JP5689304B2 - Determination method of mass transfer parameters in rock mass - Google Patents

Description

  The present invention relates to a method for determining a mass transfer parameter in a rock mass.

  As a test method for grasping mass transfer characteristics in rock mass with cracks, a tracer test in which a tracer solution containing a tracer substance is infiltrated from the water injection surface of the rock sample and the tracer concentration of the tracer solution flowing out from the discharge surface is measured. (For example, refer to Patent Document 1).

  For example, various parameters related to the movement of pollutants are acquired by conducting a tracer test on the target rocks for radioactive waste geological disposal, and the rocks that make up the natural barrier are analyzed by numerical analysis based on the acquired parameters. An evaluation may be performed.

In the tracer test for rock mass, the crack opening width and the dispersion coefficient in the crack, which are parameters related to advection / dispersion in the crack, which is the main migration path of material, are obtained. However, in rocks with a high porosity such as sedimentary rocks, in addition to these parameters, it is necessary to obtain parameters (matrix diffusion coefficient) related to diffusion from cracks to the rock matrix (matrix).
Here, advection refers to the movement of a substance due to the flow of groundwater, dispersion refers to the spread of the substance caused by the heterogeneity of the flow path and flow velocity of the substance, and diffusion refers to the movement of the substance due to a concentration gradient. Say.

  The three parameters of the crack opening width, the dispersion coefficient in the crack, and the matrix diffusion coefficient are the time-dependent data of the tracer concentration of the tracer solution flowing out from the discharge surface measured by the tracer test, the advection / dispersion in the crack, and It is obtained by matching with the solution of the governing equation considering matrix diffusion. However, it is difficult to determine the above three parameters of the crack opening width, the dispersion coefficient in the crack, and the matrix diffusion coefficient at a time by a single tracer test. For this reason, the above three parameters have been obtained by a conventional method of performing a plurality of tracer tests by changing the injection amount of the tracer solution or a method of simultaneously injecting a plurality of tracer solutions having different molecular diffusion coefficients in water. It was.

JP 2006-64394 A

However, depending on the test conditions, the sensitivity that the difference in parameters gives to the test results is low (the shape of the curve of the tracer concentration over time does not change even if the parameters change), and the three parameters (crack opening width, dispersion within the crack) In some cases, it was difficult to uniquely determine a coefficient and a matrix diffusion coefficient.
Therefore, it was necessary to set appropriate test conditions in the tracer test.

  The present invention has been made to solve such problems, and it is possible to uniquely determine three parameters consisting of the crack opening width of the rock mass, the dispersion coefficient in the crack, and the matrix diffusion coefficient. It is an object of the present invention to provide a method for determining mass transfer parameters in rock mass.

In order to solve the above problems, the method for determining the mass transfer parameter in the rock according to the present invention estimates the range of values in advance for each of the crack opening width of the target rock, the porosity of the rock matrix, and the matrix diffusion coefficient, Based on the estimated crack opening width, the porosity, and the matrix diffusion coefficient, and the relational expressions (formulas 1 and 2 described later) obtained from the theoretical solution of the governing equation considering advection and matrix diffusion in the crack Then, the size of the tracer test sample, the injection amount of the tracer solution and the injection time are set, and the injection amount of the tracer solution is applied from one side to the tracer test sample formed to the set size. Injecting over the injection time, measuring the time change of the concentration of the tracer solution discharged from the other side, and based on the measured time change of the concentration breakthrough curve Create a advection and dispersion phenomena in the crack, by a theoretical solution or numerical solution of the governing equation of mass transport phenomena considering matrix diffusion phenomenon compared to the breakthrough curve, crack opening width, dispersion coefficient of the crack And determining a combination of matrix diffusion coefficients.
Estimate the range of values for the crack opening width of the target rock, the porosity of the rock matrix, and the matrix diffusion coefficient,

  According to the method for determining the mass transfer parameter in the rock mass, it is possible to uniquely determine the three parameters including the crack opening width of the rock mass, the dispersion coefficient in the crack, and the matrix diffusion coefficient.

