Information processing device and information processing method

Abstract

This paper proposes an information processing device and method that shorten the time required to estimate the distribution of carbon dioxide injected into reservoirs beneath the seabed, and that simplify the estimation procedure. [Solution] The information processing device 100 comprises: an analysis unit 1 that performs numerical analysis using an equation that expresses minute pressure fluctuations in the gaps of a reservoir where carbon dioxide is stored as being caused by tidal loads in complex numbers; and a calculation unit 2 that calculates an amplitude reduction ratio, which is the ratio of the complex amplitudes of minute pressure fluctuations before and after carbon dioxide is injected into the reservoir, and a time shift, which is the phase difference of the minute pressure fluctuations before and after carbon dioxide is injected into the reservoir, based on the analysis results of the numerical analysis.

Description

[Technical Field]

[0001] The present invention relates to an information processing apparatus and an information processing method. [Background technology]

[0002] In recent years, there has been a surge in technological development related to carbon dioxide capture and storage (CCS), and related inventions have been published. For example, Non-Patent Document 1 discloses an invention for estimating the distribution of carbon dioxide injected into a reservoir beneath the seabed. In the invention of Non-Patent Document 1, first, tidal loads are input using a coupled fluid-geodynamic analysis, and the pressure history in the pores of the reservoir is output. Next, minute pressure fluctuation components caused by tidal fluctuations are extracted from the pressure history by curve fitting to the output pressure history. Subsequently, the amplitude and time shift of the extracted minute pressure fluctuation components are obtained. Then, the permeability and the distribution of the carbon dioxide plume (e.g., location, shape) are estimated so that the obtained amplitude and time shift match the observation results. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Akagi, Toshifumi; Yamamoto, Hajime; Sato, Kozo (2020). "Numerical analysis of pressure response of geological fluids due to ocean tides during CO2 injection into subsurface". Journal of Japan Society of Civil Engineers, Series C (Geosphere Engineering), Vol. 76, No. 3, 266-276, 2020. [Overview of the project] [Problems that the invention aims to solve]

[0004] However, the invention described in Non-Patent Document 1 requires multiple steps in the fluid-geodynamic coupled analysis because calculations are performed by dividing the time period. In addition, curve fitting to the fluid-geodynamic coupled analysis is required separately. As a result, the entire process for estimating the distribution of carbon dioxide takes a considerable amount of time, and the procedure is complicated.

[0005] From this perspective, the object of the present invention is to propose an information processing device and an information processing method that shorten the time required to estimate the distribution of carbon dioxide injected into reservoirs beneath the seabed and simplify the estimation procedure. [Means for solving the problem]

[0006] The present invention The analysis unit performs numerical analysis using a complex number equation that expresses minute pressure fluctuations in the pores of the reservoir where carbon dioxide is stored as being caused by tidal loads, The information processing device includes a calculation unit that calculates, based on the results of the numerical analysis, an amplitude reduction ratio which is the ratio of the complex amplitudes of minute pressure fluctuations before and after carbon dioxide is injected into the reservoir, and a time shift which is the phase difference of the minute pressure fluctuations before and after carbon dioxide is injected into the reservoir. Furthermore, the present invention is Information processing device, The process involves a step of performing numerical analysis using an equation that expresses minute pressure fluctuations in the pores of a reservoir where carbon dioxide is stored as being caused by tidal loads, using complex numbers, and This information processing method involves the steps of: calculating, based on the results of the numerical analysis, an amplitude reduction ratio which is the ratio of the complex amplitudes of minute pressure fluctuations before and after carbon dioxide is injected into the reservoir, and a time shift which is the phase difference of the minute pressure fluctuations before and after carbon dioxide is injected into the reservoir. With this configuration, numerical analysis becomes time-independent and can be completed in a single step. Furthermore, curve fitting for coupled fluid-geodynamic analysis is unnecessary when extracting minute pressure fluctuations. In addition, calibration for rock stiffness is unnecessary by using an amplitude reduction ratio that has little dependence on rock stiffness.

[0007] Moreover, it is preferable that the above formula is represented by formula (1) to formula (6).

Number

[0008] Moreover, it is preferable to further include an estimation unit that estimates the distribution of the carbon dioxide using the calculated amplitude reduction ratio and time shift. Thereby, using the observation result of the minute pressure fluctuation, the estimation of the distribution of carbon dioxide can be easily corrected, and the agreement with the observation result by elastic wave exploration can be easily achieved.

