Concentration calculation device, concentration calculation method, and concentration calculation program

Abstract

To easily obtain the concentrations of a plurality of chemical species dissolved in an aqueous solution.SOLUTION: A concentration calculation device comprises: a concentration calculation section for deriving concentrations of N chemical species, as unknown quantities, by solving a simultaneous equation containing N formulas; and an output section for outputting the concentrations of N chemical species. The N formulas include an N-1 formula containing a plurality of chemical equilibrium formulas, and an electric charge storage formula. The concentration calculation section includes: a setting section for setting a candidate value of a concentration of one chemical species; a calculation section for deriving a provisional value of a concentration of remaining N-1 chemical species by solving the N-1 formula by assigning the candidate value; and a determination section for determining whether or not the electric charge storage formula is established under the candidate value and the N-1 provisional value. If the determination section determines that electric charge storage formula is not established, changes of the candidate value, and derivation of the N-1 provisional value based on the changed candidate value are repeatedly executed until the determination section determines that the electric charge storage formula is established.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to a concentration calculation device, a concentration calculation method, and a concentration calculation program. [Background technology]

[0002] For example, Non-Patent Document 1 discloses a method for determining the unknown concentrations of various chemical species dissolved in an aqueous solution using simultaneous equations that hold between the concentrations of each chemical species. In this method, the concentrations of all unknown chemical species are simultaneously changed, and the concentrations of each chemical species that satisfy the simultaneous equations are simultaneously determined. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] TJ Wolery, “Calculation of chemical equilibrium between aqueous solution and minerals: The EQ3 / 6 software package”, University of California, Lawrence Livermore Laboratory, 1979. Summary of the Invention [Problem to be solved by the invention]

[0004] For example, when an aqueous solution contains multiple chemical species as solutes, or when a chemical species undergoes multiple chemical reactions in an aqueous solution, the simultaneous equations include multiple chemical equilibrium equations that hold when an equilibrium state is reached. These chemical equilibrium equations are not independent of each other, but contain terms for the concentrations of common chemical species. Therefore, when solving a simultaneous equation containing such chemical equilibrium equations, the concentration of a chemical species that satisfies one chemical equilibrium equation does not necessarily also satisfy other chemical equilibrium equations. Therefore, the above-mentioned method of simultaneously varying the concentrations of all chemical species to determine the concentrations of each chemical species poses a problem: it is difficult to determine the concentrations of each chemical species that satisfy the simultaneous equations. This problem becomes particularly pronounced as the structure of the simultaneous equations becomes more complex.

[0005] The present disclosure describes a concentration calculation device, a concentration calculation method, and a concentration calculation program that can easily determine the concentrations of multiple chemical species dissolved in an aqueous solution. [Means for solving the problem]

[0006] A concentration calculation device according to an embodiment of the present disclosure is a concentration calculation device that calculates the concentrations of N (N is an integer of 3 or more) chemical species dissolved in an aqueous solution, and includes: a concentration calculation unit that derives the concentrations of the N chemical species as unknowns by solving simultaneous equations including N equations that hold between the concentrations of the N chemical species; and an output unit that outputs the concentrations of the N chemical species derived by the concentration calculation unit, wherein the N equations include N-1 equations including a plurality of chemical equilibrium equations that hold between the concentrations of the N chemical species when the N chemical species reach an equilibrium state in the aqueous solution, and a charge conservation equation that shows that the sum of the charges of cations and the sum of the charges of anions are equal in the aqueous solution; and the concentration calculation unit calculates the concentrations of the N chemical species as unknowns by solving simultaneous equations including N equations that hold between the concentrations of the N chemical species when the N chemical species reach an equilibrium state in the aqueous solution. a setting unit that sets a candidate value for the concentration of any one of the chemical species from N, a calculation unit that derives provisional values ​​for the concentrations of the remaining N-1 chemical species excluding one of the N chemical species by substituting the candidate value and solving N-1 equations, and a determination unit that determines whether the equation of conservation of charge holds under the candidate value and the N-1 provisional values; if the determination unit determines that the equation of conservation of charge holds, the candidate value and the N-1 provisional values ​​are each provided to an output unit as true values, and if the determination unit determines that the equation of conservation of charge does not hold, the change of the candidate value and the derivation of the N-1 provisional values ​​based on the changed candidate value are repeatedly executed until the determination unit determines that the equation of conservation of charge holds.

[0007] A concentration calculation method according to one embodiment of the present disclosure is a concentration calculation method for calculating the concentrations of N (N is an integer of 3 or more) chemical species dissolved in an aqueous solution, the method comprising: deriving the concentrations of the N chemical species as unknowns by solving simultaneous equations including N equations that hold among the concentrations of the N chemical species; and outputting the derived concentrations of the N chemical species, wherein the N equations include N-1 equations including a plurality of chemical equilibrium equations that hold among the concentrations of the N chemical species when the N chemical species reach an equilibrium state in the aqueous solution, and a charge conservation equation showing that the sum of the charges of cations and the sum of the charges of anions are equal in the aqueous solution; and deriving the concentrations of the N chemical species. This includes setting a candidate value for the concentration of any one of N chemical species, substituting the candidate value and solving N-1 equations to derive provisional values ​​for the concentrations of the remaining N-1 chemical species excluding the concentration of one of the N chemical species, and determining whether or not the equation of conservation of charge holds under the candidate value and the N-1 provisional values. If it is determined that the equation of conservation of charge holds, the candidate value and the N-1 provisional values ​​are output as true values, and if it is determined that the equation of conservation of charge does not hold, the process of changing the candidate value and deriving the N-1 provisional values ​​based on the changed candidate value is repeatedly executed until it is determined that the equation of conservation of charge holds.

[0008] A concentration calculation program according to one embodiment of the present disclosure is a concentration calculation program for calculating the concentrations of N (N is an integer of 3 or more) chemical species dissolved in an aqueous solution, and causes a computer to execute the following steps: deriving the concentrations of the N chemical species as unknowns by solving simultaneous equations including N equations that hold between the concentrations of the N chemical species; and outputting the derived concentrations of the N chemical species; the N equations are N-1 simultaneous equations including a plurality of chemical equilibrium equations that hold between the concentrations of the N chemical species when the N chemical species reach an equilibrium state in the aqueous solution. and the equation of conservation of charge, which shows that the sum of the charges of cations and anions in an aqueous solution is equal; and deriving the concentrations of the N chemical species includes: setting a candidate value for the concentration of any one of the N chemical species; substituting the candidate value into N-1 equations to derive provisional values ​​for the concentrations of the remaining N-1 chemical species, excluding the concentration of one of the N chemical species; and determining whether the equation of conservation of charge holds under the candidate value and the N-1 provisional values; and if it is determined that the equation of conservation of charge holds, outputting the candidate value and the N-1 provisional values ​​as true values, respectively; and if it is determined that the equation of conservation of charge does not hold, repeatedly changing the candidate value and deriving the N-1 provisional values ​​based on the changed candidate value until it is determined that the equation of conservation of charge holds.

[0009] In the above-described concentration calculation device, concentration calculation method, and concentration calculation program, when solving a system of equations with the concentrations of N chemical species as unknowns, a candidate value for the concentration of one of the N chemical species is provisionally set, and provisional values ​​for the concentrations of the remaining N-1 chemical species are calculated based on that candidate value. Whether the provisionally set candidate value is a correct value (true value) that satisfies the simultaneous equations is then confirmed by determining whether the equation of conservation of charge holds. Once the concentration of one chemical species is provisionally determined in this way, the number of unknowns to be found is reduced by one, making it possible to easily derive the concentrations of the remaining N-1 chemical species using the equations of conservation of charge. Then, by determining whether the provisionally determined concentration of the chemical species is correct using the equation of conservation of charge, the concentrations of the N chemical species that satisfy the simultaneous equations can be found. This method of determining the concentrations of N chemical species in stages by temporarily fixing the concentration of one chemical species makes it easier to solve simultaneous equations with a complex structure including multiple chemical equilibrium equations, compared to a method of simultaneously determining the concentrations of N chemical species while simultaneously changing the concentrations of N chemical species, and makes it easier to determine the concentrations of N chemical species that satisfy the simultaneous equations.