In the method for determining the mass transfer parameter in the rock mass, the tracer test may be performed twice or more by changing the injection flow rate of the tracer solution with respect to the tracer test sample.
Moreover, you may implement the tracer test which inject | pours simultaneously the at least 2 or more types of tracer solution from which the molecular diffusion coefficient in water differs with respect to the said sample for tracer tests.

  According to the method for determining the mass transfer parameter in the rock mass, at least two or more breakthrough curves can be obtained for the same sample, and a more accurate parameter can be uniquely determined.

  The size of the sample for the tracer test, the injection amount of the tracer solution and the injection time should be set so as to satisfy the relational expression obtained from the theoretical solution of the governing equation considering the advection and matrix diffusion in the crack of the target rock. For example, the uniqueness of the three parameters is improved.

According to a second aspect of the present invention, there is provided a method for determining a mass transfer parameter in a rock mass, estimating a range of values for each of a crack opening width, a matrix diffusion coefficient, and a rock matrix porosity of the target rock, and estimating the estimated crack opening width. Based on the matrix diffusion coefficient and the porosity, and relational expressions (formulas 1 and 2 to be described later) obtained from the theoretical solution of the governing equation considering advection and matrix diffusion in the crack, The first injection of the tracer solution that sets the size and satisfies the relational expressions (formulas 1 and 2 described later) obtained from the theoretical solution of the governing equation considering the advection and matrix diffusion in the crack of the target rock The amount and the first injection time, and the second injection amount and the second injection time of the tracer solution that does not satisfy the relational expression are set. The tracer test sample is a time change in the concentration of the tracer solution injected from the one side over the first injection time and discharged from the other side with respect to the sample for the tracer test. A tracer that measures one measured value and injects the second injected amount of the tracer solution from one side over the second injection time to the sample for the tracer test and discharges it from the other side. Measure the second measurement value that is the time change in the concentration of the solution, create a breakthrough curve based on the measured first measurement value and the second measurement value, respectively , advection and dispersion phenomenon in the crack, the theoretical solution or numerical solution of the governing equation of mass transport phenomena considering matrix diffusion phenomenon by comparing with the breakthrough curve, crack opening width, the dispersion coefficient and matrix diffusion coefficient of the crack combination It is characterized by determining the.

  In addition, about the determination method of the mass transfer parameter in the rock mass concerning the said 2nd invention, the tracer test which inject | pours simultaneously the at least 2 or more types of tracer solution from which the molecular diffusion coefficient in water differs with respect to the said sample for a tracer test. Further implementation may be performed.

  According to the method for determining the mass transfer parameter in the rock mass, the three parameters can be determined more reliably.

  According to the method for determining the mass transfer parameter in the rock according to the present invention, it is possible to uniquely determine three parameters including the crack opening width of the rock, the dispersion coefficient in the crack, and the matrix diffusion coefficient.

It is a flowchart which shows the procedure of the determination method of the mass transfer parameter in rock mass which concerns on embodiment of this invention. It is a schematic diagram of the boring core used with the determination method of the mass transfer parameter in bedrock. It is a graph which shows an example of the breakthrough curve which changed opening width. It is a schematic diagram which shows the test device of a tracer test. It is a graph which shows the breakthrough curve which concerns on embodiment of this invention. It is a model figure of advection in a crack, dispersion | distribution, and matrix diffusion. (A) And (b) is the breakthrough curve which shows the analysis result of each forward analysis case in an Example. FIG. 10 is a contour diagram showing a mean square distribution of errors when each parameter of forward analysis based on the result of one tracer test by forward analysis case A1 is changed within a range of ± 1 order around a set value. FIG. 10 is a contour diagram showing a mean square distribution of errors when each parameter of forward analysis based on two tracer test results in forward analysis cases A1 and A2 is changed within a range of ± 1 order around a set value. FIG. 10 is a contour diagram showing a mean square distribution of errors when each parameter of forward analysis based on two tracer test results in forward analysis cases A1 and A3 is changed within a range of ± 1 order around a set value. FIG. 10 is a contour diagram showing a mean square distribution of errors when each parameter of forward analysis based on the result of one tracer test by forward analysis case B1 is changed within a range of ± 1 order around a set value. FIG. 10 is a contour diagram showing a mean square distribution of errors when each parameter of forward analysis based on two tracer test results in forward analysis cases B1 and B2 is changed within a range of ± 1 order around a set value. FIG. 6 is a contour diagram showing a mean square distribution of errors when each parameter of forward analysis based on two tracer test results in forward analysis cases B1 and B3 is changed within a range of ± 1 order around a set value. (A) and (b) show breakthrough curves when the opening width is changed by two orders around the set value for the forward analysis cases A1 and B1, respectively. (C) shows the time and concentration in (b). A breakthrough curve in which the axis is converted into a logarithmic display is shown. It is a breakthrough curve which shows the analysis result of forward analysis cases C1 and C2. It is a contour diagram showing the distribution of the mean square error S when three parameters are changed in a range of ± 1 order around the set value of forward analysis for forward analysis cases C1 and C2.