Advantages of the Invention

[0009] According to the present invention, the time required to estimate the distribution of carbon dioxide injected into reservoirs beneath the seabed can be reduced, and the estimation procedure can be simplified. [Brief explanation of the drawing]

[0010] [Figure 1] This is a functional configuration diagram of the information processing device according to this embodiment. [Figure 2A] This is an explanatory diagram for CCS (Carbon Capture and Storage) on the seabed. [Figure 2B] This is an enlarged view of the dashed circle in Figure 2A. [Figure 3A] This is a diagram illustrating the movement of carbon dioxide during injection. [Figure 3B] This is a diagram illustrating the movement of carbon dioxide after the injection is complete. [Figure 4] This graph shows the time-dependent changes in pressure disturbances affecting carbon dioxide in the ground. [Figure 5] This is a flowchart for monitoring carbon dioxide plumes. [Figure 6] This is an explanatory diagram of a comparative example of a small pressure fluctuation simulation. (a) is a graph showing the time change of tidal load, (b) is a graph showing the pressure history of injected carbon dioxide, and (c) is a graph when the small pressure fluctuation component is separated. [Figure 7] This is a flowchart showing the proposed method of this embodiment. [Figure 8] This is an explanatory diagram of the analysis conditions used in the proposed method of this embodiment. [Figure 9] This diagram illustrates the analysis conditions used in conventional methods. (a) is a graph of the tidal load history with a period of 1 day, (b) is a graph of the tidal load history with a period of 0.5 days, and (c) is a diagram of a square region constructed with the mesh used in the finite element method. [Figure 10] This is a heatmap of the amplitude reduction ratio obtained in an example using the proposed method of this embodiment. [Figure 11] This is a heatmap of the time shift obtained in an example using the proposed method of this embodiment. [Figure 12]This is a graph (part 1) showing the distribution of amplitude reduction ratios. [Figure 13] This is a graph (part 1) showing the distribution of time shifts. [Figure 14] This is graph (part 2) showing the distribution of amplitude reduction ratios. [Figure 15] This is graph (part 2) showing the distribution of time shifts. [Figure 16] The graphs show the distribution of minute pressure fluctuations obtained by the proposed method; (a) shows the distribution of the amplitude reduction ratio, and (b) shows the distribution of the amplitude. [Modes for carrying out the invention]

[0011] Hereinafter, embodiments for carrying out the present invention will be described in detail with reference to the drawings as appropriate. Each figure is only a schematic representation to the extent that the present invention can be fully understood. Therefore, the present invention is not limited to the illustrated examples. In each figure, common or similar components are denoted by the same reference numerals, and their redundant descriptions are omitted.

[0012] [composition] Figure 1 is a functional configuration diagram of the information processing device of this embodiment. The information processing device 100 is a computer that performs predetermined calculations. The information processing 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 composed of a CPU (Central Processing Unit), the information processing by the computer including the control unit is realized by program execution processing by the CPU. In addition, the storage unit included in the computer stores various programs to realize the functions of the computer according to the CPU's instructions. This realizes cooperation between software and hardware. The programs can be provided by recording them on a recording medium or via a network. The storage unit may also be implemented as a cloud.

[0013] The information processing device 100 comprises an analysis unit 1, a calculation unit 2, an estimation unit 3, and a display control unit 4. The information processing device 100 also stores exploration data 5 and observation data 6.

[0014] Analysis Unit 1 performs numerical analysis related to CCS. Specifically, Analysis Unit 1 performs numerical analysis using an equation that expresses minute pressure fluctuations in the pores of the reservoir where carbon dioxide is stored as being caused by tidal loads, using complex numbers. The calculation unit 2 calculates predetermined values. Specifically, based on the analysis results of the numerical analysis performed by the analysis unit 1, the calculation unit 2 calculates the amplitude reduction ratio, which is the ratio of the complex amplitudes of the minute pressure fluctuations before and after the injection of carbon dioxide into the reservoir, and the time shift, which is the phase difference of the minute pressure fluctuations before and after the injection of carbon dioxide into the reservoir. The estimation unit 3 estimates predetermined values. Specifically, the estimation unit 3 estimates the distribution of carbon dioxide using the amplitude reduction ratio and time shift calculated by the calculation unit 2. The display control unit 4 causes the display unit of the information processing device 100 to display predetermined content on the screen.

[0015] Exploration data 5 is data showing the results of seismic exploration related to CCS. For example, exploration data 5 is data showing the seepage rate at a given location in the ground, but is not limited to this. Observational data 6 represents the results of observations related to CCS. For example, observational data 6 represents data showing minute pressure fluctuations caused by tidal loads, but is not limited to this.