[0010] In some embodiments, the setting unit sets a lower limit and an upper limit for the concentration of one chemical species, and sets an intermediate value between the lower limit and the upper limit as a candidate value. When the determination unit determines that the equation of conservation of charge does not hold, the setting unit may set the current candidate value as a new lower limit or upper limit, and set a new candidate value using the new lower limit or upper limit. In this case, the search range between the lower limit and the upper limit can be narrowed each time it is determined that the equation of conservation of charge does not hold. Therefore, by repeating the above determination, the candidate values ​​can be narrowed down and the true value can be reliably determined.

[0011] In some embodiments, the aqueous solution is an aqueous solution containing water as a solvent and different chemical species A and B (A and B are any chemical formulas) as solutes, and the concentrations of the N chemical species are expressed as the concentration of hydrogen ions [H + ] and the hydroxide ion concentration [OH ―], the concentration of chemical species A, [A], and the concentration of chemical species A ionized by hydrogen ions, [AH + ], the concentration of species B [B], and the concentration of species B ionized by hydrogen ions [BH + ], and the N-1 equations are determined by the first equilibrium constant and [H + ] and [OH ― ], and when the equilibrium state is reached, the second equilibrium constant and [AH + ] and [A] and [H + ], and when the equilibrium state is reached, the third equilibrium constant and [BH + ] and [B] and [H + ] and the amount of chemical species A added to the aqueous solution is [AH + ] and [A], and the amount of chemical species B added to the aqueous solution is equal to the sum of [BH + ] and [B], and the conservation of charge is [H + ] and [AH + ] and [BH + ] and the sum is [OH ― In this case, the second and third chemical equilibrium equations have a common [H + ], which satisfies the second chemical equilibrium equation [H + ] may not simultaneously satisfy the third chemical equilibrium equation, making it difficult to simultaneously change and calculate the concentrations of N chemical species. In contrast, by temporarily fixing the concentration of one chemical species and gradually calculating the concentrations of N chemical species that satisfy the N equations, it becomes possible to easily calculate the concentrations of N chemical species, as described above.

[0012] In some embodiments, the aqueous solution is an aqueous solution containing water as a solvent and a chemical species A (A is any chemical formula) as a solute, and the concentrations of N chemical species are the concentrations of hydrogen ions [H + ] and the hydroxide ion concentration [OH ―], the concentration of chemical species A, [A], and the concentration of chemical species A ionized by hydrogen ions during the first ionization step, [AH + ] and the concentration of species A ionized by hydrogen ions during the second ionization step [AH2 2+ ], and the N-1 equations are determined by the first equilibrium constant and [H + ] and [OH ― ], and when the first stage equilibrium state is reached, the second equilibrium constant and [AH + ] and [A] and [H + ], and when the second stage equilibrium state is reached, the third equilibrium constant and [AH2 2+ ] and [AH + ] and [H + ] and the amount of chemical species A added to the aqueous solution is [AH + ] and [A], and the conservation of charge is [H + ] and [AH + ] and [AH2 2+ ] and the sum is [OH ― In this case, the second and third chemical equilibrium equations have a common [H + ], which satisfies the second chemical equilibrium equation [H + ] may not simultaneously satisfy the third chemical equilibrium equation, making it difficult to simultaneously change and calculate the concentrations of N chemical species. In contrast, by temporarily fixing the concentration of one chemical species and gradually calculating the concentrations of N chemical species that satisfy the N equations, it becomes possible to easily calculate the concentrations of N chemical species, as described above.

[0013] In some embodiments, the setting unit is + ] or [OH ― ] can be set as a candidate value. + ] and [OH ― ], the first chemical equilibrium equation is used to calculate [H + ] and [OH ―] can be easily derived, it becomes easier to derive the concentrations of N-1 chemical species using N-1 equations. This makes it easier to find the concentrations of N chemical species. [Effects of the Invention]

[0014] According to some aspects of the present disclosure, there are provided a concentration calculation device, a concentration calculation method, and a concentration calculation program that can easily determine the concentrations of multiple chemical species dissolved in an aqueous solution. [Brief explanation of the drawings]

[0015] [Figure 1] FIG. 1 is a configuration diagram showing an example of a concentration calculation device. [Figure 2] FIG. 2 is a diagram for explaining an example of a method for searching for the true value of [H+]. [Figure 3] FIG. 3 is a flow chart showing an example of a concentration calculation method. [Figure 4] FIG. 4 is a diagram illustrating an example of a hardware configuration of the concentration calculation apparatus. [Figure 5] FIG. 5 is a diagram for explaining another example of a method for searching for the true value of [H+]. [Figure 6] FIG. 6 is a flow chart showing another example of the concentration calculation method. DETAILED DESCRIPTION OF THE INVENTION

[0016] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. In the description of the drawings, the same elements are designated by the same reference numerals, and duplicated descriptions will be omitted as appropriate.

[0017] [Concentration calculation device] First, with reference to FIG. 1, a schematic configuration of a concentration calculation device 1 according to one embodiment will be described. The concentration calculation device 1 shown in FIG. 1 calculates the concentrations of N (N is an integer equal to or greater than 3) chemical species dissolved in an aqueous solution. The concentration calculation device 1 derives the concentrations of the N chemical species by solving simultaneous equations including N expressions that hold between the concentrations of the N chemical species in the aqueous solution. Note that the term "chemical species" collectively refers to ions, radicals, atoms, atomic groups, elements, compounds, and the like. Therefore, chemical species dissolved in an aqueous solution may exist, for example, in an ionic state or in an atomic state.

[0018] For example, in an aqueous solution with water as the solvent and two chemical species A and B (A and B represent any chemical formula) as the solutes, in addition to the chemical species A and B, there is also H generated by ionization of water. + (hydrogen ion) and OH - (hydroxide ion) and H + The ionized species AH + and BH + where chemical species A and B are electrochemically active species in aqueous solution, i.e., chemical species that ionize in aqueous solution. In this case, the simultaneous equations that hold between the concentrations of the chemical species present in the aqueous solution are composed of the following equations (1) to (6).

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[0019] In equations (1) to (6), [H + ] is H in aqueous solution + The concentration of [OH - ] is OH in aqueous solution - [A] is the concentration of species A in aqueous solution. [AH + ] is the chemical species AH in aqueous solution + [B] is the concentration of species B in the aqueous solution. [BH + ] is the chemical species BH in aqueous solution + The unit of concentration of each chemical species is (mol / L). T A indicates the amount of chemical species A added to the aqueous solution. B indicates the amount of chemical species B added to the aqueous solution. w is the self-dissociation constant (first equilibrium constant) of water in aqueous solution. A is the equilibrium constant (second equilibrium constant) for the equilibrium reaction of chemical species A in aqueous solution. B is the equilibrium constant (third equilibrium constant) for the equilibrium reaction of chemical species B in aqueous solution.

[0020] Equation (1) is the H produced by ionization of water in an aqueous solution. + and OH - is the first chemical equilibrium equation that holds when the ionization equilibrium is reached. + ] and [OH - ] is a constant K w Equation (2) is the second chemical equilibrium equation that holds when the chemical species A in the aqueous solution reaches ionization equilibrium. Equation (2) shows that in equilibrium, [A] and [H + ] and the product is [AH + ] and constant K A Equation (3) shows that the amount of chemical species A after a chemical reaction in an aqueous solution is equal to the product of the amount of chemical species A and the amount of chemical species AH +is equal to the amount of chemical species A before the chemical reaction occurs (i.e., the amount of chemical species A added to the aqueous solution). In other words, equation (3) is the first equation of conservation of amount of substance, which shows that the sum of the amount of [A + ] and [AH + ] is the input amount T A This shows that it is equal to

[0021] Equation (4) is the third chemical equilibrium equation that holds when the ionization equilibrium of the chemical species B in the aqueous solution is reached. Equation (4) is the equilibrium state between [B] and [H + ] is multiplied by [BH + ] and constant K B Equation (5) shows that the amount of species B after a chemical reaction in an aqueous solution is equal to the product of the amount of species BH + is equal to the amount of species B before the chemical reaction occurs (i.e., the amount of species B added to the aqueous solution). In other words, equation (5) is the equation for conservation of the amount of [B + ] and [BH + ] is the input amount T B Equation (6) is the equation (charge conservation equation) that shows that in equilibrium, the sum of the charges on the cations (i.e., the sum of the positive charges) and the sum of the charges on the anions (i.e., the sum of the negative charges) are equal. Equation (6) shows that the [H + ] and [AH + ] and [BH + ] and the sum is [OH - ].

