Estimation method

Abstract

To provide an estimation method which shortens a calculation time required for estimating a capillary pressure curve related to two-phase fluid in the ground.SOLUTION: An estimation method includes a discharge step of filling a gap 42 of a three-dimensional ground model in which the ground is reproduced by extracting an image of soil particles and an image of the gap from an X-ray CT image of a ground sample, and the lower part of solid particles 41 of the three-dimensional ground model with first fluid (water 43), and imparting a predetermined gravity value to an analysis model 4 in which the upper part of the soil particles 41 of the three-dimensional ground model is filled with second fluid (air 44), to discharge the first fluid, and a calculation step of calculating a capillary pressure in a steady state by the Bernoulli's theorem, and calculating a volume content of the first fluid in the steady state. While changing the gravity value, the discharge step and the calculation step are repeatedly performed.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to an estimation method. [Background technology]

[0002] In recent years, research into the behavior of fluids in the ground has become active. In particular, many cases are known that deal with the behavior of two or more fluids that form an interface. For example, there is a case where an unsaturated region in the ground where a two-phase fluid consisting of water and air is mixed is examined. Fluid behavior in the ground is often studied using numerical analysis based on Darcy's law. When performing numerical analysis, it is necessary to provide parameters that indicate the relationship between the two types of fluids in the target ground, that is, two-phase flow parameters. Two-phase flow parameters include, but are not limited to, capillary pressure curves and relative permeability curves.

[0003] For two-phase fluids such as water and air, standardized test methods have been established to determine two-phase flow parameters. However, these tests are not easy. For example, advanced techniques and experience are required to conduct the tests. Furthermore, if the sample (soil particles) in question has low permeability, the tests take a long time to complete. Furthermore, the difficulty of conducting the tests increases dramatically depending on the type of fluid and the temperature and pressure conditions being considered.

[0004] Patent Document 1 discloses a method for evaluating the capillary pressure curve of rock in an underground reservoir from measurements of rock debris. The invention of Patent Document 1 includes steps of measuring the permeability k of rock cuttings, centrifuging the cuttings initially saturated with a liquid (e.g., saline solution) to measure the capillary pressure curve Pc as a function of the saturation rate, and parameterizing the measured capillary pressure curve. However, the invention of Patent Document 1 involves centrifugal separation, which damages the original properties of the target ground. This reduces the reliability of the measured capillary pressure curve. Even if such a capillary pressure curve is used to perform a numerical analysis based on Darcy's law, the reliability of the analysis results is reduced, which is a problem. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Special Publication No. 2005-525574 Summary of the Invention [Problem to be solved by the invention]

[0006] As mentioned above, although testing is not easy, there is a strong desire to obtain a highly reliable capillary pressure curve. In response to this situation, efforts are being made to estimate the capillary pressure curve by calculation. However, there is a problem in that the calculations required for estimation take a long time. From this perspective, an object of the present invention is to propose an estimation method that shortens the calculation time required to estimate a capillary pressure curve for a two-phase fluid in the ground. [Means for solving the problem]

[0007] The present invention, which solves the above-mentioned problem, is an estimation method comprising: a discharge step of applying a predetermined gravity value to the voids of a three-dimensional ground model that reproduces the ground by extracting images of soil particles and voids from X-ray CT images of a ground sample, and an analytical model in which a first fluid is filled below the soil particles of the three-dimensional ground model and a second fluid is filled above the soil particles of the three-dimensional ground model, thereby discharging the first fluid; and a calculation step of calculating the capillary pressure in a steady state using the following equation (1) and calculating the volume content of the first fluid in the steady state, in which the discharge step and the calculation step are repeated while changing the gravity value. ρgz + P = constant...Equation (1) In equation (1), ρ is the density [ML -3 ] and g is the gravitational acceleration [LT -2 ] is the gravity value based on the reference plane [L], z is the height from the reference plane set in the three-dimensional ground model [L], and P is the capillary pressure [ML -1 T -2 ]. According to this configuration, by changing the gravity value, the capillary pressure P calculated using Equation (1) can be treated as the capillary pressure at a different height under normal gravity (a height with a value different from the height z in Equation (1)). For example, the capillary pressure at height z when a gravity value n times the gravitational acceleration g0 is applied to the analytical model is equivalent to the capillary pressure at height n × z when normal gravitational acceleration g0 is applied. Therefore, by plotting the relationship between capillary pressure and volume fraction each time the gravity value is changed, a capillary pressure curve can be estimated. The estimated capillary pressure curve extends beyond the dimensions of the ground sample, i.e., the dimensions of the 3D ground model. In other words, the dimensions of the 3D ground model can be made small enough to obtain a capillary pressure curve covering a range sufficient to demonstrate the desired reliability. Reducing the dimensions of the 3D ground model reduces the amount of calculation required to estimate the capillary pressure curve and shortens the calculation time. Furthermore, the capillary pressure curve can be estimated even under conditions of fluid type, temperature, and pressure that would make the test itself extremely difficult.

