Silica scale formation prediction system, geothermal power generation system, silica scale formation prediction method, and silica scale formation prediction program

Abstract

This system provides a silica scale generation prediction system that can predict the amount of silica scale generated with greater accuracy. [Solution] The silica scale generation prediction system according to the present invention is based on the temperature T at the predicted site of the target object. s A prediction formula PF for silica concentration C, which depends on the silica concentration, and the time t until the silica-containing fluid reaches the predicted site. s The system includes a silica scale generation prediction unit that predicts the amount of silica scale generated at a predicted site based on at least one of the silica concentration C prediction curve PC which depends on the silica concentration C, wherein the silica concentration C prediction formula PF and the silica concentration C prediction curve PC are obtained based on a reaction model generated using a silica polymerization reaction that includes reversible and irreversible reactions and precipitation equilibrium reactions of silica contained in the fluid, and the silica scale generation prediction unit calculates the amount of silica scale generated at the predicted site using at least one of the initial silica concentration Ci and the fluid flow rate FR.

Description

[Technical Field]

[0001] The present invention relates to a silica scale generation prediction system, a geothermal power generation system, a silica scale generation prediction method, and a silica scale generation prediction program. [Background technology]

[0002] In plant systems that use geothermal fluids, such as geothermal power generation facilities, silica scale, formed by the precipitation of silica dissolved in the geothermal fluid, generally adheres to various equipment such as machinery and piping that make up the plant system. Silica scale is mainly composed of polymers of Si and O and adheres firmly to various equipment. In geothermal power generation facilities, the adhesion of silica scale to various equipment leads to a decrease in the silica scale's reduction capacity and a decrease in the power generation efficiency of the geothermal power generation facility. Therefore, methods are being investigated to predict the amount of silica scale generated from the properties of the geothermal fluid using simulations, rather than relying on experience.

[0003] One method for predicting the amount of silica scale formation is, for example, the temperature T at the prediction site where silica scale deposition should be predicted. s and the time t until the silicic acid-containing fluid reaches the predicted site s A method for predicting silica scale formation is disclosed, which includes the steps of obtaining a prediction formula for silica saturation concentration and calculating the amount of silica deposited at a predicted site based on a temperature-dependent prediction formula for silica saturation concentration and a time-dependent prediction curve for silica dissolved concentration, and the prediction formula for silica saturation concentration and the prediction curve for silica dissolved concentration are obtained based on a three-step precipitation equilibrium reaction model (see, for example, Patent Document 1). [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] International Publication No. 2023 / 074697 [Overview of the Initiative] [Problems that the invention aims to solve]

[0005] In the silica scale generation prediction method described in Patent Document 1, the initial concentration and flow rate of the silicic acid-containing fluid were fixed to predetermined values, and fluctuations in these values ​​were not considered. Therefore, in order to improve the accuracy of silica scale generation prediction and to utilize methods that predict silica scale generation through simulation, there is a need for a method that can predict the amount of silica scale generated at the target site with higher accuracy by also considering fluctuations in the initial concentration and flow rate of the silicic acid-containing fluid.

[0006] One aspect of the present invention aims to provide a silica scale generation prediction system that can predict the amount of silica scale generated in a predicted site with greater accuracy. [Means for solving the problem]

[0007] One aspect of the present invention is, Predicting the adhesion of silica scale caused by silica contained in the fluid, using the temperature T at the predicted location on the object. s , and the time t until the silica-containing fluid reaches the predicted site s An acquisition unit that acquires at least one of the following conditions, temperature T s Prediction formula for silica concentration C dependent on PF and time t s A silica scale generation amount prediction unit predicts the amount of silica scale generated in the predicted area based on at least one of the prediction curve PC of silica concentration C which depends on the silica concentration, Equipped with, The prediction formula PF and the prediction curve PC for the silica concentration C are obtained based on a reaction model generated using a silica polymerization reaction that includes reversible and irreversible reactions and precipitation equilibrium reactions of the silica contained in the fluid. The silica scale generation prediction unit is a silica scale generation prediction system that calculates the amount of silica scale generated at the prediction site using at least one of the initial silica concentration Ci and the fluid flow rate FR.

[0008] One aspect of the present invention is that a computer acquires at least one condition of temperature T at a predicted site of an object for predicting adhesion of silica scale caused by silica contained in a fluid s , and time t until the fluid containing silica reaches the predicted site s in an acquisition step; a silica scale generation amount prediction step of predicting the generation amount of the silica scale at the predicted site based on at least one of a prediction formula PF of silica concentration C depending on temperature T s and a prediction curve PC of silica concentration C depending on time t s ; and performs The prediction formula PF of the silica concentration C and the prediction curve PC of the silica concentration C are obtained based on a reaction model generated using a silica polymerization reaction including a reversible reaction, an irreversible reaction, and a precipitation equilibrium reaction of the silica contained in the fluid. The silica scale generation amount prediction step is a prediction method of calculating the generation amount of the silica scale at the predicted site using at least one element of an initial concentration Ci of the silica and a flow rate FR of the fluid.

[0009] One aspect of the present invention is that a computer acquires at least one condition of temperature T at a predicted site of an object for predicting adhesion of silica scale caused by silica contained in a fluid s , and time t until the fluid containing silica reaches the predicted site s in an acquisition step; a silica scale generation amount prediction step of predicting the generation amount of the silica scale at the predicted site based on at least one of a prediction formula PF of silica concentration C depending on temperature T s and a prediction curve PC of silica concentration C depending on time t s ; and causes to perform The prediction formula PF and the prediction curve PC for the silica concentration C are obtained based on a reaction model generated using a silica polymerization reaction that includes reversible and irreversible reactions and precipitation equilibrium reactions of the silica contained in the fluid. The silica scale generation prediction step is a silica scale generation prediction program that calculates the amount of silica scale generated at the prediction site using at least one of the initial silica concentration Ci and the fluid flow rate FR. [Effects of the Invention]

[0010] A silica scale generation prediction system according to one aspect of the present invention can predict the amount of silica scale generated with greater accuracy. [Brief explanation of the drawing]

[0011] [Figure 1] This is a block diagram showing the schematic configuration of a prediction system according to the first embodiment of the present invention. [Figure 2] This is an explanatory diagram showing the flow of calculation for silica concentration C. [Figure 3] This figure shows an example of a prediction curve for silica concentration C, which is calculated using the prediction formula PF for silica concentration C, and illustrates the relationship between temperature T and silica concentration C. [Figure 4] This figure shows an example of a prediction curve for silica concentration C, which is calculated using the prediction formula PF for silica concentration C when the fluid is acidic or neutral, and illustrates the relationship between temperature T and silica concentration C. [Figure 5] This figure shows an example of a graph illustrating the change in the effective reaction coefficient J with respect to pH. [Figure 6] This figure shows an example of a prediction curve for silica concentration C, which is calculated using the prediction formula PF for silica concentration C when the pH of the fluid is basic, and illustrates the relationship between temperature T and silica concentration C. [Figure 7] This is a flowchart showing a prediction method according to the first embodiment of the present invention. [Figure 8] This is a block diagram showing the schematic configuration of the prediction system according to the second embodiment of the present invention. [Figure 9] This figure shows an example of a predicted curve PC for silica concentration C obtained by processes (i) to (iii). [Figure 10] This figure shows an example of a predicted curve PC for silica concentration C obtained by process (iii). [Figure 11] This is a semi-logarithmic graph showing an example of a prediction curve PC for frequency factor A. [Figure 12] This is a flowchart showing a prediction method according to a second embodiment of the present invention. [Figure 13] This block diagram shows the hardware configuration of the prediction system. [Figure 14] This is a conceptual diagram showing an example of a geothermal power generation system equipped with a prediction system according to an embodiment of the present invention. [Figure 15] This figure shows the calculated amount of silica scale generated in Examples 1-1 to 1-3 and Comparative Examples 1-1 to 1-3. [Figure 16] This figure shows the calculation results of the amount of silica scale generated per unit time in Examples 2-1 to 2-3 and Comparative Examples 2-1 to 2-3. [Modes for carrying out the invention]

[0012] The embodiments for carrying out the present invention will be described in detail below. For ease of understanding, the same reference numerals are used for identical components in each drawing, and redundant explanations are omitted. Furthermore, in this specification, the "~" indicating a numerical range means that the values ​​before and after it are included as the lower and upper limits, respectively, unless otherwise specified. If only the upper limit of a numerical range represented by "~" has a unit specified, it means that the lower limit also has the same unit.

[0013] <First Embodiment> [Silica scale generation prediction system] A silica scale generation amount prediction system (hereinafter simply referred to as the "prediction system") according to the first embodiment of the present invention (hereinafter simply referred to as the "embodiment") will be described. Figure 1 is a block diagram showing the schematic configuration of the prediction system according to this embodiment. As shown in Figure 1, the prediction system 1A has an acquisition unit 10, a model recording unit 20A, a silica concentration prediction formula creation unit (hereinafter also simply referred to as the "prediction formula creation unit") 30, a silica scale generation amount prediction unit 40, and an output unit 50. The prediction system 1A predicts the amount of silica scale generated from a silica-containing fluid when a silica-containing fluid flows through a target object.

[0014] In this embodiment, the object refers to a component installed in a plant system, such as piping and equipment, that has a flow path through which a silica-containing fluid can flow.

[0015] Examples of plant systems include geothermal power generation systems, boiler systems, systems with cooling water piping, and water treatment systems, but are not limited to these, as long as they have components with flow channels through which a silica-containing fluid can flow.

[0016] Fluids containing silica include Si(OH)4 and Si(OH)3O - SiO2(OH)2 2- Si2O2(OH)5 - , and / or Si2O3(OH)4 2- Silica refers to a fluid containing chemical species including Si and OH, but is not limited to these. A silica-containing fluid may be, for example, water that may contain silica, and may include, but is not limited to, groundwater, tap water, geothermal water, or wastewater derived therefrom. For example, if the plant system is a geothermal power generation system, the silica-containing fluid may be geothermal water. Furthermore, the term "fluid" is not limited to a liquid, and may also include a mixture of water and gases such as steam.

[0017] The acquisition unit 10 predicts the adhesion of silica scale caused by silica contained in the fluid, and the temperature T at the predicted location of the object.s The data may be obtained under the following conditions: the initial concentration of silica in the fluid (in ppm) and at least one of the fluid flow rate FR.

[0018] Silica scale refers to silica that cannot dissolve in a fluid and precipitates. The precipitated silica is usually a tetramer or a polymer with a higher degree of polymerization, but the degree of polymerization of the polymer is not particularly limited.

[0019] The predicted areas are parts of the plant system to which prediction system 1A is applied that come into contact with a silica-containing fluid and where silica scale is likely to adhere. For example, in a geothermal power generation system, these may include, but are not limited to, turbine components such as turbine blades and rotors, piping, and heat exchangers.

[0020] temperature T s (Unit: K) can be any value as appropriate. For example, the temperature of the fluid or equipment at the predicted site can be measured using a temperature measuring device such as a temperature sensor installed at a specific location, and the fluid temperature can be calculated from the measured temperature of the equipment as needed. s This can be done. In addition, the temperature of the fluid or equipment at the predicted location can be calculated by simulations that take into account the operating conditions of the plant system, and the value obtained by calculating the fluid temperature from the measured temperature of the equipment as needed can be used as the temperature T s That is also acceptable.

[0021] The initial concentration of silica (Ci) in a fluid is the initial concentration of silica in a fluid that may contain silica. The initial concentration (Ci) can be measured using a concentration sensor installed at a specific location.

