CN1563942A - Device and method of analyzing transfer parameter of liquid in saturated multiporous medium - Google Patents

Abstract

The invention is a device and method for measuring migration parameters of liquid in saturated porous media. The device is a model tank without a cover, which is divided by a porous plate: a barrier chamber for placing porous media, a diffusion source chamber and a distilled water chamber. The measurement method uses a measuring device to measure the change of the concentration of the diffusing agent over time and the concentration of the diffusing agent at different positions in the porous medium. The concentration can be expressed by the Laplace solution of the diffusion equation, and the migration parameters: diffusion coefficient D and distribution coefficient K _d can be obtained by back analysis method. The invention has the advantages of simple structure, convenient operation, low cost and reliable test results.

Description

A kind of apparatus and method of measuring liquid transfer parameter in saturated porous media

Technical field

The invention belongs to the pollutant measurement technical field, be specifically related to a kind of apparatus and method of measuring liquid transfer parameter in saturated porous media.Utilize this method and apparatus can measure diffusion coefficient D and the partition factor K of pollutant in soil _d

Technical background

Along with the growth and the industrialized development of urban population, various discharging wastes quantity sharply increase, discarded object be manipulated so the severe problem that the world today faced.At present in the world most countries to the disposal of discarded object still based on landfill.The way that landfill yard is general is that layering landfill, compacting are done the layer that binds with clay then at landfill material and underground antiseepage fender body of pollution source surrounding buildings and the artificial back cover layer of antiseepage.Countries such as present America and Europe have developed the active barrier system with high adsorption.In the design of barrier system, determine that the transfer parameter of pollutant in barrier (comprises diffusion coefficient D and partition factor K _d) be the most primary and crucial.Though the mensuration of transfer parameter most accurately can determine that doing like this can be very time-consuming, and can pollute environment from site test, so generally still the chamber model test is definite by experiment.

JP2003106974 discloses a kind of method of measuring the coefficient of diffusion in the liquid, it is because the change of the solution concentration that diffusion causes and the change of solution quality by measuring, determine diffusion flow J and concentration gradient dc/dx, according to Fick ' s first law, obtain diffusion coefficient D again.

JP9234329 discloses and has a kind ofly reached the method that certain phenomenon (particularly adsorbing quality changes) that adsorption equilibrium produces is calculated coefficient of diffusion in (oxidation) silica gel particle medium by research.

US5627329 discloses the method for definite diffusant coefficient of diffusion in solid granular thing (as plastics, metal), with inert gas by containing the granular substance of diffusant, measure a parameter that is directly proportional with diffusant concentration in the inert gas that flows out in a period of time scope, get the slope of parameter～time curve neutral line part, multiply by a constant again, promptly obtain coefficient of diffusion.The shortcoming of this device is that the temperature difficulty of heating is chosen, and will guarantee that promptly diffusant does not become liquid, makes particle can not be softened or become liquid state again, because particle is in different states, the coefficient of diffusion that obtains is different.

WO9733152 discloses the method and apparatus of charged molecule in a kind of mensuration porous medium (being ion) coefficient of diffusion, porous medium be placed on a level of making by non-conducting material to container in, a buffer container is respectively put at the container two ends, an electrode is respectively arranged in each buffer container, and the source that the generation potential difference (PD) is housed between two electrodes is to quicken the motion of charged molecule.During test charged molecule is contacted with porous medium, measure the motion (as the distance that covers behind the certain hour) of these charged molecules, and then calculate coefficient of diffusion.This device only is applicable to measures the diffusion of ion in porous medium.

Summary of the invention

The objective of the invention is to propose a kind of simple in structure, easy to use, with low cost being used for and measure the apparatus and method of liquid at the saturated media transfer parameter.

The present invention design be used for measuring the device of liquid at the saturated media transfer parameter, it is a kind of pure disperser, be specially the uncovered model groove of making by the PEF plastic plate, by porous plate (holing on the PEF plastic plate) it is divided into 3 parts: center section is the barrier chamber, the placing porous medium; Left-hand component is the diffuse source chamber, and right-hand component is the distillation hydroecium.

The advantage of this device is:

1) makes simply, only can be assembled into, do not need cover plate, only need a base plate, several side plates with several PEF plastic plates.

2) cheap.As long as such box is about 100 yuan cost.

3) in this process of the test, have only diffusion process to exist, do not have the interference of seepage flow, the diffusion coefficient D that records is pure diffusion coefficient D.