[0016] [CCS for seabed sediment] Figure 2A is an explanatory diagram of CCS for the seabed. Figure 2B is an enlarged view of the dashed circle in Figure 2A. For example, a boring machine (not shown) installed on a plant 10 on the ocean penetrates the shielding layer 11 on the seabed and drills further into the reservoir layer 12 which is below the shielding layer 11. Plant 10 inserts an injection well 13 into the borehole in the shielding layer 11 and reaches into the reservoir layer 12. The reservoir layer 12 is, for example, a sandstone layer containing saltwater (sometimes simply called "water"), but is not limited to this. When plant 10 injects carbon dioxide from the injection well 13, as shown in Figure 2B, the carbon dioxide 12-1 discharged from the tip of the injection well 13 pushes out the water 12-2 present in the voids of the reservoir layer 12.

[0017] Figure 3A is an explanatory diagram of the movement of the injected carbon dioxide during injection. Figure 3B is an explanatory diagram of the movement of the injected carbon dioxide after the injection is complete. As shown in Figure 3A, the carbon dioxide plume 14 discharged from the tip of the injection well 13 expands horizontally within the reservoir 12 and rises to the top of the reservoir 12 due to buoyancy. As shown in Figure 3B, after a predetermined time has elapsed since the injection was completed, the carbon dioxide plume 14 stagnates.

[0018] In CCS, monitoring the movement of injected carbon dioxide is crucial. For example, the movement of plume 14 can be visualized using three-dimensional seismic exploration. However, there are limitations to increasing the frequency of seismic exploration from a cost-effectiveness perspective (e.g., once a year is realistic). In this embodiment, a supplementary monitoring method different from seismic exploration is incorporated and combined with seismic exploration, which is performed infrequently. The reliability of monitoring is improved by comprehensively evaluating the results from multiple types of monitoring.

[0019] [Small pressure fluctuations caused by tidal loads] The plume 14, located within the reservoir 12 of the seabed (inside the ground), is affected by tides. Tides include oceanic tides and geospheric tides. Oceanic tides cause periodic sea level fluctuations, resulting in vertical tidal loads (tidal forces) on the plume 14. Geospheric tides cause periodic crustal strains, resulting in horizontal tidal loads (tidal forces) on the plume 14. The pressure of the carbon dioxide constituting the plume 14 depends not only on the main fluctuations caused by the injection but also on the minute pressure fluctuations caused by the tidal loads.

[0020] Figure 4 is a graph showing the time evolution of pressure disturbances on carbon dioxide in the ground. The pressure on carbon dioxide before injection (thick solid line) is linked to minute pressure fluctuations of tidal forces (solid line). As shown in Figure 4, it is known that the amplitude of the pressure on carbon dioxide after injection (dashed line) decreases compared to before injection. Also, as shown in Figure 4, it is known that the phase of the pressure on carbon dioxide after injection (dashed line) shifts (time shift) compared to before injection. The decrease in amplitude and the time shift are phenomena caused by the fact that the compressibility of carbon dioxide is greater than that of water. By evaluating the decrease in amplitude and the time shift, the movement of plume 14 can be monitored.

[0021] Figure 5 is a flowchart for monitoring carbon dioxide plumes. As shown in Figure 5, seismic exploration is performed on the seabed (Step A1). The timing of seismic exploration is indicated by white triangles in Figure 5, and the frequency of seismic exploration is low (for example, once a year). The seismic exploration provides the results of the CO2 plume exploration (Step A2). The CO2 plume exploration results are an example of exploration data 5. In seismic exploration, the permeability at each location in the reservoir 12 is measured in an observation well 15 that reaches the reservoir 12 from the surface. Since the injected carbon dioxide spreads within the reservoir 12, the permeability measured in the observation well 15 is updated as needed each time seismic exploration is performed and can be recorded as exploration results.

[0022] As shown in Figure 5, the information processing device 100 receives, for example, an initial estimate of the permeability at each location of the seabed ground from the user (Step A3). Note that it is sufficient for the information processing device 100 to receive an initial estimate of the permeability at at least each location of the reservoir in the seabed ground. Next, the information processing device 100 performs an injection analysis using the input initial estimate of the permeability (Step A4). The injection analysis is an analysis of the distribution of carbon dioxide injected into the reservoir. The injection analysis is well known, so a detailed explanation is omitted. The results of the CO2 plume analysis are obtained from the injection analysis (Step A5).