[0022] The fluid flow rate FR can be any value as appropriate. For example, the fluid flow rate at the predicted location can be measured using a flow meter installed at a specific location and used as the fluid flow rate FR. Alternatively, the fluid flow rate at the predicted location can be calculated using a simulation that takes into account the operating conditions of the plant system and used as the fluid flow rate FR.

[0023] The model recording unit 20A records the equilibrium reaction model M1. The equilibrium reaction model M1 can be used in the prediction formula creation unit 30 to create the prediction formula PF for silica concentration C.

[0024] Equilibrium reaction model M1 is a reaction model generated using a silica polymerization reaction that includes reversible and irreversible reactions of dissolved silica and a precipitation equilibrium reaction, and it is preferable that the reaction model includes an ionization equilibrium reaction of dissolved silica. It is more preferable that equilibrium reaction model M1 is a three-step precipitation equilibrium reaction model represented by the following formula (I).

[0025]

number

[0026] Silica polymerization reactions generally involve a reversible reaction that produces SiOSi(OH)6 from Si(OH)4, and a reaction that produces (SiO)3OSi(OH) from SiOSi(OH)6. 10 The calculations are based on a two-step model involving an irreversible reaction that produces (SiO)3Si(OH)9O. In this embodiment, the silica polymerization reaction employs a three-step precipitation equilibrium reaction model of formula (I) above, which further considers the precipitation equilibrium reaction, rather than this two-step model. By using the three-step precipitation equilibrium reaction model, the unconsidered (SiO)3Si(OH)9O - The formation of silica scale can be predicted, including the dynamics of the chemical species represented by [the formula].

[0027] The prediction formula creation unit 30 uses the equilibrium reaction model M1 stored in the model recording unit 20A to create a prediction formula PF for silica concentration C (unit: ppm).

[0028] The prediction formula PF for silica concentration C is an equation that represents the prediction curve for silica concentration C.

[0029] The silica concentration C given by the silica concentration prediction formula PF refers to the mass percentage concentration (unit: ppm) of a solution in which silica (including monomers and various silica polymers of dimers or more) that can be produced by the silica condensation polymerization reaction described above is dissolved at a predetermined temperature T. The silica concentration C may also be the mass percentage concentration (unit: ppm) of a solution in which silica is dissolved at a predetermined temperature T and pH.

[0030] Silica concentration C refers to the concentration of silica (dissolved silica) in a fluid, and is either the equilibrium concentration (dissolved concentration) of unsaturated silica in the fluid or the saturation concentration of silica.

[0031] Here, the prediction formula PF for silica concentration C shows the relationship between time and the silica concentration in the fluid, and the type of silica concentration input differs depending on whether the silica in the fluid is saturated or not. If the silica is not saturated, silica concentration C is the equilibrium concentration of silica in the fluid, and if the silica is saturated, silica concentration C is the saturation concentration of silica in the fluid.

[0032] The equilibrium concentration of silica refers to the state in which the silica concentration stabilizes after the silica reaction has progressed from its initial concentration.

[0033] The saturation concentration of silica refers to the mass percentage concentration (unit: ppm) of a solution in which silica (including monomers and various silica polymers of dimers or more) produced by the silica condensation polymerization reaction described above dissolves and reaches a saturated solution at a predetermined temperature T. In other words, the saturation concentration of silica refers to the maximum concentration in which silica (including monomers and various silica polymers of dimers or more) can dissolve at a predetermined temperature T. The saturation concentration of silica may be the mass percentage concentration of a solution in which a saturated solution is reached at a predetermined temperature T and pH, or it may be the maximum concentration in which silica can dissolve at a predetermined temperature T and pH.

[0034] The silica scale generation amount prediction unit 40 is determined by temperature T s Based on the prediction formula PF for silica concentration C which depends on the system, the amount of silica scale generated at any predicted site in the plant system is predicted. The silica scale generation prediction unit 40 uses at least one of the initial silica concentration Ci and the fluid flow rate FR to calculate the amount of silica scale generated at the predicted site and predicts the amount of silica scale generated at the predicted site.

[0035] Furthermore, the initial silica concentration (Ci) in the fluid and the fluid flow rate (FR) can be the values ​​obtained by the acquisition unit 10, as described above.

[0036] The prediction formula PF for silica concentration C is obtained based on the equilibrium reaction model M1 recorded in the model recording unit 20A. If the equilibrium reaction model M1 is a three-step precipitation equilibrium reaction model represented by the above formula (I), then the prediction formula PF for silica concentration C is calculated using the above formula (I), where k1, k2, k a and k B It can be obtained based on this.

[0037] Figure 2 shows an explanatory diagram of the calculation flow for silica concentration C. As shown in Figure 2, when obtaining the prediction formula PF for silica concentration C using the above formula (I), first, the free energy change ΔG in each step of the reaction in formula (I) is obtained by performing first-principles calculations or the like from the free energies of the four chemical species represented in formula (I) and the fluid in which the silica is dissolved (e.g., geothermal water). From the obtained free energy change ΔG value, the reaction equilibrium constants of the silica polymerization reaction are calculated from the following formula (i) to obtain k1 and k2. k1, k2=exp(-ΔGn / RT) ···(i) (In the equation, n represents the number of reaction steps and is an integer greater than or equal to 1, ΔGn is the change in free energy of the nth reaction step, R is a constant, and T is the temperature (unit: K).)

[0038] Temperature T may also refer to the polymerization reaction temperature Tr (unit: K) in the three-step precipitation equilibrium reaction model represented by the above formula (I).

[0039] k a This is the equilibrium coefficient of acid dissolution of silica, and the acid dissociation constant of silica, pk a It can be calculated from this.

[0040] Silica acid dissociation constant pk a This can be calculated using a general method for calculating the acid dissociation constant, and the value of the following equation (a), calculated from the free energy change ΔG using quantum chemical calculations and linear fitting correction methods, can be used. pk a =pΔG+q ···(a) (In the formula, p and q are constants, and ΔG is (SiO)3Si(OH)9O - (SiO)3OSi(OH) 10 This is the value of the change in free energy in the equilibrium reaction.

[0041] In equation (a), p may be between 0.19 and 0.24, and q may be between -56 and -51. Preferably, p may be between 0.21 and 0.22, and q may be between -54 and -52.

[0042] kB This is the ionization equilibrium constant, and the ionization equilibrium constant k B This can be obtained from the following equation (ii). k B =k² / k a ...(ii)

[0043] Precipitation equilibrium constant k sp This can be obtained from the following equation (iii). k sp =k² × k a ...(iii)

[0044] In the formula for calculating the equilibrium constant of the silica polymerization reaction, temperature T refers to the polymerization reaction temperature (unit: K) in the three-step precipitation equilibrium reaction model represented by the above formula (I). Temperature T and the calculated k1, k2, k a and k B Using the reversible reaction calculation formula, the prediction formula PF, which represents the prediction curve of silica concentration C, is calculated as shown in equation (1) below. Ce=a1[exp(b1Tr)] ···(1) (In the formula, a1 and b1 are constants, and Tr represents the polymerization reaction temperature (unit: K).)

[0045] a1 and b1 are calculated using the above formula (I), k1, k2, k a and k B These are values ​​calculated based on the following. a1 and b1 can be parameters estimated to ensure a region that falls within a predetermined range (e.g., within an error range of ±20%) from the predicted curve of silica concentration C.

[0046] a1 may be between 18 and 32, and b1 may be between 0.005 and 0.010. Preferably, a1 may be between 20 and 30, and b1 may be between 0.006 and 0.009.

[0047] The temperature range of T can be approximately 250 to 500 K.

[0048] Figure 3 shows an example of a prediction curve for silica concentration C, which shows the relationship between temperature T and silica concentration C, calculated using the prediction formula PF for silica concentration C. As shown in Figure 3, the silica concentration C corresponding to temperature T can be calculated using the prediction curve PC for silica concentration C based on the prediction formula PF for silica concentration C. As described above, temperature T refers to the polymerization reaction temperature Tr in the three-step precipitation equilibrium reaction model represented by the above formula (I). In prediction system 1A, when predicting the amount of silica scale generated, the temperature T at a predetermined prediction site where the amount of scale generated in the actual plant system should be predicted is used. s The polymerization reaction temperature Tr is used, and the effective activity coefficient γ is calculated using the pH at the predicted site. Prediction system 1A uses the calculated temperature T at the predicted site. s The effective activity coefficient γ can be used to predict the silica concentration C using the prediction formula PF.

[0049] Note that the temperature T at the predicted site s This could be, for example, the temperature of a silica-containing fluid at the predicted location of the plant system.

[0050] The pH at the predicted site may be the pH of a silica-containing fluid at the predicted site of the plant system. The pH value at the predicted site can be measured using a standard pH meter or calculated using methods such as simulation.

[0051] For predicting silica concentration C, the following formula (1-1) is preferable when the silica-containing fluid is under acidic and neutral conditions. Ce=(Ci / 1000)γ{a[exp(bTr)]} ···(1-1) (In the formula, Ci is the initial concentration of silica (unit: ppm), γ is the effective activity coefficient, a and b are constants, and Tr represents the polymerization reaction temperature (unit: K).)

[0052] Note that acidic and neutral conditions refer to situations where the pH of the fluid in which silica is dissolved is between 0 and 7.

[0053] In equation (1-1), a and b are k1, k2, and k calculated using equation (I) above. a and k B This is a value calculated based on the following. For example, a may be between 16 and 36, and b may be between 0.003 and 0.015. Preferably, a may be between 18 and 35, and b may be between 0.005 and 0.012. Most preferably, a may be between 20 and 33, and b may be between 0.006 and 0.010.

[0054] The temperature range of T can be approximately 250 to 500 K.

[0055] The effective activity coefficient γ in equation (1-1) is a value calculated based on pH. The effective activity coefficient γ can be calculated based on the following equation (b), and is a coefficient that determines the effect of pH in the acidic and neutral ranges (pH 0 to 7) on silica concentration. -logγ=A γ Z 2 {E / (1+B γ cE)} ···(b) (In the formula, A γ and B γ (where is a constant, Z is the number of charges, c is the effective diameter coefficient, and E is the effective ionic strength.)

[0056] A γ and B γ This value is derived from the Debye-Huckel theory, using the temperature T of the silica polymerization reaction system and the dielectric constant ε of water, which is the solvent for the silica polymerization reaction.

[0057] More specifically, A γ and B γ This can be expressed by the following equations (c-1) and (c-2). A γ = 1.825 × 10 6 (εTr) (-3 / 2) ...(c-1) B γ = 50.3 × (εTr) (-1 / 2) ...(c-2) (In equations (c-1) and (c-2), Tr represents the polymerization reaction temperature (unit: K), and ε represents the dielectric constant of water at polymerization reaction temperature Tr.)

[0058] The charge number Z is 1 or 2, and in the case of monovalent ions of silica monomers and dimers (SiO(OH)) 3- , Si2O(OH) 7- ) is 1, and in the case of divalent ions of silica monomer and dimer (SiO2(OH)2 2- S2O2(OH)6 2- In the case of ), the answer is 2.

[0059] The effective diameter coefficient c may be set to, for example, 4 in the silica polymerization reaction.

[0060] The effective ionic strength E can be expressed by the following equation (d). E = {I + (hydrogen ion concentration)} / [1 + B] γ c[I+(hydrogen ion concentration)] ···(d) (In the formula, I is the solute ion strength, and B γ (where c is a constant and c is the effective diameter coefficient.)

[0061] The solute ion intensity I is determined by the following equation (e). I = 1 / 2 × (Ct + (hydrogen ion concentration)) × Z ... (e) (In the formula, Ct is the total concentration of silica (unit: mol / L), and Z represents the charge number of the solute, which is either 1 or 2.)