[0022] In equations (1) to (6), the constant K w , K. A , K. B is a constant that is determined in advance by experiment, etc., and the input amount T A , T B is an arbitrary constant that is set by the user of the concentration calculation device 1. w , K. A , K. B , T A , TB are set independently and are changed as needed. + ], [OH - ], [A], [AH + ], [B], and [BH + ] is the unknown to be found, and K w , K. A , K. B , T A , T B Therefore, the simultaneous equations including equations (1) to (6) are w , K. A , K. B , T A , T B is the independent variable, and [H + ], [OH - ], [A], [AH + ], [B], and [BH + ] can be considered as a computational model with the dependent variable.

[0023] The number of unknown concentrations of chemical species is six, whereas the above simultaneous equations include six equations, equations (1) to (6). Therefore, the concentration calculation device 1 can calculate the concentrations of the six chemical species by solving these six equations. In the above equations (1) to (6), chemical species A and B are H + Although it is shown to have the property of receiving OH - Alternatively, chemical species A may have the property of accepting OH. - While species B has the property of accepting H + Conversely, if species A is H + While species B has the property of accepting OH - The signal may have a property of receiving

[0024] If the concentration of each chemical species in an aqueous solution is known, the amounts of chemical species A and B dissolved in the aqueous solution can be determined. Such information is particularly useful in fields related to capture devices that capture specific gases from exhaust gases emitted from chemical plants and thermal power plants. For example, in a capture device that captures CO2 (carbon dioxide) from exhaust gases, CO2 is absorbed by contacting a gas containing CO2 with an aqueous solution containing dissolved RNH2 (amine, R represents an appropriate hydrocarbon group), and the CO2 is released into the gas phase and captured by heating the aqueous solution.

[0025] In such capture devices, the aqueous solution into which CO2 has been absorbed (CO2 absorbing solution) is evaluated by the amount of dissolved CO2. The greater the amount of dissolved CO2 (absorbed amount) in the CO2 absorbing solution, the higher the final CO2 capture rate, and therefore the higher the performance of the CO2 absorbing solution. On the other hand, the smaller the amount of dissolved CO2 in the CO2 absorbing solution, the lower the CO2 capture rate, and therefore the lower the performance of the CO2 absorbing solution. Therefore, the concentration of the chemical species dissolved in the CO2 absorbing solution is an important indicator for predicting the performance of the CO2 absorbing solution. In the above equations (1) to (6), if chemical species A is CO2 and chemical species B is RNH2, it is possible to calculate the amount of dissolved CO2 in the aqueous solution and predict the performance of the CO2 absorbing solution.

[0026] When solving the simultaneous equations including equations (1) to (6), the concentration calculation device 1 calculates the [H + ], [OH - ], [A], [AH + ], [B], and [BH +[] is treated as an optimization problem with the concentration of any one of the chemical species as a single variable, and the concentration of each chemical species that satisfies the simultaneous equations is searched for while gradually changing the concentration. Specifically, the concentration calculation device 1 first sets a candidate value for the concentration of any one of the chemical species. Then, the concentration calculation device 1 calculates provisional values ​​for the concentrations of the remaining chemical species by substituting the set candidate value into equations (1) to (5). The concentration calculation device 1 then confirms whether the remaining equation (6) is satisfied under these candidate values ​​and each provisional value, thereby confirming whether the candidate values ​​are correct (true values).

[0027] If the concentration calculation device 1 determines that the candidate value is not a true value, it searches for the true value of the candidate value by changing the candidate value and repeating the above calculation and determination. On the other hand, if the concentration calculation device 1 determines that the candidate value is a true value, it outputs the candidate value and each provisional value as a true value. In this embodiment, a binary search method is exemplified as an algorithm for searching for a true value. In this method, an upper limit and a lower limit of the concentration of the chemical species for which the candidate value is set are set, and the true value of the candidate value is searched for by gradually narrowing the range between the upper limit and the lower limit.

[0028] The functional components of the concentration calculation device 1 will be described with reference to FIG. 1. As shown in FIG. 1, the concentration calculation device 1 includes an input unit 10, a concentration calculation unit 20, and an output unit 30. The input unit 10 acquires information necessary to solve simultaneous equations including equations (1) to (6). Specifically, the input unit 10 acquires information necessary to solve simultaneous equations including equations (1) to (6), such as K w , K. A , K. B , T A , T B The input to the input unit 10 is performed by, for example, a user operation. Alternatively, the input value of K w , K. A , K. B , T A , T B The input value may be automatically sent to the input unit 10.

[0029] The concentration calculation unit 20 calculates the Kw , K. A , K. B , T A , T B By substituting the input values ​​of equations (1) to (6), the unknown [H + ], [OH - ], [A], [AH + ], [B], and [BH + 1, the concentration calculation unit 20 includes, for example, a setting unit 21, a calculation unit 22, and a determination unit 23.

[0030] The setting unit 21 is + ], [OH - ], [A], [AH + ], [B], and [BH + In this embodiment, the setting unit 21 selects the concentration of any one of the chemical species from [H + The case where the setting unit 21 selects [H + ], but also the concentrations of other chemical species (i.e., [OH - ], [A], [AH + ], [B], or [BH + ]) may be selected. + ] is selected, [H + ] is set to an upper limit value XU and a lower limit value XL that define a search range for searching for a true value XT of [H (see FIG. 2 described later). The setting unit 21, for example, sets the lower limit value XL to zero, and sets the upper limit value XU to a sufficiently large arbitrary value. Then, the setting unit 21 sets an intermediate value XC between the upper limit value XU and the lower limit value XL to a value [H + ] is set as a candidate value.

[0031] The calculation unit 22 calculates [H + By substituting the candidate values ​​of [OH - ], [A], [AH + ], [B], and [BH + ] is derived as a provisional value. + If we temporarily fix the candidate value of [OH - ], [A], [AH+ ], [B], and [BH + For these five unknowns, the five equations (1) to (5) are included in the simultaneous equations, so by solving these five equations, the five unknowns can be found.

[0032] The determination unit 23 determines whether [H + ] and [OH - ], [A], [AH + ], [B], and [BH + ] is used as a provisional value to determine whether the remaining equation (6) of the simultaneous equations is satisfied. + ], [OH - ], [AH + ], and [BH + When the candidate value and provisional value are substituted into [H + ]+[AH + ]+[BH + ]-[OH - ]) is equal to the right-hand side of equation (6) (zero).

[0033] In this embodiment, [H + ] candidate value is changed little by little to search for the true value, and the provisional values ​​of each remaining chemical species are [H + ], the calculated value of the left side of equation (6) is determined according to the candidate value of [H + ] can be considered as a function that changes depending on the calculated value of the left side of equation (6). If the calculated value of the left side of equation (6) is the function Q, the function Q is the sum of the charges of the cations in the aqueous solution ([H + ]+[AH + ]+[BH + ]) and the sum of the charges of the cations ([OH - ]) and the value that indicates the difference.