[0023] Next, the information processing device 100 compares the CO2 plume exploration results and analysis results to determine whether the analysis results (at the timing of the seismic exploration) reproduce the CO2 plume (step A6). If it reproduces it (Yes in step A6), the information processing device 100 adopts the permeability (estimated value) input during the injection analysis (step A7). If it does not reproduce it (No in step A6), the information processing device 100 updates the permeability input during the injection analysis as appropriate and performs the injection analysis again (step A4). Ultimately, it adopts the permeability at which the CO2 plume was reproduced (step A7).

[0024] As shown in Figure 5, a supplementary monitoring method different from seismic exploration is performed. The timing of the implementation of the supplementary monitoring method is indicated by hatched triangles in Figure 5, and the frequency of implementation of the supplementary monitoring method is high (for example, daily). At the predetermined implementation timing, the CO2 plume has expanded (step B1), and a predicted result of the CO2 plume is obtained based on the CO2 plume exploration results (see step A2). The information processing device 100 receives, for example, a user input, which is an assumed value for the distance L from the CO2 plume (step B2). As shown in Figure 5, the distance L is the shortest distance between the observation well 15 and the boundary of the CO2 plume.

[0025] Next, the information processing device 100 performs a micro-pressure fluctuation simulation (step B3). The information processing device 100 can perform the micro-pressure fluctuation simulation using the permeability adopted in step A7. Details of the micro-pressure fluctuation simulation will be described later. As a result, the information processing device 100 can obtain analytical values ​​of the micro-pressure fluctuation as a result of the simulation (step B4). Next, the information processing device 100 determines whether the obtained analytical values ​​reproduce the measured values ​​of the micro-pressure fluctuation (step B5). In making this determination, the information processing device 100 can use the measured values ​​of the micro-pressure fluctuation (step B6). The measured values ​​of the micro-pressure fluctuation are an example of observation data 6. The measured values ​​of the micro-pressure fluctuation can be obtained, for example, using the measurement method described in “Sato, K., & Horne, RN (2018). Time-lapse analysis of pressure transients due to ocean tides for estimating CO2 saturation changes. International Journal of Greenhouse Gas Control, 78, 160-167.”

[0026] If the simulation is reproduced (Yes in step B5), the estimation unit 3 of the information processing device 100 adopts the assumed distance L from the CO2 plume as the estimated value (step B7). The estimation unit 3 of the information processing device 100 can estimate the distribution of the CO2 plume using the adopted estimated value. On the other hand, if the simulation is not reproduced (No in step B5), the information processing device 100 corrects the predicted result of the expansion of the CO2 plume (see step B1) using the measured value of the minute pressure fluctuation (step B6). The information processing device 100 can update the assumed value of the distance L from the CO2 plume and perform the minute pressure fluctuation simulation again (step B3). As a result, the estimation unit 3 of the information processing device 100 adopts the distance L when the measured value of the minute pressure fluctuation was reproduced as the estimated value (step B7). By following the steps above, you can monitor the carbon dioxide plume.

[0027] [Simulation of minute pressure fluctuations] The small pressure fluctuation simulation (step B3 in Figure 5) will be explained. Figure 6 is an explanatory diagram of a small pressure fluctuation simulation as a comparative example, where (a) is a graph showing the time change of tidal load, (b) is a graph showing the pressure history of injected carbon dioxide, and (c) is a graph when the small pressure fluctuation component is separated.

[0028] Tidal loads (sea level fluctuations and global tidal strains) can be measured at predetermined time intervals using well-known measurement methods. The graph in Figure 6(a) corresponds to plotting the measured tidal loads F (indicated by circles) and connecting them with a periodic curve. The analysis unit 1 of the information processing device 100 can perform a fluid-geodynamic coupled analysis using the tidal load F and seepage rate (see step A7 in Figure 5) as input. Details of the fluid-geodynamic coupled analysis are shown in Non-Patent Literature 1, so only an overview is provided in this specification.

[0029] Analysis Unit 1 can obtain the pressure history in the pores between rocks within the reservoir (pore pressure history related to the pore fluid (a fluid containing a mixture of injected carbon dioxide and water)) by performing a coupled fluid-geodynamic analysis. Specifically, Analysis Unit 1 solves the equilibrium of forces in the ground (equations (1) to (3)), the conservation of mass laws for water and CO2 (equations (4) and (5)), and the equations of motion for the pore fluid (Darcy's law, equations (6) and (7)) under the constitutive equations for porous elastic bodies (equations (8) to (15)).

