Reverse quantization-based nuclear reactor safety injection system optimization method

Abstract

The invention belongs to the technical field of reactor thermal hydraulics, and particularly relates to a nuclear reactor safety injection system optimization method based on reverse quantization. Comprising the following steps: determining a minimum injection flow demand, a maximum design parameter range of the safety injection system, and trigger and input logic of each device of the safety injection system; constructing a rapid calculation method for the injection flow of the safety injection system; determining an initial state and a transfer matrix of the Markov chain; markov chain samples are extracted to serve as design parameter values of all devices; comparing the flow calculation value with the minimum flow demand, and judging whether the Markov chain accepts transfer based on the Bayesian theory; and carrying out statistical analysis on the Markov chain to obtain an uncertainty distribution interval of each parameter. The method has the beneficial effects that the coolant loss accident phenomenon is analyzed, the coolant flow demand after the safety injection system is put into use is determined, the operation mode and hydraulic flow characteristics of the safety injection system are analyzed, and the rapid calculation method for the injection flow of the safety injection system is constructed.

Description

Technical Field

[0001] The present invention belongs to the technical field of reactor thermal-hydraulics, and particularly relates to an optimization method for the emergency core cooling system of a nuclear reactor based on reverse quantization. Background Art

[0002] The safety of nuclear reactors is the lifeline of nuclear energy development. According to the requirements of the "Design Safety Code for Nuclear Power Plants" (HAF102 - 2016), it is necessary to ensure the realization of three basic safety functions: controlling reactivity, removing the residual heat of the reactor core, and containing and limiting the radioactive release of accidents under all states of nuclear power plants. Among them, for the loss-of-coolant accident, due to the loss of the primary coolant, the premise of ensuring the cooling of the reactor core is to ensure the core flooding and the water inventory of the primary loop. An emergency core cooling system, also known as the emergency injection system, needs to be set up. If the break is large enough to rely on the break flow to remove the residual heat of the reactor core, the long-term cooling by the emergency injection system is used to maintain the safety of the reactor core; if the break flow is not sufficient to remove the residual heat of the reactor core, while the emergency injection system replenishes the water inventory of the primary loop, the residual heat removal system is also required to cool the reactor core. The means of cooling the reactor core must ensure that the cladding or fuel integrity parameters do not exceed the limits during the accident, and the reactor core cooling can be maintained for a sufficient long time.

[0003] Since most conventional nuclear reactors are pressurized water reactors with relatively high operating pressures, they will experience a pressure relief process from high pressure to low pressure during a loss-of-coolant accident. Therefore, three types of emergency injection equipment, namely high-pressure emergency injection, medium-pressure emergency injection, and low-pressure emergency injection, are set up for the loss-of-coolant accident. In addition, there are also related equipment required for the long-term cooling stage. The design of these equipment has always been an important part of the nuclear reactor design. According to different reactor types, the high-pressure emergency injection can be mainly divided into two categories: emergency injection pumps or passive core makeup tanks; the medium-pressure emergency injection is mainly a pressurized accumulator tank; and the low-pressure emergency injection can be mainly divided into two types: emergency injection pumps or passive refueling water tanks. Among them, for the design of the emergency injection pump, it is only necessary to ensure that the pump can inject a sufficient amount of coolant into the reactor coolant system. Therefore, the design and optimization difficulties of the nuclear reactor emergency injection system mainly focus on the design of passive core makeup tanks, pressurized accumulator tanks, and passive refueling water tanks.

[0004] Currently, the design method for the nuclear reactor emergency injection system is relatively passive. First, the design parameters such as the geometric structure of each system equipment are given, and then a detailed model of the reactor is established using a thermal-hydraulic system program to demonstrate the safety and conservatism of the equipment design in a loss-of-coolant accident. If the equipment design cannot meet the safety requirements of the reactor, the plan needs to be repeatedly modified and modeled for analysis. This iterative process is time-consuming and laborious, and it is difficult to carry out economic optimization. Therefore, it is necessary to develop an efficient optimization method for the nuclear reactor emergency injection system to guide the design and optimization of the emergency injection system equipment and improve the economy. Summary of the Invention

[0005] The object of the present invention is to provide an optimization method for the emergency core cooling system of a nuclear reactor based on inverse quantization, which can be used to guide the design and optimization of the equipment of the emergency core cooling system and significantly improve the economy.

[0006] The technical solution of the present invention is as follows: An optimization method for the emergency core cooling system of a nuclear reactor based on inverse quantization, comprising the following steps:

[0007] Step 1: Determine the minimum injection flow rate requirement;

[0008] Step 2: Determine the maximum design parameter range of the emergency core cooling system;

[0009] Step 3: Sort out the triggering and input logic of each device in the emergency core cooling system;

[0010] Step 4: Construct a rapid calculation method for the injection flow rate of the emergency core cooling system;

[0011] Step 5: Determine the length of the Markov chain;

[0012] Step 6: Determine the initial state and transition matrix of the Markov chain

[0013] Step 7: For each node in the Markov chain, execute Steps 8 to 11 until the length of the Markov chain reaches the length of the Markov chain determined in Step 5;

[0014] Step 8: Extract samples of the Markov chain as the design parameter values of each device;

[0015] Step 9: Use the rapid flow rate calculation method constructed in Step 4 to calculate the injection flow rate value of the emergency core cooling system in the current design state;

[0016] Step 10: Compare the calculated flow rate value with the minimum flow rate requirement, and judge whether the Markov chain accepts the transfer based on Bayesian theory;

[0017] Step 11: Increment the current length of the Markov chain by one;

[0018] Step 12: Conduct a statistical analysis on the Markov chain to obtain the uncertainty distribution interval of each parameter.