  As shown in FIG. 1, the method for determining the mass transfer parameter in the rock according to the present embodiment includes a preparation step S1, a parameter estimation step S2, a tracer test condition setting step S3, a tracer test execution step S4, and a parameter evaluation step. S5.

The preparation step S1 is a step of cutting and shaping the test sample.
As shown in FIG. 2, the test sample 2 is cut out and shaped from the boring core 1 collected from the target rock. In the present embodiment, the test sample 2 is collected so as to include a portion where the crack 3 is generated in the boring core 1.

  As the test sample 2 is cut out and shaped, preliminary test samples 4 and 4 are collected from the vicinity of the position where the test sample 2 of the same boring core 1 is cut out. In the present embodiment, two preliminary test samples 4 and 4 are collected from two places above and below the test sample 2 and used for the diffusion test and the porosity measurement. The number and shape of the preliminary test samples 4 are not limited.

  The parameter estimation step S2 is a step of estimating a range of values for each parameter of the crack opening width of the target rock, the porosity of the rock matrix portion, and the matrix diffusion coefficient.

  In the present embodiment, first, a diffusion test and a porosity measurement are performed on the preliminary test samples 4 and 4 to obtain a porosity and a matrix diffusion coefficient of the rock substrate portion (matrix portion). Based on the porosity and matrix diffusion coefficient, the range of the porosity and matrix diffusion coefficient of the test sample is estimated.

  Next, a water permeability test is performed on the test sample 2 to measure the hydraulic opening width of the crack in the test sample 2. Then, using this hydraulic opening width as a guide, the range of the crack opening width is estimated.

  The tracer test condition setting step S3 is a step of setting the size of the test sample 2, the injection amount of the tracer solution, and the injection time based on the parameter range estimated in the parameter estimation step S2.

The size of the test sample 2, the amount of the tracer solution injected, and the injection time are the theoretical solution of the governing equation considering the advection in the crack 3 of the target rock mass and the diffusion to the rock matrix (hereinafter referred to as “matrix diffusion”). Is determined so as to satisfy the relational expressions (formulas 1 and 2) obtained from
Expressions 1 and 2 are expressions obtained by solving simultaneous inequalities of Expressions 7 and 8 described later.

Equation 1 shows a time t ^{* at} which the concentration c _f / c _{0 of the} breakthrough curve BTC1 given an arbitrary crack opening width 2b = 2b ^* as shown in FIG. 3 becomes erfc (α). Thereby, the time until the breakthrough curve BTC1 reaches a predetermined concentration can be obtained.
Incidentally, c _f tracer concentration that is discharged, c ₀ is the tracer concentration injected.

Further, the equation 2 shows that the concentration c _f / c _{0 at} time t ^* is erfc (α with respect to the change when the crack opening width 2b = 2b ^* of the breakthrough curve BTC1 is γ times (breakthrough curve BTC2). ) shows a T ₀ a ² conditions that varies below erfc (beta) from.
That is, according to the formula 1 and the formula 2, it is possible to determine the test condition having the required sensitivity of the crack opening width 2b in the focused test time (injection time t).

Here, T ₀ is an average residence time, A is a transition parameter due to matrix diffusion, and is expressed by Equation 3 and Equation 4.
Further, α and β represent variables of the complementary error function (erfc) of Equation 6 described later in the breakthrough curves BTC1 and BTC2, respectively, and are in a relationship of α <1, β> α.