[0030]

number

[0031] Here, σ ij x represents stress (i,j = 1,2,3). i This represents the i-th component (i = 1, 2, 3) of the 3D coordinate (x1, x2, x3). ε ν (=ε 11 +ε 22 +ε 33 ) represents volume strain (ε ii (This is the longitudinal strain in the direction of the 3D coordinate axis). w This represents pore water pressure. nThis represents the pressure of carbon dioxide. c represents capillary pressure. r represents the degree of water saturation. φ represents the porosity. c w ρ represents the compressibility of water. w This represents the density of water. n ρ represents the compressibility of carbon dioxide. n represents the density of carbon dioxide. N represents a parameter related to the stiffness of the rock. q i w represents the flux of water. q i n k represents the flux of carbon dioxide. r w k represents the relative permeability of water (the ratio of the absolute permeability of the pore fluid to the absolute permeability of the pore water). r n μ represents the relative permeability of carbon dioxide (the ratio of the absolute permeability of the interstitial fluid to the absolute permeability of carbon dioxide in the pores). w μ represents the viscosity of water. n k represents the viscosity of carbon dioxide. k represents the permeability (absolute permeability of the interstitial fluid). g i = (0,0,-g), where g is the acceleration due to gravity.

[0032]

number

[0033] Here, ε ij σ represents strain (longitudinal strain or transverse strain). ij Δ represents stress. E represents Young's modulus. ν represents Poisson's ratio. G represents shear stiffness. b is Biot's constant. Also, Δ is the increment from the initial state. That is, Δφ is the increment of the porosity. Δp w Δp is the increment in pore water pressure. n This represents the increment in the pressure of carbon dioxide.

[0034] The graph in Figure 6(b) shows the analysis results of the coupled fluid-soil dynamics analysis. Next, analysis unit 1 separates the tidal fluctuation component (micro-pressure fluctuation component) from the pore pressure history obtained from the graph in Figure 6(b) by curve fitting. The lower graph in Figure 6(c) shows the time evolution of the separated tidal fluctuation component. The upper graph in Figure 6(c) shows the pore pressure history remaining after the separation of the tidal fluctuation component, with the pressure of injected carbon dioxide being the main trend.

[0035] The calculation unit 2 can calculate the amplitude and time shift of the pressure on carbon dioxide after injection based on the graph at the bottom of Figure 6(c). The estimation unit 3 can estimate the permeability and the position and shape of the carbon dioxide plume by selecting the permeability and the position and shape of the carbon dioxide plume so that the calculated amplitude and time shift match the observation data 6.

[0036] However, conventional fluid-soil dynamics coupled analysis inherently requires a considerable amount of time for analysis. Specifically, in the graph of Figure 6(b), the analysis unit 1 plots the pore pressure history curve at predetermined time points (t1, t2, ..., t n ,t n+1 Divide it into sections, and divide it into sections (t i ~t i+1 Analysis needs to be performed for each step. Because analysis needs to be performed in multiple steps in the time direction, there was a problem that the calculation time was enormous (approximately 10 days). In addition, there was a problem that the work of dividing the time period was complicated. Furthermore, curve fitting to the pore pressure history obtained from the graph in Figure 6(b) is required separately. For this reason, the work of obtaining the amplitude and time shift of the pressure on carbon dioxide after injection based on the graph in Figure 6(c) was time-consuming and the procedure was complicated.

[0037] This embodiment proposes a method to solve the above-mentioned problems. The proposed method will be described in detail below. First, we will make assumptions to simplify the stress and strain terms that appear in conventional methods. <1> ~Assumption <3> Prepare it. Assumption <1> The reservoir is assumed to be approximately a thin, horizontal layer. Assumption <2> The change in total vertical stress is equal to the change in pressure due to ocean tides. Assumption <3> Horizontal strain is caused by Earth tides.

[0038] Assumption <2> Based on this, in the case of ocean tides, Δσ 33 = σ T , ε 11 + ε 22 Let = 0. Here, σ T σ represents the load due to sea level fluctuations. T This is known and becomes the external force term. In this case, from equations (8) to (10), Δσ 11 and Δσ 22 Eliminating (by applying the increment Δ in equations (8) to (10)) yields equation (16).

[0039]

number

[0040] Here, ε 11 + ε 22 = 0, therefore ε ν = ε 11 + ε 22 + ε 33 Therefore, equation (17) is derived.

[0041]

number

[0042] Δp (ocean tide) is a term that explicitly indicates the pressure increment in the reservoir void caused by ocean tides, with Δp representing the pressure increment.