[0062] The hydrogen ion concentration can be calculated from a given pH of 0 to 7. For example, if the pH is 5.5, then 10 (-5.5) That is the case.

[0063] Figure 4 shows an example of a predicted silica concentration C curve, which illustrates the relationship between temperature T and silica concentration C, calculated using the prediction formula PF for silica concentration C when the fluid is acidic or neutral. As shown in Figure 4, the predicted silica concentration C curve PC based on the prediction formula PF differs for fluid pH values ​​of 5.5 and 7.0, meaning that different predicted curves PC are obtained for different fluid pH values. Although not shown in the figure, the prediction formula PF for silica concentration C can be derived using the method described above, and the predicted curve PC can be drawn for each pH range of 0 to 7. Therefore, by using the prediction formula PF for silica concentration C, the amount of silica scale generated can be predicted according to pH conditions where the fluid is acidic or neutral, and the amount of silica scale generated in acidic or neutral fluids can be predicted with greater accuracy.

[0064] When the silica-containing fluid is under basic conditions, it is preferable to use the following formula (1-2) for predicting silica concentration C, PF. Ce=(Ci / 1000)J{a[exp(bTr)]} ···(1-2) (In the formula, Ci is the initial concentration of silica (unit: ppm), J is the effective reaction coefficient, a and b are constants, and Tr represents the polymerization reaction temperature (unit: K).)

[0065] Basic conditions refer to a situation where the pH of the fluid in which silica is dissolved is greater than 7 and 14 or less.

[0066] In the above formula (1-2), a and b are k1, k2, and k calculated using the above formula (I). a and k B This is a value calculated based on the following. For example, a3 may be 6 to 34 and b3 may be 0.005 to 0.015. Preferably, a3 may be 8 to 32 and b3 may be 0.005 to 0.015. More preferably, a3 may be 10 to 30 and b3 may be 0.006 to 0.009.

[0067] The temperature range of T can be approximately 250 to 500 K.

[0068] The effective reaction coefficient J can be calculated based on the following equation (f), and is a coefficient that determines the effect of pH in the basic region on silica concentration. Based on the understanding that in the basic region, ions do not directly participate in the polymerization reaction of silica and are determined by the fraction of silica in the non-ionized molecular state, the effective reaction coefficient J can be calculated based on the following equation (f). J = (X - Xi1 - Xi2) / X ... (f) (In the formula, X is the total amount of silica (molar amount 100%), and Xi1 and Xi2 are the fractions of silica monomer ions and silica dimer ions (molar fraction %).

[0069] In equation (f), Xi1 and Xi2 are the acid dissociation constants pk of silica. a It can be calculated from this.

[0070] Silica acid dissociation constant pk a This is the equilibrium constant when considering the dissociation reaction in which protons (hydrogen ions) are released from silica monomers, silica dimers, and silica tetramers.

[0071] Silica monomer ions are Si(OH)3O - This refers to a silica dimer ion, which is Si2(OH)7O - This refers to the following.

[0072] The effective reaction coefficient J is a number between 0 and 1, and it varies between pH values ​​greater than 7 and 14. An example graph of the change in the effective reaction coefficient J with respect to pH is shown in Figure 5. As shown in Figure 5, the effective reaction coefficient J can be obtained when the fluid is at a specific pH in the basic range.

[0073] Furthermore, Figure 6 shows an example of a predicted silica concentration C curve that illustrates the relationship between temperature T and silica concentration C, calculated using the prediction formula PF for silica concentration C when the fluid pH is basic. As shown in Figure 6, the predicted silica concentration C curve PC based on the prediction formula PF differs for fluid pH values ​​of 5.5, 7.0, and 9.0, meaning that different predicted curves PC are obtained for different pH values. Although not shown in the figure, the prediction formula PF can be derived using the method described above, and the predicted curve PC can be drawn for each pH range of the fluid pH from 7 to 14. Therefore, by using the prediction formula PF for silica concentration C, the amount of silica scale generated can be predicted according to the pH conditions of a basic fluid, just as it can be predicted when the fluid is acidic or neutral, and the amount of silica scale generated in a basic fluid can be predicted with greater accuracy.

[0074] The silica scale generation prediction unit 40 preferably calculates the amount of silica scale generated per unit time in the prediction site M using the following formula (2-1) when the fluid is acidic or neutral. M=Ci-[γ{a[exp(bT s / Tr)]}QS+Ci] / 1000 ···(2-1) (In the formula, M is the amount of silica scale produced, Ci is the initial silica concentration (in ppm), γ is the effective activity coefficient, a and b are constants, Tr is the polymerization reaction temperature (in K), Q is the fluid velocity per unit time (hereinafter also referred to as relative flow rate) (in m / s), and S is the cross-sectional area of ​​the fluid channel (in cm) 2 ) is. )

[0075] As described above, the initial silica concentration Ci in the fluid can be the value obtained by the acquisition unit 10.

[0076] The effective activity coefficient γ is calculated based on pH. The effective activity coefficient γ is calculated based on the abundance of silica monomer and dimer ions.

[0077] The constants a and b are k1, k2, k a and k B It is calculated based on this.

[0078] The flow path through which the fluid flows is, for example, the cross-sectional area (unit: cm 2 ) of a pipe used for transporting the fluid provided in a system plant.

[0079] The silica scale generation amount prediction unit 40 may calculate the flow rate FR of the fluid based on the relative flow rate Q (unit: m / s) and the cross-sectional area S (unit: cm 2 ) of the flow path through which the fluid flows.

[0080] When the fluid is under basic conditions, the silica scale generation amount prediction unit 40 preferably calculates the generation amount M of silica scale per unit time at the prediction site using the following formula (2-2). M = Ci - [J{a[exp(bTr)]}QS + Ci] / 1000 ···(2-2) (In the formula, M is the generation amount of silica scale, Ci is the initial concentration of silica (unit: ppm), J is the effective reaction coefficient, a and b are constants, Tr is the polymerization reaction temperature (unit: K), Q is the relative flow velocity of the fluid (unit: m / s), and S is the cross-sectional area (unit: cm 2 ) of the flow path through which the fluid flows.)

[0081] a and b are calculated based on k1, k2, k a and k B .

[0082] The effective reaction coefficient J is calculated based on the pH. The effective reaction coefficient J is calculated based on the abundance ratios of monomeric silica ions and dimeric ions.

[0083] The flow path through which the fluid flows is, similar to the above formula (2-1), for example, the cross-sectional area (unit: cm 2 ) of a pipe used for transporting the fluid provided in a system plant.

[0084] The silica scale generation amount prediction unit 40 may include a prediction site silica concentration calculation unit 41, a total silica concentration calculation unit 42, and a silica scale generation amount calculation unit 43.

[0085] The predicted-site silica concentration calculation unit 41 calculates the silica concentration C at the predicted site where silica scale adhesion is to be predicted, based on the temperature T at the predicted site obtained by the acquisition unit 10 s and the prediction formula PF of the silica concentration C created by the prediction formula creation unit 30

[0086] When the fluid is under acidic and neutral conditions, the prediction formula PF of the silica concentration C can be calculated using the above formula (1-1), and when the fluid is under basic conditions, it can be calculated using the above formula (1-2).

[0087] The total silica concentration calculation unit 42 obtains the total silica concentration C in the fluid containing silica t

[0088] Note that the total silica concentration C t is equal to the initial concentration C of silica i Therefore, the total silica concentration calculation unit 42 can calculate the initial concentration C of silica as the total silica concentration C i t

[0089] The total silica concentration C t is the total concentration of silica present in the fluid supplied to the plant system to which the prediction system 1A is applied. In terms of calculation, the mass% concentration (ppm) of silica monomer (Si(OH)4) in the fluid, calculated based on the amount of all Si atoms present in the fluid, is taken as the total silica concentration C t Of this, the amount exceeding the silica concentration C is considered to precipitate and adhere as silica scale

[0090] For example, when the plant system to which the prediction system 1A is applied is a geothermal power generation system, the total silica concentration C t can be calculated, for example, as follows. First, the geothermal water pumped out from the production well is analyzed to obtain the mass or molar amount of Si atoms in the geothermal water. Then, assuming that all Si atoms form silica monomer (Si(OH)4), the mass% concentration of silica monomer in the geothermal water is obtained by calculation. In the prediction system 1A, the total silica concentration C t ​​​The portion of the total silica concentration that exceeds the silica concentration, i.e., the total silica concentration C t It is assumed that the amount of silica removed from the silica concentration will precipitate as silica scale.

[0091] The silica scale generation amount calculation unit 43 calculates the total silica concentration C obtained by the total silica concentration calculation unit 42. t Based on the silica concentration C at the predicted site calculated by the predicted site silica concentration calculation unit 41, the amount of silica scale generated at the predicted site can be calculated. Specifically, the total silica concentration C obtained by the total silica concentration calculation unit 42 t Then, by calculating the difference in silica concentration C at the predicted site created by the prediction formula creation unit 30, and calculating the change in silica concentration C at the predicted site, the amount of silica scale generated at the predicted site can be obtained.

[0092] In other words, the silica concentration C at the predicted site is given by the above formula (2-1) "[γ{a[exp(bT s This corresponds to " / Tr)]}QS+Ci] / 1000", and when the fluid is under basic conditions, it corresponds to "[J{a[exp(bTr)]}QS+Ci] / 1000" in the above formula (2-2).

[0093] The change in silica concentration C can be calculated using the following formula (A). That is, the change in silica concentration C is equal to the initial silica concentration C in the fluid. i It is preferable to use an amount obtained by subtracting the equilibrium concentration of unsaturated silica in the fluid or the saturation concentration of silica from the above. Change in silica concentration = Initial silica concentration C in the fluid i -(Equilibrium concentration of unsaturated silica in a fluid or saturation concentration of silica) ···(A)

[0094] Furthermore, the silica scale generation amount calculation unit 43 calculates the total silica concentration C in the silica-containing fluid obtained by the total silica concentration calculation unit 42. tUsing this method, the amount of silica scale M generated per unit time at the predicted site can be calculated using equation (2-1) above when the fluid is acidic or neutral, or using equation (2-2) above when the fluid is basic.

[0095] The output unit 50 outputs the predicted result of the amount of silica scale generated in the predicted area, which was predicted by the silica scale generation amount prediction unit 40, by displaying or transmitting it.

[0096] The prediction system 1A comprises an acquisition unit 10 and a silica scale generation amount prediction unit 40. The silica scale generation amount prediction unit 40 predicts the amount of silica scale generated at a prediction site using a prediction formula PF for silica concentration C obtained based on a reaction model generated using a silica polymerization reaction that includes reversible and irreversible reactions and precipitation equilibrium reactions of silica, as well as the initial silica concentration Ci and the fluid flow rate FR. Since the silica scale generation amount prediction unit 40 calculates the amount of silica scale generated at the prediction site including the initial silica concentration Ci and the fluid flow rate FR, it can improve the prediction accuracy of the amount of silica scale generated at the prediction site. Therefore, the prediction system 1A can predict the amount of silica scale generated at the prediction site with greater accuracy.