Here, the width of the crack of W, L is the distance from the injection position of the tracer to the discharge position, _Qf is the flow rate of the tracer, _nm is the porosity of the rock matrix part, and _Dm is the diffusion coefficient of the rock matrix part. Show. The crack width W, the distance L, and the inflow flow rate _Qf are known values.

As the crack opening width 2b, the porosity n _{m of} the rock matrix part, and the diffusion coefficient D _m of the rock matrix part, using the range of values estimated in the parameter estimation process, the size of the test sample 2 to determine the conditions such as the inlet flow Q _f of (width W and length L of the crack in equation 3) and the tracer.

Hereinafter, examples in which parameters are assumed using Equation 1 and Equation 2 are shown below.
For example, when the time when the concentration c _f / c ₀ is 0.5 is considered using Equation 1, α = 0.5 (erfc (0.5) = 0.47≈0.5) The test time can be determined by the relational expression of Expression 5 assigned to 1.

Further, Equation 2 shows the condition of T ₀ A ² such that the concentration c _f / c _{0 at} time t ^* changes from erfc (α) to erfc (β) or less with respect to a change of γ times the opening width. Show. That is, it is possible to determine the test condition having the sensitivity of the required aperture width on the time scale of interest by using the formulas 2 and 5.

As a practical example, with respect to 2-fold change in the opening width, in the time-density _c f / _{c 0} in the crack of approximately 0.5 ^{t *,} concentration _c f / _{c 0} is more than about 5% change In such a case, α = 0.5 (erfc (α) = 0.47), β = 0.55 (erfc (β) = 0.44), γ = 2.0, and Equation 2 Is T ₀ A ² <5.76 (≈6).

Equation 6 is based on the knowledge that the sensitivity to the crack opening width test results is not affected by the crack dispersion coefficient, and is the governing equation for the one-dimensional mass transfer phenomenon in a single crack considering matrix diffusion (formula 9) is a theoretical solution when the dispersion phenomenon in the crack is ignored (when D _f = 0 in Equation 9).

For each of the breakthrough curve BTC1 and breakthrough curve BTC2 shown in FIG. 3, when the concentration c _f / c ₀ in the crack at time t = t ^* is expressed by erfc (α) and erfc (β), The relational expression of Expression 8 holds.

Tracer tests performed step S4 is tracer tracer test condition setting step size of the tracer test specimen 2 set in S3, also the set infusion amount c ₀ and the injection time t in the tracer test condition setting process S3 This is a process of conducting a test.

  In the tracer test, as shown in FIG. 4, the tracer solution is injected into the tracer test sample 2 from one side through the pump 5 and the tracer solution discharged from the other side is collected. Measure the concentration of the collected tracer solution. The configuration of the test apparatus used for the tracer test is not limited to that shown in FIG.

In this embodiment, the tracer test is performed by changing the injection flow rate Q _f (Q1, Q2) with the tracer solution E1 and performing the tracer test twice.

The tracer test method is not limited to the above-described method. For example, the tracer test sample 2 may be performed two or more times by changing the injection flow rate of the tracer solution, or the tracer test sample 2 The test sample 2 may be measured by a method in which at least two kinds of tracer solutions having different molecular diffusion coefficients in water are simultaneously injected to measure the concentration. Moreover, you may implement combining the method of changing the injection | pouring flow rate of a tracer solution, and implementing a tracer test twice, and the tracer test which inject | pours two or more types of different tracer solutions simultaneously.
Here, the tracer test performed at least twice by changing the injection flow rate of the tracer solution may be a case where the condition of the expression 2 is satisfied in all cases, or the case where the condition of the expression 2 is satisfied. It may be a case where it is combined with a case that is not present.

  The parameter evaluation step S5 compares the result measured in the tracer test execution step S4 with the analysis result based on the theoretical solution or numerical solution, and determines the combination of the crack opening width, the dispersion coefficient in the crack, and the matrix diffusion coefficient. It is a process to do.