[0043] Assumption <3> Based on this, in the case of Earth tides, Δσ 33 = 0, ε 11 + ε 22 = ε T Let ε TThis represents the strain caused by Earth's tides. ε T This is known and becomes the external force term. In this case, from equations (8) to (10), Δσ 11 and Δσ 22 Eliminating (by applying the increment Δ in equations (8) to (10)) yields equation (18).

[0044]

number

[0045] Here, by rearranging equation (18), we derive equation (19).

[0046]

number

[0047] Δp (earth tides) is a term that explicitly indicates the pressure increment in the reservoir void caused by earth tides, with Δp representing the pressure increment.

[0048] As shown in equations (17) and (19), the only unknown variable is pressure, as stress and strain are eliminated. Furthermore, adding equations (4) and (5) together yields equations (20) and (21).

[0049]

number

[0050] For further simplification, assume <4> ~Assumption <6> Prepare it. Assumption <4> : Capillary pressure is 0 (p c = 0) Assumption <5> : Density and viscosity are constant (ρ w ρ n ,μ w ,μ n (Position partial derivative = 0) Assumption <6> : Relative osmotic pressure is constant (k r w , k r nPosition partial derivative = 0)

[0051] By assumptions <4> to <6>, the non-linearity is removed. By combining equations (6) and (7) with equations (20) and (21), equation (22) is obtained. For convenience of description, the subscript 0 indicates approximation by a constant. That is, in equation (22), based on assumptions <5> and <6>, μ w ≈ μ w0 (constant), μ n ≈ μ n0 (constant), k r w ≈ k r0 w (constant), k r n ≈ k r0 n is expressed as (constant).

[0052]

Equation

[0053] Substituting equation (17) or equation (19) into equation (22) gives equations (23) to (26).

[0054]

Equation

[0055] Here, f T * represents the external force due to the earth tide or ocean tide. In equation (25), φ ≈ φ0 is approximated by a constant. In equation (26), s r ≈ s r0 is approximated by a constant. c p is a function of various compressibility factors, and β T is the porous elastic coefficient, and they are given by equations (27) to (29) respectively.

[0056]

Equation

[0057] Here, c represents the compression rate of the rock skeleton. G is the shear rigidity. c s represents the compression rate of the rock particles. Depending on the assumed conditions, relational expressions other than the above may be used, but this method can still be applied without change.

[0058] TIFF2026083845000013.tif27170

[0059]

Number

[0060] In Equation (30), consider the component of frequency ω of f T * . Let Δp * = P * exp(iωt), and f T * = F T * exp(iωt). Then, Equation (31) can be derived from Equation (30).

[0061]

Number

[0062] P * and F T * are complex numbers. The absolute value of P * is the amplitude (complex amplitude) of the micro-pressure fluctuation, and the argument is the phase shift (time shift) of the micro-pressure fluctuation. Regarding the amplitude of the micro-pressure fluctuation, the ratio of the complex amplitudes of the micro-pressure fluctuations before and after injecting carbon dioxide into the storage layer is defined as the "amplitude reduction ratio". In this embodiment, the amplitude reduction ratio is used to estimate the distance L from the CO2 plume (see step B7 in FIG. 5).

[0063] Equation (31), a partial differential equation of a complex variable, can be solved using numerical methods such as the finite element method. Since equation (31) is a time-independent equation, the amplitude and time shift can be obtained in a single step of analysis. Therefore, computation time can be reduced and the procedure simplified.

[0064] Figure 7 is a flowchart of the proposed method in this embodiment. The flowchart in Figure 7 is part of the small pressure fluctuation simulation (step B3 in Figure 5). First, the analysis unit 1 of the information processing device 100 receives a frequency input (step S1). For example, the input frequency ω can be a plurality of frequencies ω1, ω2, ... selected by the user as appropriate. Next, the analysis unit 1 of the information processing device 100 performs numerical analysis using the input frequency (step S2). Specifically, the analysis unit 1 substitutes the frequencies ω1, ω2, ... into equation (31) and solves equation (31). The numerical analysis can be, for example, the finite element method, but is not limited to this. Next, the calculation unit 2 of the information processing device 100 calculates the amplitude reduction ratio and time shift using the results of the numerical analysis (step S3). The processing shown in Figure 7 reduces the time required for numerical analysis compared to conventional methods. Furthermore, it eliminates the need to extract minute pressure fluctuation components using curve fitting (see Figures 6(b) and 6(c)).