The concrete steps of assay method of the present invention are: (1) puts into the center section of model groove with porous medium, is sidelong by porous medium at porous plate and puts a filter paper, in case porous medium spills from the hole; (2) the right and left at the model groove partly adds distilled water (can not fill it up with), and it is saturated that porous medium is slowly absorbed water, and gets rid of the air in the medium hole, makes porous medium closely knit, and the time that this process continues is longer; (3) treat that porous medium is saturated after, add the liquid that contains diffusant in the side (left side) of model groove, opposite side (right side) adds distilled water, and the water level of liquid and distilled water is equated, does not so just have the generation of seepage flow phenomenon; The water level face will be lower than the porous medium face in addition, overflows in order to avoid contain the liquid and the distilled water of diffusant; (4) along with the carrying out of diffusion, the concentration of diffusant descends gradually in the liquid diffuse source; In process of the test, the concentration of measuring on the one hand diffusant in the diffuse source is measured in the porous medium concentration of diffusant on the diverse location over time on the other hand.

The calculating of coefficient of diffusion:

The determinator of the present invention's design is pure disperser, and transport equation is represented with the one dimension diffusion equation of pollutant in saturated porous media:

$R_f\frac{\∂c}{\∂t}=D\frac{{\∂}^{2}c}{\∂x^2}---\left(1\right)$

In the formula: R _fBe the retardance factor, suppose that absorption is linear absorption, then R _f=1+ (ρ _bk _d/ n), n is a porosity; ρ _bIt is the porous medium dry density; k _dIt is the line balancing coefficient (partition factor) of adsorption isothermal.

The boundary condition of this assay method is as follows:

C(x＞0；t＝0)＝0 (2)

C(x＝0；t＝0)＝C ₀ (3)

C(x＝L；t＞0)＝0 (4)

In the formula: the length of L-porous medium part, i.e. barrier chamber length L in the determinator ₂Before formula 2 expression diffusions take place, there is not this kind diffusant in the porous medium; The initial concentration of diffusant is a constant C in formula (3) the express liquid diffuse source ₀Formula (4) is illustrated in the whole diffusion process, and porous medium is always 0 by the concentration of distilled water side diffusant.

Here preceding two conditions are understandable fully.Formula 4 can be understood like this: what put on the right side of device is distilled water because test period is shorter, the amount that the diffusant diffusion arrives the distilled water side seldom, again because the diluting effect of distilled water, so hypothesis is set up.

Along with the carrying out of diffusion, diffusant concentration reduces owing to diffusing in the porous medium in the liquid diffuse source:

$C(0,t)=C_0-\frac{1}{H_f}{\∫}_0^{t}f(0,\mathrm{\τ})\mathrm{d\τ}---\left(5\right)$

In the formula: f (0, be that the x=0 place diffuses into the diffusion flux in the porous medium τ), f=-D (dc/dx), H _fThe thickness that is diffuse source (pollution source) (is the length L of diffuse source chamber in the determinator ₁).

This migration models can not get analytic solution, adopts La Pula to tear (Laplace) transform method here, earlier equation (1) is carried out the Laplace conversion, obtains the general type that the Laplace of equation (1) separates

c＝B ₁exp(φ ₁x)+B ₂exp(φ ₂x) (6)

f＝nDB ₁φ ₂exp(φ ₁x)+nDB ₂φ ₁exp(φ ₂x) (7)

B ₁, B ₂-integration constant; φ ₁, φ ₂---following equation root:

${\mathrm{\φ}}_1=\frac{v}{2D}+\sqrt{\frac{v^2}{{4D}^2}+\frac{R_{f}s+\mathrm{\λ}}{D}}=\sqrt{\frac{R_{f}s}{D}}=\sqrt{\frac{s}{D^{*}}}$

${\mathrm{\φ}}_2=\frac{v}{2D}-\sqrt{\frac{v^2}{{4D}^2}+\frac{R_{f}s+\mathrm{\λ}}{D}}=-\sqrt{\frac{R_{f}s}{D}}=-\sqrt{\frac{s}{D^{*}}}$

B ₁, B ₂Try to achieve after the Laplace conversion by boundary condition, with B ₁, B ₂Value substitution equation (6), (7), the Laplace of concentration C separates as follows:

$\stackrel{\‾}{C}=\frac{C_0}{\exp \left(\sqrt{{\mathrm{sR}}_f/\mathrm{Dx}}\right)}\frac{\exp \left(2\sqrt{s{R}_f/\mathrm{Dx}}\right)-\exp \left(2\sqrt{{\mathrm{sR}}_f/\mathrm{DL}}\right)}{s[1-\exp (2\sqrt{{\mathrm{sR}}_f/\mathrm{DL}}]-\frac{\mathrm{nD}}{H_f}\sqrt{{\mathrm{sR}}_{f/D}}[1+\exp \left(2\sqrt{{\mathrm{sR}}_f/\mathrm{DL}}\right)]}---\left(8\right)$

Wherein S is Laplace (La Pula a tears) operator, is multiple parameter.

