Method for predicting the amount of silica scale formation

Abstract

The present invention accurately predicts a generated amount of silica scale under complicated conditions.　A method for predicting a generated amount of silica scale comprises: a step for acquiring a temperature Ts(K) at a prediction portion at which the adhesion of the silica scale should be predicted, and / or a time ts(min.) until a fluid including silicic acid reaches the prediction portion; and a step for computing an adhesion amount of the silica at the prediction portion on the basis of a prediction equation of silica saturation concentration dependent on the temperature, and / or a prediction curve of silica dissolved concentration dependent on the time, wherein the prediction equation of the silica saturation concentration and the prediction curve of the silica dissolved concentration are obtained on the basis of k1, k2, kB, ka in a three-step precipitation equilibrium reaction model that is expressed as the following formula (1).

Description

[Technical field]

[0001] The present invention relates to a method and system for predicting the amount of silica scale formation, and a geothermal power generation system equipped with said prediction system. In particular, the present invention relates to a method and system for predicting the amount of silica scale formation by simulation without collecting data through experiments, and a geothermal power generation system equipped with said prediction system. [Background technology]

[0002] In plant systems that use groundwater, such as geothermal power generation systems, silica dissolved in the water causes silica scale to adhere to the equipment and piping that make up the plant system. Silica scale is a strong deposit that is mainly composed of polymers of Si and O. In particular, in geothermal power plants, the formation of silica scale causes problems such as a decrease in reduction ability and a decrease in power generation efficiency.

[0003] Various methods have been proposed to predict the amount of scale formation from the properties of hot water.

[0004] The kinetics of the reaction between silicic acid and the surface of amorphous silica in aqueous NaCl solutions is known (see, for example, Non-Patent Document 1).

[0005] A scale growth prediction method is known that predicts the thickness of scale that will form in a well from the velocity of the fluid in the well (see, for example, Patent Document 1). A scale quantitative evaluation method is known that weighs a device that can be heated locally and measures the scale mass by comparing the mass before and after heating (see, for example, Patent Document 2). A method is known that estimates scale thickness based on the fluid flowing through a pipe, the temperature of the outer surface of the pipe, the thermal conductivity of the scale, etc. (see, for example, Patent Document 3). A scale inhibition method is known that sprays a scale inhibitor according to the scale components contained in steam (see, for example, Patent Document 4). [Prior art documents] [Patent documents]

[0006] [Patent Document 1] JP 2002-257030 A [Patent Document 2] JP 2019-027961 A [Patent Document 3] International Publication 2019 / 202981 [Patent Document 4] JP 2020-12456 A [Non-patent literature]

[0007] [Non-Patent Document 1] Journal of Colloid and Interface Science Volume 110, Issue 1, March 1986, Pages 40-64 Summary of the Invention [Problem to be solved by the invention]

[0008] However, the method disclosed in Non-Patent Document 1 is an empirical technique, and since a large amount of measured values ​​is required to establish a prediction formula, and since the experimental conditions cannot be accurately controlled, accurate predicted values ​​cannot be obtained. Moreover, since it is necessary to repeat measurements and correct the empirical prediction formula every time the conditions change, the method lacks versatility.

[0009] The methods disclosed in Patent Documents 1 to 4 require empirical values ​​such as large amounts of experimental data and actual measurement data to establish a prediction formula for predicting the amount of silica scale generated. Acquisition of data requires the use of special equipment, or the stopping of a plant system such as a geothermal power generation system and the disassembly of part of the equipment. Furthermore, prediction formulas established by empirical methods are very vulnerable to changes in conditions, and a huge amount of data is required to obtain an accurate prediction formula.

[0010] As described above, it was difficult to accurately predict the amount of silica scale generated in conventional technologies. Therefore, for example, maintenance was performed after a plant system such as a geothermal power generation system suddenly stopped or its power generation capacity decreased. This resulted in a disadvantage of a decrease in sales due to a decrease in the amount of electricity sold. In addition, when performing maintenance in advance to avoid a decrease in power generation capacity and a sudden stop, the amount of silica scale generated cannot be accurately grasped, so the maintenance timing cannot be optimized, and there was also a problem of higher maintenance costs due to an increase in the number of maintenance operations. [Means for solving the problem]

[0011] The present inventors have investigated the quantification of the amount of silica scale formation by simulation without relying on experiments. As a result, they have come up with the idea of ​​devising a reaction model of the silica polymerization reaction in hot water, and have established a method for calculating various parameters required for predicting the silica saturation concentration and the silica dissolved concentration, thereby completing the present invention.

[0012] The object of the present invention can be achieved by the following preferred embodiments. [1] The temperature T at the predicted location where silica scale deposition should be predicted s (K), and / or the time it takes for the silicic acid-containing fluid to reach the predicted location t s (min.) calculating the amount of silica attached at the predicted portion based on a prediction equation for a silica saturation concentration depending on temperature and / or a prediction curve for a silica dissolved concentration depending on time; Including, The prediction equation for the silica saturation concentration and the prediction curve for the silica dissolved concentration are a three-stage precipitation equilibrium reaction model represented by the following equation (1): [ka] (In formula (1), k 1 is Si(OH) 4 and SiOSi(OH) 6is the reaction equilibrium constant between it and k 2 is the reaction equilibrium constant between SiOSi(OH) 6 and (SiO) 3 S i(OH) 10 and is the reaction equilibrium constant between it and k B is the reaction equilibrium constant between SiOSi(OH) 6 and (SiO) 3 Si(OH) 9 O - and is the ionization equilibrium constant between it and k a is the silica acid dissociation constant between (SiO) 3 Si(OH) 9 O - and (SiO) 3 S i(OH) 10 and is the method for predicting the amount of silica scale formation obtained based on k in, k 1 , k 2 , k B , k a and k [2] The silica acid dissociation constant k a is based on the free energy change ΔG in the equilibrium reaction between (SiO) 3 Si(OH) 9 O - and (SiO) 3 S i(OH) 10 and is the method described in [1] obtained by quantum chemical calculation and the linear fitting correction method. [3] The relationship between the silica acid dissociation constant k a and the free energy change ΔG is pk a = pΔG + q (where p and q are constants) and is the method described in [2]. [4] The method described in [3], where p is 0.19 to 0.24 and q is -56 to -51. [5] The prediction curve of the dissolved silica concentration C is the initial silica concentration C iPlots of the dissolved silica concentration at two or more different time points obtained by first-principles calculations based on Equation (1) are obtained by fitting, The frequency factor A used for correcting the fitting at the initial stage of the reaction is A = m[exp(nT)] (3) (In Equation (3), m and n are constants, and k 1 , k 2 , k B , k a are calculated based on) The method according to [1], represented by [6] The method according to [5], where m is 2.0 to 3.1 and n is 0.083 to 0.085. [7] The prediction formula for the silica saturation concentration Ce is the silica saturation concentration Ce at temperature T 1 : Ce 1 = a 1 [exp(b 1 T)] (2) (In Equation (2), a 1 , b 1 are constants calculated based on k 1 , k 2 , k B , k a and T represents the polymerization reaction temperature) The method according to [1], represented by [8] The method according to [7], where a 1 is 18 to 32 and b 1 is 0.005 to 0.010. [9] The prediction formula for the silica saturation concentration Ce 2 is the silica saturation concentration Ce at temperature T and pH of 0 or more and less than 7 2 : Ce 2 = R{a 2 [exp(b 2 T)]} (4) (In Equation (4), a 2 , b 2 are constants calculated based on k 1 , k 2 , kB , k a is a constant calculated based on R is the effective activity coefficient calculated based on pH, T represents the polymerization reaction temperature. The method according to [1], represented as

[10] The formula for calculating the effective activity coefficient R is: -logR = A R Z 2 {E / (1+B R cE)} (5) {In formula (5), A R =1.825*10 6 (εT) -3 / 2 , B R =50.3*(εT) -1 / 2 It is expressed as the charge number Z is a constant selected from 1 or 2, the effective diameter coefficient c is 4, E is the effective ionic strength expressed by the following formula (6) E = {I+(hydrogen ion concentration)} / [1+B R c[I+(hydrogen ion concentration)] (6) (In formula (6), I is the solute ionic strength.) is} The method according to [9], represented as

[11] a 2 is 16 to 36, and b 2 The method according to [9], wherein the n-th order number is 0.003 to 0.015.

