JP6357720B2 - Simulation method of behavior of water-insoluble liquid in unsaturated soil - Google Patents

Description

The present invention relates to a method for simulating the behavior of a water-insoluble liquid in unsaturated soil.

  In response to the nationwide groundwater contamination survey conducted by the Environment Agency in 1982, volatile organic chlorine compounds such as trichlorethylene, tetrachloroethylene, 1,1,1-trichloroethane, gasoline, kerosene, light oil, heavy oil (oils) It has been confirmed that soil and groundwater contamination due to such factors exists nationwide, especially in urban areas.

  On the other hand, in order to effectively and efficiently purify and repair such contaminated soil and groundwater, it is important to capture the behavior of the pollutant, that is, the diffusion region and concentration distribution as accurately as possible. In particular, NAPL (Non-Aqueous Phase Liquid) such as trichlorethylene, tetrachlorethylene, gasoline, light oil, and kerosene can stay in the ground for a long time and cause serious pollution. It is important to capture

  Conventionally, as a technique for predicting the behavior of pollutants in the ground, 1) a technique for analyzing water infiltration in a saturated ground (single phase), and 2) analyzing an arbitrary two-phase infiltration phenomenon Techniques (two phases), 3) Techniques (three phases) for analyzing water-NAPL-air seepage phenomena are used.

  1) The method (single phase) of analyzing the infiltration phenomenon of water in saturated ground simulates the infiltration (movement) phenomenon of pore water (groundwater) in saturated ground where the soil particle gap is filled with water, such as deeper than the groundwater surface. It is a technique to do. The permeation phenomenon in the state where the soil particle gap is filled with a single fluid is discretized by the finite element method, the finite difference method, or the finite volume method using the Darcy law and the continuity equation (mass conservation law of pore water) as governing equations. By solving the above, it is possible to accurately simulate the behavior of groundwater, and hence the behavior of pollutants contained in the groundwater.

2) The method of analyzing any two-phase seepage phenomenon (two-phase) is, for example, the penetration of pore water and pore air in unsaturated ground where water and air are present in the gap between soil particles, such as shallower than the groundwater surface ( This is a method of simulating the (movement) phenomenon. In addition to the Darcy and mass conservation laws for pore water and air, respectively, the water-air seepage phenomenon is analyzed using a moisture characteristic curve that gives the relationship between the pressure and saturation of the water phase and air phase. Proposed and put into practical use a water-air two-phase coupled permeation analysis method that solves by the finite element method or the finite difference method using the relationship between saturation and permeability / air permeability coefficient, and the state equation of air phase (assuming ideal gas) as the governing equation. ing.
Note that van Genuchten's equation (see Non-Patent Document 1) and Brooks-Corey's equation (see Non-Patent Document 2) are often used as moisture characteristic curves that give the relationship between the water phase and air phase pressure and saturation. Yes. Further, several methods using the Mualem formula (see Non-Patent Document 3) and the like have been proposed for the relationship between the saturation of each phase and the water permeability / air permeability coefficient.
In addition, the two-phase water-NAPL or NAPL-air permeation phenomenon with different pore fluid combinations is based on the pore fluid pressure and scaled water-air moisture characteristic curves taking into account the difference in interfacial tension between pore fluids. The saturation relationship is used to analyze the water-air infiltration phenomenon in almost the same way. Water-NAPL analysis is performed in saturated ground, NAPL-air analysis is performed in the infiltration (movement) of NAPL in dry ground. ).

  The finite element method, finite difference method, and finite volume method are often used as numerical analysis methods for multiphase infiltration phenomena, but the infiltration phenomenon of ground where multiple fluids exist in the gap is relative to the saturation change. Since the change in permeability is large and nonlinearity becomes a problem, studies on discretization of governing equations and numerical calculation techniques have been continued.

  In the 1990s, the development of two-phase permeate flow analysis techniques was promoted, and Celia and Bouloutas (see Non-Patent Document 4) developed a spatially discrete governing equation for the analysis of water-air unsaturated permeation. When the pressure is displayed and solved, the law of conservation of mass (mass balance) is not satisfied and numerical vibration occurs. When the mixed equation expressed by pressure and saturation is solved, the law of conservation of mass is satisfied, but numerical vibration occurs. It was shown that if the modified Picard method applying the Picard method to the mixed equation is used, the law of conservation of mass is satisfied and pressure oscillation does not occur. Furthermore, Hibi et al. (See Non-Patent Document 5) compared the applicability of analysis methods such as the Fully upwind method (see Non-Patent Document 6) with respect to the water-NAPL two-phase permeation analysis method, and applied the modified Picard method. The solution method was shown to be a rational method that satisfies the law of conservation of mass for infiltration analysis of water-NAPL two-phase system and does not cause pressure oscillation.

  3) The method of analyzing the water-NAPL-air infiltration phenomenon (three phases) is that NAPL leaks near the ground surface and penetrates into the ground without mixing with water and air, and is independent of the water and air phases. This is a method for simulating the multiphase infiltration (movement) phenomenon of water, NAPL and air in multiphase ground where water and air and NAPL intervene in the gap between soil particles when forming a flow.

  And in this method of analyzing the water-NAPL-air infiltration phenomenon, in addition to the Darcy law and the mass conservation law of the water phase, the air phase and the NAPL phase, respectively, the relationship between the pressure and saturation of the three-phase pore fluid, and It is necessary to solve the relationship between the saturation of each phase and water permeability, NAPL (oil), air permeability coefficient (or relative permeability), and the state equation of air phase (compression characteristics of the ideal gas) as governing equations by the finite element method etc. There is.