[0008] It is also preferable to set the same pressure at the upper end and the lower end of the three-dimensional ground model. This allows for the creation of boundary conditions that prevent the generation of conductive flows above and below the 3D ground model for both the first and second fluids. This allows for faithful reproduction of the movement of the first and second fluids within the ground sample. Furthermore, the constraints on the Courant number caused by the conductive flows above and below the 3D ground model are less likely to occur, which helps prevent the calculation time from becoming too long. [Effects of the Invention]

[0009] According to the present invention, it is possible to reduce the calculation time required to estimate the capillary pressure curve for a two-phase fluid in the ground. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 2 is a functional configuration diagram of the estimation device according to the present embodiment. [Figure 2] FIG. 1 is an explanatory diagram of an analysis model. [Figure 3]3 is a flowchart showing an estimation method according to the present embodiment. [Figure 4] 1 is a graph of an estimated capillary pressure curve. DETAILED DESCRIPTION OF THE INVENTION

[0011] Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. Each drawing is merely a schematic illustration to allow a sufficient understanding of the present invention. Therefore, the present invention is not limited to the illustrated examples. In each drawing, common or similar components are designated by the same reference numerals, and redundant explanations thereof will be omitted.

[0012] [composition] FIG. 1 is a functional configuration diagram of the estimation device of this embodiment. The estimation device 100 is a computer equipped with hardware such as an input unit, an output unit, a control unit, and a storage unit. For example, if the control unit is configured with a CPU (Central Processing Unit), information processing by a computer including the control unit is realized by program execution processing by the CPU. Furthermore, a storage unit included in the computer stores various programs for realizing the functions of the computer in response to instructions from the CPU. This realizes collaboration between software and hardware. The programs can be recorded on a recording medium or provided via a network. The storage unit may also be implemented as a cloud. Note that a console can be communicatively connected to the estimation device 100, and the console can display the processing details of the estimation device 100. For example, the console can display image data generated by image processing by the estimation device 100 on a screen.

[0013] The estimation device 100 is a computer that performs numerical analysis of fluid behavior in the ground. The estimation device 100 can estimate two-phase flow parameters required for the numerical analysis. In this embodiment, a capillary pressure curve is used as the two-phase flow parameter. The estimation device 100 includes an analysis unit 1, a calculation unit 2, and a display control unit 3. The estimation device 100 also stores an analysis model 4.

[0014] The analysis unit 1 analyzes the behavior of two-phase fluid in the ground. In this embodiment, water (first fluid) and air (second fluid) are used as the two-phase fluid. The analysis unit 1 can construct an analysis model 4 for the analysis. The analysis unit 1 can perform the analysis by inputting predetermined values ​​into the analysis model 4. The calculation unit 2 calculates values ​​necessary for estimating the capillary pressure curve based on the analysis results of the analysis unit 1. The calculations of the calculation unit 2 enable the estimation of the capillary pressure curve. The display control unit 3 displays the estimated capillary pressure curve in a predetermined display format. For example, the display control unit 3 can display the calculated values ​​of the calculation unit 2 in a table format via the output unit of the estimation device 100. Furthermore, if the output unit of the estimation device 100 is a display unit capable of displaying on a screen, the display control unit 3 can display the estimated capillary pressure curve on a screen via the display unit. Furthermore, the display control unit 3 can display on a screen the analysis model 4 and a simulation performed when the analysis model 4 is used.