[12] The silica saturation concentration Ce 3 The prediction formula for the silica saturation concentration Ce at temperature T and pH greater than 7 and less than 14 is 3 : Ce 3 =(1-J){a 3 [exp(b 3 T)]} (7) (In formula (7), a 3 , b 3 is k 1 , k 2 , k B , k ais a constant calculated based on J is the effective reaction coefficient calculated based on the fraction of silica monomer ions and silica dimer ions, T represents the polymerization reaction temperature. The method according to [1], represented as

[13] The formula for calculating the effective reaction coefficient J is: J=(X-Xi 1 -Xi 2 ) / X (8) (In formula (8), X is the total amount of silica, Xi 1 is the acid dissociation constant k aj is the fraction of silica monomer ions calculated from Xi 2 , acid dissociation constant k aj (The fraction of silica dimer ions is calculated from The method according to

[12] , represented as

[14] a 3 is 6 to 34, and b 3 The method according to

[12] , wherein

[15] The total silica concentration, C, in the silicic acid-containing fluid. t and obtaining The total silica concentration C t and calculating the silica deposition amount based on the silica saturation concentration. The method according to [1], wherein the silica adhesion amount is predicted by

[16] The method according to [1], wherein the amount of silica adhesion is predicted by a step of calculating the amount of silica adhesion based on a prediction curve of the dissolved silica concentration.

[17] The temperature T at the predicted location where silica scale deposition should be predicted s (K), and / or the time it takes for the silicic acid-containing fluid to reach the predicted location t s (min.) and a device for calculating the amount of silica adhesion at the predicted portion based on a prediction formula for a silica saturation concentration depending on temperature and / or a prediction curve for a silica dissolved concentration depending on time; Including, The prediction equation for the silica saturation concentration and the prediction curve for the silica dissolved concentration are a three-stage precipitation equilibrium reaction model represented by the following equation (1): [ka] (In formula (1), k 1 is Si(OH) 4 and SiOSi(OH) 6 is the reaction equilibrium constant between k 2 is SiOSi(OH) 6 and (SiO) 3 S i(OH) 10 is the reaction equilibrium constant between k B is SiOSi(OH) 6 and (SiO) 3 Si(OH) 9 O - is the ionization equilibrium constant between k a is (SiO) 3 Si(OH) 9 O - and (SiO) 3 S i(OH) 10 is the silica acid dissociation constant between In, k 1 , k 2 , k B , k a A system for predicting the amount of silica scale formation based on the above.

[18] a gas-liquid separator that separates the geothermal fluid pumped from the production well into gas and liquid components; a turbine disposed downstream of the gas-liquid separator and configured to be rotatable by the gas components separated by the gas-liquid separator; A pipe for delivering the liquid component separated by the gas-liquid separator to a reinjection well;

[17] A prediction system for the amount of silica scale formation described in A geothermal power generation system comprising: Effect of the Invention

[0013] According to the method for predicting the amount of silica scale formation of the present invention, the amount of silica scale formation can be predicted easily and accurately even under complicated conditions without relying on empirical values ​​such as experimental values ​​and actual measured values. This makes it possible to reduce costs associated with shutdowns of the plant system and increased frequency of maintenance, and to operate the plant system stably and efficiently. Furthermore, the method is also effective in designing plant systems where silica scale formation is a concern. [Brief description of the drawings]

[0014] [Figure 1] FIG. 1 is a flowchart showing the calculation of the silica saturation concentration Ce1 and the dissolved silica concentration C1 in the prediction method according to the first embodiment of the present invention. [Diagram 2] FIG. 2 is a graph showing an example of a prediction curve showing the relationship between the polymerization reaction temperature T and the saturation concentration Ce1 at pH 7, which can be used in the prediction method according to the first embodiment of the present invention. [Diagram 3] FIG. 3 is a graph showing an example of a prediction curve showing the relationship between the polymerization reaction time t and the dissolved silica concentration C1 and the amount of precipitated silica at 100° C. and pH 7, which can be used in the prediction method according to the first embodiment of the present invention. [Figure 4] Figure 4 is a semi-logarithmic graph showing the prediction curve of the frequency factor A used in fitting to accurately predict the dissolved concentration in the early stage of the reaction, with the vertical axis being on a logarithmic scale. By using the frequency factor A, the experimental values ​​at each temperature can be reproduced at the 5 min time point. [Diagram 5] FIG. 5 is a flowchart showing the calculation of the silica saturation concentration Ce2 and the dissolved silica concentration C2 in the prediction method according to the second embodiment of the present invention. [Figure 6] FIG. 6 is a graph showing an example of a prediction curve showing the relationship between the polymerization reaction temperature T and the saturation concentration Ce2 at pH 5.5 and pH 7.0, which can be used in the prediction method according to the second embodiment of the present invention. [Figure 7]FIG. 7 is a graph showing an example of a prediction curve showing the relationship between the polymerization reaction time t and the dissolved silica concentration C2 and the amount of precipitated silica at 150° C. and pH 5.5, which can be used in the prediction method according to the second embodiment of the present invention. [Figure 8] FIG. 8 is a flowchart showing the calculation of the silica saturation concentration Ce3 and the dissolved silica concentration C3 in the prediction method according to the third embodiment of the present invention. [Figure 9] FIG. 9 is a graph showing the change in effective reaction coefficient J in the pH range of 7 to 14. [Figure 10] FIG. 10 is a graph showing an example of a prediction curve showing the relationship between the polymerization reaction temperature T and the saturation concentration Ce3 at pH 5.5, pH 7.0, and pH 9.0, which can be used in the prediction method according to the third embodiment of the present invention. [Figure 11] FIG. 11 is a graph showing an example of a prediction curve showing the relationship between the polymerization reaction time t and the dissolved silica concentration C3 and the amount of precipitated silica at 100° C. and pH 9.0, which can be used in the prediction method according to the third embodiment of the present invention. [Figure 12] FIG. 12 is a conceptual diagram illustrating a geothermal power generation system including a system for predicting the amount of silica scale formation according to one embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. However, the present invention is not limited to the embodiment described below.

[0016] [First embodiment: Method for predicting the amount of silica scale formation] According to a first embodiment, the present invention relates to a method for predicting the amount of silica scale formation. The method for predicting the amount of silica scale formation includes the following steps. Temperature T at the predicted location where silica scale deposition should be predicted s (K), and / or the time it takes for the silicic acid-containing fluid to reach the predicted location t s (min.) A step of calculating the amount of silica adhesion at the predicted portion based on a prediction formula for the temperature-dependent silica saturation concentration and / or a prediction curve for the time-dependent silica dissolved concentration.