In the water-NAPL-air three-phase ground, only the water-NAPL interface and NAPL-air interface appear, but the Leverett assumption (see Non-Patent Document 7) that the water-air interface does not appear is used. A formula (see Non-Patent Document 8) combining a water-NAPL two-phase system and a NAPL-air two-phase model is used.
In addition, Stone (see Non-Patent Document 9) and Parker and Lenhard (see Non-Patent Document 10, Non-Patent Document 11, and Non-Patent Document 12) are saturation and relative transmission of each phase of water-NAPL-air three-phase ground. A degree relation is proposed.

  In the infiltration analysis of water-NAPL-air three-phase system ground, as in the case of two-phase system, the problem is pointed out that the mass balance is not maintained (the law of conservation of mass is not satisfied) if the governing equation with pressure unknown is discretized. However, Oostrom et al. (See Non-Patent Document 13) uses the analysis method based on the Fully upwind type finite difference method, and Hibiki and Fujinawa (see Non-Patent Document 14) apply the modified Picard method to the three-phase system. As a result, analysis that maintains mass balance is realized.

van Genuchten, M. Th. (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, pp. 892-898. Brooks, R.J and Corey, A.T. (1964) Hydraulic properties of porous media, Hydrol.Pap.3, Colo.State Univ., Fort Collins. Mualem, Y. (1976) A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour.Res., 12, pp. 513-522 Celia, M. and Bouloutas, E. T. (1990) A general mass-conservative numerical solution for the unsaturated flow equation, Water Resources Research, 26 (7), p.1483-1496. Yoshihiko Hibiki, Katsuyuki Fujinawa, Yukihiko Fujiwara (2002) Comparison of numerical models of water-NAPL two-phase flow in porous media, Journal of Japan Society of Civil Engineers, No.720 / VII-25, pp.27-38. Thomson, N. R., Graham, D. N., and Farquhar, G. J. (1992) One-dimensional immiscible displacement experiments, J. Contamination Hydrology, 10, p.197-223. Leverett, M.C. (1941) Capillary behavior in porous solids, Trans. Am. Inst. Min. Metal.Eng., 142, pp. 152-169. Lenhard, R.J. and Parker, J.C. (1987) A model for hysteretic constitutive relations governing multiphase flow 2. Permeability-saturation relations, Water Resour.Res., 23 (12), pp.2197-2206. Stone, H.I. (1973) Estimation of three-phase relative permeability and residual oil data, J. Can. Pet. Tech. 12 (4), pp.53-61. Parker, J.C. and Lenhard, R.J. (1990) Determining three-phase permeability-saturation-pressure relations from two-phase system measurements, J. Pet. Sci. Eng. 4, pp. 57-65, 1990. R. J. Lenhard and Parker, J. C .: Water Resour. Res. Vol.24 (3), pp.373-380, 1988. Parker, J.C., R.J.Lenhard, and T. Kuppusamy: Water Resour.Res. Vol.23 (4), pp.618-624, 1987. Oostrom, M., Hofstee, C., Lenhard, RJ and Wietsma, TW (2003) Flow behavior and residual saturation formation of liquid carbon tetrachloride in unsaturated heterogeneous porous media, Journal of Contaminant Hydrology, 64 (1-2), p. 93-112. Hibiki, Fujinawa (2005) Comparison of numerical models of air-water-NAPL three-phase flow in porous media, Journal of Japan Society of Civil Engineers, 79781-94.

  However, in the conventional water-NAPL-air three-phase permeation analysis, the mass conservation law, Darcy law and pressure-saturation (p-S) relationship, saturation-relative permeability (Sk) of each phase. The governing equation obtained from the relation is spatially discretized by the finite element method, the finite volume method, etc., but in the past model that gives the pressure-saturation relationship, the pressure of NAPL (water-insoluble fluid) is relatively small, that is, NAPL There was a problem that the three-phase pressure-saturation relationship could not be correctly grasped under the condition that the degree of saturation was low.

  In the conventional water-NAPL-air three-phase analysis method, the NAPL saturation is extremely underestimated under relatively low NAPL pressure conditions, so the relative permeability of the NAPL phase must be underestimated. become. For this reason, there is a problem that the pressure-saturation relationship and the saturation-specific permeability relationship cannot be correctly grasped when NAPL enters the ground or discharges NAPL from the ground (such as purification). .

  In other words, in the conventional water-NAPL-air three-phase coupled infiltration analysis method described above, there is no model that can properly express the pressure-saturation relationship in a situation where the saturation is low when NAPL permeates, and the pressure of NAPL However, the hysteresis at the time of NAPL intrusion / discharge cannot be considered under relatively low conditions. For this reason, there has been a problem that it is impossible to accurately simulate the water-NAPL-air three-phase infiltration phenomenon when NAPL enters the unsaturated ground or when the soil contaminated with NAPL is purified.

In view of the above circumstances, the present invention can accurately simulate the infiltration phenomenon of pore fluid in a multiphase ground where water, air, and a water-insoluble fluid (NAPL) are interposed in the gap of soil particles. The purpose is to provide a method for simulating the behavior of water-insoluble liquids in unsaturated soil, which makes it possible to more accurately evaluate and verify the extent and extent of pollution and the effects of soil pollution remediation measures. .