[0034] Figure 2 shows the relationship between the function Q and [H + ]. In FIG. 2, the vertical axis represents the function Q, and the horizontal axis represents [H + ]. As shown in Figure 2, the function Q is +] shows a monotonically increasing tendency. + As [H + The lower limit XL of [H + The upper limit XU of [H + The candidate value of [H + ] can take various values ​​depending on the function Q, but it becomes zero when equation (6) is satisfied. Therefore, when the function Q becomes zero, + ] is the true value XT.

[0035] Therefore, whether or not equation (6) holds depends on [H + ] can be determined by whether or not the function Q for the candidate value of [H + ], the determining unit 23 determines that the formula (6) is satisfied. + ] is judged to be the true value XT, and [H + ] and the provisional values ​​of the remaining chemical species are provided to the output unit 30 as true values. + If it is determined that the function Q for the candidate value of [H + ] is not the true value XT, and [H + ] is provided to the setting unit 21 with an instruction signal instructing the setting unit 21 to change the candidate value.

[0036] The setting unit 21 is + When an instruction signal to change the candidate value of [H + ]. Specifically, we change the candidate value of [H + If the function Q shows a negative value when the candidate values ​​of [H + ] is smaller than the true value XT (i.e., in Figure 2, [H + ] is located to the left of the true value XT), the setting unit 21 sets the current [H +] as a new lower limit value. In this case, the setting unit 21 sets the intermediate value between the new lower limit value and the upper limit value XU as a new [H + ] is set as a candidate value. + If the function Q shows a positive value when the candidate values ​​of [H + ] is a value that is greater than the true value XT (i.e., in Figure 2, [H + ] is located to the right of the true value XT), the setting unit 21 sets the current [H + In this case, the setting unit 21 sets the intermediate value between the new upper limit value and the lower limit value XL as the new [H + ] is set as a candidate value.

[0037] Setting section 21 is [H + ], the new [H + Based on the candidate values ​​of [H + ] and the candidate value of [H + ] is determined to be the true value XT. In this way, by repeating a series of search processes including the setting of candidate values ​​by the setting unit 21, the calculation by the calculation unit 22, and the determination by the determination unit 23, the value of [H + ], the search range (i.e., the range between the upper and lower limits) for finding the true value XT of [H + ] can be found as the true value XT.

[0038] When the binary search method is used as in this embodiment, [H + The search range for [H + ] search range is 1 / 2 50 (i.e., a range about 15 orders of magnitude smaller). + By narrowing the search range of [H + ] can be reliably and quickly searched for the true value XT of [H +When determining whether the function Q for the candidate value of [ ] becomes zero, the function Q does not need to be zero strictly, but only needs to be within a range that can be considered as zero. Therefore, the determination unit 23 determines whether the function Q becomes zero when the function Q becomes zero by a predetermined threshold (for example, 10 -4 ), the function Q may be determined to be zero, and the function Q may be determined to be non-zero if the function Q is greater than the threshold.

[0039] The output unit 30 outputs [H + When the output unit 30 receives the candidate value of [ ] and the provisional values ​​of the remaining chemical species as true values ​​from the determination unit 23, it outputs these true values ​​to a display device or the like. The destination and method of output by the output unit 30 are not particularly limited, and the output unit 30 may output data to an external device or to a display screen of a personal computer or the like, for example. The information output from the output unit 30 allows the user to know the amounts of chemical species A and B dissolved in the aqueous solution. For example, if CO2 is assumed to be chemical species A, the amount of CO2 dissolved can be known, and the performance of the aqueous solution into which CO2 has been absorbed can be evaluated.

[0040] [Concentration calculation method] Next, a concentration calculation method performed by the concentration calculation device 1 will be described with reference to FIG.

[0041] First, in the concentration calculation device 1, the input unit 10 inputs K w , K. A , K. B , T A , T B This process may be performed, for example, by a user operating the concentration calculation device 1. Alternatively, a previously acquired K w , K. A , K. B , T A , T B The input value of is sent to the concentration calculation device 1, and the concentration calculation device 1 calculates K w , K. A , K. B , T A , T BThe input value may be acquired.

[0042] Next, the setting unit 21 of the concentration calculation unit 20 calculates the unknowns [H + ], [OH - ], [A], [AH + ], [B], and [BH + ] from [H + ] is selected (step S02). This process may be performed by the user operating the concentration calculation device 1, for example.

[0043] Next, the setting unit 21 sets [H + An upper limit value XU and a lower limit value XL that define a search range for searching for the true value XT of [H + The lower limit XL of [H + The upper limit XU of [ ] may be set to any sufficiently large value.

[0044] Next, the setting unit 21 sets [H + ] candidate values ​​are set (step S03). + The candidate value for [ ] is set to, for example, an intermediate value XC between the upper limit value XU and the lower limit value XL.

[0045] Next, the calculation unit 22 of the concentration calculation unit 20 calculates K w , K. A , K. B , T A , T B Input value and [H + ] are substituted into equations (1) to (5), which allows the remaining [OH - ], [A], [AH + ], [B], and [BH + A provisional value of ] is calculated (step S04).

[0046] Next, the determination unit 23 of the concentration calculation unit 20 determines [H + ] and [OH - ], [A], [AH + ], [B], and [BH+ ], it is determined whether or not the formula (6) is satisfied (step S05). If the determination unit 23 determines that the formula (6) is not satisfied (No in step S05), the setting unit 21 sets [H + ] is changed (step S06). + If the function Q indicates a negative value when the candidate value of [H + ] candidate value is the new [H + ] is set as the lower limit of [H + If the function Q indicates a positive value when the candidate value of [H + ] candidate value is the new [H + ] is set as the upper limit value of

[0040] . Thereafter, steps S04 and S05 are repeated until the decision unit 23 decides that the formula (6) does not hold.

[0047] On the other hand, if the determination unit 23 determines that the formula (6) is true (Yes in step S05), the determination unit 23 determines that [H + ] and [OH - ], [A], [AH + ], [B], and [BH + The provisional values ​​of [ ] are provided as true values ​​to the output unit 30, which then outputs the true values ​​to a display device or the like (step S07).

[0048] [Hardware configuration] Next, the hardware configuration of the concentration calculation apparatus 1 will be described with reference to Fig. 4. Fig. 4 is a diagram showing an example of the hardware configuration of the concentration calculation apparatus 1. The concentration calculation apparatus 1 includes one or more computers 100. The computer 100 has a CPU (Central Processing Unit) 101, a main memory unit 102, an auxiliary memory unit 103, a communication control unit 104, an input device 105, and an output device 106. The concentration calculation apparatus 1 is configured by one or more computers 100 configured by this hardware and software such as a program.

[0049] When the concentration calculation device 1 is configured by multiple computers 100, these computers 100 may be connected locally or via a communication network such as the Internet or an intranet. This connection logically constructs a single concentration calculation device 1.

[0050] The CPU 101 executes an operating system, application programs, etc. The main memory 102 is composed of a read-only memory (ROM) and a random access memory (RAM). The auxiliary memory 103 is a storage medium composed of a hard disk, a flash memory, etc. The auxiliary memory 103 generally stores a larger amount of data than the main memory 102. At least a portion of each component constituting the concentration calculation apparatus 1 is realized by the auxiliary memory 103. The communication control unit 104 is composed of a network card or a wireless communication module. At least a portion of each component constituting the concentration calculation apparatus 1 may be realized by the communication control unit 104. The input device 105 is composed of a keyboard, a mouse, a touch panel, a microphone for voice input, etc. For example, at least a portion of the input unit 10 is realized by the input device 105. The output device 106 is composed of a display, a printer, etc. At least a portion of the output unit 30 is realized by the output device 106. For example, the output device 106 may display data output by the output unit 30 on a display, etc.