[0097] Generally, in power generation facilities such as geothermal power generation systems, the timing of maintenance aimed at removing silica scale is determined by predicting the amount of scale generated, for example, based on prediction formulas derived from experiments or actual measurements at the facility, or based on the amount of power generated measured at the power generation facility. Establishing a prediction formula for predicting the amount of silica scale generated requires a large amount of empirical data, such as experimental and actual measurement data. Furthermore, acquiring this data requires the use of specialized equipment. In addition, it is necessary to shut down the plant system, such as a geothermal power generation system, and disassemble parts of the equipment multiple times in order to acquire the data. However, with these conventional methods, it is difficult to accurately predict the amount of silica scale generated. As a result, maintenance is often carried out only after the plant system, such as a geothermal power generation system, has unexpectedly shut down or experienced a decrease in power generation capacity, which can lead to a decrease in revenue due to reduced electricity sales. Moreover, when maintenance is carried out in advance to avoid a decrease in power generation capacity and unexpected shutdowns, it is difficult to accurately grasp the amount of silica scale generated, making it impossible to optimize the timing of maintenance, and potentially increasing maintenance costs due to an increase in the number of maintenance sessions. Furthermore, prediction formulas established empirically to forecast silica scale formation are highly susceptible to conditional variations. Establishing accurate prediction formulas requires a vast amount of data, necessitating numerous tests and significant costs. Additionally, precisely controlling experimental conditions during data acquisition is difficult, making accurate predictions challenging. Moreover, the need to repeat measurements and revise the prediction formulas each time conditions change results in a lack of versatility.

[0098] The prediction system 1A does not rely on empirical values, such as by collecting data through experiments and making decisions based on experimental or measured values. Instead, the silica scale generation prediction unit 40 predicts the silica concentration C at a desired prediction site through simulation and predicts the amount of silica scale generated at that site. Therefore, even when the initial silica concentration Ci and fluid flow rate FR fluctuate and conditions are complex, the prediction system 1A can easily improve the accuracy of predicting the amount of silica scale generated at the prediction site while keeping time and cost down.

[0099] Furthermore, in prediction system 1A, the silica scale generation prediction unit 40 calculates the amount of silica scale generated by including the initial silica concentration Ci as a condition. Therefore, even when the initial silica concentration Ci is a value other than the value that has generally been used as a specified value (e.g., 1000 ppm), the prediction accuracy of the amount of silica scale generated at the prediction site can be improved. Thus, prediction system 1A can also predict the amount of silica scale generated in systems where the initial silica concentration Ci is a concentration other than the predetermined concentration (e.g., 1000 ppm).

[0100] Furthermore, in prediction system 1A, the silica scale generation prediction unit 40 calculates the amount of silica scale generated by including the fluid flow rate FR as a condition. Even with the same initial concentration of Ci, the amount of silica scale generated fluctuates due to changes in the fluid flow rate FR, such as the relative fluid velocity. By including the fluid flow rate FR as a condition in the calculation of the amount of silica scale generated by the silica scale generation prediction unit 40, the accuracy of predicting the amount of silica scale generated at the prediction site can be improved even when the fluid flow rate FR fluctuates. Therefore, prediction system 1A can predict the amount of silica scale generated, including the fluctuations in the fluid flow rate FR, even in systems where the fluid flow rate FR fluctuates.

[0101] In prediction system 1A, it is preferable to use equation (1-1) above for the prediction formula PF of silica concentration C when the fluid is acidic or neutral, and equation (1-2) above when the fluid is basic. This allows the silica scale generation prediction unit 40 to appropriately calculate the amount of silica scale M generated at the prediction site according to the pH state of the fluid. Therefore, prediction system 1A can predict the amount of silica scale generated at the prediction site with even greater accuracy.

[0102] In the prediction system 1A, the silica scale generation prediction unit 40 preferably calculates the amount of silica scale generated per unit time at the prediction site using equation (2-1) above when the fluid is acidic or neutral, and using equation (2-2) above when the fluid is basic. This allows the silica scale generation prediction unit 40 to appropriately calculate the amount of silica scale generated per unit time at the prediction site according to the pH state of the fluid. Therefore, the prediction system 1A can predict the amount of silica scale generated at the prediction site with even greater accuracy.

[0103] In prediction system 1A, it is preferable that the equilibrium reaction model M1 is a model that includes the ionization equilibrium reaction of silica contained in the fluid. This allows the equilibrium reaction model M1 to more appropriately represent the silica polymerization reaction, and thus more appropriately represent the prediction formula PF for silica concentration C. As a result, the silica scale generation prediction unit 40 can more appropriately calculate the amount of silica scale generated per unit time M at the prediction site. Therefore, prediction system 1A can predict the amount of silica scale generated at the prediction site with even greater accuracy.

[0104] Prediction system 1A uses the three-step precipitation equilibrium reaction model represented by equation (I) above as the equilibrium reaction model M1, and the prediction formula PF for silica concentration C is calculated using equation (I) above, with k1, k2, k a and k BIt is preferable to obtain it based on this. This allows the equilibrium reaction model M1 to more appropriately represent the silica polymerization reaction, and thus to more appropriately represent the prediction formula PF for silica concentration C. For this reason, the silica scale generation prediction unit 40 can calculate the amount of silica scale generated per unit time M at the prediction site with even greater accuracy. Thus, the prediction system 1A can further improve the prediction accuracy of the amount of silica scale generated at the prediction site.

[0105] In the prediction system 1A, it is preferable that the silica scale generation amount prediction unit 40 has a prediction site silica concentration calculation unit 41, a total silica concentration calculation unit 42, and a silica scale generation amount calculation unit 43. t Based on the silica concentration C, the amount of silica scale generated can be calculated. Therefore, prediction system 1A can predict the amount of silica scale generated at the prediction site with even greater accuracy.

[0106] [Method for predicting silica scale generation] Next, the method for predicting the amount of silica scale generated according to this embodiment (hereinafter sometimes simply referred to as the "prediction method") will be described. The prediction method according to this embodiment can be performed using the prediction system 1A described above. Therefore, in each step, some of the contents already explained in the prediction system 1A described above will be omitted.

[0107] Figure 7 is a flowchart of the prediction method according to this embodiment. As shown in Figure 7, in the prediction method according to this embodiment, the acquisition unit 10 predicts the adhesion of silica scale caused by silica contained in the fluid, and the temperature T at the predicted part of the object. s The system may obtain, under the condition that at least one of the initial silica concentration Ci in the fluid and the fluid flow rate FR be obtained (acquisition process: step S11).

[0108] Next, the prediction formula creation unit 30 uses the equilibrium reaction model M1 stored in the model recording unit 20A to create a prediction formula PF for the silica concentration C (unit: ppm) (silica concentration C prediction formula creation process: step S12).

[0109] Next, the silica scale generation prediction unit 40 uses the temperature T, which was created in the silica concentration C prediction formula creation step (step S12). s Based on the prediction formula PF for silica concentration C which depends on the system, the amount of silica scale generated at any predicted site in the plant system is predicted (silica scale generation prediction step: step S13).

[0110] In the silica scale formation prediction step S13, the prediction site silica concentration calculation unit 41 calculates the temperature T at the prediction site where silica scale adhesion should be predicted, which was obtained in the acquisition step S11. s Then, based on the silica concentration prediction formula PF created in step S12, the silica concentration C at the predicted site is calculated (predicted site silica concentration calculation step: step S131).

[0111] Next, the total silica concentration calculation unit 42 calculates the total silica concentration C in the silica-containing fluid. t Calculate (total silica concentration calculation step: step S132).

[0112] Next, the silica scale generation amount calculation unit 43 calculates the total silica concentration C calculated in the total silica concentration calculation step S132. t Based on the silica concentration C at the predicted site calculated in the predicted site silica concentration calculation step S131, the amount of silica scale generated at the predicted site can be calculated (silica scale generation amount calculation step: step S133).

[0113] Furthermore, the silica scale generation amount calculation unit 43 calculates the total silica concentration C in the silica-containing fluid obtained in the total silica concentration calculation step S132. tUsing this method, the amount of silica scale M generated per unit time at the predicted site can be calculated using equation (2-1) above when the fluid is acidic or neutral, or using equation (2-2) above when the fluid is basic.

[0114] Next, the output unit 50 outputs the predicted result of the amount of silica scale generated at the predicted site, which was predicted in the prediction step (step S13), by displaying or transmitting it (output step: step S14).

[0115] The prediction method according to this embodiment includes an acquisition step S11 and a silica scale generation amount prediction step S13. In the silica scale generation amount prediction step S13, the amount of silica scale generated is calculated using the prediction formula PF for silica concentration C, the initial silica concentration Ci, and the fluid flow rate FR, and the amount of silica scale generated at the prediction site is predicted. Since the silica scale generation amount prediction step S13 calculates the amount of silica scale generated at the prediction site including the initial silica concentration Ci and the fluid flow rate FR, the prediction accuracy of the amount of silica scale generated at the prediction site can be improved. Therefore, the prediction method according to this embodiment can predict the amount of silica scale generated with higher accuracy.

[0116] <Second Embodiment> [Silica scale generation prediction system] A prediction system according to a second embodiment of the present invention (hereinafter sometimes simply referred to as "this embodiment") will be described. Figure 8 is a block diagram showing the schematic configuration of the prediction system according to this embodiment. As shown in Figure 8, the prediction system 1B according to this embodiment further comprises a prediction curve creation unit 60 and a second silica scale generation amount prediction unit 70 in addition to the prediction system 1A according to the first embodiment shown in Figure 1. That is, the prediction system 1B has an acquisition unit 10, a model recording unit 20B, a prediction formula creation unit 30, a first silica scale generation amount prediction unit 40, a prediction curve creation unit for silica concentration C (hereinafter simply referred to as "prediction curve creation unit") 60, a second silica scale generation amount prediction unit 70, and an output unit 50.

[0117] In this embodiment, the silica scale generation amount prediction unit 40 of the prediction system 1A according to the first embodiment described above is referred to as the first silica scale generation amount prediction unit 40, and the amount of silica scale generated calculated by the first silica scale generation amount prediction unit 40 is referred to as the first silica scale generation amount. The prediction formula creation unit 30, the first silica scale generation amount prediction unit 40, and the output unit 50 are the same as those of the prediction system 1A according to the first embodiment described above, so details are omitted.

[0118] The acquisition unit 10 predicts the adhesion of silica scale caused by silica contained in the fluid, and the temperature T at the predicted location of the object. s , and the time t until the silica-containing fluid reaches the predicted site s The data is obtained using the condition (unit: minutes). The acquisition unit 10 may also acquire at least one of the following elements: the initial silica concentration Ci in the fluid and the fluid flow rate FR.

[0119] The time t for a silica-containing fluid to reach the predicted site where silica scale deposition should be predicted. s (Unit: minutes) can be calculated using the relative flow velocity of the silica-containing fluid in the plant system and the distance from the point where time t is 0 (time t=0) to the predicted point. Alternatively, time t s This can also be obtained through simulation based on the operating conditions of the plant system. For example, if the plant system is a geothermal power generation system, time t s This could also be the time required for the geothermal water pumped from the production well to reach a predetermined predicted location.

[0120] The model recording unit 20B records the equilibrium reaction model M1, similar to the model recording unit 20A. The equilibrium reaction model M1 can be used in the prediction formula creation unit 30 to create the prediction formula PF for silica concentration C, and can also be used in the prediction curve creation unit 60 to create the prediction curve PC for silica concentration C.

[0121] As mentioned above, silica concentration C refers to the concentration of dissolved silica in the fluid, specifically the equilibrium concentration of unsaturated dissolved silica in the fluid, or (dissolved concentration) the saturation concentration of dissolved silica. The prediction curve PC for silica concentration C shows the relationship between time and the silica concentration of dissolved silica in the fluid, and its shape may differ depending on whether the dissolved silica in the fluid is saturated or not. Therefore, if the dissolved silica is not saturated, silica concentration C is considered the equilibrium concentration of dissolved silica in the fluid, and if the dissolved silica is saturated, silica concentration C is considered the saturation concentration of dissolved silica in the fluid.