  In order to achieve the above object, the present invention provides the following means.

The method for simulating the behavior of a water-insoluble liquid in unsaturated soil according to the present invention is a method for water-insoluble in an unsaturated soil in a multiphase ground where water, air, and a water-insoluble fluid (NAPL) are interposed in the gaps between soil particles. The method of simulating the behavior of an ionic liquid , as shown in the following formulas (1) and (2), a gap in a multiphase ground where water, air, and a water-insoluble fluid are interposed in a gap between soil particles In addition to constructing a model representing the permeation phenomenon of the fluid, a governing equation for the three-phase flow of water-air-NAPL is set as shown in the following equations (3), (4), and (5), and the equation (3 ), (4), and (5), the space is discretized by the Galerkin finite element method, the time is discretized by the backward difference method, and the modified Picard method is applied, and the following equations (6) and (7) ), And the behavior of the water-insoluble liquid is analyzed using the formula (8).

here,
n: Soil porosity, S: Saturation, p: Pressure, _kr : Relative permeability coefficient, K: Saturation permeability coefficient, γ: Unit volume weight, _Kv : Volume compression coefficient, q: Flow rate, ρ: Density, b: object force, μ _r : inviscidity coefficient, E _j ⁱ : ∂S _i / ∂p _j ,
[Superscript / Subscript w, a, n, l]: [Water, Air, Water-insoluble liquid (NAPL), Liquid (Water + NAPL), [Superscript m, k]: [Time step, respectively] [Repetition step], [•]: time differentiation, [-(superscript)]: average value in element, [-(subscript)]: value at boundary.

In the method for simulating the behavior of a water-insoluble liquid in unsaturated soil according to the present invention, the transition between any two phases and three phases of water, air, and a water-insoluble fluid in a gap between soil particles is expressed as follows. Using the intermediate fluid pressure coefficient μ expressed by the equation (9), it is expressed by a variable from 0 to 1 as in the following equations (10), (11), and (12), and the following equation (13) Β ^w , β ^l and μ satisfying) are given by a Bezier curve, and the water-air suction s _aw is a scale variable β ^{w of} the water phase determined by μ and the liquid phase of water and water-insoluble fluids, It is desirable to obtain a characteristic curve indicating the degree of saturation of the water phase and the liquid phase by multiplying β ^l and substituting it into the van Genuchten equation of the following equation (14).

Here, S is the saturation, and S _max and S _min are the maximum and minimum saturations, respectively. s is a suction, and p is a pressure, and s _ij = p _i -p _j (subscripts i and j indicate a low wettability fluid and a high fluid, respectively, of the two phases).

Furthermore, in the method for simulating the behavior of a water-insoluble liquid in an unsaturated soil of the present invention, state variables I _w and I _l reflecting the inflow and outflow history of the water phase and the liquid phase are set to 1 in the inflow process of water and liquid. The following equation (15) that satisfies the relationship of approaching −1 in the discharge process is given by the following equation (15), and μ is expressed as I _w and I _l taking into account the inflow / outflow history of water and liquid as in the following equation (16): _{w ^*,} and said that it has to be fixed for μ _l ^*.

Here, i corresponds to the water phase w and the liquid phase l. ζ _w and ζ _l are parameters that determine the rate of change of I _w and I _{l with} respect to the saturation change of water and liquid. m _i is a parameter that determines the strength of the effect of the hysteresis of the outflow Nyutoki.

In the method for simulating the behavior of water-insoluble liquid in unsaturated soil of the present invention, the permeation phenomenon of pore fluid in the multiphase ground where water, air, and water-insoluble fluid (NAPL) are interposed in the gap of soil particles. It becomes possible to simulate with high accuracy.

It is a schematic diagram showing the penetration phenomenon of LNAPL and DNAPL. Is a diagram showing an analysis model used in simulation example by behavior simulation method of the water-insoluble liquid unsaturated soil according to the first embodiment of the present invention. Is a diagram showing the permeation analysis of LNAPL conducted with behavior simulation method of the water-insoluble liquid unsaturated soil according to the first embodiment of the present invention. Is a diagram showing the permeation analysis of DNAPL conducted with behavior simulation method of the water-insoluble liquid unsaturated soil according to the first embodiment of the present invention. It is a figure which shows Leverett's assumption that the three-phase fluid of water-water-insoluble liquid (NAPL) -air fills the contact point vicinity of soil particles in the order of water, NAPL, and air having high wettability in the soil particle gap. Is a diagram showing the relationship between the model parameters β and intermediate pressure coefficient number μ of the present invention used in the description of the behavior simulation method of a water-insoluble liquid in the unsaturated soil according to the second embodiment of the present invention. It is a figure which shows the relationship of parameter (beta) and intermediate pressure coefficient (micro | micron | mu) of the conventional LP model (FIG. 7 (a)) and the model of this invention (FIG.7 (b)). It is a figure which shows the schematic diagram and pressure assumption of the oil layer thickness experiment (column experiment) by Tanahashi et al. Result of a second simulation performed for confirming the superiority of the behavior simulation method of the water-insoluble liquid unsaturated soil according to the embodiment results of the present invention, the oil layer thickness experiments by Tanahashi et al (column experiment) (FIG. 9A), the result of the conventional LP model (FIG. 9B), and the result of the model of the present invention (FIG. 9C) are compared. An intermediate fluid pressure coefficient number mu employed in the description of the behavior simulation method of the water-insoluble liquid of the third in the unsaturated soil according to the embodiment of the present invention, an intermediate fluid pressure coefficient number mu ^* Considering history, saturation S It is a figure which shows the relationship. It is the figure which compared the simulation result of the model of LP model, the model of 2nd Embodiment, and the model of 3rd Embodiment.