[0017] More specifically, the present embodiment relates to a method for predicting the amount of silica scale generation in a plant system through which a fluid containing silicic acid flows. The fluid containing silicic acid is Si(OH) 4 , Si(OH) 3 O - , SiO 2 (OH) 2 2- , Si 2 O 2 (OH) 5 - and / or Si 2 O 3 (OH) 4 2- The term "silicic acid" refers to a fluid containing chemical species containing Si and OH, including, but not limited to, those mentioned above. The plant system may be a plant system equipped with piping and equipment through which a fluid containing silicic acid flows, and is, for example, a plant system in which the deposition of silica scale may cause the plant system to stop or malfunction. Examples of plant systems include, but are not limited to, geothermal power generation systems, boiler systems, systems equipped with cooling water piping, and water treatment systems.

[0018] The fluid containing silicic acid may be, for example, water that may contain silicic acid, and may include, but is not limited to, groundwater, tap water, geothermal water, or wastewater derived from these. For example, if the plant system is a geothermal power generation system, the fluid containing silicic acid may be geothermal water. Note that the fluid is not limited to liquid, and may also be a mixture of water and gas such as steam.

[0019] In this embodiment, three types of prediction formulas are established for the temperature-dependent silica saturation concentration. In addition, based on each of these prediction formulas, a method for deriving a prediction curve of time-dependent silica dissolved concentration is established. Each aspect will be described below.

[0020] (First aspect) In the first embodiment of the method according to the present invention, the saturation concentration of silica Ce depending on the temperature T is 1 The amount of silica scale generated at any part of the plant system is predicted based on the prediction formula. In the first embodiment, a prediction formula is provided for a pH of 7. Here, the silica saturation concentration Ce given by the prediction formula is 1 The term "saturation concentration" refers to the weight percent concentration (unit: ppm) of a solution in which silica (including monomers and various silica polymers of dimers or higher) that can be produced by the above-mentioned condensation polymerization reaction of silicic acid dissolves and reaches a saturated solution at a specified temperature T. In other words, it refers to the maximum concentration at which silica (including monomers and various silica polymers of dimers or higher) can be dissolved at a specified temperature T. Furthermore, 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.

[0021] Silica saturation concentration Ce 1 In order to obtain a prediction equation for the above, the present inventors established a three-stage precipitation equilibrium reaction model represented by the following equation (1). [ka] (In formula (1), k 1 is Si(OH) 4 and SiOSi(OH) 6 is the reaction equilibrium constant between k 2 is SiOSi(OH) 6 and (SiO) 3 S i(OH) 10 is the reaction equilibrium constant between k B is SiOSi(OH) 6 and (SiO) 3 Si(OH) 9 O - is the ionization equilibrium constant between k ais the silicic acid dissociation constant between (SiO) 3 Si(OH) 9 O - and (SiO) 3 S i(OH) 10 and)

[0022] Conventionally, the silica polymerization reaction has been calculated based on a two-step model consisting of a reversible reaction that generates SiOSi(OH) 4 from Si(OH) 6 and an irreversible reaction that generates (SiO) 6 from SiOSi(OH) 3 S i(OH) 10 In the present invention, instead of this two-step model, by adopting the model of the above formula (1) that further considers the precipitation equilibrium reaction, it becomes possible to predict the behavior of chemical species represented by (SiO) 3 Si(OH) 9 O - which has not been considered conventionally.

[0023] Next, the prediction formula for the silica saturation concentration Ce 1 and the derivation of the silica dissolved concentration C 1 curve will be explained. Figure 1 is a flowchart of the calculation of the silica saturation concentration Ce 1 and the silica dissolved concentration C 1

[0024] In this method, first, from the four chemical species represented by formula (1) and the free energy of the fluid (e.g., water) in which silicic acid is dissolved, the free energy change ΔG in each step of the reaction of formula (1) is obtained. Also, from the value of the free energy change ΔG, k 1 , k 2 are obtained. The temperature T in the calculation formula of the equilibrium constant of the polymerization reaction is the polymerization reaction temperature. The acid dissociation constant k a can use the following values calculated from the free energy change ΔG by quantum chemical calculation and the linear fitting correction method. pk a =pΔG+q ​In the formula, p and q are constants, and ΔG is the (SiO 3 Si(OH) 9 O - and (SiO) 3 S i(OH) 10 It is a value of free energy change in an equilibrium reaction with. More specifically, p may be 0.19 to 0.24, and q may be -56 to -51. Preferably, p may be 0.21 to 0.22, and q may be -54 to -52.

[0025] From these calculations, the polymerization reaction temperature T and the silica saturation concentration Ce 1 The relationship between the concentration and ppm is calculated as shown in the following formula (2). Ce 1 =a 1 [exp(b 1 T)] (2) In formula (2), a 1 , b 1 is a constant, and is a value obtained by the calculation described in the above flow chart. T (K) represents the polymerization reaction temperature. The temperature range of T may be about 250K to 500K. More specifically, a 1 is 18 to 32, and b 1 may be 0.005 to 0.010. 1 is 20 to 30, and b 1 may be 0.006 to 0.009.

[0026] Figure 2 shows the silica saturation concentration Ce 1 2 is an example of the formula (2) showing a prediction curve of the silica saturation concentration Ce. In FIG. 2, the prediction formula according to the present invention is shown by a solid line. 1 In the three-stage precipitation equilibrium reaction model represented by formula (1), the temperature T is the polymerization reaction temperature (unit: K). In the prediction method according to the present embodiment, when predicting the amount of silica scale adhesion, the temperature T s can be used as the polymerization temperature in the prediction calculation. smay be, for example, the temperature of a fluid that may contain silica at a predicted location in a plant system.

[0027] A specific method for predicting the amount of silica scale adhesion based on formula (2) will be described below. The prediction method includes the following steps a) to d). a) Temperature T at the predicted location where silica scale deposition is to be predicted s (K) Obtaining process b) Temperature T s From the prediction formula (2), the silica saturation concentration Ce at the predicted portion is 1 The process of calculating c) Total silica concentration in the siliceous fluid, C t The process of obtaining d) Total silica concentration C t and silica saturation concentration Ce 1 Calculating the amount of silica deposited based on

[0028] In step a), the predicted portion where deposition of silica scale should be predicted is a portion that comes into contact with a fluid containing silicic acid in a plant system in which the prediction method according to the present embodiment is carried out, and is a portion where deposition of silica scale is possible. For example, in a geothermal power generation system, the predicted portion may be a turbine component such as a turbine blade or rotor, a pipe, a heat exchanger, etc., but is not limited to these. Temperature T s The method of acquiring (K) is not particularly limited. For example, the temperature of the fluid or the equipment at the prediction location is actually measured by a temperature measuring device such as a temperature sensor installed at a specific location, and the fluid temperature is calculated from the actual measured temperature of the equipment as necessary. s Alternatively, the temperature of the fluid or equipment at the predicted location can be calculated by a simulation that takes into account the operating conditions of the plant system, and the fluid temperature can be calculated from the actual measured temperature of the equipment as necessary. s It can also be written as:

[0029] Step b) can be performed by a calculation device capable of executing the calculation according to the prediction formula (2). The calculation device may be, for example, a computer with a specific calculation program installed, but is not particularly limited.

[0030] In step c), the total silica concentration C t is the total concentration of silica present in the fluid supplied to the plant system implementing the present invention. For calculation purposes, it is calculated based on the amount of silica monomer (Si(OH) 4 ) in the fluid is expressed as the total silica concentration C t Of this, the amount exceeding the silica saturation concentration Ce is thought to precipitate and adhere as silica scale. For example, in a geothermal power generation system, the total silica concentration C t can be calculated, for example, as follows. First, the geothermal water pumped from the production well is analyzed to obtain the mass or molar amount of the Si atoms in the geothermal water. Then, the mass or molar amount of the Si atoms is calculated by determining whether all of the Si atoms are silica monomers (Si(OH) 4 ) is formed, and the weight percent concentration of silica monomer in geothermal water is calculated. In the method of this embodiment, the total silica concentration C t It is assumed that the portion exceeding the saturation concentration precipitates as silica scale.