First, as shown in FIG. 5, a plurality of breakthrough curves obtained as a result of the tracer test are created.
Next, the breakthrough curve created from the test result is compared with the breakthrough curve calculated by Equation 13, and the plurality of breakthrough curves created and the plurality of breakthrough curves calculated by Equation 13 are simultaneously displayed. determining a combination of the best average residence time to conform T ₀ and Peclet number P _e and migration parameters a by matrix diffusion.

And migration parameters A the average residence time T ₀ and Peclet number P _e and matrix diffusion obtained above, Equation 19, the opening width 2b crack by Formula 20 and Formula 22, the longitudinal dispersion length alpha _L, the matrix diffusion coefficient D _m Can be requested.

Equations (9) and (10) are governed equations for a one-dimensional mass transfer phenomenon in a single crack expressed in consideration of the advection / dispersion phenomenon in a parallel plate crack and the matrix diffusion phenomenon in the direction perpendicular to the crack. It is.
Here, x is the coordinate in the flow axis of the crack, y coordinates on the axis perpendicular to the crack, c _f is the tracer concentration in the crack, c _m is the tracer concentration in the rock matrix unit, t is time, v _f is the actual flow velocity in the crack, _nm is the porosity of the rock matrix portion, and b is 1/2 of the crack opening width (2b = crack opening width) (see FIG. 6). D _f and D _m represent the hydraulic dispersion coefficient in the crack and the diffusion coefficient (matrix diffusion coefficient) of the rock matrix part, respectively, and are expressed by Expression 11 and Expression 12, respectively.

Here, D ′ is a mechanical dispersion coefficient, α _L is a longitudinal dispersion length in a crack, D _d is a molecular diffusion coefficient of a solute in free water, and τ is a degree of bending of a rock substrate.

When the dispersion phenomenon in the crack is not ignored (when D _f = 0 is not set), the theoretical solution shown in Equation 13 is obtained from the governing equations shown in Equation 9 and Equation 10 by giving the following initial conditions and boundary conditions. Can be derived. The theoretical solution is not limited to Equation 13, and different theoretical solutions may be used depending on the boundary conditions of the tracer test to be performed.
Depending on the boundary conditions, a theoretical solution may not be obtained. In that case, a combination of parameters is obtained by numerical solution.

Here, c ₀ represents the source concentration, and ξ represents an integral variable.
Y, T, and l are expressed by Expression 14, Expression 15, and Expression 16, respectively.

Here, the average residence time _{T 0,} Peclet number _{P e} and migration parameters A by matrix diffusion, respectively formula 17 is expressed by the equation 18 and equation 19.

However, usually, the mechanical dispersion coefficient D 'relationship between the molecular diffusion coefficient _{D d} is, D'»D _d becomes, _{D f} ≒ D' for can be approximated as, Peclet number _{P e} (equation 15), the formula 20 It can be expressed as

Further, when the tracer solution is injected at a constant flow rate, the relationship shown in Equation 21 is established between the actual flow velocity v _f in the crack and the opening width 2b, and if this is substituted into Equation 17, the average residence time T ₀ Can be expressed as in Equation 22.

Here, W is the width of the crack, with the tracer infusion rate Q _f, is a known parameter determined from the test conditions.
Therefore, according to Equation 22, it is possible to determine the opening width 2b from the average residence time T _0.

Further, the matrix diffusion coefficient D _m can be obtained by substituting the opening width 2b and porosity n _m in Equation 19. As the porosity _nm , a value obtained by a laboratory test using a test sample is adopted.
Furthermore, according to Equation 20, it is possible to determine the longitudinal dispersion length alpha _L from Peclet number P _e.

As described above, according to the method for determining the mass transfer parameter in the rock according to the present embodiment, by obtaining at least two breakthrough curves for the same sample, the crack opening width of the rock, the dispersion coefficient in the crack, and the matrix Three parameters consisting of diffusion coefficients can be uniquely determined.
By using these three parameters, the movement state of the solute in the target rock can be grasped, and for example, it can be used when appropriately predicting the movement state of the pollutant.

  In addition, since an appropriate test condition based on the theoretical formula is set, the tracer test can be performed efficiently and accurately, and each parameter can be grasped more accurately. Since the test conditions can be easily set, an efficient test plan is possible.

  The preferred embodiments of the present invention have been described above. However, the present invention is not limited to the above-described embodiments, and the above-described constituent elements can be appropriately changed without departing from the spirit of the present invention.