Hereinafter, the behavior simulation method (behavior analysis method) of the water-insoluble liquid in the unsaturated soil according to the first embodiment of the present invention will be described with reference to FIGS. Here, this embodiment can accurately simulate the permeation phenomenon of pore fluid in the multiphase ground where water, air, and NAPL (non-aqueous fluid) are interposed in the gap between the soil particles. The present invention relates to a method for simulating the behavior of a water-insoluble liquid in unsaturated soil, which makes it possible to more accurately evaluate and verify the effect of the countermeasures for soil contamination, and the prediction of the spread and degree of soil contamination.

First, in order to solve the soil contamination phenomenon by NAPL and subsequent purification problems, a numerical analysis method that properly considers the infiltration characteristics and fluid retention characteristics of the ground is necessary. In particular, for NAPL pollution in shallow unsaturated ground, a characteristic curve that accurately reflects the relationship between the pressure and saturation of the water-NAPL-air three phases mixed in the soil and a multiphase flow analysis method based thereon are effective.
As a conventional three-phase system characteristic curve, Lenhard and Parker's model using water-NAPL and NAPL-air two-phase characteristic curves (Non-Patent Documents 10, 11, 12: hereinafter, this conventional model is referred to as “LP model”. ") Is simple and has been often used to analyze initial value problems. In the model, as shown in the following equations (17) and (18), water saturation is given by water pressure and NAPL pressure, and liquid saturation (water saturation + NAPL saturation) is given by taking NAPL pressure and air pressure as variables. Yes.

Here, in this embodiment, the symbols used are defined as follows.
n: Porosity, S: Saturation, p: Pressure, _kr : Specific permeability coefficient, K: Saturation permeability coefficient, γ: Unit volume weight, _Kv : Volume compression coefficient, q: Flow rate, ρ: Density, b: Body force, μ _r : inviscid coefficient, E _j ⁱ : ∂S _i / ∂p _j ,
[Superscript / Subscript w, a, n, l]: [Water, Air, NAPL, Liquid (Water + NAPL], [Superscript m, k]: [Time step, Repeat step, respectively], [・]: Time derivative, [-(superscript)]: Average value in element, [-(subscript)]: Value at boundary

As shown in the equations (17) and (18), in the LP model, the water saturation and the liquid saturation are given independently of the air pressure and the water pressure, respectively, and the interaction between the phases is not taken into consideration. That is, the interaction between water and air is ignored, and the two-phase characteristic curves of water-NAPL and NAPL-air are simply expressed. For this reason, the saturation degree of NAPL is low and the saturation distribution in the ground that is close to the water-air two-phase system (pressure-saturation relationship of the three-phase ground) cannot be expressed properly. It is not possible to accurately solve the pollution mechanism and the purification process of unsaturated ground due to (see FIG. 9 described later).
Note that the four partial differential coefficients E in the equations (17) and (18) can be calculated by, for example, an equation (32) described later.

On the other hand, in the behavior analysis method (behavior simulation method) of the water-insoluble liquid in the unsaturated soil of the present embodiment, a model is constructed using the following equations (19) and (20), Accurately simulate pore fluid permeation phenomenon in multiphase ground where water, air, and water-insoluble fluid (NAPL) are interspersed in the gap between soil particles, using a three-phase characteristic curve that takes pressure interaction into account. It can be so.

Specifically, in the method for analyzing the behavior of a water-insoluble liquid in an unsaturated soil according to the present embodiment, a characteristic curve describing a mass conservation law and a change in the degree of saturation of pore fluid as a governing equation of multiphase flow in the ground ( It is assumed that the equations (19) and (20) are considered, and the permeation phenomenon of each phase follows the Darcy law.
Here, the relationship between the saturation and the specific transmission coefficient uses the Mualem equation (Non-Patent Document 3). Assuming that water and NAPL are incompressible fluids and air is an ideal gas, the governing equations of water-air-NAPL three-phase flow are as shown in the following equations (21), (22), and (23).

  Then, for the equations (21), (22), and (23), the space is discretized by the Galerkin finite element method, the time is discretized by the backward difference method, and the modified Picard method is applied. ), Formula (25), and formula (26) are obtained.

In Expression (24), Expression (25), and Expression (26), {} is a vector indicating a value at a node.

_Next, organized by Taylor expansion with ^{_{S w m + 1, k +}} 1, S n m + 1, k + 1, S a m + 1, k + 1 to _{p w, p n, p a} , the following equation (27), equation (28), wherein (29) is obtained.

Here, δ ^{m + 1, k + 1} = pm ^{+ 1, k + 1−} pm ^{+ 1, k} , and δ is an unknown variable and calculation is repeated until δ≈ (nearly equal) 0.

In addition, the matrix in Formula (27)-Formula (29) is given by the following formula (30).

  Next, a description will be given of a calculation example (simulation result) by the behavior analysis method of the water-insoluble liquid in the unsaturated soil of the present embodiment formulated using the modified Picard method as described above.