[0122] The prediction curve generation unit 60 uses the equilibrium reaction model M1 stored in the model recording unit 20B to calculate time t s Create a predictive curve PC for silica concentration C, which depends on [the specified factor].

[0123] The prediction curve PC for silica concentration C is a time-dependent curve that shows the relationship between time t and silica concentration C. The prediction curve PC for silica concentration C is obtained based on the equilibrium reaction model M1.

[0124] The method for obtaining the prediction curve PC for silica concentration C includes the following steps (i) to (iii).

[0125] First, the initial silica concentration C i Obtain (step (i)).

[0126] Next, in the three-step precipitation equilibrium reaction model of equation (I), k1, k2, k a and k B Calculate the effective activity coefficient γ and the initial silica concentration C i and k1, k2, k a and k B Then, the predicted value of the silica concentration C is calculated from the effective activity coefficient γ (step (ii)).

[0127] Next, the silica concentration C is plotted against time t, and a curve fitting is performed based on the plot results (step (iii)). This yields a predicted curve PC for the silica concentration C.

[0128] The method for obtaining the prediction curve PC of silica concentration C can be carried out in the same manner as in the first embodiment described above, except that in step (ii) above, when calculating the predicted value of silica concentration C, it is necessary to calculate the effective activity coefficient γ of the prediction formula PF for silica concentration C (see, for example, formula (1-1)) taking pH conditions into consideration. Furthermore, the method for calculating the frequency factor A, which will be described later, and the preferred values ​​of the constants m and n that determine the frequency factor A may also be the same as in the first embodiment described above.

[0129] An example of a predicted curve PC for silica concentration C obtained by steps (i) to (iii) is shown in Figure 9. The predicted curve PC for silica concentration C shown in Figure 9 is the predicted curve PC when the initial silica concentration Ci is approximately 1300 ppm, the temperature is 150°C, and the pH is 5.5. In Figure 9, the solid line represents the silica concentration C (unit: ppm), and the dashed line represents the amount of precipitated silica (also called silica precipitate amount) (unit: ppm). As shown in Figure 9, the predicted curve PC for silica concentration C is time-dependent and becomes a nearly stable value after a predetermined time has elapsed.

[0130] The amount of silica precipitated refers to the mass of silica tetramers produced from a unit volume (1 L) of fluid. When the fluid is geothermal water, the mass of silica tetramers produced from a unit volume of fluid can be approximated by the mass of silica tetramers produced from a unit mass (1 kg) of fluid.

[0131] The second silica scale generation amount prediction unit 70 uses the prediction curve creation unit 60 to predict time t s Based on a prediction curve PC of silica concentration C which depends on the second silica scale generation amount, the amount of silica scale generated at time t at any predicted site in the plant system is predicted. The second silica scale generation amount prediction unit 70 calculates the amount of silica scale generated at time t at the predicted site using at least one of the elements of the initial silica concentration Ci and the fluid flow rate FR.

[0132] Time t sThe silica concentration C, which depends on the total silica concentration, is the concentration of silica dissolved in the fluid at time t (in minutes), with the polymerization start time being set to zero. The silica concentration C referred to here is the same as the total silica concentration C mentioned above. t Similar to the explanation given earlier, this is the mass percentage concentration (unit: ppm) of silica monomer (Si(OH)4) in the fluid, calculated based on the amount of Si atoms dissolved in the fluid.

[0133] Initial silica concentration C i This refers to the concentration of silica dissolved in the fluid at the start of polymerization (time t=0). Initial silica concentration C i This is expressed as the mass percentage concentration (unit: ppm) of silica monomer (Si(OH)4) in the fluid, calculated based on the amount of Si atoms dissolved in the fluid.

[0134] In the three-step precipitation equilibrium reaction model represented by equation (I) above, time t is the time (in minutes) with the point in time when Si(OH)4 is dissolved in the fluid set to 0. In this embodiment, the point in time considered to be the start of the polymerization reaction in an actual plant system can be used as 0 for prediction calculations. For example, if the plant system is a geothermal power generation system, the point in time when geothermal water is pumped from the production well can be set to 0.

[0135] This section describes an example of how to obtain a predictive curve PC for silica concentration C.

[0136] In the method for obtaining the prediction curve PC for silica concentration C, the initial silica concentration C i Obtain (step (i)).

[0137] Initial silica concentration C i In calculations, the total silica concentration C t It can be assumed that this is equal to the total silica concentration C mentioned above. t Using the same method, the initial silica concentration C i You can obtain it.

[0138] Next, as shown in the flowchart in Figure 2, the k1, k2, and k in the three-step precipitation equilibrium reaction model of equation (I) above were calculated. a and k B Using this method, the initial silica concentration C obtained in step (i) is used. i And, k1, k2, and k obtained from the three-step precipitation equilibrium reaction model of equation (I) above. a and k B From this, the predicted value of silica concentration C is calculated (step (ii)).

[0139] It is preferable to obtain predicted values ​​of the silica concentration C at multiple different time points t, for example, at 10 or more points, preferably 50 or more points, and more preferably 100 or more points. This makes it possible to obtain predicted values ​​of the silica concentration C from the start of the reaction to a desired time point.

[0140] Next, the silica concentration C is plotted against time t, and a predicted curve PC of the silica concentration C is obtained by curve fitting based on the plot results (step (iii)).

[0141] Figure 10 shows an example of a predicted curve PC for silica concentration C obtained by process (iii). Note that the predicted curve PC for silica concentration C in Figure 10 is obtained when the initial silica concentration Ci is approximately 1100 ppm, the fluid temperature is 100°C, and the fluid pH is 7. In Figure 10, the solid line represents the silica concentration C (unit: ppm), and the dashed line represents the silica precipitation amount (unit: ppm). As mentioned above, the silica precipitation amount refers to the mass of silica tetramers produced from a unit volume (1 L) of fluid. When the fluid is geothermal water, the mass of silica tetramers produced from a unit volume of fluid can be approximated by the mass of silica tetramers produced from a unit mass (1 kg) of fluid. Therefore, the sum of the silica concentration C and the silica precipitation amount equals the initial silica concentration C. i This is the result.

[0142] Here, a frequency factor A is necessary to fit the temperature T (unit: K) with the predicted silica concentration C in the initial stage of the reaction. The initial stage of the reaction refers to the period approximately 5 to 10 minutes after the start of the reaction, although this varies depending on the reaction apparatus and conditions. The relationship between temperature T and frequency factor A is expressed by the following equation (f). A = m × exp(nTr) ... (f) (In the formula, m and n are constants, obtained by the calculations shown in the flowchart above. Tr represents the polymerization reaction temperature (unit: K).)

[0143] The polymerization reaction temperature Tr is in the range of approximately 250 to 500 K.

[0144] m may be between 2.0 and 3.1, and n may be between 0.083 and 0.085. Preferably, m may be between 2.3 and 2.8, and n may be between 0.0835 and 0.0845.

[0145] Figure 11 is a semi-logarithmic graph showing the prediction curve for frequency factor A, with the vertical axis on a logarithmic scale. By using frequency factor A, experimental values ​​at each temperature can be reproduced in the initial stages of the reaction, for example, at a time point of 5 to 10 minutes.

[0146] The second silica scale generation prediction unit 70 includes a predicted site silica concentration calculation unit 71, a total silica concentration calculation unit 72, and a silica scale generation amount calculation unit 73 at time t.

[0147] The predicted site silica concentration calculation unit 71 calculates the time t obtained by the acquisition unit 10 until the silica-containing fluid reaches the predicted site. s Then, the silica concentration C at the predicted site is calculated from the prediction curve PC of silica concentration C created by the prediction curve creation unit 60.

[0148] The total silica concentration calculation unit 72 calculates the total silica concentration C in a silica-containing fluid. t The total silica concentration calculation unit 72 can be performed in the same manner as the total silica concentration calculation unit 42.

[0149] Note that the total silica concentration is C t The initial silica concentration C i It is equal to the initial silica concentration C used to derive the silica concentration C. i Total silica, dilution C t It can be calculated as follows.

[0150] The silica scale generation amount calculation unit 73 calculates the total silica concentration C obtained by the total silica concentration calculation unit 72. t Then, based on the silica concentration C at the predicted site calculated by the predicted site silica concentration calculation unit 71, the amount of silica scale generated at the predicted site at time t is calculated as the amount of silica scale generated in the second silica scale. Specifically, the total silica concentration C at time t of the predicted site obtained by the total silica concentration calculation unit 72 is used. t Then, by calculating the difference in silica concentration C at the predicted site, calculated by the predicted site silica concentration calculation unit 71, and calculating the change in silica concentration C at time t in the predicted site, the amount of silica scale generated at time t in the predicted site can be obtained as the amount of silica scale generated in the second silica scale.

[0151] Furthermore, the silica scale generation amount calculation unit 73 can calculate the amount of silica scale generated per unit time up to time t at the predicted site from the amount of silica scale generated at time t at the predicted site. Specifically, the total silica concentration C at time t at the predicted site obtained by the total silica concentration calculation unit 72 t Then, by calculating the difference in silica concentration C at the predicted site, calculated by the predicted site silica concentration calculation unit 71, and calculating the change in silica concentration C at time t in the predicted site, the amount of silica scale generated per unit time at time t in the predicted site can be obtained as the amount of silica scale generated in the second silica scale.

[0152] The change in silica concentration C can be calculated using the following formula (B). That is, the change in silica concentration C is equal to the initial concentration C of dissolved silica in the fluid. i It is preferable to use an amount obtained by subtracting the equilibrium concentration of unsaturated dissolved silica in the fluid or the saturation concentration of dissolved silica from the above. Change in silica concentration = Initial concentration C of dissolved silica in the fluid i -(Equilibrium concentration of unsaturated dissolved silica in the fluid or saturation concentration of dissolved silica) ···(B)

[0153] The prediction system 1B comprises an acquisition unit 10, a first silica scale generation amount prediction unit 40, and a second silica scale generation amount prediction unit 70. The second silica scale generation amount prediction unit 70 is based on a reaction model generated using a silica polymerization reaction that includes reversible and irreversible reactions of dissolved silica and precipitation equilibrium reactions, and is obtained over time t s The amount of silica scale generated at time t in the predicted site is predicted using a prediction curve PC of silica concentration C which depends on the initial silica concentration Ci and the fluid flow rate FR. The first silica scale generation prediction unit 40 can accurately predict the amount of silica scale generated at the predicted site as the first silica scale generation amount by considering the initial silica concentration Ci and the fluid flow rate FR. The second silica scale generation prediction unit 70 calculates the amount of silica scale generated at time t in the predicted site including the initial silica concentration Ci and the fluid flow rate FR, thereby improving the prediction accuracy of the amount of silica scale generated at time t in the predicted site. Therefore, the second silica scale generation prediction unit 70 can accurately predict the amount of silica scale generated at time t in the predicted site as the second silica scale generation amount. Thus, the prediction system 1B can further improve the prediction accuracy of the amount of silica scale generated.

[0154] In the prediction system 1B, it is preferable that the second silica scale generation prediction unit 70 includes a prediction site silica concentration calculation unit 71, a total silica concentration calculation unit 72, and a silica scale generation amount calculation unit 73 at time t. t Based on the silica concentration C, the amount of silica scale generated at the predicted site at time t can be calculated. Therefore, prediction system 1B can predict the amount of silica scale generated at the predicted site at time t with even higher accuracy.

[0155] [Method for predicting silica scale generation] Next, the method for predicting the amount of silica scale generated according to this embodiment (hereinafter simply referred to as the "prediction method") will be described. The prediction method according to this embodiment can be performed using the prediction system 1B described above. Therefore, in each step, some of the contents already explained in the prediction system 1B described above will be omitted.