  For example, the estimation method of the range of values for the crack opening width of the target rock mass, the porosity of the rock matrix and the matrix diffusion coefficient can be carried out by conducting a diffusion test or porosity measurement on a preliminary test sample, It is not limited to the case where the estimation is performed by carrying out the water permeability test.

  Moreover, although the said embodiment demonstrated the case where a sample (sample for a test, a sample for preliminary tests) was extract | collected from a boring core, the collection | recovery method of a sample is not limited, For example, even if it cuts out from an excavation slot Good.

In the following, the results of the examination on the uniqueness of the results when evaluating the three parameters from the tracer test results are shown.
In this study, using the theoretical solution of Equation 13, a forward analysis result in which arbitrary test conditions and parameters were set was assumed to be a virtual tracer test result, and an inverse analysis was performed on this result.

Table 1 shows the setting conditions for the forward analysis case simulating the tracer test.
The scale of the tracer test was 5 cm assuming an indoor tracer test using a core sample.

  In the tracer test, dimensions such as the length and width of the sample are usually determined by the size of the collected sample. Therefore, the test conditions that can be changed are the injection flow rate of the tracer solution and the type of the tracer to be injected.

In this study, the analysis was performed on the assumption that the injection flow rate _Qf is large (forward analysis case A1) and the injection flow rate _Qf is small (forward analysis case B1).
In addition, for the forward analysis cases A1 and B1, the forward analysis cases A2 and B2 when the injection flow rate _Qf was changed were also analyzed.
Furthermore, the analysis was also performed for the forward analysis cases A3 and B3 when the injection flow rate was the same as the forward analysis cases A1 and B1 and the matrix diffusion coefficient _Dm was changed.

  7A and 7B show the analysis results (breakthrough curves) of each forward analysis case. FIGS. 7A and 7B are obtained by adding a concentration measurement error of ± 2% to the concentration data at each time obtained by the theoretical solution of Equation 13, assuming an actual tracer test.

When the analysis results shown in FIGS. 7A and 7B are considered as tracer test results, three parameters (rock opening width of rock mass, dispersion coefficient in crack, matrix diffusion coefficient) are obtained by inverse analysis. Check for uniqueness.
For confirmation of uniqueness, a combination of a plurality of arbitrary parameters is designated, and the square mean S of errors between the observation data (forward analysis result) and the analysis result shown in Expression 23 is used for each combination.

  To confirm the uniqueness, a combination of parameters that can be fitted to one breakthrough curve obtained from a single tracer test result is obtained for each of a case with a large injection flow rate and a case with a small injection flow rate. In addition, a combination of parameters that can fit two breakthrough curves obtained from two tracer test results with different flow rates simultaneously and a parameter that can be fitted simultaneously to a breakthrough curve obtained from two tracer test results with different matrix diffusion coefficients Find a combination of

8 to 13 show the examination results.
Here, FIGS. 8 and 11 show the case where the parameters are evaluated from the results of one tracer test according to the forward analysis cases A1 and B1, respectively.
FIGS. 9 and 12 show cases where parameters are evaluated from the results of two tracer tests in which the flow rates in forward analysis cases A1 and A2 and B1 and B2 are changed, respectively.
Further, FIGS. 10 and 13 show cases where parameters were evaluated from the results of a single tracer test in which two kinds of tracers having different molecular diffusion coefficients in water were respectively injected according to forward analysis cases A1 and A3 and B1 and B3, respectively. ing.

  8, 9, and 10 are contours showing the distribution of the mean square error S when the three parameters are changed in the range of ± 1 order around the set value of the forward analysis for the forward analysis cases A1 to A3. FIG.

  The hatched portion in the drawing (the portion surrounded by the 0.02 line) shows that the mean square S value is small, and the breakthrough curve obtained by the combination of parameters and the forward analysis result agree well with each other. Show. If a clear peak concentrated at one point is seen, the inverse analysis solution converges to that peak, indicating that the parameter can be uniquely determined.