[0051] The auxiliary storage unit 103 stores the program 110 and data necessary for processing in advance. The program 110 causes the computer 100 to execute each functional element of the concentration calculation apparatus 1. The program 110 causes the computer 100 to execute, for example, the processes related to steps S01 to S07 described above. For example, the program 110 is loaded by the CPU 101 or the main storage unit 102 and causes at least one of the CPU 101, the main storage unit 102, the auxiliary storage unit 103, the communication control unit 104, the input device 105, and the output device 106 to operate. For example, the program 110 reads and writes data from and to the main storage unit 102 and the auxiliary storage unit 103. The program 110 may be provided in the form of a tangible recording medium such as a CD-ROM, a DVD-ROM, or a semiconductor memory. The program 110 may be provided as a data signal via a communication network.

[0052] [Action and effect] The effects achieved by the concentration calculation device 1, the concentration calculation method, and the concentration calculation program described above will be described.

[0053] When solving a system of simultaneous equations containing the concentrations of multiple chemical species as unknowns by numerical calculation, it is conceivable to simultaneously change the concentrations of each chemical species little by little and search for the concentration of each chemical species that satisfies the simultaneous equations. However, when chemical species A and B are included as solutes in the aqueous solution as in this embodiment, the simultaneous equations include Equation (2), which is a chemical equilibrium equation for chemical species A, and Equation (4), which is a chemical equilibrium equation for chemical species B. In this case, Equation (2) and Equation (4) have in common the equation [H + ] exists, and for example, [H + ] simultaneously satisfies equation (4). Therefore, it is difficult to determine the concentration of each chemical species that satisfies simultaneous equations including equations (1) to (6) when determining the concentration of each chemical species by changing the concentration of all chemical species simultaneously. As a result, it may take a long time to determine the concentration of each chemical species, or it may not be possible to determine the concentration of each chemical species under certain conditions.

[0054] In contrast, in this embodiment, when solving the simultaneous equations including equations (1) to (6), [H + A candidate value for [ ] is provisionally set, and provisional values ​​for the concentrations of the remaining chemical species are calculated based on that candidate value. Then, whether the provisionally set candidate value is the correct value (true value) that satisfies the simultaneous equations is confirmed by determining whether Equation (6) holds. Once the concentration of one chemical species is provisionally determined in this way, the number of unknowns to be calculated is reduced by one, and the concentrations of the remaining five chemical species can be easily derived using Equations (1) to (5). Then, by changing the concentration of the fixed chemical species and searching for the true value that satisfies Equation (6), the concentrations of the six chemical species that satisfy the simultaneous equations can be calculated. This method of temporarily fixing the concentration of one chemical species and gradually calculating the concentrations of N chemical species can easily calculate the concentrations of N chemical species that satisfy the simultaneous equations. As a result, it is possible to quickly and reliably calculate the concentrations of N chemical species that satisfy the simultaneous equations compared to a method of simultaneously calculating the concentrations of N chemical species while simultaneously changing the concentrations of N chemical species.

[0055] In this embodiment, when the determination unit 23 determines that the formula (6) does not hold, the change of the candidate value and the derivation of the provisional values ​​of the concentrations of the remaining chemical species based on the changed candidate value are repeatedly executed until the determination unit 23 determines that the formula (6) holds. In this case, the concentrations of each chemical species that satisfy the simultaneous equations can be reliably obtained.

[0056] In this embodiment, the setting unit 21 sets [H + ], and sets an intermediate value XC between the lower limit value XL and the upper limit value XU as a candidate value. If the determination unit 23 determines that formula (6) does not hold, the setting unit 21 may set the current candidate value as a new lower limit value or upper limit value, and set a new candidate value using the new lower limit value or upper limit value. In this case, the search range between the lower limit value and the upper limit value can be narrowed each time it is determined that formula (6) does not hold, and by repeating the above determination, the candidate values ​​can be narrowed down and the true value can be reliably found.

[0057] In this embodiment, when the equilibrium state is reached, K A and [AH + ] and [A] and [H + ] and when the equilibrium state is reached, K B and [BH + ] and [B] and [H + ] and equation (3) which holds between them are included in the simultaneous equations. In this case, equations (2) and (3) have a common [H + ] is included, and satisfies Eq. (2) [H + ] may not simultaneously satisfy equation (3), so it is difficult to simultaneously calculate the concentration of each chemical species while changing it simultaneously. + According to the method of this embodiment in which the concentration of each chemical species is determined stepwise by temporarily fixing [(amount of chemical species)], it is possible to easily determine the concentration of each chemical species, as described above.

[0058] In this embodiment, the setting unit 21 sets [H + In this case, the candidate value of [OH ― ] can be easily derived, so the remaining [A], [AH + ], [B], and [BH + This makes it easier to derive the provisional value of [OH ― ] can be set as a candidate value. In this case, using equation (1), + ] can be easily derived, the concentrations of the six chemical species can be more easily calculated. + ] appears in many expressions, so [H + ] or [OH ― ], the concentration of each chemical species can be more easily determined.

[0059] If we consider a situation in which CO2-containing gas is brought into contact with an aqueous solution containing dissolved RNH2, causing the aqueous solution to absorb CO2, equations (1) to (6) can be written as the following equations (7) to (14), where chemical species A is CO2 and chemical species B is RNH2.

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[0060] In equations (7) to (14), [CO2] is the concentration of CO2 in the aqueous solution. [HCO3 - ] is HCO3 in aqueous solution - The concentration of [CO3 2- ] is the CO3 in aqueous solution 2- [RNH2] is the concentration of RNH2 in aqueous solution. [RNH3 + ] is the RNH3 + The concentration of [RNHCOO - ] is RNHCOO in aqueous solution -is the concentration of CO2 in the aqueous solution. T1 indicates the amount of CO2 added to the aqueous solution. T2 indicates the amount of RNH2 added to the aqueous solution. K1 is the equilibrium constant (second equilibrium constant) for the first-stage equilibrium reaction of CO2 in the aqueous solution. K2 is the equilibrium constant for the second-stage equilibrium reaction of CO2 in the aqueous solution. K3 is the equilibrium constant (third equilibrium constant) for the equilibrium reaction of RNH2 in the aqueous solution. K4 is the equilibrium constant for the equilibrium reaction between CO2 and RNH2 in the aqueous solution.

[0061] Equation (7) is the same as equation (1). Equation (8) corresponds to equation (2). Equation (8) is a chemical equilibrium equation that holds when the chemical reaction of CO2 in an aqueous solution reaches the first equilibrium state. Equation (8) expresses the chemical equilibrium equation [HCO3 - ] and [H + ] is equal to the product of [CO2] and the constant K1. Equation (9) is the chemical equilibrium equation that holds when the chemical reaction of CO2 in an aqueous solution reaches the second equilibrium state. Equation (9) shows that at equilibrium, [CO3 2- ] and [H + ] and the product is [HCO3 - ] and the constant K2. Equation (10) corresponds to equation (4). Equation (10) is a chemical equilibrium equation that holds when the chemical reaction of RNH2 in an aqueous solution reaches equilibrium. Equation (10) shows that at equilibrium, [RNH2] and [H + ] is multiplied by [RNH3 + ] and a constant K3.

[0062] Equation (11) is a chemical equilibrium equation that holds when the chemical reaction (salt formation reaction) between CO2 and RNH2 in an aqueous solution reaches equilibrium. Equation (11) expresses the equilibrium state between [RNH2] and [HCO3 - ] and the product is [RNHCOO -] and the constant K4. Equation (12) corresponds to equation (3). Equation (12) indicates that the number of CO2 in the aqueous solution is equal to the number of CO2 before the chemical reaction that is introduced into the aqueous solution. In other words, equation (12) indicates that [CO2] in the aqueous solution is equal to the amount of input T1. Equation (13) corresponds to equation (5). Equation (13) indicates that the number of RNH2 in the aqueous solution and the number of RNH3 + Number of RNHCOO - is equal to the number of RNH2 before the chemical reaction. In other words, equation (13) shows that the sum of [RNH2] and [RNH3 + ] and [RNHCOO - ] is equal to the input amount T2. Equation (14) corresponds to equation (6). Equation (14) shows that the sum of [H + ] and [RNH3 + ] and the sum is [OH - ] and [HCO3 - ] and [RNHCOO - ] and 2 × [CO3 2- ] is equal to the sum of

[0063] When solving the above equations (7) to (14), the unknown quantity [H + ], [OH - ], [CO2], [HCO3 - ], [CO3 2- ], [RNH2], [RNH3 + ], and [RNHCOO - Specifically, first, the input values ​​of K1, K2, K3, K4, T1, and T2 are input, and the unknown [H + ], [OH - ], [CO2], [HCO3 - ], [CO3 2- ], [RNH2], [RNH3 + ], and [RNHCOO - ], for example, [H + Then, using the set candidate values, the remaining [OH- ], [CO2], [HCO3 - ], [CO3 2- ], [RNH2], [RNH3 + ], and [RNHCOO - A provisional value of ] is calculated.