[0156] Figure 12 is a flowchart of the prediction method according to this embodiment. As shown in Figure 12, in the prediction method according to this embodiment, the acquisition unit 10 predicts the adhesion of silica scale caused by silica contained in the fluid, and the temperature T at the predicted part of the object. s , and the time t until the silica-containing fluid reaches the predicted site s The data is obtained using the condition (unit: minutes) (acquisition process: step S21).

[0157] Furthermore, the acquisition unit 10 may acquire at least one of the elements of the initial silica concentration Ci in the fluid and the fluid flow rate FR.

[0158] Next, the prediction formula creation unit 30 creates a prediction formula PF for silica concentration C using the equilibrium reaction model M1 stored in the model recording unit 20B, similar to the prediction formula creation step S12 for silica concentration C in the silica scale generation amount prediction method according to the first embodiment shown in Figure 7 above (prediction formula creation step for silica concentration C: step S22).

[0159] Next, the first silica scale generation amount prediction unit 40 predicts the amount of silica scale generated at any prediction site in the plant system as the first silica scale generation amount, based on the silica concentration prediction formula PF created in the silica concentration prediction formula creation step (step S22), similar to the silica scale generation amount prediction step S13 of the silica scale generation amount prediction method according to the first embodiment shown in Figure 7 above (first silica scale generation amount prediction step: step S23).

[0160] The first silica scale generation amount prediction step S23, specifically the predicted site silica concentration calculation step S231, the total silica concentration calculation step S232, and the silica scale generation amount calculation step S233, are the same as the predicted site silica concentration calculation step S131, the total silica concentration calculation step S132, and the silica scale generation amount calculation step S133 of the silica scale generation amount prediction step S13 of the silica scale generation amount prediction method according to the first embodiment shown in Figure 7 above, so details are omitted.

[0161] Furthermore, the first silica scale generation amount prediction unit 40 calculates the total silica concentration C obtained in the total silica concentration calculation step S132. t Alternatively, the amount of silica scale generated may be calculated as the amount of first silica scale generated based on the silica concentration C at the predicted site obtained in the predicted site silica concentration calculation step S131.

[0162] Next, the prediction curve creation unit 60 uses the equilibrium reaction model M1 stored in the model recording unit 20B to calculate time t s A prediction curve PC for silica concentration C, which depends on (prediction curve creation process: step S24), is created.

[0163] Next, the second silica scale generation amount prediction unit 70 generates a prediction curve created in the prediction curve creation step S24, time t s Based on the prediction curve PC of silica concentration C which depends on the second silica scale, the amount of silica scale generated at any predicted site in the plant system at time t is predicted as the amount of second silica scale generated (second silica scale generation prediction step: step S25).

[0164] In the second silica scale generation prediction step S25, the prediction site silica concentration calculation unit 71 calculates the time t obtained in the acquisition step S21 until the silica-containing fluid reaches the prediction site. s Then, the silica concentration C at the predicted site is calculated from the prediction curve PC created in the prediction curve creation process S24 (silica concentration calculation process: step S251).

[0165] Next, the total silica concentration calculation unit 72 calculates the total silica concentration C in the silica-containing fluid.t Calculate the total silica concentration (total silica concentration calculation step: step S252).

[0166] Next, the silica scale generation amount calculation unit 73 calculates the total silica concentration C calculated in the total silica concentration calculation step S252. t Then, based on the silica concentration C at the predicted site calculated in the silica concentration calculation step S251, the amount of silica scale generated at the predicted site at time t is calculated as the amount of second silica scale generated (silica scale generation amount calculation step: step S253).

[0167] Specifically, the total silica concentration C at time t of the predicted site, obtained in the total silica concentration calculation step S252. t Then, by calculating the difference in silica concentration C at the predicted site, which was calculated in the prediction curve creation process S24, and calculating the change in silica concentration C at time t in the predicted site, the amount of silica scale generated at time t in the predicted site can be obtained as the amount of second silica scale generated.

[0168] Next, the output unit 50 outputs the calculation result of the amount of silica scale generated at time t in the predicted area, which was predicted in the second silica scale generation amount prediction step (step S25), by displaying or transmitting it (output step: step S26).

[0169] The prediction method according to this embodiment includes an acquisition step S21, a first silica scale generation amount prediction step S23, and a second silica scale generation amount prediction step S25. In the first silica scale generation amount prediction step S23, the prediction method according to this embodiment predicts the amount of silica scale generated at the prediction site as the first silica scale generation amount. In the second silica scale generation amount prediction step S25, the prediction method according to this embodiment predicts the amount of silica scale generated at time t at the prediction site as the second silica scale generation amount using a prediction curve PC of silica concentration C, the initial silica concentration Ci, and the fluid flow rate FR. Since the second silica scale generation amount prediction step S25 calculates the amount of silica scale generated at time t at the prediction site, including the initial silica concentration Ci and the fluid flow rate FR, the prediction accuracy of the silica scale generation amount at time t at the prediction site can be improved. Therefore, the second silica scale generation amount prediction step S25 can accurately predict the amount of silica scale generated at time t at the prediction site as the second silica scale generation amount. Thus, the prediction method according to this embodiment can further improve the prediction accuracy of the amount of silica scale generated.

[0170] In this embodiment, the prediction system 1B includes a first silica scale generation amount prediction unit 40, but it may also consist only of a second silica scale generation amount prediction unit 70.

[0171] As described above, prediction systems 1A and 1B can predict silica scale formation with greater accuracy, without relying on empirical values ​​such as experimental or measured values. Therefore, they can be effectively used in various plant systems such as geothermal power generation systems. By predicting silica scale formation with greater accuracy, prediction systems 1A and 1B can reduce plant system downtime and the increase in costs due to increased maintenance frequency, enabling stable and efficient plant system operation. They can also be effectively used in the design of plant systems where silica scale formation is a concern.

[0172] <Hardware configuration of the prediction system> Next, an example of the hardware configuration of prediction systems 1A and 1B will be described. Figure 13 is a block diagram showing the hardware configuration of prediction systems 1A and 1B. As shown in Figure 13, prediction systems 1A and 1B are composed of information processing devices (computers) and can be configured as computer systems that include a CPU (Central Processing Unit: processor) 101 which is the arithmetic processing unit, RAM (Random Access Memory) 102 and ROM (Read Only Memory) 103 which are the main memory, an input device 104 which is the input device, an output device 105 which is the input device, a communication module 106, and an auxiliary storage device 107 such as a hard disk. These are interconnected by a bus 108. Note that the input device 104, the output device 105 and the auxiliary storage device 107 may be provided externally.

[0173] The CPU 101 controls the overall operation of the prediction systems 1A and 1B and performs various information processing. The CPU 101 can predict the amount of silica scale generated with even greater accuracy by executing, for example, the prediction method described above or the prediction program described later, which is stored in the ROM 103 or the auxiliary storage device 107.

[0174] RAM102 is used as the work area of ​​CPU101 and may include non-volatile RAM for storing major control parameters and information.

[0175] ROM103 stores basic input / output programs, etc. Prediction programs may also be stored in ROM103.

[0176] The input device 104 is an input device such as a keyboard, mouse, operation buttons, touch panel, or display screen, which receives information input by the user as an instruction signal and outputs that instruction signal to the CPU 101.

[0177] The output device 105 includes display devices such as monitor displays, speakers, and printing devices such as printers. In the output device 105, for example, information such as the predicted amount of silica scale generated is displayed on a display device such as a monitor display, and the displayed screen is updated in response to input operations via the input device 104 or the communication module 106.

[0178] The communication module 106 is a data transmission and reception device such as a network card, and functions as a communication interface that receives information from an external data acquisition server and outputs the analyzed information to other electronic devices.

[0179] The auxiliary storage device 107 is a storage device such as an SSD (Solid State Drive) or HDD (Hard Disk Drive), and stores various data, files, etc., necessary for the operation of the prediction systems 1A and 1B.

[0180] Each function of the prediction systems 1A and 1B is realized by reading predetermined computer software (including a prediction program) from the main memory such as RAM 102 or the auxiliary storage device 107, executing it with the CPU 101, thereby reading and writing data to the main memory such as RAM 102 and the auxiliary storage device 107, and operating the input device 104, output device 105, and communication module 106.

[0181] Therefore, the parts of the prediction systems 1A and 1B shown in Figures 1 and 8 are realized through the collaborative action of software and hardware in a computer equipped with prediction systems 1A and 1B, where the processor executes predetermined computer software (including a prediction program) that is pre-stored.

[0182] A computer program implementing at least some of the functions of the parts of the prediction systems 1A and 1B shown in Figures 1 and 8 may be installed on the storage of one or more computers. The CPU 101 of one or more computers may perform the functions of the parts of the prediction systems 1A and 1B shown in Figures 1 and 8 by reading the computer program installed on its own machine into main memory and executing it.

[0183] The prediction systems 1A and 1B shown in Figures 1 and 8 may be implemented by one or more CPUs 101. Here, CPU 101 may refer to one or more electronic circuits located on a single chip, or one or more electronic circuits located on two or more chips or two or more devices. When multiple electronic circuits are used, each electronic circuit may communicate by wired or wireless means.

[0184] Furthermore, the functions of each part of the prediction systems 1A and 1B shown in Figures 1 and 8 may be executed by a single computer or by a distributed system of multiple computers. When the functions of each part of the prediction systems 1A and 1B shown in Figures 1 and 8 are executed by a distributed system of multiple computers, these multiple computers may send and receive data via a communication network including a LAN (Local Area Network), WAN (Wide Area Network), PAN (Personal Area Network), or the Internet.

[0185] The prediction program can be stored, for example, in the main memory or auxiliary storage device 107 of a computer. Alternatively, the prediction program may be stored on a computer connected to a communication line such as the Internet, and provided by allowing users to download part or all of the prediction program via the communication line. Furthermore, the prediction program may be configured to be provided or distributed via a communication line.

[0186] The prediction program may be recorded (including installed) into a computer from a state where part or all of it is stored on a portable storage medium such as an optical disc like a CD-ROM or DVD-ROM, or a semiconductor memory like flash memory.

[0187] <Third Embodiment> [Plant Systems] A plant system to which the silica scale formation prediction system according to this embodiment is applied will be described. Here, the case in which the prediction system 1A according to the first embodiment described above is used as the silica scale formation prediction system according to this embodiment, and the plant system is a geothermal power generation system will be described. Note that the prediction system 1B according to the second embodiment described above may be used instead of the prediction system 1A according to the first embodiment described above. The plant system may be a boiler system, a system equipped with cooling water piping, and a water treatment system, etc., instead of a geothermal power generation system.

[0188] Figure 14 is a conceptual diagram showing an example of a geothermal power generation system equipped with prediction system 1A. As shown in Figure 14, the geothermal power generation system 100 includes a production well 110, a gas-liquid separator 120, a turbine 130, a generator 140, a condenser 150, an injection well 160, a silica scale formation prediction system 170, a temperature measuring unit 181, a concentration measuring unit 182, a pH measuring unit 183, and piping L10. Note that the silica scale formation prediction system 170 is the same as prediction system 1A described above, so details are omitted.

[0189] The prediction site where the adhesion of silica scale in the geothermal power generation system 100 should be predicted is not particularly limited and may be any location where geothermal fluid can adhere. In FIG. 14, the prediction site is described as the pipe L11 that connects the production well 110 and the gas-liquid separator 120 among the pipes L10. Note that the prediction site is not limited to the pipe L11 and may be the turbine 130 or the like. Further, the prediction site may be a member not specifically shown in FIG. 14. The prediction site may be one location within the geothermal power generation system 100 or two or more locations, and the number of prediction sites is not limited.