[0031] In step d), the total silica concentration C obtained in step c) t and silica saturation concentration Ce 1 The amount of silica scale adhesion can be obtained by calculating the difference between the above amounts using a calculation device. The calculation device may be a computer having a specific calculation program installed therein, as in the case of step b), but is not particularly limited.

[0032] Next, in the first embodiment, the time-dependent silica dissolved silica concentration C 1 The amount of silica scale generated at any part of the plant system is predicted based on the prediction curve. In this prediction method, the time t and the silica dissolved concentration C 1A prediction curve showing the relationship between the above and the amount of silica adhesion is obtained from the prediction curve.

[0033] Dissolved silica concentration C at time t 1 is the concentration of silica dissolved in the fluid at time t (min), with the start of polymerization set to zero. The silica concentration here is the total silica concentration C t The amount of silica monomer (Si(OH)) was calculated based on the amount of dissolved Si atoms in the fluid, similar to that described for 4 ) in the fluid in weight percent (ppm). Initial silica concentration C i is the concentration of silica dissolved in the fluid at the start of polymerization (t = 0). The initial silica concentration C i The amount of silica monomer (Si(OH)) calculated based on the amount of Si atoms dissolved in the fluid 4 ) in the fluid in weight percent concentration (ppm). Time t is expressed as Si(OH) 4 is dissolved in the fluid is set as 0 (min). In the prediction method according to the present embodiment, the time recognized as the start time of the polymerization reaction in an actual plant system can be used for prediction calculation as 0. For example, in a geothermal power generation system, the time when geothermal water is pumped up from a production well can be set as 0.

[0034] First, let us consider the time t and the silica dissolved concentration C 1 A method for obtaining a prediction curve showing the relationship between the above will be described. The method for obtaining a prediction curve includes the following steps i) to iii). i) Initial silica concentration C i The process of obtaining ii) In the three-stage precipitation equilibrium reaction model of equation (1), k 1 , k 2 , k B , k a Calculate the initial silica concentration C i and k 1 , k 2 , k B , k a From the above, the silica dissolved concentration C 1Calculating a predicted value of iii) Dissolved silica concentration C versus time t 1 By plotting and fitting the curve based on the plot results, the silica dissolved concentration C 1 A process of obtaining a predicted curve of

[0035] Step i) is the initial silica concentration C i This is the process of obtaining the initial silica concentration C i is calculated as the total silica concentration C t Therefore, the total silica concentration C can be calculated by the method described above. t In the same manner, the initial silica concentration C i can be obtained.

[0036] In step ii), k is added according to the flow chart of FIG. 1 , k 2 , k B , k a Calculate the initial silica concentration C i and k 1 , k 2 , k B , k a From the above, the silica dissolved concentration C 1 Calculate the predicted value of the dissolved silica concentration C 1 The predicted value of is preferably obtained at multiple different times t, and can be calculated, for example, at 10 or more different times t, preferably 50 or more different times, and more preferably 100 or more different times t. This allows the dissolved concentration C 1 A predicted value of can be obtained.

[0037] In step iii), the silica dissolved concentration C 1 Plot the silica dissolved concentration C based on the plot results. 1 A predicted curve of the silica dissolved concentration C obtained by step iii) is obtained. 1 This is an example of a predicted curve for the silica dissolved concentration C, which is obtained when the initial concentration is about 1100 ppm, at a temperature of 100° C. and a pH of 7. In FIG. 1The graph shows the silica concentration (unit: ppm) and the dashed line shows the amount of silica precipitation (unit: ppm). The amount of silica precipitation refers to the mass of silica tetramers generated from fluid per unit volume (1 L). When the fluid is geothermal water, the mass of silica tetramers generated from fluid per unit volume can be approximated to the mass of silica tetramers generated from fluid per unit mass (1 kg). Therefore, the silica dissolved concentration C 1 The sum of the initial silica concentration C i It becomes.

[0038] Polymerization temperature T and dissolved silica concentration C at the initial stage of the reaction 1 In order to fit the predicted value of , the frequency factor A is required. Here, the initial stage of the reaction means a stage of about 5 to 10 minutes from the start of the reaction, although it varies depending on the reaction apparatus, conditions, etc. The relationship between the polymerization temperature T and the frequency factor A is expressed by the following formula (3). A = m[exp(nT)] (3) In formula (3), m and n are constants and are values ​​obtained by the calculation described in the above flow chart. T (K) represents the polymerization reaction temperature. The temperature range of T is about 250K to 500K. More specifically, m may be 2.0 to 3.1, and n may be 0.083 to 0.085. Preferably, m may be 2.3 to 2.8, and n may be 0.0835 to 0.0845.

[0039] Figure 4 is a semi-logarithmic graph showing the predicted curve of the frequency factor A, with the vertical axis being a logarithmic scale. By using the frequency factor A, it is possible to reproduce the experimental values ​​at each temperature at the initial stage of the reaction, for example, at a time point of 5 to 10 minutes.

[0040] Silica dissolved concentration C 1 A specific method for predicting the amount of silica scale deposition based on the prediction curve will be described below. The prediction method includes the following steps A) to D). A) The time t until the silicic acid-containing fluid reaches the predicted location s (min.) B) temperature time ts and silica dissolved concentration C 1 A step of obtaining a silica dissolved concentration C at the predicted portion from the predicted curve. C) Total silica concentration in silicic acid-containing fluids C t The process of obtaining D) Total silica concentration C t and the silica dissolved concentration C 1 Calculating the amount of silica deposited at time t based on

[0041] In step A), the time t until the fluid containing silicic acid reaches the predicted site where the deposition of silica scale is to be predicted s (min.) can be calculated from the flow rate of the fluid containing silicic acid in the plant system and the distance from the point where time t = 0 to the predicted point. s can be obtained by simulation based on the plant system operation status. For example, in a geothermal power generation system, s (min.) may be the time it takes for geothermal water pumped from a production well to reach a predetermined predicted location.

[0042] Step B) is to calculate the silica dissolved concentration C from the predicted curve. 1 The calculation of can be performed by a computing device capable of executing the calculation.

[0043] Steps C) and D) can be carried out in the same manner as in steps c) and d) above. However, the total silica concentration C t is the initial silica concentration C i Therefore, the silica dissolved concentration C 1 The initial silica concentration C used in the derivation of i is the total silica concentration C t It can be calculated as:

[0044] As described above, according to the method for predicting the amount of silica scale adhesion according to the first aspect of the present embodiment, it is possible to predict the silica saturation concentration Ce at a desired portion without needing empirical values ​​such as experimental values ​​or actual measured values. 1 and / or dissolved silica concentration C 1It is possible to predict the amount of silica scale formation, which can be handled under complex conditions in a short time and at a low budget.

[0045] (Second aspect) Next, in the second aspect of the method according to the present embodiment, the saturation concentration Ce of silica depending on the temperature T and pH is calculated. 2 The amount of silica scale generated at any part of the plant system is predicted based on the prediction formula. In the second embodiment, a prediction formula is provided that is particularly useful when the pH of the fluid in which silicic acid is dissolved is 0 or more and less than 7. Therefore, the prediction formula according to this embodiment may also be referred to as a prediction formula for the acidic region. The silica saturation concentration Ce given by the prediction formula of this embodiment is 2 refers to the weight percent concentration (unit: ppm) of a solution in which silica that can be produced by the above-mentioned condensation polymerization reaction of silicic acid dissolves and reaches a saturated solution at a given temperature T and pH. In other words, it refers to the maximum concentration at which silica can dissolve at a given temperature T and pH. The definitions of silicic acid, silica, and silica scale are the same as those in the first embodiment.