  In FIG. 8 created only by one tracer test result (case A1), a clear peak concentrated on one point is not seen, and the three parameters cannot be determined uniquely. On the other hand, in FIG. 9 by the tracer test (cases A1 and A2) in which the flow rate is changed, or in FIG. 10 by the tracer test (cases A1 and A3) in which two kinds of tracers having different molecular diffusion coefficients are injected simultaneously, the forward analysis is performed. In the vicinity of the setting parameter, a clear peak is seen in the distribution of the mean square S, and it can be seen that the uniqueness of the parameter is improved.

  Therefore, it is possible to more accurately determine the three parameters by performing two or more tracer tests with varying flow rates, or by using two or more tracer solutions with different molecular diffusion coefficients in water. It turns out that it can be done.

  11, 12, and 13 are contours showing the distribution of the mean square error S when the three parameters are changed in the range of ± 1 order around the set value of the forward analysis for the forward analysis cases B1 to B3. FIG.

As shown in FIGS. 11, 12, and 13, when the flow rate is small, the longitudinal dispersion length α _L and the matrix diffusion coefficient D _m can be uniquely evaluated, but the opening width 2 b is compared with the case where the flow rate is large. As a result, the sensitivity to the shape of the breakthrough curve is small, and the result cannot be evaluated uniquely. This is because the shape of the breakthrough curve hardly changes even if the opening width 2b is changed to any value under the low flow rate condition.

  From the above results, it can be seen that in order to uniquely evaluate the three parameters, it is necessary to carry out under the flow rate conditions in which the sensitivity of the opening width 2b is sufficiently ensured.

  Next, the result of examining the relationship between the test conditions and the sensitivity of the opening width is shown.

  For forward analysis cases A1 and B1, as shown in FIGS. 14 (a) and 14 (b), a breakthrough curve is created when the order value of the opening width 2b is changed by two orders.

  In case A1 where the flow rate is large, as shown in FIG. 14A, the shape of the breakthrough curve changes greatly before and after the plot, and it can be seen that the sensitivity of the opening width 2b is within a large range.

  On the other hand, when the flow rate is small, as shown in FIG. 14B, even if the set value of the opening width 2b is changed, there is a range in which the breakthrough curve shows substantially the same shape, and the sensitivity of the opening width 2b is low. You can see that it is in range. However, the sensitivity of the opening width 2b varies depending on the time of interest and the scale of the space.

FIG. 14 (c) shows a breakthrough curve in which the time and concentration axes in FIG. 14 (b) are converted into logarithmic representations.
As shown in FIG. 14 (c), depending on the time and space scales of interest, a difference appears in the shape of the breakthrough curve even in a range where almost no change was found in the shape of the breakthrough curve.

  Therefore, in order to evaluate the three parameters, it is necessary to determine the test conditions having the sensitivity of the aperture width so that the parameters can be evaluated practically after determining the time of interest and the transition distance. .

Here, the time scale indicates the length of the test implementation period, and is determined based on Equation 1 in the test plan. The transition distance indicates the length of the crack in the flow direction, and is given as a known condition depending on the size of the target sample.
On the other hand, the flow rate condition (test condition) having the sensitivity of the opening width can be determined by the dimensionless parameter T ₀ A ² , and may be determined by the test condition that satisfies Expression 2.

  Next, the certainty was confirmed by combining the tracer test under the test conditions satisfying Formula 2 and the tracer test under the test conditions not satisfied.

As shown above, even if it can uniquely determine the three parameters (FIG. 9, FIG. 10) the peak of the mean square S of error, in the range of about one order of aperture width 2b and longitudinal dispersion length alpha _L Distributed, with high uncertainty.
However, even when the three parameters cannot be determined uniquely, the longitudinal dispersion length α _L and the matrix diffusion coefficient D _m are highly sensitive and unique (see FIGS. 11, 12, and 13).

  Therefore, it is confirmed whether the uniqueness of the evaluation results of the three parameters can be improved by combining the unsatisfied case with the case satisfying the relational expression (Equation 1 and Equation 2) obtained from the theoretical solution of the governing equation. To do.

  Tracer test (forward analysis case C1) with injection volume and injection time satisfying the relational expressions (Equation 1 and 2) obtained from the theoretical solution of the governing equation, and tracer test (forward analysis) with injection volume not satisfying the relational expression Table 2 shows a list of conditions and parameters for forward analysis with case C2). FIG. 15 shows a breakthrough curve based on the result of forward analysis.