[0190] The production well 110 is a well that draws out hot water (geothermal water), steam, or a mixture thereof (hereinafter referred to as geothermal fluid) in a subterranean geothermal reservoir layer to the surface.

[0191] The gas-liquid separator 120 separates the geothermal fluid pumped up from the production well 110 into a gas component and a liquid component.

[0192] The turbine 130 is disposed downstream of the gas-liquid separator 120. The turbine 130 is configured to be rotatable by the gas component separated by the gas-liquid separator 120. Note that the turbine 130 may include both a mode in which the steam separated by the gas-liquid separator 120 directly rotates the turbine and a mode in which the steam heats a low-boiling-point solvent and the low-boiling-point solvent rotates the turbine.

[0193] The generator 140 generates electricity by being driven by the rotation of the turbine 130.

[0194] The condenser 150 condenses the geothermal steam discharged from the turbine 130.

[0195] The reinjection well 160 is connected to the pipe L10 and is a well that leads the liquid component separated by the gas-liquid separator 120 back into the ground.

[0196] The temperature measurement unit 181 is provided in the pipe L10 and measures the temperature of the geothermal fluid pumped up from the production well 110. Examples of the temperature measurement unit 181 include a thermometer.

[0197] The concentration measurement unit 182 is provided in the pipe L10 and measures the concentration of silica in the geothermal fluid such as the initial concentration Ci of silica in the geothermal fluid pumped up from the production well 110. Examples of the concentration measurement unit 182 include a concentration sensor and the like.

[0198] The pH measurement unit 183 is provided in the pipe L10 and measures the pH of the geothermal fluid pumped up from the production well 110. Examples of the pH measurement unit 183 include a pH meter and the like.

[0199] The pipe L10 connects the respective members constituting the geothermal power generation system 100 and has pipes L11 and L12. The pipe L11 is a pipe that introduces the geothermal fluid pumped up from the production well 110 to the gas-liquid separator 102. The geothermal fluid is pumped up from the production well 110 by, for example, a water supply pump (not shown) and supplied to the gas-liquid separator 102. The pipe L12 is a pipe that delivers the geothermal water separated by the gas-liquid separator 120 to the reinjection well.

[0200] In the geothermal power generation system 100, the geothermal fluid led out from the production well 110 is sent through the pipe L11 to the gas-liquid separator 120, and in the gas-liquid separator 120, it is separated into steam, which is a gas component, and geothermal water, which is a liquid component. The steam separated by the gas-liquid separator 120 is guided to the turbine 130 and used for the rotation of the turbine 130 to generate electricity by the generator 140. The steam that has passed through the turbine 130 is cooled by the condenser 150 and guided to the reinjection well 160 through a pipe (not shown). On the other hand, the geothermal water separated by the gas-liquid separator 120 is guided to the reinjection well 160 through the pipe L12. The geothermal water may be cooled by a cooling tower (not shown) or the like in the middle of the pipe L12.

[0201] In the geothermal power generation system 100, the temperature of the geothermal fluid is measured by a temperature measuring unit 181 installed in the piping L11, the concentration of silica in the geothermal fluid is measured by a concentration measuring unit 182, and the pH of the geothermal fluid is measured by a pH measuring unit 183. The measurement results from the temperature measuring unit 181, the concentration measuring unit 182, and the pH measuring unit 183 are sent to the silica scale generation prediction system 170. Based on these measurement results, the silica scale generation prediction system 170 predicts the amount of silica scale generated from the geothermal fluid.

[0202] Thus, by installing a silica scale generation prediction system 170 in the pipe L11, which is the prediction area, the geothermal power generation system 100 can accurately predict the amount of silica scale generated from the geothermal fluid that adheres to the pipe L11. As a result, the geothermal power generation system 100 can minimize downtime and perform maintenance at the appropriate time, enabling stable and highly efficient power generation.

[0203] As described above, embodiments have been explained, but each of the above embodiments is presented as an example, and the present invention is not limited by each of the above embodiments. Each of the above embodiments can be implemented in various other forms, and various combinations, omissions, substitutions, and modifications are possible without departing from the spirit of the invention. The above embodiments and their variations are included in the scope and spirit of the invention, as well as in the scope of the invention and its equivalents as described in the claims. [Examples]

[0204] The following describes the embodiment in more detail with reference to examples, but this embodiment is not limited to these examples.

[0205] <Example 1-1> [Creation of a model corresponding to silica polymerization reaction] As a reaction model for silica polymerization in hot water, we used the three-step precipitation equilibrium reaction model represented by equation (I) below, and created a model corresponding to silica polymerization using the reaction module of the calculation software (COMSOL Multiphysics® modeling software).

[0206]

number

[0207] [Creation of a predictive curve PC for silica concentration C] Using the three-step precipitation equilibrium reaction model represented by equation (I) above, a predictive curve PC for silica concentration C was created.

[0208] [Calculation of silica scale generation amount] In the prediction curve creation unit 60 of the prediction system 1B shown in Figure 8, the silica concentration prediction curve PC created based on the three-step precipitation equilibrium reaction model represented by equation (I) prepared as described above was used in the second silica scale generation prediction unit 70, which used calculation software (COMSOL Multiphysics® modeling software) to calculate the difference between the initial concentration and the silica concentration (equilibrium concentration). The amount of silica scale generated in the pipe when hot water containing silica under the following hot water condition 1-1 was flowed through the pipe for a unit time was calculated. The calculation results of the silica scale generation are shown in Figure 15. (Hydrogen conditions 1-1) • Hot water temperature: 100℃ (373.15K) • pH of hot water: 7.0 · Relative flow rate of hot water: 1 m / s · Initial concentration of silica in hot water: 1500 ppm

[0209] <Example 1-2> In Example 1-1, the amount of silica scale generated was calculated in the same manner as Example 1-1, except that the initial concentration of silica in the hot water was changed to 500 ppm according to the following conditions 1-2 of the hot water. The calculation results of the amount of silica scale generated are shown in Fig. 15. (Conditions 1-2 of hot water) · Temperature of hot water: 100 °C (373.15 K) · pH of hot water: 7.0 · Relative flow rate of hot water: 1 m / s · Initial concentration of silica in hot water: 500 ppm

[0210] <Example 1-3> In Example 1-1, the amount of silica scale generated was calculated in the same manner as Example 1-1, except that the initial concentration of silica in the hot water was changed to 1100 ppm according to the following conditions 1-3 of the hot water. The calculation results of the amount of silica scale generated are shown in Fig. 15. (Conditions 1-3 of hot water) · Temperature of hot water: 100 °C (373.15 K) · pH of hot water: 7.0 · Relative flow rate of hot water: 1 m / s · Initial concentration of silica in hot water: 1100 ppm

[0211] <Example 2-1> In Example 1-1, the amount of silica scale generated per unit time was calculated in the same manner as Example 1-1, except that the relative flow rate of the hot water was changed to 2 m / s according to the following conditions 2-1 of the hot water and the initial concentration of silica in the hot water was changed to 1100 ppm. The calculation results of the amount of silica scale generated are shown in Fig. 16. (Conditions 2-1 of hot water) · Temperature of hot water: 100 °C (373.15 K) · pH of hot water: 7.0 • Relative flow velocity of hydrothermal fluid: 2 m / s Initial silica concentration in hydrothermal fluid: 1100 ppm

[0212] <Example 2-2> In Example 2-1, the procedure was the same as in Example 2-1, except that the relative flow velocity of the hydrothermal water was changed to 0.5 m / s, as described in hydrothermal water conditions 2-2 below. The calculation results of the amount of silica scale generated per unit time are shown in Figure 16. (Hydrogen conditions 2-2) • Hot water temperature: 100℃ (373.15K) • pH of hot water: 7.0 • Relative flow velocity of hydrothermal fluid: 0.5 m / s Initial silica concentration in hydrothermal fluid: 1100 ppm

[0213] <Example 2-3> In Example 2-1, the procedure was carried out in the same manner as in Example 1-3, except that the conditions for the hydrothermal water were the same as in Example 1-3, as described in Hydrothermal Water Conditions 2-3 below. The calculation results of the amount of silica scale generated per unit time are shown in Figure 16. (Conditions for hydrothermal fluids 2-3) • Hot water temperature: 100℃ (373.15K) • pH of hot water: 7.0 • Relative flow velocity of hydrothermal fluid: 1.0 m / s Initial silica concentration in hydrothermal fluid: 1100 ppm

[0214] <Comparative Example 1-1> In Example 1-1, the calculation of silica scale formation was performed in the same manner as in Example 1-1, except that the initial silica concentration and relative flow velocity in the hydrothermal water were not used as elements when calculating the silica scale formation amount using the prediction system 1B shown in Figure 8. The calculation results of the silica scale formation amount are shown in Figure 15.

[0215] <Comparative Example 1-2> In Comparative Example 1-1, the procedure was the same as in Comparative Example 1-1, except that the initial concentration of silica in the hydrothermal water was changed to 500 ppm. The calculation results for the amount of silica scale generated are shown in Figure 15.

[0216] <Comparative Example 1-3> The procedure was the same as in Comparative Example 1-1, except that the initial silica concentration in the hydrothermal water was changed to 1100 ppm. The calculation results for the amount of silica scale generated are shown in Figure 15.

[0217] <Comparative Example 2-1> In Example 2-1, the process was carried out in the same manner as in Example 2-1, except that the initial concentration of silica in the hydrothermal water and the relative flow velocity were not used as elements when calculating the amount of silica scale generated using the prediction system 1B shown in Figure 8. The calculation results of the amount of silica scale generated per unit time are shown in Figure 16.

[0218] <Comparative Example 2-2> The procedure was the same as in Comparative Example 2-1, except that the relative flow velocity of the hydrothermal fluid was changed to 0.5 m / s. The calculation results for the amount of silica scale generated per unit time are shown in Figure 16.

[0219] <Comparative Example 2-3> The procedure was the same as in Comparative Example 2-1, except that the relative flow velocity of the hydrothermal fluid was changed to 1.0 m / s. The calculation results for the amount of silica scale generated per unit time are shown in Figure 16.

[0220] As shown in Figure 15, in Comparative Examples 1-1 to 1-3, even when the initial silica concentration was set to 500 ppm, 1100 ppm, and 1500 ppm, the amount of silica scale generated was approximately 572 ppm, similar to the case where the initial concentration was 1100 ppm. Furthermore, as shown in Figure 16, in Comparative Examples 2-1 to 2-3, even when the relative flow velocity of the hydrothermal water was changed to 0.5 m / s, 1 m / s, and 2 m / s, the amount of silica scale generated per unit time was approximately 572 mg / s, similar to the case where the relative flow velocity of the hydrothermal water was 1 m / s. Therefore, in each comparative example, the predicted amount of silica scale generated remained almost unchanged even when the initial silica concentration and the relative flow velocity of the hydrothermal water were varied, indicating that the amount of silica scale generated cannot be accurately predicted.

[0221] On the other hand, as shown in Figure 15, in Examples 1-1 to 1-3, when the initial silica concentrations were 500 ppm, 1100 ppm, and 1500 ppm, the silica scale generation amounts were approximately 260 ppm, 572 ppm, and 780 ppm, respectively. Therefore, in Examples 1-1 to 1-3, the silica scale generation amount increased as the initial silica concentration increased, and the silica scale generation amount corresponding to the initial silica concentration was appropriately predicted. Furthermore, as shown in Figure 16, in Examples 2-1 to 2-3, when the relative flow velocity of the hot water was 0.5 m / s, 1 m / s, and 2 m / s, the silica scale generation amount per unit time was approximately 260 mg / s, 572 mg / s, and 1140 mg / s, respectively. Therefore, in Examples 1-1 to 1-3, the silica scale generation amount increased as the relative flow velocity of the hot water increased, and the silica scale generation amount corresponding to the relative flow velocity of the hot water was appropriately predicted.