[0015] The analytical model 4 is a three-dimensional ground model that reproduces the ground in which a two-phase fluid flows. The analytical model 4 is created using X-ray CT images of a ground sample. To capture an X-ray CT image, for example, soil particles of the target ground filled in a cylindrical container are prepared as the ground sample. This ground sample is then photographed using an X-ray CT device. The X-ray CT device photographs the interior of the ground sample, and an X-ray CT image of the ground sample can be output. The X-ray CT image is input to the estimation device 100. The analysis unit 1 extracts images of the soil particles and voids from the X-ray CT image. The image extraction can be performed using well-known techniques. The analysis unit 1 processes the extracted images to place a cylindrical three-dimensional ground model consisting of soil particles and voids in a digital space.

[0016] [Water-air two-phase flow behavior] When a water source exists deep underground, the interior of the ground above the water source is an unsaturated region where both water and air exist. In the unsaturated region, an interface between water and air is formed, and negative pressure due to interfacial tension, i.e., capillary pressure, is generated. Note that below the groundwater table (the top surface of the water source) is a saturated region where the fluid is only water, and since there is no interface, the interfacial tension is 0 and no capillary pressure is generated. The degree of saturation decreases the further away from the groundwater table. The lower the degree of saturation, the greater the interfacial tension and the greater the capillary pressure.

[0017] For fluids, Bernoulli's principle, which represents the conservation of mechanical energy in fluids, applies. When dealing with steady states, the velocity term in Bernoulli's principle can be ignored, and the following equation (1) is obtained: ρgz + P = constant...Equation (1) In equation (1), ρ is the density of water [ML -3 ] and g is the gravitational acceleration [LT -2 ], z is the height from the reference plane [L], and P is the water pressure (capillary pressure) [ML -1 T -2 ]. If the groundwater level is taken as the reference level (z=0), then as mentioned above, no capillary pressure occurs at the groundwater level, so P=0. Therefore, the "constant" on the right-hand side of equation (1) becomes 0, and P=-ρgz (negative pressure). The degree of saturation can be calculated from the water content in the soil sample. As a result, a capillary pressure curve is obtained, which shows the relationship between capillary pressure and degree of saturation.

[0018] [About the test to obtain the capillary pressure curve] The capillary pressure curve can be determined by laboratory testing. For reference, the test methods for obtaining the capillary pressure curve for water-air two-phase flow are explained below. There are three known test methods: the earth column method, the pressure plate method, and the centrifugal method.

[0019] The earth column method is a test method in which a cylindrical container is filled with soil particles from the ground in a vertical direction, and water is then filled and drained from the bottom of the container by gravity. For a specimen in a steady state, a capillary pressure curve can be created by measuring the saturation distribution at each height position of the soil column from the free water surface. One possible approach is to apply the soil column method to a numerical model that replicates a water-filled soil column and estimate the capillary pressure curve. In this case, an X-ray CT scanner would be used to image the entire soil column, which may be several meters tall, and the voids would be reconstructed from the X-ray CT images. However, due to height limitations, the X-ray CT scanner cannot image the entire soil column. Therefore, applying the soil column method makes analysis difficult because it is unable to replicate the voids throughout the soil column. Even if the voids could be replicated, the scale of the numerical model would be extremely large, resulting in a huge number of analysis grids. This would result in an excessive computational load for the analysis, and the calculations required to estimate the capillary pressure curve would take a significant amount of time. Therefore, the estimation method using the soil column method is not practical.

[0020] The pressure plate method is a testing method in which a specimen filled with water to a depth of several centimeters is placed on a ceramic filter placed inside a pressure chamber, and the pressure chamber is pressurized to drain water from below the specimen. The air infiltration pressure of the ceramic filter is large enough that only the water inside the specimen is discharged in response to pressure application; both the water and air inside the specimen are not discharged together due to pressure application. A capillary pressure curve can be created by evaluating the relationship between the pressure and the amount of water discharged for a specimen in a steady state. One possible approach is to apply the pressure plate method to a numerical model that replicates a soil sample filled to saturation with water and estimate the capillary pressure curve. Compared to the soil column method, the soil sample dimensions are sufficiently small, allowing for a significantly smaller scale of the numerical model and a significantly reduced number of analysis grids. This significantly reduces the computational load and the time required to estimate the capillary pressure curve. However, since the pressure plate method imposes a pressure condition, a pressure difference occurs between the top and bottom of the numerical model. This results in airflows passing through the top and bottom of the numerical model, which differs significantly from actual tests (no airflows passing through the top and bottom of actual tests). This means that the estimated capillary pressure curve is not very reliable. Furthermore, the presence of airflows passing through the top and bottom limits the time step during analysis due to the constraints of the Courant number, which prolongs the analysis time. The Courant number constraint refers to the requirement that the Courant number (= flow velocity × time interval ÷ analysis grid size) not exceed 1.