[0064] Then, by determining whether or not equation (14) holds, [H + ] is determined to be a true value. By performing the same process as in the above-described embodiment, it is possible to determine whether the candidate value of [H + ], [OH - ], [CO2], [HCO3 - ], [CO3 2- ], [RNH2], [RNH3 + ], and [RNHCOO - ] can be calculated. If we can calculate the concentration of each chemical species in the aqueous solution in this way, we can understand the amount of CO2 dissolved in the aqueous solution. Of the chemical species dissolved in the aqueous solution, [HCO3 - ], [CO3 2- ], and [RNHCOO - ] indicates the amount of CO2 present in dissolved form, so the amount of dissolved CO2 in an aqueous solution can be obtained from these concentration values.

[0065] [Variations] As described above, the present disclosure is not necessarily limited to the above-described embodiments, and various modifications are possible without departing from the spirit of the present disclosure.

[0066] For example, only chemical species A may dissolve in an aqueous solution, and that chemical species A may undergo a two-step chemical equilibrium reaction. In this case, in addition to chemical species A, the aqueous solution may also contain H produced by ionization of water. + and OH - And, H + The ionized species AH + and AH2 2+ In this case, the simultaneous equations that hold between the concentrations of chemical species present in the aqueous solution are composed of the following equations (15) to (19): [AH2 2+] is AH2 in aqueous solution 2+ is the concentration of K A is the equilibrium constant (second equilibrium constant) of the first equilibrium reaction of chemical species A in aqueous solution. AH is the equilibrium constant (third equilibrium constant) for the second equilibrium reaction of chemical species A in aqueous solution.

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[0067] Equation (15) is the H produced by ionization of water in an aqueous solution. + and OH - Equation (16) is the equation (second chemical equilibrium equation) that holds when the chemical reaction of chemical species A in an aqueous solution reaches the first equilibrium state. Equation (17) is the equation (third chemical equilibrium equation) that holds when the chemical reaction of chemical species A in an aqueous solution reaches the second equilibrium state. Equation (18) expresses the relationship between the amount of chemical species A and the amount of chemical species AH after a chemical reaction has occurred in an aqueous solution. + Amount and species of AH2 2+ Equation (19) is an equation (conservation of substance) that shows that the sum of the charges on the cations (i.e., the sum of the positive charges) and the sum of the charges on the anions (i.e., the sum of the negative charges) is equal to the amount of chemical species A before the chemical reaction begins (i.e., the amount of chemical species A added to the aqueous solution). Equation (19) is an equation (conservation of charge) that shows that at equilibrium, the sum of the charges on the cations (i.e., the sum of the positive charges) and the sum of the charges on the anions (i.e., the sum of the negative charges) are equal.

[0068] When solving the above equations (15) to (19), the unknown quantity [H + ], [OH - ], [A], [AH + ], and [AH2 2+ Specifically, first, K A , K. AH , T A The input value of is entered and the unknown [H + ], [OH - ], [A], [AH + ], and [AH2 2+ ], for example, [H + ] is set as a candidate value. Then, using the set candidate value, the remaining [OH - ], [A], [AH + ], and [AH2 2+ ] is calculated. Then, by determining whether or not Equation (19) is satisfied, the provisional value of [H + ] is determined to be a true value. By performing the same process as in the above-described embodiment, it is possible to determine whether the candidate value of [H + ], [OH - ], [A], [AH + ], and [AH2 2+ ] can be obtained.

[0069] Therefore, even when solving such simultaneous equations including equations (15) to (19), the unknown quantity [H + ], [OH - ], [A], [AH + ], and [AH2 2+ ] can be easily obtained. In addition, this simultaneous equation contains the equation K A and [AH + ] and [A] and [H + ] and when the second stage equilibrium state is reached, K A and [AH2 2+ ] and [AH + ] and [H +In this case, the formula (16) and the formula (17) contain the common formula [H + ] is included, and satisfies Eq. (16) [H + ] may not simultaneously satisfy equation (17), making it difficult to simultaneously calculate the concentration of each chemical species while simultaneously changing it. + According to this method, in which the concentration of each chemical species is determined stepwise by temporarily fixing [(a) / (b)], it is possible to easily determine the concentration of each chemical species, as described above.

[0070] In the above-described embodiment, a binary search method is used to find [H + ] was explained, but the Newton-Raphson method can be used to find the true value of [H + In the Newton-Raphson method, as shown in FIG. 6, the true value of K included in equations (1) to (6) is searched for by the input unit 10, similar to the binary search method. w , K. A , K. B , T A , T B The input value of [H + ], [OH - ], [A], [AH + ], [B], and [BH + ] from [H + ] is selected (step S12).

[0071] Next, the setting unit 21 sets [H + ] is set as a candidate value (step S13). + The sum of the provisional value of [H + The candidate value of [ ] may be any value. The minute amount is set in order to obtain a line L (that is, a tangent to the function Q) in FIG.

[0072] Next, the calculation unit 22 of the concentration calculation unit 20 calculates [H +] are substituted into equations (1) to (5), which allows the remaining [OH - ], [A], [AH + ], [B], and [BH + ] is calculated (step S15). + The provisional value + minute amount of ] is substituted into equations (1) to (5), and the remaining [OH - ], [A], [AH + ], [B], and [BH + The sum of the provisional value of [ ] and the minute amount (i.e., provisional value + minute amount) is calculated (step S16). Note that steps S13 and S15 may be performed simultaneously with steps S14 and S16, or may be performed at a timing different from steps S14 and S16.

[0073] Next, the determination unit 23 of the concentration calculation unit 20 determines [H + ] and [OH - ], [A], [AH + ], [B], and [BH + It is determined whether or not the formula (6) is satisfied under each provisional value of [ ] (step S17). As explained in the above embodiment, whether or not the formula (6) is satisfied can be determined by whether or not the function Q indicating the calculated value of the left side of the formula (6) is zero.

[0074] Figure 5 shows the relationship between the function Q and [H + ]. In FIG. 5, the vertical axis represents the function Q, and the horizontal axis represents [H + ]. [H + ] is the candidate value of X1, and [H + If the value of the function Q when [H is the candidate value X1 is Y1, the point P1(X1, Y1) can be obtained in steps S13 and S15. + ] candidate value + minute amount is X1 + ΔX, [H + If the value of function Q when [X1+ΔX] is the candidate value X1+ΔX is Y1+ΔY, point P2(X1+ΔX, Y1+ΔY) can be obtained in steps S14 and S16.

[0075] If these two points P1 and P2 are known, a straight line L connecting points P1 and P2 (i.e., a tangent to the function Q at point P1) can be obtained. Then, the determining unit 23 determines the intersection PL(X2, 0) between the straight line L and the horizontal axis of FIG. 6, and calculates [H + ] is X1, the function Q is determined to be zero or not, and the formula (6) is determined to be true or not. If the determination unit 23 determines that the formula (6) is not true (No in step S17), the process returns to step S13 and step S14, and the setting unit 21 determines that [H + Specifically, the setting unit 21 changes the candidate value of X2, which indicates the intersection PL with the horizontal axis in FIG. + ] is set as a candidate value for [ 0 . 0 . 0 . ]. Thereafter, steps S13 to S17 are repeated until the decision unit 23 decides that the formula (6) does not hold.