[0046] Figure 5 shows the silica saturation concentration Ce 2 and silica dissolved concentration C 2 This is a flow chart of the calculation. The calculation formula for the acidic region is also derived based on the three-stage precipitation equilibrium reaction model of silica polymerization, represented by the above formula (1). Silica acid dissociation constant k a Formula for calculating pk a =pΔG+q, and the preferred values ​​of the constants p and q are also similar to those in the first embodiment.

[0047] Saturation concentration of the acidic region according to the second embodiment Ce 2 is calculated as shown in the following formula (4) based on the relationship between the polymerization reaction temperature T and the effective activity coefficient R. Ce 2 =R{a 2 [exp(b 2 T)]} (4) (In formula (4), a 2 , b 2 is a constant, and k1 , k 2 , k B , k a T(K) is the polymerization reaction temperature. R is the effective activity coefficient, which is calculated based on pH.

[0048] Based on the specific calculation results, for example, a 2 is 16 to 36, and b 2 may be 0.003 to 0.015. 2 is 18-35, b 2 may be 0.005 to 0.012. Most preferably, a 2 is 20 to 33, and b 2 may be 0.006 to 0.010. The temperature range of T may be about 250K to 500K.

[0049] R can be calculated based on the following formula and is a coefficient that determines the effect of pH in the acidic range (pH 0 or more and less than 7) on the silica saturation concentration. -logR = A R Z 2 {E / (1+B R cE)} (5) {In formula (5), A R , B R is a value calculated based on the Debye-Huckel theory from the temperature T of the silica polymerization reaction system and the dielectric constant ε of water, which is the silica polymerization reaction solvent, The charge number Z is 1 or 2, the effective diameter coefficient c is 4, E is the effective ionic strength represented by the following formula (6), and can be expressed by the following formula. E = {I+(hydrogen ion concentration)} / [1+B R c[I+(hydrogen ion concentration)](6) (In formula (6), I is the solute ionic strength.)

[0050] More specifically, A R , B R can be expressed by the following formula: AR =1.825*10 6 (εT) -3 / 2 B R =50.3*(εT) -1 / 2 ε represents the dielectric constant of water at temperature T, and T(K) represents the polymerization reaction temperature.

[0051] The charge number Z is 1 or 2, and in the case of monovalent ions of silica monomers and dimers (Si(OH) 3 O - , Si 2 O 2 (OH) 5 - ) is 1, and in the case of divalent ions of silica monomer and dimer (SiO 2 (OH) 2 2- , S i 2 O 3 (OH) 4 2- ) is 2. The effective size coefficient c is a constant 4 in the polymerization reaction of silica.

[0052] The solute ionic strength I is determined from the following formula: I=1 / 2*(Ct+(hydrogen ion concentration))*Z 2 In the formula, Ct is the total concentration of silica (unit: mol / L), and Z represents the number of charges on the solute, which is 1 or 2.

[0053] The hydrogen ion concentration can be calculated from a given pH greater than or equal to 0 and less than 7; for example, for a pH of 5.5, it is 10^(-5.5).

[0054] Figure 6 shows the silica saturation concentration Ce 2FIG. 6 shows a predicted curve at pH 5.5 based on the prediction formula according to the second embodiment of the present invention, and a predicted curve at pH 7.0 (in the first embodiment). As shown in FIG. 6, according to the second embodiment, different predicted curves are obtained when the pH is different. Although not shown, the prediction formula according to the second embodiment can be derived by the above method at each pH in the range of 0 or more and less than 7, and a predicted curve can be drawn. On the other hand, the predicted curve of the comparative example was obtained based on the empirical rule by the method disclosed in Non-Patent Document 1, but the pH is not strictly considered, and the predicted curve is different from that of the present embodiment.

[0055] According to the prediction formula of the second aspect, the silica saturation concentration Ce 2 In the three-stage precipitation equilibrium reaction model represented by formula (1), the temperature T is the polymerization reaction temperature (unit: K). In the prediction method according to the second aspect, when predicting the amount of silica scale adhesion, the temperature T s The polymerization temperature is used as the polymerization temperature, and the effective activity coefficient R is calculated using the pH at the predicted portion, which can be used in the prediction calculation. s can be determined in the same manner as in the first embodiment. The pH at the predicted location may be the pH of a fluid that may contain silica at the predicted location in the plant system.

[0056] Next, a specific method for predicting the amount of silica scale adhesion based on formula (4) will be described. The prediction method includes the following steps a) to d). a) Temperature T at the predicted location where silica scale deposition is to be predicted s (K), and a step of acquiring pH b) Temperature T s From the pH and prediction formula (4), the silica saturation concentration Ce at the predicted portion is calculated. 2 The process of calculating c) Total silica concentration in the siliceous fluid, C t The process of obtaining d) Total silica concentration C tand silica saturation concentration Ce 2 Calculating the amount of silica deposited based on

[0057] The method for predicting the amount of silica scale adhesion can be carried out in the same manner as in the first embodiment, except that in step a) the pH at the predicted portion is obtained, and in step b) calculation is performed using prediction formula (4). The pH value at the predicted portion can be measured using a normal pH meter, or can be calculated using a method such as simulation.

[0058] According to the method for predicting the amount of silica scale adhesion of the present embodiment, it is possible to predict the amount of silica scale adhesion according to the acidic pH condition of a fluid in which silica scale is a problem, and more accurate prediction is possible compared to the conventional techniques.

[0059] Next, in the second embodiment, the time-dependent silica dissolved concentration C 2 The amount of silica scale generated at any part of the plant system is predicted based on the prediction curve. In this prediction method, the time t and the silica dissolved concentration C 2 A prediction curve showing the relationship between the time and the silica deposition amount is calculated from the prediction curve. 2 The method for obtaining the prediction curve includes the following steps i) to iii). i) Initial silica concentration C i The process of obtaining ii) In the three-stage precipitation equilibrium reaction model of equation (1), k 1 , k 2 , k B , k a Calculate the effective activity coefficient R and the initial silica concentration C i and k 1 , k 2 , k B , k a , R, silica dissolved concentration C 2 Calculating a predicted value of iii) Dissolved silica concentration C versus time t 2 By plotting and fitting the curve based on the plot results, the silica dissolved concentration C2 A process of obtaining a predicted curve of

[0060] In the second embodiment, the silica dissolved concentration C 2 The method for obtaining the predicted curve of the silica dissolved concentration C 2 The calculation of the predicted value of may be the same as that of the first embodiment, except that it is necessary to calculate the effective activity coefficient R of the prediction formula (4) taking into account the pH condition. In addition, the calculation method of the frequency factor A and the preferable values ​​of the constants m and n that determine the frequency factor may also be the same as those of the first embodiment.

[0061] FIG. 7 shows the silica dissolved concentration C obtained by steps i) to iii) of the second embodiment. 2 7 is an example of a predicted curve for the case where the initial concentration is about 1300 ppm, the temperature is 150° C., and the pH is 5.5. In FIG. 7, the solid line represents the dissolved silica concentration C (unit: ppm), and the dashed line represents the amount of precipitated silica (unit: ppm).

