DD218681B3 - METHOD FOR DETERMINING THE THROUGHPROOF AND NONPURROUT POROSITAET - Google Patents

Description

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Method for determining porosity parameters

The invention relates to a method for determining the flowed through and non-perfused porosity of disturbed or undisturbed samples of porous media as a function of the saturation of the sample with the fluid under consideration. These parameters are z. B. for the investigation of heat and mass transport with the flowing soil and groundwater needed.

For the laboratory determination of the flowed through and non-perfused porosity, column run tests on samples with L> 5 0 (L column length, 0 diameter of the sample) using conservative tracers are known. From the measured values of the tracer concentration C (z, t) (t-time, 0 = S ζ = SL), the desired porosity parameters по and n _s are determined from the process-describing equations (1) by computer-aided parameter identification:

5 ² C 5C. _. 5C

-Γ- - ν ~ - (n ₀ + k ₃ ) -

δζ δζ 6t

ζ -ν - (по + кз) - £ - k, C - Ic ₂ C ₈ , Па)

0 = (n _s , + W - ^ r ¹ - + k, C - k ₂ Cs, (1 b)

ot

D - dispersion coefficient

ν - filter speed (flow per area)

n ₀ - porosity flowed through

n _St - non-perfused porosity (P. with stagnant fluid)

ki, k ₂ - Velocity coefficients of the 1st order kinetic exchange reaction between the tracer in the

flowed through and non-perfused pore space k ₃ , k, - Speicheroeffiiienten the solid phase

The disadvantages of this method arise

- from the high computational effort

- out of necessity, 4 of the 8 parameters of Eq. (1) (D, v, n ₀ , n _st , k _{1 (} k ₂ , k ₃ , k ")) must be determined by other methods, since only 4 independent parameters are identifiable from Eq. (1), and

- from the difficulties encountered in taking undisturbed L> 5 0 soil samples. The object of the invention is to provide a method with which all variables which are necessary for determining the aforementioned porosity parameters, both disturbed and undisturbed samples taken with little effort can be determined.

According to the invention, the object is achieved in that, when flowing through the sample with a tracer fluid, the quantities listed below are determined successively in three process steps:

Process step I:

The disturbed or undisturbed sample of the porous medium to be examined is installed in a sample chamber. It is flowed through with the fluid to be examined, to which a conservative tracer is admixed, at about constant velocity ν until this tracer is in thermodynamic equilibrium in the flow-through and non-perfused fluid-filled pore space. This state is reached when the tracer concentration in the process is the same as in the feed {C _A = C _z = C |). The desired Gesamtfiuidsättigung of the porous medium η _Σ = n ₀ + n _St is generated by the fact that the porous medium wetting phase is placed in the pore space under appropriate negative pressure or the non-wetting under appropriate pressure

 The sample contains the following amount of tracer when the thermodynamic equilibrium is reached:

Μ, = C, n _s V with С, = C _A

To be measured, the tracer concentrations in the inlet and outlet as well as the volume V of the sample are to be recorded.

Process step II:

At the inlet of the sample, the fluid to be examined with an altered tracer concentration (eg tracer-free) is now supplied, the pressure conditions (capillary pressure) and the flow rate remaining unchanged compared to method step I. In the case of using a tracer-free fluid, which is considered below, the tracer is washed out of the perfused pore space. The flow of tracer-free fluid is carried out until the concentration of the conservative tracer has reached about the value of 0.8 to 0.5Q in the course. The flow rate must be as constant as possible in this process step. The tracer concentration decrease as a function of time (at the times ti) at the outlet (ДС _А -Q-Cn [L, t] = QiM), the washed-out tracer quantity Мц and the filter speed v.