[0076] On the other hand, if the determination unit 23 determines that the formula (6) is true (Yes in step S17), the determination unit 23 determines that [H + ] and [OH - ], [A], [AH + ], [B], and [BH + ] are provided as true values ​​to the output unit 30, which then outputs these true values ​​to a display device or the like (step S18). In this way, even when the Newton-Raphson method is used, the same effects as those of the above-described embodiment can be achieved.

[0077] In the above-described embodiment, the setting unit 21 + ], [OH - ], [A], [AH + ], [B], and [BH + ], [H + However, the setting unit 21 may be configured to select [H + ] and not just [OH - ], [A], [AH + ], [B], and [BH +In the above-described embodiment, a case where two types of chemical species A and B are introduced and dissolved in the aqueous solution has been described. However, three or more types of chemical species may be introduced into the aqueous solution. In the above-described embodiment, CO2 is exemplified as the chemical species A, and RNH2 is exemplified as the chemical species B. However, the chemical species A and B introduced into the aqueous solution may be CO 2、 The chemical species is not limited to RNH2, but may be other chemical species such as CH3COOH (acetic acid), HCl (hydrochloric acid), NH3 (ammonia), and NaOH (sodium hydroxide). Note that CH3COOH, HCl, and NH3 dissolve in water to form H + NaOH dissolves in water and releases or receives OH. - It has the property of releasing

[0078] The gist of the present invention will be described below. [1] A concentration calculation device that calculates the concentration of N (N is an integer of 3 or more) chemical species dissolved in an aqueous solution, a concentration calculation unit that derives the concentrations of the N chemical species as unknowns by solving a system of equations including N expressions that hold between the concentrations of the N chemical species; an output unit that outputs the concentrations of the N chemical species calculated by the concentration calculation unit, The N equations are N-1 equations including a plurality of chemical equilibrium equations that hold between the concentrations of the N chemical species when the N chemical species reach an equilibrium state in the aqueous solution; and a charge conservation equation indicating that the sum of the charges of the cations and the sum of the charges of the anions in the aqueous solution are equal, The concentration calculation unit a setting unit that sets a candidate value for the concentration of any one of the N chemical species; a calculation unit that derives provisional values ​​of concentrations of the remaining N-1 chemical species excluding the concentration of the one chemical species from the concentrations of the N chemical species by substituting the candidate value and solving the N-1 equations; a determination unit that determines whether the equation of conservation of charge is satisfied based on the candidate value and the N-1 provisional values; When the determination unit determines that the equation of conservation of charge is established, the candidate value and the N-1 provisional values ​​are each provided to the output unit as a true value; a concentration calculation device in which, when the determination unit determines that the equation of conservation of charge does not hold, changing the candidate value and deriving the N-1 provisional values ​​based on the changed candidate value are repeatedly executed until the determination unit determines that the equation of conservation of charge holds. [2] the setting unit sets a lower limit value and an upper limit value of the concentration of the one chemical species, and sets an intermediate value between the lower limit value and the upper limit value as the candidate value; [1] The concentration calculation device according to [1], wherein, when the determination unit determines that the equation of conservation of charge does not hold, the setting unit sets the candidate value as a new lower limit value or upper limit value, and sets the new candidate value using the new lower limit value or upper limit value. [3] The aqueous solution is an aqueous solution containing water as a solvent and different chemical species A and B (A and B are any chemical formulas) as solutes, The concentrations of the N species are the concentrations of hydrogen ions [H + ] and the hydroxide ion concentration [OH ― ], [A] being the concentration of the chemical species A, and [AH + ], the concentration of the chemical species B [B], and the concentration of the chemical species B ionized by the hydrogen ions [BH + ] and, The N-1 formulas are When equilibrium is reached, the first equilibrium constant and the [H + ] and the [OH ― ] and a first chemical equilibrium equation that holds between When equilibrium is reached, the second equilibrium constant [AH + ] and the above [A] and the above [H + ] and a second chemical equilibrium equation that holds between When equilibrium is reached, the third equilibrium constant and the [BH + ] and the above [B] and the above [H + ] and a third chemical equilibrium equation that holds between The amount of the chemical species A added to the aqueous solution is [AH + ] and the sum of [A], and the first amount of substance conservation equation, The amount of the chemical species B added to the aqueous solution is [BH + and a second equation for conservation of amount of substance showing that [A] is equal to the sum of [B] and [C], The charge conservation equation is expressed as [H + ] and the above [AH + ] and the aforementioned [BH + ] is the sum of the above [OH ― ] is equal to the concentration calculation device described in [1] or [2]. [4] The aqueous solution is an aqueous solution containing water as a solvent and a chemical species A (A is any chemical formula) as a solute, The concentrations of the N species are the concentrations of hydrogen ions [H + ] and the hydroxide ion concentration [OH ― ], [A] being the concentration of the chemical species A, and [AH + ] and the concentration of the chemical species A ionized by the hydrogen ions during the second ionization [AH2 2+ ] and, The N-1 formulas are When equilibrium is reached, the first equilibrium constant and the [H + ] and the [OH ― ] and a first chemical equilibrium equation that holds between When the first equilibrium state is reached, the second equilibrium constant and the [AH + ] and the above [A] and the above [H + ] and a second chemical equilibrium equation that holds between When the second equilibrium state is reached, the third equilibrium constant and the [AH2 2+ ] and the above [AH + ] and the above [H + ] and a third chemical equilibrium equation that holds between The amount of the chemical species A added to the aqueous solution is [AH + and the equation of conservation of amount of substance, which shows that [A] is equal to the sum of [A] and [B], The charge conservation equation is expressed as [H + ] and the above [AH + ] and the aforementioned [BH + ] is the sum of the above [OH ― ] is equal to the concentration calculation device described in [1] or [2]. [5] The setting unit + ] or the [OH ― The concentration calculation device according to [3] or [4], wherein the candidate value is set to [0.01]. [6] A concentration calculation method for calculating the concentration of N (N is an integer of 3 or more) chemical species dissolved in an aqueous solution, Deriving the concentrations of the N chemical species as unknowns by solving a system of equations including N expressions that hold between the concentrations of the N chemical species; and outputting the derived concentrations of the N chemical species; The N equations are N-1 equations including a plurality of chemical equilibrium equations that hold between the concentrations of the N chemical species when the N chemical species reach an equilibrium state in the aqueous solution; and a charge conservation equation indicating that the sum of the charges of the cations and the sum of the charges of the anions in the aqueous solution are equal, deriving the concentrations of the N chemical species setting a candidate value for the concentration of any one of the N chemical species; deriving tentative values ​​of the concentrations of the remaining N-1 chemical species, excluding the concentration of the one chemical species, from the concentrations of the N chemical species by substituting the candidate value and solving the N-1 equations; determining whether the charge conservation equation is satisfied under the candidate value and the N-1 provisional values; When it is determined that the equation of conservation of charge is established, the candidate value and the N-1 provisional values ​​are output as true values, respectively; A concentration calculation method in which, when it is determined that the equation of conservation of charge does not hold, changing the candidate value and deriving the N-1 provisional values ​​based on the changed candidate value are repeatedly performed until it is determined that the equation of conservation of charge holds. [7] A concentration calculation program for calculating the concentrations of N (N is an integer of 3 or more) chemical species dissolved in an aqueous solution, Deriving the concentrations of the N chemical species as unknowns by solving a system of equations including N expressions that hold between the concentrations of the N chemical species; outputting the derived concentrations of the N chemical species; The N equations are N-1 equations including a plurality of chemical equilibrium equations that hold between the concentrations of the N chemical species when the N chemical species reach an equilibrium state in the aqueous solution; and a charge conservation equation indicating that the sum of the charges of the cations and the sum of the charges of the anions in the aqueous solution are equal, deriving the concentrations of the N chemical species setting a candidate value for the concentration of any one of the N chemical species; deriving tentative values ​​of the concentrations of the remaining N-1 chemical species, excluding the concentration of the one chemical species, from the concentrations of the N chemical species by substituting the candidate value and solving the N-1 equations; determining whether the charge conservation equation is satisfied under the candidate value and the N-1 provisional values; When it is determined that the equation of conservation of charge is established, the candidate value and the N-1 provisional values ​​are output as true values, respectively; a concentration calculation program that, when it is determined that the equation of conservation of charge does not hold, repeatedly changes the candidate value and derives the N-1 provisional values ​​based on the changed candidate value until it is determined that the equation of conservation of charge holds. [Explanation of symbols]