To one group of given parameter (D, R _f), can obtain the concentration C value of diffusant on random time, the optional position by formula (8) by numerical transformation, so ask D and k by test _dValue is the utilization inverse analysis method.Concrete steps are as follows: diffusion test proceeds to a certain moment t, can record in the porous medium concentration value of diffusant on the diverse location, obtains the relation curve of concentration C and diffusion length x, adjusts diffusion coefficient D and partition factor k _dValue obtains half analytic solution of concentration by formula (8), and the concentration curve with these theoretical half analytic solution go the match experiment to record pushes over out D and k thus _dValue.Concentration that also can be by measuring diffusant in the diffuse source is adjusted D and k over time _dValue uses the theoretical solution that is obtained by formula (8) to remove the match concentration time curve, D that obtains estimating and k _dValue.About the D value, can go to estimate with the analytic solution in the infinite half plane earlier.

The present invention utilizes self-designed pure disperser, and the concentration value by on the soil sample diverse location after measuring the concentration change in the diffuse source or spreading certain hour goes the match test figure with theoretical curve, D that obtains mating and k _dValue.The advantage of the method is that device is simple and practical, and is with low cost; Pure diffusion measurement process computing method are simple relatively.

Description of drawings

Fig. 1 is a determinator of the present invention.

Fig. 2 is the Ca of two examples of use the present invention acquisition ²⁺The relation curve of distance (C-X) of concentration.

Fig. 3 is the K of an example of use the present invention acquisition ⁺The relation curve of distance (C-X) of concentration.

Fig. 4 is the Zn of an example of use the present invention acquisition ²⁺The relation curve of distance (C-X) of concentration.

Number in the figure: B-model well width; H-model groove height, L ₁-diffuse source chamber length, L ₂-porous medium chamber length, L ₃-distillation hydroecium length.

Embodiment

Further introduce the present invention below by embodiment.

Embodiment 1

Porous media material adopts area, Shanghai shallow soil (silty clay) (liquid limit ω _L=30.5%, plastic limit ω _P=18.9%, plasticity index I _P=11.6), diffusant is CaCl ₂Moulded dimension is as follows: B=10cm, H=15cm, L ₁=10cm, L ₂=10cm, L ₃=10cm.Test procedure is as follows: before (1) test, with the soil sample natural air drying, remove the above bulky grain of 2mm; (2) soil sample of natural air drying is put into the center section of device, tamping in layers, recording the soil sample dry density is 1.5g/cm ³, porosity is 0.43; (3) add distilled water at the right and left of model groove, it is saturated to make that soil sample absorbs water at leisure, gets rid of the air in the soil pores, and this process will continue the long time (about two weeks～1 month); (4) treat that soil sample is fully saturated after, be sidelong CaCl in diffuse source into the normal concentration for preparing ₂(Ca ²⁺Concentration be 0.1mol/L), opposite side adds distilled water, attention will make the height of water level on native barrier both sides equate, so just can not produce seepage flow, is also noted that the water level face on both sides will be lower than about porous medium face 3cm slightly.Diffusion process has just begun like this, along with the carrying out of diffusion, Ca in the diffuse source ²⁺Concentration descend gradually.After test proceeds to 63 days, measure in the native porous medium Ca on the diverse location ²⁺Concentration.

In order to calculate diffusion coefficient D and partition factor k _dValue, what leave diffuse source with test point is horizontal ordinate apart from x, with this diffusant Ca ²⁺Concentration C be ordinate, the data preparation that experiment is recorded is seen Fig. 2 in the C-X coordinate system.With the method for telling about previously, suppose different D, ρ _bk _dValue returns theoretical curve to experimental data, successfully obtained D, R with the experimental data coupling _fValue, Ca ²⁺Diffusion coefficient D value in native porous medium is 11.1 * 10 ⁶Cm ²/ s, ρ _bk _dValue is 0.6, blocks factor R accordingly _fValue is 2.40.