Process step III:

The sample is then fed into the inlet of the outlet (creation of a closed fluid circuit). The pressure conditions (capillary pressure) and the flow rate remain unchanged compared to the method steps I and II, the closed fluid circuit is operated until a thermodynamic equilibrium has again been established between the tracerten fluid portions of the flowed through and non-perfused pore space. This is achieved when Cz = Ca = Cm. The sample then contains the amount of tracer

Mm = СщПіѴ. (З)

By measurement, the tracer concentration in the inlet and outlet and thus Qn is to be recorded. From the balance equation of the tracer quantity of the three method steps, it follows:

Μ, = M _n + Μ ,,, (4)

and thus the fluid-saturated total porosity of the porous medium η to:

", Mi. (5)

V (Q-C ,,,)

The determination of n ₀ is based on the assumption that for the front tip of the tracer-free water particles at the outlet for v / L> k _{2 the} following equation describes with sufficient accuracy the concentration at the outlet of the sample:

In order to determine n ₀ from equation (6), the measured values Qi (t _w ) are graphically plotted in an X, Y coordinate system

Y = inferf (- ^ - 1, o) (7a)

X = in t | i (t _M time since the beginning of method step II)

α Υ (α) α Υ (α) α Υ (α) α Υ (α) α Υ (α)

0.00 0.00 0.25 0.23 0.50 0.48 3 0.75 0.81 0.875 1.07 0.05 0.04 0.30 0.27 0.55 0.54 0.775 0.85 0.900 1.15 0.10 0.09 0.35 0.32 0.60 0.60 0,800 0.90 0.925 1.25 0.15 0.13 0.40 0.37 0.65 0.66 0.825 0.97 0.950 1.40 0.20 0.18 0.45 0.42 0.70 0.73 0,850 1.02 0,975 1.65 inf erf (-α) = - inf erf (α) lim inf erf (α) = °

plotted and the values Y ₁ , starting from the smallest Xj values starting with a straight line: = irechend Eq. (6)

Y = A - BX (8)

balanced. For increasing values Xi, the Yj values may be above the compensation amount. The through-flow and non-perfused porosity result from this:

"O = - to, 5

with: to, s = exp X (Q, = 0.5 Q) (9a)

nst = π _Σ - n ₀ = - (v / L) to, 6. If)

V (L | - Lin)

In the following exemplary embodiment, a sample chamber which is known in principle for hydraulic permeability measurements is used to carry out the method. The specific device is shown in the drawing. The sample chamber is completely filled with a soil sample 1. It is applied laterally with a constant overpressure ρ relative to the atmospheric pressure p _a , _m . At the front, the sample chamber is bounded by ceramic plates 5. Fluid and tracer flow through the ceramic plates (lower end side) and out (upper end side). At the inlet two Boyle-Mariottesche vessels 2 and 3 are connected. In Fig. 2 is tracer-free water; in 3 water and NaCl as a tracer. The vessels are height adjustable for adjusting the flow rate. They can be connected separately via the inlet tap 11 to the line to the inlet 10-stroke tap.

The position of the taps in the three process steps is shown. At the drain a drain pipe and a standpipe 7 are connected via a three-way cock 10A. Between 10A and 10Z there is another line with which the drain can be returned to the inlet. For this purpose, a pump 6 and a standpipe 7 are connected in the line. Both are used to set the constant filter speed to about the value previously set with the adjusted height of the Boyle-Mariottesian vessels. In each of the supply and discharge a measuring cell 8 is connected for measuring the Tracerkonzentration. A burette 9 serves to determine the discharge rate. The individual measuring steps and their evaluation have already been explained above.

Claims (2)

1. A method for determining the flowed through and the non-perfused porosity by measuring changes in concentration and time when flowing through a sample with a fluid and a tracer, characterized in that successively the concentration of the tracer in the thermodynamic equilibrium state of traversed by the tracer fluid at a constant fluid velocity sample , the time to decrease of the tracer concentration to 0.5 to 0.8 times the concentration value measured in the first step after addition of fluid with a lower tracer concentration and, after the sample inlet and outlet are connected together, the concentration of the tracer in the thermodynamic equilibrium continuous circulation of the remaining after the second step in the device fluid can be measured. 2. The method according to claim 1, characterized in that in the second step, a tracer-free fluid is added.