[0021] The centrifugal method is a testing method in which a soil sample filled with water (about a few centimeters deep) is placed in a centrifugal loading device, and water is drained from the sample by changing the gravitational field.Drainage forces a high suction field (high capillary pressure field), and a capillary pressure curve can be created by evaluating the relationship between the gravitational field and water content of the sample in a steady state. One possible method is to apply the centrifugal method to analyze a water-filled soil sample using a numerical model that reproduces it, and estimate the capillary pressure curve. Because the soil sample dimensions are sufficiently small, this method has the advantage of significantly reducing the computational load required for analysis, as with the pressure plate method, and significantly shortening the calculation time required to estimate the capillary pressure curve. Furthermore, unlike the pressure plate method, there is no need to apply pressure conditions.

[0022] [Analysis model 4] Based on the above test method, in this embodiment, an analytical model 4 was constructed with reference to the centrifugal method. Fig. 2 is an explanatory diagram of the analytical model. For ease of explanation, Fig. 2 illustrates the analytical model 4 as a cross-sectional view of the three-dimensional ground model cut by a vertical plane passing through the central axis of the cylindrical three-dimensional ground model.

[0023] As shown in Figure 2, in the analytical model 4, soil particles 41 are arranged within a cylindrical region. Furthermore, voids 42 are arranged within the cylindrical region of the soil particles 41. Water 43 is filled throughout the voids 42 and below the soil particles 41. The water 43 present below the soil particles 41 represents a water source deep underground. Furthermore, air 44 is filled above the soil particles 41. The same pressure P1 is set at the top and bottom of the three-dimensional ground model. The pressure P1 is a fixed value. This setting makes it possible to create boundary conditions that do not generate vertically conducting air flows, as occurs with the pressure plate method.

[0024] [Estimation method] FIG. 3 is a flowchart illustrating the estimation method of this embodiment. Referring to FIG. 3, the process of the estimation device 100 estimating a capillary pressure curve using the analytical model 4 will be described. First, the analysis unit 1 of the estimation device 100 executes a drainage process on the analytical model 4 (step S1). Specifically, the analysis unit 1 assigns a predetermined gravity value to the analytical model 4 based on input from the input unit of the estimation device 100. Then, the water 43 filling the voids 42 moves downward and is drained from the soil particles 41. Fluid analysis of the water 43 can be performed using, but is not limited to, the continuity equation and the Navier-Stokes equation. As the water drains, air 44 enters the voids 42, and the cylindrical region of the soil particle 41 becomes an unsaturated region (suction field). Furthermore, an interface is formed between the water 43 and the air 44, generating capillary pressure due to interfacial tension. The drainage rate follows the assigned gravity value, and reaches a steady state when the gravity of the gravity value and the interfacial tension balance each other.

[0025] Next, the analysis unit 1 calculates the capillary pressure and the volumetric water content in a steady state (step S2). Specifically, the analysis unit 1 calculates the capillary pressure P using the following equation (2) based on Bernoulli's theorem, ignoring the velocity term. P = -ρ×g1×z...Equation (2) In equation (1), ρ is the density of water [ML -3 ]. g1 is the gravity value [LT -2 ] and the acceleration due to gravity [LT -2 ] is the reference plane. z is the height from the reference plane [L], and P is the water pressure (capillary pressure) [ML -1 T -2 The reference plane (z=0) is the upper surface of the water 43 present below the soil particle 41, that is, the lower end of the soil particle 41.

