of the soil the initial source concentration is a constant C0;Eq.(6c) samples. means that the contaminant concentration at the exit of 1.3 Transport modeling simulations the soil barrier is zero because of the presence of large Based on the migration mechanism of contaminant amount of water. in porous medium,a one—dimensional migration equation is given asD3] c(0,,)=co—At where A is a reduction factor. (7) e + ef} v 一。 o + The contaminant source concentration is reduced nearly linearly with time to account for transfer into the soil barrier. The contaminant transport through the soil samples where is seepage velocity;刀e effective porosity;C con— taminant concentration in the aqueous phase;D disper— sion coeficifent;S equilibrium adsorbed concentration;P was analyzed using Eqs.(5)一(7).These equations were solved by a specially developed FORTRAN 95一based inifte difference program.The central difference scheme was used.Some parameters used in this program are listed in Tab.2.The values of isotherm parameters b and dry density;t time;and x distance from the domain en— trance. The results of the batch tests were used as input pa— rameters and the Langmuir model was found to fit well to the test data based on calculated correlation coe伍cients. qm were obtained from batch tests as shown in Tab-3. Tab・2 Parameters used in inifte difference program Parameter Initial time step/d Time step multiplier For this study the adsorption model of Cr(VI)on all soi1 samples was a Langmuir isotherm model ofthe form ̄ ] S: 1+bC Value O.01 1.2 0.5 0 0l O.1 Maximum time step/d Minimum time step/d where b and qm are isotherm parameters. Time step reduction factor Combining Eq.(2)and Eq.(3)gives a one— Spacing between grid lines/era O.1 dimensional migration equation of contaminant in soil as 53— Transactions ofTianjin University Vo1.j 7No.i 2011 Tab.3 The values of b and qm at different pH values and temperatures 5 6 O.0l9 2 0.O16 8 284.4 261.2 0 9720 974.——.——.————————.——.——.——.——.——.——-——.——-——-——-—— -—— 7 9 0.0141 0.013 2 207.6 190.2 O.98l 0 988O.016 5 ,——260.9 .—— 0.985 ——0.017 5 ———271.6 .——0.979 .——0.019 0 .——284.1 .——0.973 .—— 2 Results and discussion 2.1 Dif sion test results The concentration of source solution is 1.27 mg/L at f=1 000 d.therefore the value of in Eq.(7)is found to be 0.061 23.For any given diffugion coeffieient D.the concentration at any specified place and time can be ob— tained by numerical calculation.The values of D were back..calculated by varying D values until the concentra.. (a)z=2.5 cm tion profile predicted by F0RTRAN program fit the ex- perimental data wel1.The concentrations of Cr(Ⅵ)in the pore water of the soil versus at different depths in the soil are shown in Fig.3.where C is contaminant concen— tration.T is temperature and f is time. Fig.3 shows that the predicted concentration profiles of that Cr(VI)well fit the observed ones.Atier a stand— ing time Of 1 000 d.the concentration of source solution decreases from 62.5 mg/L to 1.27 mg/L.Some ions may (b)z=5.0 cm be adsorbed by soil.The cOncentrations at x=3.5 cm and the exit are both zero,which means Cr(VI)did not break through 5 cm soil sample after a standing time of 1 000 d. The di sion distance is only 3.5 cm.The diffusion coef- ifcients of Cr(VI)are basically consistent at three diff.er— ent depths.which are 1.50x 1 0 cm /s.1.62×1 0 cm /s and 2.08x 10 cm /s from top to bottom ofthe test device. The dif Lsion coeficient on the bottom ifs a little higher. which may be caused by a higher concentration on the boRom.It is shown in Fig.3 that at the interface between the source and soil sample.there is a sudden change of concentration.This phenomenon agrees with the testing (c)z=7.5 cm Fig.3 Measured and predicted concentration of Cr(Ⅵ) versus x at diferent depths results of Xi et ,L and indicates that there is some kind (T=295K,f=1 000 d,pH=7,P=1.72 cm ) of chemical reaction at the interface.The same phenome— piing effect was not considered.While one parameter non was found in laboratory and neld tests abroad.which changed.the other parameters kept constant.Under the needs to be further studied. 