Embodiment 2

Other condition is the same, just changes diffuse source into CaCl ₂, KCl mixed solution (Ca ²⁺, K ⁺Initial concentration be 0.1mol/L), after test proceeds to 63 days, measure in the native porous medium Ca on the diverse location ²⁺, K ⁺Concentration.The method of calculating coefficient of diffusion is the same, Ca ²⁺The results are shown in Figure 2, K ⁺The results are shown in Figure 3, the Ca that obtains ²⁺Diffusion coefficient D value in native porous medium is 11.1 * 10 ^-6Cm ²/ s, ρ _bk _dValue is 0.15, blocks factor R accordingly _fValue is 1.34; K ⁺Diffusion coefficient D value in native porous medium is 4.76～6.3 * 10 ^-6Cm ²/ s, ρ _bk _dValue is 5～7, blocks factor R accordingly _fValue is 12.63～17.28.

Embodiment 3

Other condition is the same, just changes diffuse source into ZnSO ₄Solution (Zn ²⁺Initial concentration be 0.1mol/L), after test proceeds to 63 days, measure in the native porous medium Zn on the diverse location ²⁺Concentration.The method of calculating coefficient of diffusion is the same, the results are shown in Figure 4, the Zn that obtains ²⁺Diffusion coefficient D value in native porous medium is 9.5 * 10 ^-6m ²/ s, ρ _bk _dValue is 0.8, blocks factor R accordingly _fValue is 2.83.

Above-mentioned diffusion coefficient D that this patent records and partition factor k _dValue through with foreign literature in the result that records of other method of usefulness of reporting relatively, quite approaching, some phenomenon of discovery (as being different with transfer parameter under the multiple diffusant situation) also existence in the bibliographical information abroad at the phenomenon of diffusion source concentration sudden change, single diffusant of planting.Illustrate that the transfer parameter value that the present invention tries to achieve is that method is feasible reliably.

Claims (5)

1. A device for measuring the migration parameters of liquid in saturated porous media, characterized in that it is a coverless model tank made of polyethylene plastic plate, which is divided into three parts by a porous plate: the middle part is used to place porous The barrier chamber of the medium, the left part is the diffusion source chamber, and the right part is the distilled water chamber. 2. A method for measuring liquid migration parameters in saturated porous media, characterized in that the specific steps are as follows: (1) Put the porous medium into the middle part of the model tank, and place a piece of filter paper on the side of the porous plate near the porous medium to prevent the porous medium from leaking out of the holes; (2) Add distilled water to the left and right sides of the model tank to slowly absorb water and saturate the porous medium, remove the air in the pores of the medium, and make the porous medium dense; (3) After the porous medium is saturated, add a liquid containing a diffusing agent to one side of the model tank, and add distilled water to the other side to make the water levels of the liquid and distilled water equal; in addition, the water level should be lower than the surface of the porous medium; (4) As the diffusion proceeds, the concentration of the diffusing agent in the liquid diffusion source gradually decreases; during the test, on the one hand, the concentration of the diffusing agent in the diffusion source is The concentration of the diffusing agent. 3. The method for measuring liquid migration parameters in saturated porous media according to claim 2, characterized in that the concentration C of the diffusion agent is given by the Laplace solution of the diffusion equation: $\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\sqrt{\mathrm{<span\; class="notranslate">\; the\; s</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}\frac{\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; the\; s</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; the\; s</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; the\; s</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}\sqrt{\mathrm{<span\; class="notranslate">\; the\; s</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; the\; s</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$ Among them, R _f is the retardation factor, R _f =1+(ρ _b k _d /n), n is the porosity, ρ _b O porous medium dry density, k _d is the distribution coefficient, H _f is the thickness of the diffusion source, D is the diffusion coefficient, S is the Laplac operator, and is a complex parameter, and L is the length of the porous medium part in the model tank. 4. The method for measuring liquid migration parameters in saturated porous media according to claim 3 is characterized in that the diffusion coefficient D and the distribution coefficient K _d are obtained by using the following back analysis method: the diffusion test is carried out to a certain moment t, The concentration value of the diffusing agent at different positions in the porous medium can be measured, the relationship curve between the concentration C and the diffusion distance x can be obtained, the diffusion coefficient D and the distribution coefficient k _d can be adjusted, and the semi-analytic solution of the concentration can be obtained by formula (8). This theoretical semi-analytical solution is used to fit the experimentally measured concentration curve, and thus the D and k _d values are deduced. 5. The method for measuring liquid migration parameters in saturated porous media according to claim 3 is characterized in that the following back analysis method is used to obtain the diffusion coefficient D and the distribution coefficient _Kd : by measuring the concentration of the diffusing agent in the diffusion source As time changes, adjust the D and k _d values, use the theoretical solution obtained by formula (8) to fit the concentration-time curve, and obtain the estimated D and k _d values.