[0026] The volumetric water content in the steady state, that is, the degree of saturation, is the value obtained by dividing the volume of water 43 present in the cylindrical region of the soil particle 41 by the lattice volume (void volume) of the cylindrical region of the soil particle 41. For example, the volume of water 43 present in the cylindrical region of soil particle 41 can be found by counting the amount of data of water 43 present in the cylindrical region of soil particle 41. It may also be found by dividing the amount of drainage by the density of water. It may also be found as the product of the circular area (known) of the cylindrical region of soil particle 41 and the distance from the bottom end of soil particle 41 to the interface between water 43 and air 44. Furthermore, for example, the lattice volume of the cylindrical region of the soil particle 41 is the volume of the voids 42 arranged within the cylindrical region of the soil particle 41, and can be obtained in advance when the analytical model 4 is constructed.

[0027] Next, the estimation device 100 determines whether to continue the calculation in step S2 (step S3). Specifically, if the user inputs a request to continue the calculation in step S2 into the estimation device 100, the calculation continues. If the user inputs a request to end the calculation in step S2 into the estimation device 100, the calculation ends. For example, the estimation device 100 can determine whether there are any remaining different gravity values ​​to be assigned when calculating the capillary pressure and volumetric water content by changing the gravity value assigned to the analytical model 4, and continues the calculation if there are any remaining numbers. Note that the number of gravity values ​​to be assigned when calculating the capillary pressure and volumetric water content may be determined manually or automatically.

[0028] If the process does not continue (No in step S3), the analysis unit 1 creates and outputs a capillary pressure curve using the capillary pressure and volumetric water content calculated for each gravity value (step S4). For example, the analysis unit 1 can create and output a capillary pressure curve in response to a user's request for a specific spreadsheet process. The display control unit 3 of the estimation device 100 can display the output capillary pressure curve on the display unit. Figure 4 is a graph of the estimated capillary pressure curve. The display control unit 3 can plot the correspondence between capillary pressure and volumetric water content for each gravity value on a graph with the horizontal axis representing volumetric water content and the vertical axis representing capillary pressure. The display control unit 3 can also draw a curve for the plot using, for example, the least squares method.

[0029] On the other hand, if the drainage is to continue (Yes in step S3), the analysis unit 1 assigns a gravity value to the analysis model 4 that is different from the gravity value assigned previously (step S5). For example, a different gravity value may be input from the input unit of the estimation device 100 and assigned to the analysis model 4, or a different gravity value that is automatically set may be input and assigned to the analysis model 4. Thereafter, the analysis unit 1 executes the drainage process (step S1) in accordance with the input gravity value. Note that by assigning a gravity value to the analysis model 4 that is greater than the gravity value assigned previously, drainage can be made continuous. This completes the processing in FIG.

[0030] [supplement] In the analysis using the analytical model 4, by applying the centrifugal method, it is possible to simulate the condition in which a gravity greater than normal gravity acts on the specimen. Therefore, it is possible to obtain the capillary pressure when normal gravity acts on the specimen over a height range that exceeds the dimensions of the specimen. In the processing of Figure 3, the gravity value g1 assigned to the analytical model 4 is set to g1 = n × g0. g0 is the gravitational acceleration (9.81 m / s 2 ) where n is a positive number. Equation (2) can be transformed into the following equation (3). P = -ρ×(n×g0)×z = -ρ×g0×(n×z)...Equation (3) According to equation (3), the capillary pressure at height z when a gravity value n times the gravitational acceleration g0 is applied to the analytical model 4 is equivalent to the capillary pressure at height n × z when normal gravitational acceleration g0 is applied. In other words, by changing the gravity value, the capillary pressure P calculated by equation (2) can be treated as the capillary pressure at a different height under normal gravity (a height showing a value different from height z in equation (2)). Even if n × z indicates a height position that exceeds the dimensions of the test specimen, the capillary pressure P at that height position can be calculated.

[0031] According to the above concept, the capillary pressure curve estimated by performing the process shown in Figure 3 will be a curve that extends over a range that exceeds the dimensions of the ground sample, i.e., the dimensions of the 3D ground model. In other words, the dimensions of the 3D ground model can be made small enough to obtain a capillary pressure curve that spans a range sufficient to exhibit the desired reliability. Reducing the dimensions of the 3D ground model reduces the amount of calculation required to estimate the capillary pressure curve, thereby shortening the calculation time.