[0062] Silica dissolved concentration C 2 A specific method for predicting the amount of silica scale buildup based on the prediction curve of the silica dissolved concentration C 2 The steps may be the same as steps A) to D) of the first embodiment, except that the calculation is performed using the predicted curve of

[0063] As described above, according to the method for predicting the amount of silica scale adhesion according to the second aspect of the present embodiment, it is possible to predict the silica saturation concentration Ce, which depends on the temperature and pH at a desired portion, without requiring empirical values ​​such as experimental values ​​or actual measured values. 2 and / or dissolved silica concentration C 2 It is possible to predict the amount of silica scale formation that can be handled under complex conditions in a short time and with a low budget. In particular, it is possible to predict the amount of silica scale formation that takes into account the polymerization reaction of silica in the acidic pH range.

[0064] (Third aspect) Next, in the third aspect of the method according to the present embodiment, the saturation concentration Ce of silica depending on the temperature T and pH is calculated.3 The amount of silica scale generated at any part of the plant system is predicted based on the prediction formula. In the third embodiment, a prediction formula is provided that is particularly useful when the pH of the fluid in which silicic acid is dissolved is greater than 7 and equal to or less than 14. Therefore, the prediction formula according to this embodiment is also referred to as a prediction formula for the basic region. The silica saturation concentration Ce given by the prediction formula of the third embodiment is 3 are the same as in the second aspect, and the definitions of silicic acid, silica, and silica scale are the same as in the first aspect.

[0065] Figure 8 shows the silica saturation concentration Ce 3 and silica dissolved concentration C 3 This is a flow chart of the calculation. The basic region prediction formula is also derived based on the three-stage precipitation equilibrium reaction model of silica polymerization, represented by the above formula (1). Acid dissociation constant k a Formula for calculating pk a =pΔG+q is the same as in the first embodiment, and the preferable values ​​of the constants p and q are also the same.

[0066] The saturation concentration of the basic region according to the third embodiment, Ce 3 is calculated as shown in the following formula (7) based on the relationship between the polymerization reaction temperature T and the effective reaction coefficient J. Ce 3 =(1-J)[a 3 {exp(b 3 T)}] (7) (In formula (7), a 3 , b 3 is a constant, and k 1 , k 2 , k B , k a where T(K) represents the polymerization reaction temperature. J is the effective reaction coefficient, which is calculated based on the fraction of silica monomer ions and silica dimer ions.

[0067] Based on the specific calculation results, for example, a 3 is 6 to 34, and b 3 may be 0.005 to 0.015.3 is 8 to 32, and b 3 may be 0.005 to 0.015. Most preferably, a 3 is 10 to 30, and b 3 may be 0.006 to 0.009, and the temperature range of T may be approximately 250K to 500K.

[0068] J can be calculated based on the following formula, and is a coefficient that determines the effect of pH in the basic region on the silica saturation concentration. It is based on the discovery by the inventors that in the basic region, ions are not directly involved in the polymerization reaction of silica, and is determined by the fraction of silica in a non-ionized molecular state. The effective reaction coefficient J can be expressed by the following formula (8). J=(X-Xi 1 -Xi 2 ) / X (8) In the formula, X is the total amount of silica (molar amount, 100%), and Xi 1 , Xi 2 is the molar fraction of silica monomer ions and silica dimer ions, and can be calculated from the acid dissociation constant ka. Silica monomer ions are Si(OH) 3 O - , silica dimer ion is Si 2 O 2 (OH) 5 - The acid dissociation constant k aj is the equilibrium constant when considering the dissociation reaction in which protons (hydrogen ions) are released from silica monomer, silica dimer, and silica tetramer molecules.

[0069] J is a number between 0 and 1, and varies with pH between 7 and 14. A graph of the change in J versus pH is shown in Figure 9. Based on the graph in Figure 9, the effective reaction coefficient J at a specific pH in the basic region can be obtained.

[0070] Figure 10 shows the silica saturation concentration Ce 310 is an example of the formula (7) representing the predicted curve of. A predicted curve at pH 9.0 based on the prediction formula according to the third aspect of the present invention and a predicted curve at pH 7.0 (in the first aspect) are shown. Although not shown, the prediction formula according to the third aspect can be derived by the above method at each pH in the range of pH 7 to 4, and a predicted curve can be drawn. A predicted curve at pH 5.5 based on the prediction formula according to the second aspect is also shown in the graph. As shown in FIG. 10, according to the third aspect, different predicted curves are obtained when the pH is different. On the other hand, the predicted curve of the comparative example was obtained based on the empirical rule according to the method disclosed in Non-Patent Document 1, but the pH is not strictly considered, and the predicted curve is different from that of this aspect.

[0071] According to the prediction formula of the third aspect, the silica saturation concentration Ce 3 The temperature T and pH dependency of the silica scale deposition amount can be calculated. In the three-stage precipitation equilibrium reaction model represented by formula (1), the temperature T is the polymerization reaction temperature (unit: K). In the prediction method according to the third aspect, each step of predicting the silica scale deposition amount is performed by calculating the silica saturation concentration Ce 3 is calculated based on formula (7). The method for predicting the amount of silica scale adhesion according to the third embodiment makes it possible to predict the amount of silica scale adhesion according to the basic pH conditions of a fluid in which silica scale is a problem, and in particular makes it possible to accurately predict the amount of silica scale adhesion in a basic fluid.

[0072] In the third embodiment, as in the second embodiment, the time-dependent silica dissolved concentration C 3 Based on the prediction curve, the amount of silica scale generated at any part of the plant system can be predicted. In this prediction method, the time t and the silica dissolved concentration C 3 A prediction curve showing the relationship between the time and the silica deposition amount is calculated from the prediction curve. 3 In each step of the method for obtaining the predicted curve, in step ii) of the second embodiment, k 1 , k 2 , k B , k aCalculate the effective reaction coefficient J and the initial silica concentration C i and k 1 , k 2 , k B , k a , J, silica dissolved concentration C 3 This is the same as the second embodiment, except that the predicted value of the silica dissolved concentration C 3 The calculation of the predicted value of may be the same as that of the first embodiment, except that it is necessary to calculate the effective reaction coefficient J of the prediction formula (7) taking into account the alkaline pH condition. In addition, the calculation method of the frequency factor A and the preferable values ​​of the constants m and n that determine the frequency factor may also be the same as those of the first embodiment.

[0073] FIG. 11 shows the silica dissolved concentration C obtained by steps i) to iii) similar to the second embodiment. 3 This is an example of a predicted curve for the silica dissolved concentration C, which is obtained when the initial concentration is about 1050 ppm, at a temperature of 100° C. and a pH of 9. In FIG. 3 The dashed dotted line represents the amount of silica precipitation (unit: ppm).

[0074] As described above, according to the method for predicting the amount of silica scale adhesion according to the third aspect of the present embodiment, it is possible to predict the silica saturation concentration Ce, which depends on the temperature and pH at a desired portion, without requiring empirical values ​​such as experimental values ​​or actual measured values. 3 and / or dissolved silica concentration C 3 It is possible to predict the amount of silica scale formation that can be handled under complex conditions in a short time and with a low budget. In particular, it is possible to predict the amount of silica scale formation that takes into account the polymerization reaction of silica in the basic pH range.

[0075] [Second embodiment: Prediction system for silica scale formation amount] According to a second embodiment, the present invention provides a system for predicting the amount of silica scale deposition, which includes the following: Temperature T at the predicted location where silica scale deposition should be predicted s(K), and / or the time it takes for the silicic acid-containing fluid to reach the predicted location t s (min.) Acquisition device Temperature dependent silica saturation concentration Ce 1 , Ce 2 , or Ce 3 and / or time-dependent silica dissolved concentration C 1 , C 2 , or C 3 An apparatus for calculating the amount of silica deposition at the predicted portion based on the predicted curve.