Here, NAPL flows into the unsaturated ground with the groundwater surface, referring to the two-dimensional analysis of Tosaka et al. (Tosaka et al .: Journal of Groundwater Science, 38 (3), pp.167-180, 1996.) The phenomenon is simulated.
Specifically, the analysis model has a two-dimensional cross section as shown in FIGS. 1 and 2, and is provided with an impermeable layer that does not penetrate both two and three phases below the groundwater surface.

  The main physical property values are shown in Table 1.

In this simulation, the calculation is performed for two types of LNAPL lighter than water and DNAPL heavier than water shown in Table 1. Moreover, the penetration of NAPL was given by flow rate control, and the flow rate was constant at 2.0 × 10 ⁻⁴ m ² / sec per unit depth. Furthermore, as the boundary condition, the groundwater surface was kept constant at the lateral boundary, and the position of zero flow rate was used as the boundary for NAPL, excluding the entry point.

3 and 4 show simulation results and show changes in the saturation distribution of NAPL.
As shown in FIGS. 3 and 4, when NAPL flows from the ground surface, it stays in the impervious layer and gradually penetrates downward, and DNAPL heavier than water flows down faster than LNAPL, which is lighter than water. Obtained. Also, the difference due to the specific gravity of NAPL becomes clearer after reaching the groundwater surface, while LNAPL stays near the groundwater surface and spreads in the horizontal direction, whereas DNAPL does not stay on the groundwater surface and does not stay with the water. Due to the difference in density, the result was that it entered the groundwater surface and stayed at the bottom. Furthermore, it was confirmed that LNAPL pushed down the water table slightly when it stayed on the water table.
That is, the penetration phenomenon of LNAPL and DNAPL shown in FIG. 1 was well captured.

  In this way, the spread of contaminated fluid when DNAPL (water-insoluble fluid heavier than water, trichlorethylene, etc.) or LNAPL (water-insoluble fluid lighter than water, heavy oil, light oil, kerosene, etc.) leaks in the vicinity of the ground surface in the past However, according to the method for analyzing the behavior of the water-insoluble liquid in the unsaturated soil according to the present embodiment, it can be accurately obtained by combining with the existing investigation method. It is possible to identify the spread of pollution in the ground.

  In the present embodiment, a two-dimensional result is shown as a calculation example. However, the analysis method of the present invention can basically be solved in one or three dimensions.

  Therefore, in the behavior analysis method of the water-insoluble liquid in the unsaturated soil according to the present embodiment, the control of the three-phase flow of water-air-NAPL as shown in Equation (21), Equation (22), and Equation (23). The equation was set, the space was discretized by the Galerkin finite element method, the time was discretized by the backward difference method, the modified Picard method was applied, and it was formulated as shown in Equation (24), Equation (25), Equation (26) Therefore, it is possible to accurately simulate the permeation phenomenon of the pore fluid in the multiphase ground where water, air, and a water-insoluble fluid (NAPL) are interposed in the gap between the soil particles.

  In addition, when purifying the soil contaminated with NAPL, it is more rational by preliminarily verifying the purification effect etc. using the behavior analysis method of the water-insoluble liquid in the unsaturated soil of this embodiment. It becomes possible to select a purification measure law.

Next, with reference to FIG. 5 to FIG. 9, a behavior analysis method for a water-insoluble liquid in unsaturated soil according to a second embodiment of the present invention will be described.
Here, this embodiment, like the first embodiment, accurately simulates the permeation phenomenon of pore fluid in a multiphase ground where water, air, and a water-insoluble fluid (NAPL) are interposed in the gap between soil particles. A method for analyzing the behavior of water-insoluble liquids in unsaturated soil, which can predict the extent and extent of soil contamination, and more accurately evaluate and verify the effects of soil contamination purification measures, In particular, from the pressure-saturation relationship of the water-NAPL-air three-phase system, which could not be grasped by the conventional analysis method, to the pressure-saturation relationship of the water-air two-phase system, continuously and accurately. The present invention relates to a method for analyzing the behavior of a water-insoluble liquid in unsaturated soil.
In the present embodiment, detailed description of the same matters as in the first embodiment is omitted.

  First, a characteristic curve (Non-Patent Document 12) obtained by expanding the van Genuchten equation to an arbitrary two-phase fluid is given by the following equation (31).

Here, S is the saturation, and S _max and S _min are the maximum and minimum saturations, respectively. s is a suction, and s _ij = p _i −p _j where p is a pressure. Α is a material parameter, β is a parameter determined by a combination of two-phase interstitial fluid, and β _aw = 1. Subscripts i and j indicate a fluid having low wettability and a fluid having high wettability, respectively.

  And, as shown in FIG. 5, Lenhard and Parker (Non-Patent Document 11) says that the three-phase fluid in the gap satisfies the vicinity of the contact point of soil particles in the order of water, NAPL, and air with high wettability. Based on the assumptions, pay attention to each boundary, and as shown in the following equation (32), the water saturation is the water-NAPL two-phase characteristic curve, the sum of water and NAPL saturation (liquid saturation) ) Is given by the NAPL-air two-phase characteristic curve.

As in the first embodiment, the subscripts w, a, n, and l represent water, air, NAPL, and liquid (water + NAPL), respectively, the subscript is a combination of fluids, and the superscript is saturation. Indicates the fluid to be applied.