[0065] [Examples] An example of the proposed method of this embodiment will be described. Figure 8 is an explanatory diagram of the analysis conditions used in the proposed method of this embodiment. In Figure 8, a reservoir is simulated by constructing a 10km × 10km square region using the mesh used in the finite element method. A carbon dioxide plume with radius R = 400m exists at the center of the square region. Carbon dioxide saturation rate (volume ratio S of carbon dioxide to pore volume) g The ratio is 20%. The boundary condition for the square region is an amplitude reduction ratio of 1.

[0066] For comparison, analysis using a conventional method was also performed. Figure 9 is an explanatory diagram of the analysis conditions used in the conventional method, where (a) is a graph of the history of tidal loads with a period of 1 day, (b) is a graph of the history of tidal loads with a period of 0.5 days, and (c) is a diagram of a square region composed of the mesh used in the finite element method. The conventional method requires the history of tidal loads as input. Figure 9(a) shows the history of the 1-day period component, and Figure 9(b) shows the history of the semi-daily period component. In the example in Figure 9, a periodic displacement is applied to one side to simulate Earth tides (periodic strain of the ground). Also, the seepage rate is 1.0 × 10⁻⁶. -13 m 2 and 1.0 × 10 -12 m 2 These two values ​​were used.

[0067] Figure 10 is a heatmap of the amplitude reduction ratio obtained in an example using the proposed method of this embodiment. Figure 11 is a heatmap of the time shift obtained in an example using the proposed method of this embodiment. In Figures 10 and 11, the period is 1 day and the penetration rate is 1.0 × 10⁻⁶. -12 m 2 The display control unit 4 can display the heatmap shown in Figures 10 and 11 on the display unit of the information processing device 100. The proposed method can directly acquire the amplitude of minute pressure fluctuations without relying on curve fitting. Therefore, obtaining the amplitude reduction ratio and time shift distributions shown in Figures 10 and 11 is much easier compared to conventional methods.

[0068] Figure 12 is a graph (1) showing the distribution of amplitude reduction ratio. Figure 13 is a graph (1) showing the distribution of time shift. Figure 14 is a graph (2) showing the distribution of amplitude reduction ratio. Figure 15 is a graph (2) showing the distribution of time shift. The graphs in Figures 12 to 15 show the distribution along the "Result Display Cross Section" in Figures 8 and 9. In addition, the conventional method and the proposed method are compared for periods of 1 day and 0.5 days. The display control unit 4 can display the graphs shown in Figures 12 to 15 on the display unit of the information processing device 100.

[0069] The amplitude reduction ratio and time shift values ​​change depending on the distance from the carbon dioxide plume. Furthermore, the amplitude reduction ratio obtained by the conventional method and the results obtained by the proposed method show good agreement. In the conventional method of this embodiment, after a 2000-step fluid-soil dynamics coupled analysis, minute pressure fluctuation components were extracted from 36 pressure histories by curve fitting. The total time required per case with the conventional method is approximately 2 hours. In contrast, the proposed method can obtain the amplitude reduction ratio for all points in a single step of analysis, so the required time is only about 10 seconds.

[0070] Figure 16 is a graph showing the distribution of minute pressure fluctuations obtained by the proposed method, where (a) is the distribution of the amplitude reduction ratio and (b) is the distribution of the amplitude. Figure 16 shows the distribution when the stiffness (Young's modulus E) of the rock mass is changed. The display control unit 4 can display the graph shown in Figure 16 on the display unit of the information processing device 100.

[0071] As shown in Figure 16(b), the amplitude changes significantly depending on the stiffness of the rock mass, so care must be taken in handling the stiffness of the rock mass, making the procedure complicated. In contrast, as shown in Figure 16(a), the effect of stiffness on the amplitude reduction ratio is small, so it is convenient as it is not necessary to know the exact value of the rock mass stiffness. Therefore, it is preferable to use the amplitude reduction ratio when estimating the distance to the CO2 plume.

[0072] [effect] According to this embodiment, the time required to estimate the distribution of carbon dioxide injected into the reservoir beneath the seabed can be shortened, and the estimation procedure can be simplified. More specifically, the proposed method obtains the amplitude reduction ratio for each frequency component of pressure fluctuations by solving the boundary value problem of the complex partial differential equation (31) before and after CO2 injection. It also estimates the position of the carbon dioxide plume by selecting the position that reproduces the amplitude reduction ratio obtained from actual observational data. Since the analysis is time-independent, it can be completed in one step. Furthermore, it does not require the extraction of minute fluctuation components of pore pressure by curve fitting. In addition, by using an amplitude reduction ratio that has little dependence on rock mass stiffness, rock mass stiffness calibration is unnecessary. Therefore, it is possible to shorten the time and simplify the procedure of forward simulation.