  For forward analysis cases C1 and C2, combinations of parameters that can fit the breakthrough curve of FIG. 15 are obtained. FIG. 16 is a contour diagram showing the distribution of the mean square error S when the three parameters are changed in the range of ± 1 order around the set value of the forward analysis for the forward analysis cases C1 and C2.

As shown in FIG. 16, the distribution range of the peak of the mean square error S is smaller than the result (see FIG. 9) of the parameter combination obtained only under the test conditions that satisfy the relational expression, and the certainty is further improved. did. In particular, the evaluation of the longitudinal dispersion length α _L resulted in higher reliability.

  Therefore, it has been proved that the reliability of the combination of the three parameters is further improved by combining the test with the value satisfying the relational expressions (Equation 1 and Expression 2) and the test with the value not satisfying the relational expression. It was.

1 Boring core 2 Test sample 3 Crack 4 Preliminary test sample

Claims (5)

Estimate the range of values for the crack opening width of the target rock, the porosity of the rock matrix, and the matrix diffusion coefficient,
Equations 1 and 2 which are relational equations obtained from the theoretical solution of the governing equation considering the estimated crack opening width, the porosity and the matrix diffusion coefficient, and advection and matrix diffusion in the crack of the target rock Set the size of the sample for the tracer test, the injection amount of the tracer solution and the injection time so as to satisfy
A change in the concentration of the tracer solution discharged from the other side is injected over the injection time from one side to the injection amount of the tracer solution with respect to the sample for the tracer test formed in the set size. Measure and
Create a breakthrough curve based on the time variation of the measured concentration,
By comparing the theoretical solution or numerical solution of the governing equation of the mass transfer phenomenon considering the advection / dispersion phenomenon and matrix diffusion phenomenon in the crack with the breakthrough curve , the crack opening width, the dispersion coefficient in the crack and the matrix diffusion coefficient A method for determining a mass transfer parameter in a rock mass, characterized by determining a combination of the two.

  The method for determining a mass transfer parameter in a rock mass according to claim 1, wherein the tracer test is performed twice or more by changing an injection flow rate of the tracer solution for the tracer test sample.   The tracer test is performed by simultaneously injecting at least two types of tracer solutions having different molecular diffusion coefficients in water into the tracer test sample. A method for determining mass transfer parameters in bedrock. Estimate the range of values for the crack opening width of the target rock, the porosity of the rock matrix, and the matrix diffusion coefficient,
Based on the estimated crack opening width, the porosity, and the matrix diffusion coefficient, and Equations 1 and 2 that are relational equations obtained from the theoretical solution of the governing equation considering advection and matrix diffusion in the crack, While setting the size of the tracer test sample,
A first injection amount and a first injection time of a tracer solution satisfying Expressions 1 and 2 , which are relational expressions obtained from a theoretical solution of a governing equation considering advection and matrix diffusion in the crack of the target rock; A second injection amount and a second injection time of the tracer solution that does not satisfy the relational expressions ( 1) and (2) are set,
The tracer test sample formed to a set size is injected with the first injection amount of the tracer solution from one side over the first injection time and discharged from the other side. While measuring the first measurement value, which is a change in the concentration of the solution over time, the second injection amount of the tracer solution is injected into the tracer test sample from one side over the second injection time. Measuring the second measured value, which is the time change of the concentration of the tracer solution discharged from the other side,
Create breakthrough curves based on the measured first and second measured values,
By comparing the theoretical solution or numerical solution of the governing equation of the mass transfer phenomenon considering the advection / dispersion phenomenon and matrix diffusion phenomenon in the crack with the breakthrough curve , the crack opening width, the dispersion coefficient in the crack and the matrix diffusion coefficient A method for determining a mass transfer parameter in a rock mass, characterized by determining a combination of the two.

5. The mass transfer in rock mass according to claim 4 , wherein the tracer test is performed by simultaneously injecting at least two kinds of tracer solutions having different molecular diffusion coefficients in water into the tracer test sample. How to determine parameters.

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