As can be seen from this equation (32), the LP model is simple in that it uses a two-phase characteristic curve. However, when S ^w _anw > S ^l _anw and NAPL saturation is negative, it is convenient. In each case, NAPL disappears and S ^w _anw = S ^l _anw is considered, and S ^w _anw and S ^l _anw are _given by a water-air two-phase characteristic curve.

In the LP model, focusing on the equation (31), when the NAPL pressure coincides with the water pressure, the NAPL is controlled by water and disappears to become a water-air two-phase system. Furthermore, NAPL pressure when satisfying _{p w <p n <p a} , water - becomes 3-phase system of air -NAPL. Furthermore, when the NAPL pressure matches the air pressure, NAPL loses air and becomes a water-NAPL two-phase system.

  On the other hand, the inventors of the present application newly define such transition between any two phases and three phases by the following formula (33), and the following formula (34), formula (35), formula (36) ) So that it can be expressed by a variable from 0 to 1 by the intermediate fluid pressure coefficient μ. That is, when the state of the gap described above is shown by using μ, the following equations (34), (35), and (36) are obtained.

  Here, in order to obtain the relationships of the equations (34) to (36), the function β (μ) needs to satisfy the equation (37).

In the present embodiment, β ^w and β ^l satisfying Expression (37) are each given by a cubic Bezier curve. In order to draw a Bezier curve, three control points r ₁ , r ₂ , and r ₃ are required, and control points r ₁ on the (μ, β) plane shown in FIG. 6 are respectively provided for β ^w and β ^l . ^w , r ₂ ^w , r ₃ ^w , and r ₁ ^l , r ₂ ^l , r ₃ ^l are used. The Bezier curve passes through r ₁ and r ₃ at both ends, and the curvature is determined by the control point r ₂ between them. In addition, the tangent lines at r ₁ and r ₃ are parallel to r ₁ -r ₂ and r ₂ -r ₃ , respectively, so that the curves are smoothly connected. An arbitrary point r on the Bezier curve is given by a linear sum as in the following equation (38).

k ₁ , k ₂ , and k ₃ are parameters t (0 ≦ t ≦ 1) and are given by the following equation (39).

In addition, r at t = 0 and r is the _{r 3} with _r 1, t = 1. Here, a curvature parameter a (−2 ≦ a ≦ 2) is introduced so that the curvature of the Bezier curve can be adjusted, and the following equation (40) is used instead of equation (39).

K ₀ to k ₃ are given by the following equation (41).

Then, transition between any two phases and three phases is defined by a new equation (33), and β ^l , β ^w and s _aw obtained by equations (33) to (41) are expressed by the following equation (42) ), It is possible to give the six partial differential coefficients E of the equations (19) and (20).

Considering the features of the LP model through μ, first, the following equation (43) is obtained by substituting equation (33) into equation (32).
Furthermore, Expression (43) can be expressed simply as Expression (44).

From the equation (44), as shown in FIG. 7 (a), the LP model is defined by separate equations for the two-phase system of water-air and the three-phase system of water-air-NAPL. It is not always continuous at the point of transition. The water at the time of β ^l> β ^w not when the mu = 0 - the two-phase system of air.

On the other hand, as in the present embodiment, the relationship between β ^w , β ^l and μ satisfying the equation (37) is given as shown in FIG. The transition of the water-air two-phase system can be expressed smoothly. Further, as shown in FIG. 7B, when μ approaches 0, both β ^w and β ^l approach 1, and the water saturation and the liquid saturation approach each other and the NAPL saturation approaches 0.
Therefore, by using the behavior analysis method of the water-insoluble liquid in the unsaturated soil of this embodiment, the gap in the multiphase ground where water, air, and the water-insoluble fluid (NAPL) are interposed in the gap between the soil particles. It is possible to accurately simulate the fluid penetration phenomenon.

  Next, a simulation performed using the method for analyzing the behavior of a water-insoluble liquid in unsaturated soil according to the present embodiment was performed using a three-phase column experiment by Tanahashi et al. (Hideyuki Tanahashi, Ken Sato, Junichi Konishi: Proceedings of the Japan Society of Civil Engineers) C Vol.62 No.2, pp. 320-334, 2006.), the result of confirming the superiority of the behavior analysis method of the water-insoluble liquid in the unsaturated soil of this embodiment will be described.

  In the column experiment by Tanahashi et al., We observed the saturation distribution of the three phases in the ground after a long period of time when oil (NAPL) was accumulated on the surface of the well in the model ground. The ground pressure distribution assumes a steady state after a long time, and assumes a linear distribution as shown in FIG.

  FIG. 9 shows the result of comparison between the experimental value of the column experiment and the analytical value obtained by the LP model and the behavioral analysis method of the water-insoluble liquid in the unsaturated soil of the present embodiment.

  First, as shown in FIG. 9A, in the column experiment, it was confirmed that the oil spreads on the oil surface even when the oil layer thickness is small. From this, it is estimated that the oil well thickness of the order of several centimeters is detected at the observation well at the site of the contaminated site, and there is a concern about soil contamination below the oil level.

  In contrast, as shown in FIG. 9 (b), the LP model does not calculate the presence of oil shallower than the oil level, underestimates the oil saturation, and gives a dangerous solution for actual soil contamination. It was confirmed. On the other hand, as shown in FIG. 9 (c), in the method for analyzing the behavior of the water-insoluble liquid in the unsaturated soil according to the present embodiment, the presence of the oil in the ground on the oil surface is calculated. I capture the value well.