[0073] [Other embodiments] The equations used by the analysis unit 1 when performing numerical analysis are not limited to equation (31). The complex partial differential equation in equation (31) is assumed to be: <1> ~Assumption <6> This is an equation obtained by preparing the original equations (1) to (15), linearizing them, and approximating them to the degree of simplification possible (e.g., ignoring all terms for which the approximation is valid). Here, for example, the degree of approximation can be adjusted (e.g., selectively deciding which terms to ignore), and numerical analysis can be performed using an equation with some approximation removed from the linearized equation. Also, assumptions <1> ~Assumption <6> It is not necessary to incorporate all of these factors; you may selectively make assumptions depending on the environment of the target ground. In other words, there are various formulas that can be used in numerical analysis.

[0074] Examples of equations that do not involve approximations are as follows. For water, equations (4) and (6) are derived by substituting them into equation (17) or equation (19). Also, pore water pressure p w Small fluctuations p w * = P * exp(iωt), and water saturation s r small fluctuations s r * = S * Substituting exp(iωt) into the derived equation, we obtain equation (32). Note that S * It is a complex number.

[0075]

number

[0076] For carbon dioxide, we derive equations by substituting equations (5) and (7) into equation (17) or equation (19). Also, the pore water pressure p w Small fluctuations p w * = P * exp(iωt), and water saturation s r small fluctuations s r * = S * Substituting exp(iωt) into the derived equation, we obtain equation (33).

[0077]

number

[0078] The analysis unit 1 can perform numerical analysis using equations (32) and (33). <1> ~Assumption <6> Set the parameters and keep only the terms in the square boxes in equations (32) and (33), and in the remaining terms, the density ρ w0 ρ n0 Dividing by and adding together, we can derive equation (31).

[0079] [others] (a) It is also possible to realize a technology that appropriately combines the various technologies described in this embodiment. (b) The software described in this embodiment can be implemented as hardware, and the hardware can be implemented as software. (c) Other components of the present invention may be modified as appropriate without departing from the spirit of the present invention. [Explanation of Symbols]

[0080] 100 Information Processing Devices 1 Analysis section 2. Calculation Section 3 Estimation part 4 Display Control Unit 5. Exploration Data 6. Observational Data

Claims

1. The analysis unit performs numerical analysis using a complex number equation that expresses minute pressure fluctuations in the pores of the reservoir where carbon dioxide is stored as being caused by tidal loads, An information processing apparatus comprising: a calculation unit that calculates, based on the results of the numerical analysis, an amplitude reduction ratio which is the ratio of the complex amplitudes of minute pressure fluctuations before and after carbon dioxide is injected into the reservoir, and a time shift which is the phase difference of the minute pressure fluctuations before and after carbon dioxide is injected into the reservoir.

2. The information processing apparatus according to claim 1, wherein the above formula is represented by formulas (A) to (F). [Math 1] In formula (A), P * represents a minute pressure fluctuation, F * T represents the complex amplitude of the tidal load, k represents the permeability, k r0 w represents the relative permeability of water approximated by a constant, k r0 n represents the relative permeability of carbon dioxide approximated by a constant, μ w0 represents the viscosity of water approximated by a constant, μ n0 represents the viscosity of carbon dioxide approximated by a constant In equation (B), G represents the shear stiffness. In formula (C), φ 0 This represents the porosity approximated by a constant, In formula (D), s r0 This represents the degree of water saturation approximated by a constant, and c w This represents the compressibility of water, and c n This represents the compressibility of carbon dioxide. In equation (E), b represents the Biot constant, ν represents Poisson's ratio, and c represents the compressibility of the rock skeleton. In formula (F), c s This represents the compressibility of rock particles.

3. The information processing apparatus according to claim 1 or claim 2, further comprising an estimation unit that estimates the distribution of carbon dioxide using the calculated amplitude reduction ratio and time shift.

4. Information processing device, The process involves a step of performing numerical analysis using an equation that expresses minute pressure fluctuations in the pores of a reservoir where carbon dioxide is stored as being caused by tidal loads, using complex numbers, and An information processing method that performs the steps of calculating, based on the results of the numerical analysis, an amplitude reduction ratio which is the ratio of the complex amplitudes of minute pressure fluctuations before and after the injection of carbon dioxide into the reservoir, and a time shift which is the phase difference of the minute pressure fluctuations before and after the injection of carbon dioxide into the reservoir.

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