[0076] In the second embodiment, the silica saturation concentration Ce 1 , Ce 2 , or Ce 3 Prediction formula for silica dissolved concentration C versus time 1 , C 2 , or C 3 The predicted curve of temperature T can be obtained in the same manner as in the first to third aspects of the first embodiment, and the description thereof will be omitted. s (K), and / or time t s The apparatus for acquiring the amount of silica adhered (min.), the apparatus for calculating the amount of silica adhered, and the apparatus for measuring pH can also be selected from the same options as the apparatuses specifically listed for carrying out each step in each aspect of the first embodiment.

[0077] The system for predicting the amount of silica scale formation according to this embodiment can be incorporated into various plant systems, making it possible to predict the amount of silica scale formation suited to the conditions of the plant system.

[0078] [Third embodiment: geothermal power generation system] According to a third embodiment, the present invention relates to a geothermal power generation system, A gas-liquid separator that separates the geothermal fluid pumped from the production well into a gas component and a liquid component; a turbine disposed downstream of the gas-liquid separator and configured to be rotatable by the gas components separated by the gas-liquid separator; A pipe for delivering the liquid component separated by the gas-liquid separator to a reinjection well; A system for predicting the amount of silica scale formation according to a second embodiment Equipped with.

[0079] Fig. 12 is a conceptual diagram illustrating a geothermal power generation system according to the third embodiment. Referring to Fig. 12, the geothermal power generation system 1 is mainly composed of a production well 6, a gas-liquid separator 2, a turbine 3, a generator 4, a condenser 5, a reinjection well 7, and a prediction system for the amount of silica scale generation. The prediction system for the amount of silica scale generation is the system described in the second embodiment, and is a system capable of implementing the prediction method described in the first embodiment.

[0080] The flow of materials in the geothermal power generation system 1 will be described. The production well 6 is a well that draws out hot water, steam, or a mixture thereof (hereinafter referred to as geothermal fluid) from a geothermal reservoir underground into the ground. The geothermal fluid drawn out from the production well 6 is separated into steam, which is a gas component, and hot water, which is a liquid component, in the gas-liquid separator 2. The separated steam is guided to the turbine 3 and used to rotate the turbine 3, and electricity is produced in the generator 4. The steam that has passed through the turbine 3 is cooled in the condenser 5 and guided to the reinjection well 7 through a pipe not shown. On the other hand, the hot water separated in the gas-liquid separator 2 is cooled and guided to the reinjection well 7. Note that there are two possible modes: the steam separated in the gas-liquid separator 2 directly rotates the turbine, and the steam heats a low boiling point solvent, which then rotates the turbine. In the present invention, when the term "turbine configured to be rotatable by the gas component separated in the gas-liquid separator" is used, both of these modes are included.

[0081] The predicted portion in the plant system where the deposition of silica scale should be predicted is not particularly limited, and may be any portion to which geothermal fluid may deposit. The predicted portion may be, but is not limited to, the turbine component exemplified in the first embodiment. The predicted portion may be a component not specifically shown in FIG. 12. The predicted portion may be one location or two or more locations in the plant system, and theoretically there is no upper limit to the number of predicted portions.

[0082] According to the geothermal power generation system of this embodiment, it is possible to accurately predict the amount of silica scale adhesion, and it is possible to minimize system shutdowns and perform maintenance at appropriate times, thereby enabling stable and highly efficient power generation. In particular, it is possible to predict the amount of silica scale adhesion taking into account the pH of the geothermal fluid flowing through the geothermal power generation system. EXAMPLES

[0083] The present invention will be described in more detail below with reference to examples of the present invention. However, the present invention is not limited to the scope of the following examples.

[0084] As a reaction model of the silica polymerization reaction in hot water, the formula (1) was used, and a model corresponding to the silica polymerization reaction was created using the reaction module of calculation software (COMSOL Multiphysics (registered trademark) modeling software).

[0085] (1) Calculation results according to the first mode Using the density functional method of first-principles calculations, the ΔG n was calculated. n represents the order of the polymerization reaction, and calculations were performed for the first stage (n=1), which is the polymerization reaction of the monomer, and the second stage (n=2), which is the polymerization reaction of the dimer. Based on the definition of thermodynamics, ΔG n From the equilibrium constant k 1 , k 2 was calculated. [ka]

[0086] Calculated ΔG of silica acid dissociation reaction n The pKa was calculated using the acid dissociation constant prediction formula for silica established by the applicant, and the Ka was calculated using a general definition formula for the acid dissociation constant. The results are shown in Table 1, in comparison with the comparative example, which is a conventional method, and experimental values. [Table 1]

[0087] By the way, the acid dissociation reaction shown below [ka] where HA is the general formula for an acid. Based on the definition of the acid dissociation constant, the acid dissociation constant is calculated as follows: [ka] Since the proton has no electron, G(H + ) cannot be calculated, so in the comparison example, we use the approximate G(H 3 O + ) was substituted to calculate ΔG. On the other hand, the experimental value is the literature value of the acid dissociation constant of the monomer.

[0088] The formula derived from the chemical reaction model is the ionization equilibrium constant k B , and the precipitation equilibrium constant k sp It could be calculated as follows: [ka] The above parameters and frequency factor A are substituted into the software to obtain the silica dissolved concentration C 1 The predicted curve of the silica dissolved concentration C was obtained. 1 From the predicted curve, the saturation concentration was estimated at the equilibrium state.

[0089] Dissolved silica concentration at T = 373.15K C 1An example of a predicted curve is shown in Figure 3. Here, the dissolved experimental value indicates the saturation concentration of silica based on the results of a hydrothermal synthesis experiment using a small-scale experimental device to simulate the fluid of a power generation facility. The comparative example shows the saturation concentration of silica predicted by a conventional method. With the conventional method, it is not possible to obtain calculation results with time dependency, so only one point is plotted.

[0090] A variance analysis was performed on the obtained saturation curve, and a prediction formula for the silica saturation concentration was established. The prediction formula is expressed by the above formula (2). The predicted values ​​of the saturation concentration (Example) were compared with the calculation results and experimental values ​​of the comparative example described above, and the established saturation concentration prediction formula was verified. In FIG. 2, the solid line is the calculation result of the Example, the dashed line is the calculation result of the Comparative Example, and the white circle is the experimental value. From FIG. 2, it was shown that the predicted values ​​of the Example by this method matched well with the experimental values, and accurate prediction was possible.

[0091] A method for correcting the frequency factor A required for fitting the initial reaction concentration was devised, and an analysis of variance was performed. The frequency factor A was plotted at pH 7 under temperature conditions of 373.15 K, 423.15 K, and 448.15 K. The results are shown in Figure 4. From Figure 4, equation (3) was obtained, and an equation showing the temperature dependence of the frequency factor A was established.

[0092] (2) Calculation results according to the second method In the second embodiment, the same k as in the first embodiment 1 , k 2 , k B , k a The calculation was performed using the effective activity coefficient R and the effective activity coefficient ε = 55.72 [F / m] for T = 373.15 [K], C t =1103.07[ppm], I=0.006[mol / L], A R =0.609, B R = 0.349, and R was calculated to be 0.908. For T = 423.15 [K], ε = 44.24 [F / m], C = 1335.43 [ppm], I = 0.007 [mol / L], A R =0.713, B R= 0.368, and R was calculated to be 0.885. For T = 448.15 K, ε = 39.20 F / m, C = 1474.43 ppm, I = 0.008 mol / L, and A R =0.784, B R = 0.380, and the R was calculated to be 0.869.