  Therefore, in the method for analyzing the behavior of the water-insoluble liquid in the unsaturated soil of the present embodiment, it was proved that the column experiment of Tanahashi et al. Can be accurately reproduced by using a model based on the intermediate fluid pressure coefficient μ. .

  Therefore, according to the method for analyzing the behavior of the water-insoluble liquid in the unsaturated soil according to the present embodiment, the pore fluid in the multiphase ground where water, air, and the water-insoluble fluid (NAPL) are interposed in the gap between the soil particles. It is possible to more accurately simulate the infiltration phenomenon of soil, and to more accurately evaluate and verify the effect of soil pollution spread and degree prediction and soil contamination purification measures.

  Next, with reference to FIG. 10, FIG. 11, the behavior analysis method of the water-insoluble liquid in the unsaturated soil which concerns on 3rd Embodiment of this invention is demonstrated. In the present embodiment, detailed description of the same matters as in the first and second embodiments is omitted.

Here, in the second embodiment, it was demonstrated that the column experiment of Tanahashi et al. Can be well reproduced by using a model based on the intermediate fluid pressure coefficient μ. On the other hand, in the second embodiment, since a unique relationship is given to the suction s between the fluids and the saturation S of each phase, the hysteresis phenomenon associated with inflow and discharge of NAPL is not considered.
For this reason, in this embodiment, a state variable that defines the inflow and outflow of the aqueous phase and the liquid phase (the sum of the aqueous phase and the NAPL phase) is newly introduced so that the hysteresis phenomenon can be considered.

Specifically, as shown in the second embodiment, the intermediate fluid pressure coefficient μ (= (p _n −p _w ) / (p _a −p _w )) is a variable representing the relative relationship of the pressures of the three-phase fluid. The change from 0 to 1 corresponds to the transition from the water-air two-phase system to the water-NAPL-air three-phase system and the water-NAPL two-phase system. In the second embodiment, the water-air suction s _aw is multiplied by the water phase and liquid phase scale variables β ^w , β ^l determined by μ, and is substituted into the van Genuchten's formula, The characteristic curve model for obtaining the saturation degree of the liquid phase was explained. That is, in the model of the second embodiment, since the saturation is uniquely determined with respect to the three-phase pressure variables s _aw and μ, the response depending on the pressure history is not reflected.

On the other hand, in the method for analyzing the behavior of the water-insoluble liquid in the unsaturated soil of the present embodiment, β ^w , β taking into account the state variables I _w , I _l reflecting the inflow / outflow history of the water phase and the liquid phase. ^The hysteresis phenomenon is expressed by giving ^l .

First, I _w and I _l are assumed to approach 1 in the inflow process of water and liquid and to −1 in the discharge process, respectively. The following formula (45) is given as an evolution rule satisfying such a relationship.

Here, i corresponds to the water phase w and the liquid phase l. ζ _w and ζ _l are parameters that determine the rate of change of I _w and I _{l with} respect to the saturation change of water and liquid.

The history dependency is expressed as in the following equation (46) by correcting μ to μ _w ^* and μ _l ^* with I _w and I _l taking into account the inflow and outflow history of water and liquid.

Here, m _i is a parameter that determines the strength of the effect of the hysteresis of the outflow Nyutoki. That is, in the method for analyzing the behavior of the water-insoluble liquid in the unsaturated soil of this embodiment, the coefficient μ of the water and liquid corrected by the state variables I _w and I _l instead of μ determined uniquely for the three-phase pressure. _{w ^*,} and taking into account the history dependence by using the μ _l ^*.

FIG. 10 shows a calculation process by the behavior analysis method of the water-insoluble liquid in the unsaturated soil of the present embodiment. The upper left and lower left diagrams of FIG. 10 are processes for obtaining μ _w ^* and μ _l ^* in consideration of hysteresis by state variables I _w and I _l reflecting the history dependence with respect to μ. When I _i = 0, μ _i = μ _i ^* (45 degree broken line), and the model of the behavior analysis method of the water-insoluble liquid in the unsaturated soil of the present embodiment is the model of the first embodiment that does not consider hysteresis Gives the same solution (black dotted line in FIG. 10).
Further, the middle left of FIG. ^10, μ _{w ^*,} μ _{l *} and scale variables beta ^w water phase and a liquid ^phase, shows a relationship between beta ^l. The influence of history dependence is already reflected in μ _w ^* and μ _l ^* .
Finally, β ^w and β ^l are multiplied by s _aw and substituted into the van Genuchten equation as shown in the middle right diagram of FIG. 10 to obtain water and liquid saturations S _w and S _l .

Thereby, in the behavioral analysis method of the water-insoluble liquid in the unsaturated soil of the present embodiment, the hysteresis phenomenon can be reliably reflected with the state variable I _i as a mediator variable while maintaining the advantages of the second embodiment. .

  Next, the simulation using the behavior analysis method of the water-insoluble liquid in the unsaturated soil of this embodiment will be described.

Here, after the column experiment of a well in which NAPL (L _n = 0.067 m) is thinly stretched on the groundwater surface, the oil level is raised to the top of the well (L _n = 1.6 m), By returning to the original position again, NAPL was made to flow in and out.

  A model based on the behavior analysis method of the water-insoluble liquid in the unsaturated soil according to the present embodiment (model of the third embodiment), a Lenhard & Parker model (LP model), and a model not considering hysteresis (second Each model) was simulated and the results were compared. The pressure distribution is assumed to be a hydrostatic pressure and a hydrostatic pressure distribution assuming a steady state after a long time.