[0032] [effect] According to this embodiment, it is possible to reduce the calculation time required to estimate the capillary pressure curve for the water-air two-phase flow in the ground. More specifically, since a capillary pressure curve showing the desired reliability can be obtained even if the dimensions of the three-dimensional ground model are made sufficiently small, the amount of calculation required to estimate the capillary pressure curve can be reduced, and the calculation time can be shortened. Furthermore, the capillary pressure curve can be estimated even under conditions of fluid type, temperature, and pressure that would make the test itself extremely difficult. Furthermore, highly reliable analytical results can be obtained from numerical analysis based on Darcy's law, which is performed by applying the capillary pressure curve estimated in this embodiment.

[0033] Furthermore, by setting the same pressure P1 as the upper and lower boundary pressures in the analytical model 4 of Figure 2, it is possible to create boundary conditions for both water 43 and air 44 that do not generate a conductive flow between the top and bottom of the 3D ground model. This allows faithful reproduction of the movement of water and air in the ground sample. Furthermore, it also makes it less likely that constraints on the Courant number caused by a conductive flow between the top and bottom of the 3D ground model will occur, thereby preventing the calculation time from becoming too long.

[0034] [others] (a): Two types of fluids of a two-phase fluid can be selected. For example, water and a non-aqueous phase liquid (NAPL) may be selected to investigate soil contamination or groundwater contamination. Also, water (or hot water) and supercritical CO2 may be selected to investigate CCS (Carbon dioxide Capture and Storage) or geothermal power generation using CO2 as a heat medium. The estimation device 100 can estimate capillary pressure curves for the two selected types of fluid. (b): In this embodiment, the estimation device 100 outputs a capillary pressure curve through the drainage process. However, the drainage process may be replaced with a water absorption process. For example, as the initial state of the analysis model 4, water 43 is filled below the soil particles 41, and air 44 is filled in the entire void 42 and above the soil particles 41. The analysis unit 1 applies a predetermined gravity value and executes the water absorption process. Then, the water 43 moves upward below the soil particles 41 and is absorbed by the soil particles 41. As a result, the cylindrical region of the soil particles 41 becomes an unsaturated region (suction field). Also, as in the process of FIG. 3, a gravity value different from the previously applied gravity value is applied to the analysis model, and the water absorption process is executed. As a result, the analysis unit 1 can create and output a capillary pressure curve using the capillary pressure and volumetric water content calculated for each gravity value. Note that by applying a gravity value smaller than the previously applied gravity value to the analysis model 4, water absorption can be continuous. The drainage process and the water absorption process may also be combined. (c): When estimating the capillary pressure curve, the height position of the reference plane can be set appropriately.

[0035] (d) It is also possible to realize a technology that appropriately combines the various technologies described in this embodiment. (e) The software described in this embodiment can be realized as hardware, and vice versa. (f) In addition, the components of the present invention may be modified as appropriate within the scope of the invention. [Explanation of symbols]

[0036] 100 Estimator 1 Analysis section 2 Calculation section 3 Display control section 4. Analysis model 41 Soil particles 42 void 43 Water (first fluid) 44 Air (second fluid)

Claims

1. a discharging step of filling a first fluid into the voids of a three-dimensional ground model that reproduces the ground by extracting images of soil particles and voids from an X-ray CT image of a ground sample and below the soil particles of the three-dimensional ground model, and discharging the first fluid by applying a predetermined gravity value to an analytical model in which a second fluid is filled above the soil particles of the three-dimensional ground model; a calculation step of calculating a capillary pressure in a steady state by the following formula (1) and calculating a volume content of the first fluid in the steady state, An estimation method characterized by repeatedly performing the discharging step and the calculation step while changing the gravity value. ρgz + P = constant...Formula (1) In formula (1), ρ is the density [ML -3 ] and g is the gravitational acceleration [LT -2 ] is the gravity value based on the reference plane [L], z is the height from the reference plane set in the three-dimensional ground model [L], and P is the capillary pressure [ML -1 T -2 ].

2. The estimation method according to claim 1 , wherein the same pressure is set at the upper end and the lower end of the three-dimensional ground model.

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