[0093] Dissolved silica concentration at 150℃ (423.15K) and pH 5.5 C 2 An example of the predicted curve is shown in FIG. 7. The experimental dissolution values ​​were the same as those in the dissolution experiment according to the first embodiment, except that the dissolution experiment was carried out at pH 5.5. A variance analysis was performed on the obtained saturation curve, and a prediction formula for the silica saturation concentration was established. The same value as in the first embodiment was used for the frequency factor A. The prediction formula is expressed by the above formula (4). The plot of the experimental dissolution values ​​was in good agreement with the predicted values ​​at pH 5.5 by this method, indicating that accurate prediction was possible.

[0094] (3) Calculation results according to the third method In the third embodiment, the same k as in the first embodiment 1 , k 2 , k B , k a The calculation was performed using the value of and the effective reaction coefficient J. The parameters used in deriving the effective reaction coefficient J were Xi1 = 15.20 mol%, Xi2 = 27.35 mol%, and X = 100, and the final J was calculated to be 0.575.

[0095] Dissolved silica concentration at 100℃ (373.15K) and pH 9.0 C 3 An example of the predicted curve is shown in FIG. 11. The experimental dissolution values ​​were the same as those in the dissolution experiment according to the first embodiment, except that the dissolution experiment was carried out at pH 9.0. A variance analysis was performed on the obtained saturation curve, and a prediction formula for the silica saturation concentration was established. The same value as in the first embodiment was used for the frequency factor A. The prediction formula is expressed by the above formula (7). The plot of the experimental dissolution values ​​was in good agreement with the predicted values ​​at pH 9.0 by this method, indicating that accurate prediction was possible. [Explanation of symbols]

[0096] 1 Geothermal power plant, 2 Gas-liquid separator, 3 Turbine 4 generator, 5 condenser, 6 production well, 7 injection well

Claims

1. The temperature T at the predicted location where the deposition of silica scale is to be predicted ｓ (K), and / or the time it takes for the fluid containing silicic acid to reach the predicted site t ｓ (min.); calculating the amount of silica attached at the predicted portion based on a prediction equation for a silica saturation concentration depending on temperature and / or a prediction curve for a silica dissolved concentration depending on time; Including, The prediction equation for the silica saturation concentration and the prediction curve for the silica dissolved concentration are a three-stage precipitation equilibrium reaction model represented by the following formula (1): 【Chemistry 1】 (In formula (1), k １ is Si(OH) ４ and SiOSi(OH) ６ is the reaction equilibrium constant between k ２ is SiOSi(OH) ６ and (SiO)3 Si(OH) １０ is the reaction equilibrium constant between k Ｂ is SiOSi(OH) ６ and (SiO) ３ Si(OH) ９ O － is the ionization equilibrium constant between k ａ is (SiO) ３ Si(OH) ９ O － and (SiO)3 Si(OH) １０ is the silica acid dissociation constant between In k １ , k ２ , k Ｂ , k ａ is obtained based on (a) the predicted curve of the silica dissolved concentration C is obtained by fitting a plot of the silica dissolved concentration at two or more different time points obtained by the first principle calculation based on the initial silica concentration C i and the formula (1); The frequency factor A used to correct the fitting at the beginning of the reaction is A=m[exp(nT)] (3) (In formula (3), m and n are constants and are calculated based on k 1 , k 2 , k B , and k a .) Represented by: (b) The prediction formula for the silica saturation concentration Ce is: Ce 1 =a 1 [exp(b 1 T)] (2) (In formula (2), a 1 and b 1 are constants calculated based on k 1 , k 2 , k B , and k a ; T represents the polymerization reaction temperature. Represented by: (c) The prediction formula for the silica saturation concentration Ce 2 is: Silica saturation concentration Ce 2 at a temperature T and a pH of 0 or more and less than 7: Ce 2 =R{a 2 [exp(b 2 T)]} (4) (In formula (4), a 2 and b 2 are constants calculated based on k 1 , k 2 , k B , and k a ; R is the effective activity coefficient calculated based on pH; T represents the polymerization reaction temperature. or (d) The prediction formula for the silica saturation concentration Ce 3 is as follows: Silica saturation concentration Ce 3 at a temperature T and a pH greater than 7 and equal to or less than 14: Ce 3 = (1-J) {a 3 [exp(b 3 T)]} (7) (In formula (7), a 3 and b 3 are constants calculated based on k 1 , k 2 , k B , and k a ; J is an effective reaction coefficient calculated based on the fraction of silica monomer ions and silica dimer ions present, T represents the polymerization reaction temperature. A method for predicting the amount of silica scale formation, expressed as:

2. The silica acid dissociation constant k ａ But (SiO) ３ Si(OH) ９ O － and (SiO)3 Si(OH) １０ The method according to claim 1, wherein the free energy change ΔG in an equilibrium reaction with is obtained by quantum chemical calculation and linear fitting correction method.

3. The silica acid dissociation constant k ａ and the free energy change ΔG is pk ａ =pΔG+q (wherein p and q are constants) The method according to claim 2 , wherein

4. 4. The method of claim 3, wherein p is from 0.19 to 0.24 and q is from −56 to −51.

5. The method according to claim 1, wherein m in formula (3) of (a) is 2.0 to 3.1, and n is 0.083 to 0.

085.

6. In the formula (2) of (b), １ is 18 to 32, and b １ The method according to claim 1, wherein is 0.005 to 0.

010.

7. The calculation formula for the effective activity coefficient R in the formula (4) of (c) is -logR= A Ｒ Z ２ {E / (1+B) Ｒ (cE)} (5) {In formula (5), A Ｒ 111122251 ６ (εT) －３／２ 、 B Ｒ =50.3*(εT) －１／２ It is expressed as The charge number Z is a constant selected from 1 or 2, the effective diameter coefficient c is 4, E is the effective ionic strength represented by the following formula (6): E = {I + (hydrogen ion concentration)} / [1 + B Ｒ c [I+ (hydrogen ion concentration)] (6) (In formula (6), I is the solute ionic strength.) is The method of claim 1 , wherein

8. In the formula (4) of (c), ２ is 16 to 36, and b ２ The method according to claim 1, wherein is 0.003 to 0.

015.

9. The calculation formula for the effective reaction coefficient J in the formula (7) of (d) is J=(X-Xi 1 -Xi ２ ) / X (8) (In formula (8), X is the total amount of silica, Xi 1 is the acid dissociation constant k ａｊ is the fraction of silica monomer ions calculated from Xi ２ , acid dissociation constant k ａｊ (The fraction of silica dimer ions is calculated from The method of claim 1 , wherein

10. In the formula (7) of (d), ３ is 6 to 34, and b ３ The method according to claim 1, wherein is 0.005 to 0.

015.

11. The total silica concentration C in the silicic acid-containing fluid ｔ and obtaining The total silica concentration C ｔ and calculating the silica deposition amount based on the silica saturation concentration. The method of claim 1 , wherein the silica deposition amount is predicted by:

12. The method of claim 1 , wherein the amount of silica deposition is predicted by calculating the amount of silica deposition based on a predicted curve of the dissolved silica concentration.

13. The temperature T at the predicted location where the deposition of silica scale is to be predicted ｓ (K), and / or the time it takes for the fluid containing silicic acid to reach the predicted site t ｓ (min.) and A device for calculating the amount of silica adhesion at the predicted portion based on the method for predicting the amount of silica scale formation according to claim 1; A system for predicting the amount of silica scale formation, comprising:

14. A gas-liquid separator that separates the geothermal fluid pumped from the production well into a gas component and a liquid component; a turbine disposed downstream of the gas-liquid separator and configured to be rotatable by the gas components separated by the gas-liquid separator; A pipe for delivering the liquid component separated by the gas-liquid separator to a reinjection well; The system for predicting the amount of silica scale formation according to claim 13; A geothermal power generation system comprising:

Images