FIG. 11 shows a model of Lenhard & Parker (LP model) in the upper stage, a model that does not take hysteresis into consideration (model of the second embodiment), and an analysis of the behavior of the water-insoluble liquid in the unsaturated soil in the lower stage. An example of an analysis result by a method model is shown. Further, the left column shows the saturation distribution in the ground at L _n = 0.8 m in the inflow process and the right column in the outflow process.

  And as shown in FIG. 11, the Lenhard & Parker model (upper) calculates the difference in water saturation distribution due to hysteresis for the same oil layer thickness, but NAPL saturation is extremely underestimated. Yes.

  In addition, the model that does not consider hysteresis (middle stage) captures the distribution of NAPL saturation under the thin NAPL layer thickness reported in previous experiments, but does not consider hysteresis characteristics, so the inflow / outflow process It becomes exactly the same solution.

  In contrast, the model (bottom) of the method for analyzing the behavior of the water-insoluble liquid in the unsaturated soil of the embodiment calculates that NAPL saturation is higher in the NAPL outflow process than in the NAPL inflow process. The NAPL saturation is difficult to increase during NAPL intrusion and NAPL saturation is difficult to decrease during discharge.

  Therefore, in the method for analyzing the behavior of the water-insoluble liquid in the unsaturated soil of this embodiment, the hysteresis phenomenon is well understood, and water, air, and a water-insoluble fluid (NAPL) are interspersed between the soil particles. It is possible to more accurately simulate the phenomenon of pore fluid penetration in the ground. Therefore, it becomes possible to more accurately evaluate and verify the prediction of the extent and degree of soil contamination and the effect of soil contamination purification measures.

As mentioned above, although embodiment of the behavior simulation method (behavior analysis method) of the water-insoluble liquid in the unsaturated soil which concerns on this invention was described, this invention is limited to said 1st, 2nd, 3rd embodiment. However, the present invention can be changed as appropriate without departing from the spirit of the invention.

Claims (3)

A method for simulating the behavior of water-insoluble liquid in unsaturated soil of multiphase ground where water, air, and water-insoluble fluid (NAPL) are interspersed between the soil particles ,
As shown in the following formulas (1) and (2), a model representing a permeation phenomenon of pore fluid in a multiphase ground where water, air, and a water-insoluble fluid are interposed in the gap between soil particles,
Set the governing equations of the three-phase flow of water-air-NAPL as in the following formula (3), formula (4), formula (5),
For the equations (3), (4), and (5), the following equation (6) obtained by discretizing the space with the Galerkin finite element method, discretizing the time with the backward difference method, and applying the modified Picard method: A behavioral simulation method of a water-insoluble liquid in unsaturated soil, characterized in that the behavior of the water-insoluble liquid is analyzed using the equations (7) and (8).
here,
n: Soil porosity, S: Saturation, p: Pressure, _kr : Relative permeability coefficient, K: Saturation permeability coefficient, γ: Unit volume weight, _Kv : Volume compression coefficient, q: Flow rate, ρ: Density, b: object force, μ _r : inviscidity coefficient, E _j ⁱ : ∂S _i / ∂p _j ,
[Superscript / Subscript w, a, n, l]: [Water, Air, Water-insoluble liquid (NAPL), Liquid (Water + NAPL), [Superscript m, k]: [Time step, respectively] [Repetition step], [•]: time differentiation, [-(superscript)]: average value in element, [-(subscript)]: value at boundary. In the behavior simulation method of the water-insoluble liquid in the unsaturated soil according to claim 1,
Using the intermediate fluid pressure coefficient μ expressed by the following equation (9), the transition between any two and three phases of water, air, and water-insoluble fluid in the gap between the soil particles is expressed by the following equation (10 ), Expression (11), and expression (12) as 0 to 1 variables,
In addition, a relationship between β ^w , β ^l and μ satisfying the following expression (13) is given by a Bezier curve,
By multiplying the water-air suction s _aw by the water phase determined by μ and the scale variables β ^w and β ^l of the liquid phase of water and water-insoluble fluid, and substituting them into the following equation (14), A method for simulating the behavior of a water-insoluble liquid in unsaturated soil, characterized in that a characteristic curve indicating the degree of saturation of the phase and the liquid phase is obtained.
Here, S is the saturation, and S _max and S _min are the maximum and minimum saturations, respectively. s is a suction, and p is a pressure, and s _ij = p _i -p _j (subscripts i and j indicate a low wettability fluid and a high fluid, respectively, of the two phases). In the behavior simulation method of the water-insoluble liquid in the unsaturated soil according to claim 2,
State variables I _w and I _l reflecting the inflow and outflow history of the water phase and the liquid phase are given by the following equation (15) that satisfies a relationship approaching 1 in the inflow process of water and liquid and −1 in the discharge process, respectively.
Unsaturated soil characterized in that μ is corrected to μ _w ^* and μ _l ^* with I _w and I _l taking into account the inflow and outflow history of water and liquid as in the following equation (16) Simulation method for water-insoluble liquids.
Here, i corresponds to the water phase w and the liquid phase l. ζ _w and ζ _l are parameters that determine the rate of change of I _w and I _{l with} respect to the saturation change of water and liquid. m _i is a parameter that determines the strength of the effect of the hysteresis of the outflow Nyutoki.