[0079] 1 Concentration calculation device 20 Concentration calculation section 21 Setting section 22 Calculation section 23 Judgment section 30 Output section 100 computers XC Median XL Lower Limit XT true value XU upper limit

Claims

1. A concentration calculation device for calculating the concentrations of N (N is an integer of 3 or more) chemical species dissolved in an aqueous solution, a concentration calculation unit that derives the concentrations of the N chemical species as unknowns by solving a system of equations including N expressions that hold between the concentrations of the N chemical species; an output unit that outputs the concentrations of the N chemical species calculated by the concentration calculation unit, The N equations are N-1 equations including a plurality of chemical equilibrium equations that hold between the concentrations of the N chemical species when the N chemical species reach an equilibrium state in the aqueous solution; and a charge conservation equation indicating that the sum of the charges of the cations and the sum of the charges of the anions in the aqueous solution are equal, The concentration calculation unit a setting unit that sets a candidate value for the concentration of any one of the N chemical species; a calculation unit that derives provisional values ​​of concentrations of the remaining N-1 chemical species, excluding the concentration of the one chemical species, from the concentrations of the N chemical species by substituting the candidate value and solving the N-1 equations; a determination unit that determines whether the charge conservation equation is satisfied based on the candidate value and the N-1 provisional values; When the determination unit determines that the equation of conservation of charge is established, the candidate value and the N-1 provisional values ​​are each provided to the output unit as a true value; When the determination unit determines that the equation of conservation of charge does not hold, the change of the candidate value and the derivation of the N-1 provisional values ​​based on the changed candidate value are repeatedly executed until the determination unit determines that the equation of conservation of charge holds.

2. the setting unit sets a lower limit value and an upper limit value of the concentration of the one chemical species, and sets an intermediate value between the lower limit value and the upper limit value as the candidate value; 2. The concentration calculation device according to claim 1, wherein, when the determination unit determines that the equation of conservation of charge does not hold, the setting unit sets the current candidate value as a new lower limit value or a new upper limit value, and sets the new candidate value using the new lower limit value or the new upper limit value.

3. The aqueous solution is an aqueous solution containing water as a solvent and different chemical species A and B (A and B are any chemical formulas) as solutes, The concentrations of the N chemical species are the concentrations of hydrogen ions [H ＋ ] and the hydroxide ion concentration [OH ― ], [A] being the concentration of the chemical species A, and [AH ＋ ], [B] being the concentration of the chemical species B, and [BH ＋ ] and The N-1 formulas are When the equilibrium state is reached, the first equilibrium constant and the [H ＋ ] and the [OH ― a first chemical equilibrium equation that holds between When the equilibrium state is reached, the second equilibrium constant and the [AH ＋ ] and the [A] and the [H ＋ ] a second chemical equilibrium equation that holds between When the equilibrium state is reached, the third equilibrium constant and the [BH ＋ ] and the [B] and the [H ＋ ] a third chemical equilibrium equation that holds between The amount of the chemical species A added to the aqueous solution is [AH ＋ a first equation for conservation of amount of substance showing that [A] is equal to the sum of [A] and [B]; The amount of the chemical species B added to the aqueous solution is [BH ＋ a second equation for conservation of amount of substance showing that [A] is equal to the sum of [B] and [C], The charge conservation equation is ＋ ] and the above [AH ＋ ] and the above [BH ＋ ] is the sum of the [OH ― 2. The concentration calculation device of claim 1, wherein the concentration is expressed as:

4. The aqueous solution is an aqueous solution containing water as a solvent and a chemical species A (A is any chemical formula) as a solute, The concentrations of the N chemical species are the concentrations of hydrogen ions [H ＋ ] and the hydroxide ion concentration [OH ― ], [A] being the concentration of the chemical species A, and [AH ＋ ] and the concentration of the chemical species A ionized by the hydrogen ions during the second ionization [AH ２ ２＋ ] and The N-1 formulas are When the equilibrium state is reached, the first equilibrium constant and the [H ＋ ] and the [OH ― a first chemical equilibrium equation that holds between When the first equilibrium state is reached, the second equilibrium constant and the [AH ＋ ] and the [A] and the [H ＋ ] a second chemical equilibrium equation that holds between When the second equilibrium state is reached, the third equilibrium constant and the [AH ２ ２＋ ] and the above [AH ＋ ] and the above [H ＋ ] a third chemical equilibrium equation that holds between The amount of the chemical species A added to the aqueous solution is [AH ＋ and the equation of conservation of substance showing that [A] is equal to the sum of [A] and [B], The charge conservation equation is ＋ ] and the above [AH ＋ ] and the above [AH ２ ２＋ ] is the sum of the [OH ― 2. The concentration calculation device of claim 1, wherein the concentration is expressed as:

5. The setting unit ＋ ] or the [OH ― 5. The concentration calculation device according to claim 3, wherein the candidate value is set to:

6. A concentration calculation method for calculating the concentrations of N (N is an integer of 3 or more) chemical species dissolved in an aqueous solution, comprising: Deriving the concentrations of the N chemical species as unknowns by solving a system of equations including N expressions that hold between the concentrations of the N chemical species; and outputting the derived concentrations of the N chemical species; The N equations are N-1 equations including a plurality of chemical equilibrium equations that hold between the concentrations of the N chemical species when the N chemical species reach an equilibrium state in the aqueous solution; and a charge conservation equation indicating that the sum of the charges of the cations and the sum of the charges of the anions in the aqueous solution are equal, Deriving the concentrations of the N chemical species includes: setting a candidate value for the concentration of any one of the N chemical species; deriving tentative values ​​of the concentrations of the remaining N-1 chemical species, excluding the concentration of the one chemical species, from the concentrations of the N chemical species by substituting the candidate value and solving the N-1 equations; determining whether the charge conservation equation holds for the candidate value and the N-1 provisional values; When it is determined that the equation of conservation of charge is established, the candidate value and the N-1 provisional values ​​are output as true values, When it is determined that the equation of conservation of charge does not hold, the method repeatedly changes the candidate value and derives the N-1 provisional values ​​based on the changed candidate value until it is determined that the equation of conservation of charge holds.

7. A concentration calculation program for calculating the concentrations of N (N is an integer of 3 or more) chemical species dissolved in an aqueous solution, Deriving the concentrations of the N chemical species as unknowns by solving a system of equations including N expressions that hold between the concentrations of the N chemical species; outputting the derived concentrations of the N chemical species; The N equations are N-1 equations including a plurality of chemical equilibrium equations that hold between the concentrations of the N chemical species when the N chemical species reach an equilibrium state in the aqueous solution; and a charge conservation equation indicating that the sum of the charges of the cations and the sum of the charges of the anions in the aqueous solution are equal, Deriving the concentrations of the N chemical species includes: setting a candidate value for the concentration of any one of the N chemical species; deriving tentative values ​​of the concentrations of the remaining N-1 chemical species, excluding the concentration of the one chemical species, from the concentrations of the N chemical species by substituting the candidate value and solving the N-1 equations; determining whether the charge conservation equation holds for the candidate value and the N-1 provisional values; When it is determined that the equation of conservation of charge is established, the candidate value and the N-1 provisional values ​​are output as true values, respectively; A concentration calculation program that, when it is determined that the equation of conservation of charge does not hold, repeatedly changes the candidate value and derives the N-1 provisional values ​​based on the changed candidate value until it is determined that the equation of conservation of charge holds.

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