2.2 Analysis of influencing factor assumption that the concentration of source solution was constant (1.2 mg/L) and diffusion coeficifent was Dif-fusion coef五cient of contaminant in soil can be 1.62x 1 0 cm /s.the influence of each factor on diffusion affected by many factors,such as dry density,tempera was calculated.The values of b and口 at different tern- ture,pH value and standing time.In this study the COU一 peratures and PH values are listed in Tab.3.The results 一54一 YANGQinglei etnl:Determination ofDiffusionCoeficifentandAnalysis ofDiffusionFactors ofCr(Ⅵ)IoninClaySoil are shown in Fig.4一Fig.7 density increases.The ef.fect of dry density is mainly on geometric condition.Diflusion meander ratio increases as 1.2 1.o dry density does.It is shown in Fig.4 that the concentra— tion of contaminant decreases as dry density increases at the same place,temperature,pH value and time.When 0 8 0 6 0.4 dry density increases from 1.42 g/cm to 1.72 g/cm .the concentration of contaminant at 0.2 =1.5 cm decreases from 0.298 mg/L to 0.248 mg/L.Dif.fusion can be re— O 0 2 3 4 5 /c11] Fig.4 Concentration of Cr(V1)versus x at diferent dry densities l 2 —●}一T=295K 1.0 +71-3O3 K —._r:31 3 K 0 ——._T=333 K 0 6 1=l 000 d pH:7 0 4 p:1 72 g/cm O 2 D:1.62 x 10 cm /s 0 0 2 3 4 5 /rm Fig.5 Concentration of Cr(VI)versus x at diferent temperatures Fig.6 Concentration of Cr("qI)versus x at different pH values Fig.7 Concentrati。n。f Cr(Ⅵ)vP s at diferent time 2.2.1 The effect ofdry density on diffusion The calculation results fit well with the test data done by Xi et al『15_,i…e diffusion decreases as the dry duced by increasing soil dry density. 2.2.2 The effect oftemperature on diflusion Fig.5 shows the diffusion results of Cr(VI)ion in clay soil at different temperatures.It can be seen that the concentration of contaminant in porous water decreases as temperature rises,because when diffusion coefficient is constant.the adsorption of Cr(VI)onto soil increases with temperature. en temperature rises from 295 K to 333 K.the cOncentratiOn of contaminant at x=1.5 cm decreases from 0.246 mg/L to 0.1 07 mg/L. 2.2.3 The ef-fect ofpH on diffusion It is shown in Fig.6 that diffusion distance increases as pH value rises.When pH value is 5,6,7 and 9,the concentration of contaminant at x=1.5 cm is 0.1 08 mg/L. 0.1 55 mg/L.0.248 mg/L and 0.290 mg/L respectively.It can be seen that the initial PH value of the solution has a signiifcant influence on the adsorption of Cr(VI)onto soil.When pH rises the amount of Cr(VI)adsorbed onto soiI decreases.and the concentration of the solution be— comes larger.The influence of pH value is stronger in acid environment than in alkaline one.This phenomenon may be interpreted as the adsorption of Cr(VI)onto soil is related to the number of net negative charges in the solution. 2.2.4 The ef.fect of standing time on diflusion It is shown in Fig.7 that diffusion distance increases with time.The growth rate of dif sion decreases gradu. ally with the same increase amplitude of time.When standing time increases from 500 d to 2 000 d,diffusion distance increases from 2 cm to 4 cm and the concentra. tion of contaminant at x=1.5 cm increases from 0.089 9 mg/L to 0.447 0 mg/L.which has a breakthrough trend. The effect of time is more significant compared with other factors. 3 Conclusions This paper describes a number of laboratory tests involving the diffusion migration of Cr(VI)ion through Dalian red clay samples.Back—calculation of diffusion 55— Transactions ofTianjin Universi VoL17No.j 2011 coeficifent of Cr(VI)was made using a specially devel— oped finite diference program.Parametric analysis was conducted to simulate variations in soil dry density.tem. perature,pH and standing time.The following conclu— concentration in batch tests on the partition coeficifents of organic pollutants in landfill liner—soil materials[JJ.J Ma— terCycles WasteManag,2003,5(1):55・62. [6] Lu Haijun,Luan Maotian,Zhang Jinli et a1.Study on the adsorption of Cr(VI)onto landfill liners containing granu— sions are drawn. (1)The diffusion test device used in this PaDer is simple and useful,and diffusion progress of contaminant through soil can be easily analyzed. lar activated carbon or bentonite activated by acid[J]. Journal of China University of Mining&Technology, 2008.18(1):125一l30. (2)The concentration of source solution decreases with time.Some ions diffuse into porous water.and oth— 1 7] Wang Yan,Tang Xiaowu,Chen Yunmin et a1.Adsorption ers may be adsorbed by soil. (3)The diffusion coefficient of Cr(Ⅵ)in Dalian red clay varies from 1.50xl0 cm /s to 2.08×l0 cm /s. ARer 1 000 d diflusion effect.the concentration of me source solution drops down to 1.27 mg/L from 62.5 mg/L.and the diffusion distance is 3.5 cm. (4)Under the assumption that diffusion coefficient is constant,the diffusion effect becomes more obvious with lower density,lower temperature,higher pH value, and much more time. 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