[0222] Therefore, the prediction system according to this embodiment can improve the accuracy of predicting the amount of silica scale generated in response to changes in the initial silica concentration or the relative flow velocity of the hydrothermal fluid, even when the initial silica concentration or the relative flow velocity of the hydrothermal fluid is changed. Thus, it can be said that the amount of silica scale generated can be predicted with greater accuracy.

[0223] The embodiments of the present invention are, for example, as follows. [1] Predicting the adhesion of silica scale caused by silica contained in the fluid, using the temperature T at the predicted site of the object. s , and the time t until the silica-containing fluid reaches the predicted site s An acquisition unit that acquires at least one of the following conditions, temperature T s Prediction formula for silica concentration C dependent on PF and time t s A silica scale generation amount prediction unit predicts the amount of silica scale generated in the predicted area based on at least one of the prediction curve PC of silica concentration C which depends on the silica concentration, Equipped with, The prediction formula PF and the prediction curve PC for the silica concentration C are obtained based on a reaction model generated using a silica polymerization reaction that includes reversible and irreversible reactions and precipitation equilibrium reactions of the silica contained in the fluid. The silica scale generation prediction unit is a silica scale generation prediction system that calculates the amount of silica scale generated at the prediction site using at least one of the initial silica concentration Ci and the fluid flow rate FR. [2] The prediction formula PF for the silica concentration C is: When the fluid is acidic or neutral, formula (1-1): Ce = (Ci / 1000)γ{a[exp(bTr)]} (In the formula, Ci is the initial concentration of silica, γ is the effective activity coefficient, a and b are constants, and Tr represents the polymerization reaction temperature.) Using, When the fluid is under basic conditions, equation (1-2): Ce = (Ci / 1000)J {a[exp(bTr)]} (In the formula, Ci is the initial concentration of silica, J is the effective reaction coefficient, a and b are constants, and Tr represents the polymerization reaction temperature.) A silica scale generation prediction system described in [1], using the following. [3] The silica scale generation amount prediction unit determines the amount M of silica scale generated in the predicted area within a unit time, When the fluid is acidic or neutral, equation (2-1) applies: M=Ci-[γ{a[exp(bT s / Tr)]}QS+Ci] / 1000 (In the formula, M is the amount of silica scale produced, Ci is the initial concentration of silica, γ is the effective activity coefficient, a and b are constants, Tr is the polymerization reaction temperature, Q is the fluid velocity per unit time, and S is the cross-sectional area of ​​the channel through which the fluid flows.) Using, When the fluid is under basic conditions, equation (2-2): M=Ci-[J{a[exp(bTr)]}QS+Ci] / 1000 (In the formula, M is the amount of silica scale produced, Ci is the initial concentration of silica, J is the effective reaction coefficient, a and b are constants, Tr is the polymerization reaction temperature, Q is the fluid velocity per unit time, and S is the cross-sectional area of ​​the fluid channel.) A prediction system for silica scale generation, as described in [1] or [2], which is calculated using [the specified method]. [4] The reaction model is a silica scale generation prediction system according to any one of [1] to [3], which includes the ionization equilibrium reaction of the silica contained in the fluid. [5] The reaction model is given by the following equation (I):

[0224]

number

[10] To the computer, Predicting the adhesion of silica scale caused by silica contained in the fluid, using the temperature T at the predicted location on the object. s , and the time t until the silica-containing fluid reaches the predicted site s A process to obtain at least one of the following conditions, temperature T s Prediction formula for silica concentration C dependent on PF and time t s A silica scale generation amount prediction step that predicts the amount of silica scale generated in the predicted area based on at least one of the prediction curve PC of silica concentration C which depends on the silica concentration, Make it run, The prediction formula PF and the prediction curve PC for the silica concentration C are obtained based on a reaction model generated using a silica polymerization reaction that includes reversible and irreversible reactions and precipitation equilibrium reactions of the silica contained in the fluid. The silica scale generation prediction step is a silica scale generation prediction program that calculates the amount of silica scale generated at the prediction site using at least one of the initial silica concentration Ci and the fluid flow rate FR. [Explanation of symbols]

[0225] 1A, 1B Prediction System 10 Acquisition Department 20A, 20B Model Recording Unit 30 Silica concentration prediction formula creation section 40 Silica scale generation amount prediction unit, first silica scale generation amount prediction unit 41, 71 Predicted site silica concentration calculation unit 42, 72 Total Silica Concentration Calculation Unit 43, 73 Silica scale generation amount calculation unit 50 Output section 60 Silica concentration C prediction curve generation section 70 Second silica scale generation amount prediction unit 100 Geothermal power generation systems

Claims

1. Predicting the adhesion of silica scale caused by silica contained in the fluid, using the temperature T at the predicted location on the object. ｓ , and the time t until the fluid containing silica reaches the predicted site. ｓ An acquisition unit that acquires at least one of the following conditions, Temperature T ｓ Prediction formula for silica concentration C, dependent on PF and time t ｓ A silica scale generation amount prediction unit predicts the amount of silica scale generated in the predicted area based on at least one of the prediction curve PC of silica concentration C which depends on the silica concentration, Equipped with, The prediction formula PF and the prediction curve PC for the silica concentration C are obtained based on a reaction model generated using a silica polymerization reaction that includes reversible and irreversible reactions and precipitation equilibrium reactions of the silica contained in the fluid. The silica scale generation amount prediction unit is a silica scale generation amount prediction system that calculates the amount of silica scale generated at the prediction site using at least one of the initial silica concentration Ci and the fluid flow rate FR.

2. The prediction formula PF for the silica concentration C is, When the fluid is acidic or neutral, formula (1-1): Ce=(Ci / 1000)γ{a[exp(bTr)]} (In the formula, Ci is the initial concentration of silica, γ is the effective activity coefficient, a and b are constants, and Tr represents the polymerization reaction temperature.) Using, When the fluid is under basic conditions, equation (1-2): Ce=(Ci / 1000)J{a[exp(bTr)]} (In the formula, Ci is the initial concentration of silica, J is the effective reaction coefficient, a and b are constants, and Tr represents the polymerization reaction temperature.) A silica scale generation prediction system according to claim 1, using the method described above.

3. The silica scale generation amount prediction unit determines the amount M of silica scale generated in the predicted area within a unit time, When the fluid is acidic or neutral, formula (2-1): M=Ci-[γ{a[exp(bT ｓ / Tr)]}QS+Ci] / 1000 (In the formula, M is the amount of silica scale produced, Ci is the initial concentration of silica, γ is the effective activity coefficient, a and b are constants, Tr is the polymerization reaction temperature, Q is the fluid velocity per unit time, and S is the cross-sectional area of ​​the fluid channel.) Using, When the fluid is under basic conditions, equation (2-2): M=Ci-[J{a[exp(bTr)]}QS+Ci] / 1000 (In the formula, M is the amount of silica scale produced, Ci is the initial concentration of silica, J is the effective reaction coefficient, a and b are constants, Tr is the polymerization reaction temperature, Q is the fluid velocity per unit time, and S is the cross-sectional area of ​​the fluid channel.) A silica scale generation prediction system according to claim 1 or 2, which calculates using the method described above.

4. The silica scale generation prediction system according to claim 1 or 2, wherein the reaction model includes the ionization equilibrium reaction of the silica contained in the fluid.

5. The reaction model is given by the following equation (I): [Math 1] (where k １ is the reaction equilibrium constant between Si(OH) ４ and SiOSi(OH) ６ ; k ２ is the reaction equilibrium constant between SiOSi(OH) ６ and (SiO) ３ OSi(OH) １０と ; k Ｂ is the ionization equilibrium constant between SiOSi(OH) ６ and (SiO) ３ Si(OH) ９ O － ; and k ａ is the acid dissociation constant of silica between (SiO) ３ Si(OH) ９ O － and (SiO) ３ OSi(OH) １０ .) This is a three-step precipitation equilibrium reaction model represented by: The prediction formula PF and the prediction curve PC for the silica concentration C are calculated using the formula (I). １ , k ２ , k ａ and k Ｂ A silica scale generation prediction system according to claim 1 or 2, obtained based on the above.

6. The silica scale generation amount prediction unit is, Temperature T ｓ Based on the prediction formula PF for the silica concentration C, the silica concentration C in the predicted region is calculated. Total silica concentration C in the aforementioned fluid ｔ Obtain, The total silica geothermal C ｔ A silica scale generation prediction system according to claim 1 or 2, which calculates the amount of silica scale generated based on the silica concentration C.

7. The silica scale generation amount prediction unit is, The aforementioned time t ｓ Based on the prediction curve PC of the silica concentration C, the silica concentration C at the predicted site is calculated. Total silica concentration C in the aforementioned fluid ｔ Obtain, The total silica geothermal C ｔ A silica scale generation prediction system according to claim 1 or 2, wherein the amount of silica scale generated at the predicted site at time t is calculated based on the silica concentration C.

8. A gas-liquid separator separates the geothermal fluid pumped from the production well into gaseous and liquid components, A turbine configured to be rotatable by the gaseous components separated by the gas-liquid separator, A piping system for delivering the geothermal fluid from the production well to the gas-liquid separator, and for delivering the liquid component separated by the gas-liquid separator to the reinjection well, A silica scale generation amount prediction system according to claim 1 or 2, which predicts the amount of silica scale generated in the liquid component flowing through the piping, A geothermal power generation system equipped with [the necessary components].

9. Computers Predicting the adhesion of silica scale caused by silica contained in the fluid, using the temperature T at the predicted location on the object. ｓ , and the time t until the fluid containing silica reaches the predicted site. ｓ A process to obtain at least one of the following conditions, Temperature T ｓ Prediction formula for silica concentration C, dependent on PF and time t ｓ A silica scale generation amount prediction step that predicts the amount of silica scale generated in the predicted area based on at least one of the prediction curve PC of silica concentration C which depends on the silica concentration, Execute, The prediction formula PF and the prediction curve PC for the silica concentration C are obtained based on a reaction model generated using a silica polymerization reaction that includes reversible and irreversible reactions and precipitation equilibrium reactions of the silica contained in the fluid. The silica scale generation prediction step is a method for predicting the amount of silica scale generated at the predicted site, which uses at least one of the initial silica concentration Ci and the fluid flow rate FR to calculate the amount of silica scale generated at the predicted site.

10. On the computer, Predicting the adhesion of silica scale caused by silica contained in the fluid, using the temperature T at the predicted location on the object. ｓ , and the time t until the fluid containing silica reaches the predicted site. ｓ A process to obtain at least one of the following conditions, Temperature T ｓ Prediction formula for silica concentration C, dependent on PF and time t ｓ A silica scale generation amount prediction step that predicts the amount of silica scale generated in the predicted area based on at least one of the prediction curve PC of silica concentration C which depends on the silica concentration, Make it run, The prediction formula PF and the prediction curve PC for the silica concentration C are obtained based on a reaction model generated using a silica polymerization reaction that includes reversible and irreversible reactions and precipitation equilibrium reactions of the silica contained in the fluid. The silica scale generation prediction step is a silica scale generation prediction program that calculates the amount of silica scale generated at the prediction site using at least one of the initial silica concentration Ci and the fluid flow rate FR.

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