[0019] In the said Step 1,

[0020] The total core heat Q = residual fission energy + decay heat + metal heat storage;

[0021] The enthalpy rise of the emergency core cooling coolant = the enthalpy value of the gas phase at the reactor outlet * the gas phase fraction at the outlet + the enthalpy value of the liquid phase at the reactor outlet * the liquid phase fraction at the outlet - the enthalpy value of the liquid phase at the reactor inlet;

[0022] The injection flow rate requirement = the total core heat Q / the enthalpy rise of the emergency core cooling coolant.

[0023] In step 2, the design parameters of the emergency core cooling system include the shape, height, inner diameter, water filling volume, and pressure of each structural device. The maximum design parameter range of the emergency core cooling system is determined based on engineering experience and the limitations of the actual plant.

[0024] In step 4, the coolant injection process of the emergency core cooling system, such as the passive core makeup tank, accumulator injection tank, and passive refueling water tank, follows the basic fluid flow law, which is single-phase or two-phase liquid flow based on the pressure difference. By calculating the injection driving head of each device in the emergency core cooling system and combining with the resistance coefficient of the injection pipeline, the injection flow rate of each device in the emergency core cooling system is calculated using the Darcy formula in the form shown in Equation (1):

[0025] ΔP=R·q 2 (1)

[0026] In the formula, ΔP represents the total driving head, R represents the resistance coefficient of the injection pipeline of the emergency core cooling system, and q represents the injection flow rate.

[0027] In step 5, the length of the Markov chain to be constructed in uncertainty quantification is determined, and the length is not less than 10,000.

[0028] In step 8, based on the transition matrix determined in step 6, the design parameter values of each device in the current state are extracted using the random sampling method. The devices include the emergency core cooling system such as the passive core makeup tank, accumulator injection tank, and passive refueling water tank. These design parameter values are all the design parameters determined in steps 2 and 3. The design parameters include the shape, height, inner diameter, water filling volume, and pressure of each structural device, as well as the "trigger parameter" mentioned in step 3.

[0029] In step 10, the injection flow rate value of the emergency core cooling system calculated in step 9 is compared with the minimum injection flow rate requirement determined in step 1. The difference between the two injection flow rates is compared, the variance of the two injection flow rate data is calculated, and the transition probability in the Markov chain Monte Carlo algorithm is calculated based on the Bayesian theory to determine whether the current Markov chain accepts the transition.

[0030] In step 12, when the Markov chain is constructed, statistical analysis is performed on the Markov chains corresponding to each design parameter to obtain the uncertainty distribution interval of all the design parameters determined in steps 2 and 3. This interval is the interval of the emergency core cooling system equipment that makes the injection flow rate of the emergency core cooling system meet the minimum required flow rate, that is, the optimal value range of the design of the emergency core cooling system equipment.

[0031] The beneficial effects of the present invention are as follows: By analyzing the phenomena of loss-of-coolant accidents, determining the coolant flow rate requirements after the emergency core cooling system (ECCS) is put into use, and analyzing the operation mode and hydraulic flow characteristics of the ECCS, a rapid calculation method for the injection flow rate of the ECCS is constructed. Subsequently, given the design parameter ranges of all equipment, based on the constructed rapid calculation method, by using Bayesian theory and Markov chain Monte Carlo algorithm, reverse uncertainty quantification is carried out with the minimum coolant flow rate requirement as the design target value, and the uncertainty distribution intervals of the design parameters of each equipment are obtained, so as to guide the equipment design and optimal value selection of the ECCS. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 FIG. is a flow chart of an optimization method for a nuclear reactor emergency core cooling system based on reverse quantification provided by the present invention;

[0033] Figure 2 FIG. is a Markov chain diagram of the "height" and "water inventory" of a passive core makeup tank;

[0034] Figure 3 FIG. is a frequency histogram for statistical analysis of the Markov chain. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0035] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] An optimization method for a nuclear reactor emergency core cooling system based on reverse quantification provided by the present invention, based on the analysis of the operation mode and hydraulic flow characteristics of the ECCS, starting from the perspective of meeting the minimum flow rate requirement for accident safety, obtains the optimal value range for the equipment design of the ECCS through the reverse quantification technology using Bayesian theory and Markov chain Monte Carlo algorithm. Compared with the long-cycle iterative design demonstration or the only optimization algorithm such as genetic algorithm used in traditional design methods, this technology not only greatly shortens the time for the optimal design of the ECCS, but also gives an optimization design interval for actual designers to select, which helps to optimize the equipment design, reduce the equipment floor area, and lower the construction cost, etc., and has important economic significance and application value.

[0037] As Figure 1 shown, an optimization method for a nuclear reactor emergency core cooling system based on reverse quantification includes the following steps:

[0038] Step 1: Determine the minimum injection flow rate requirement

[0039] The design purpose of the safety injection system is to remove the residual heat in the core during accident conditions, including residual fission energy, decay heat, metal heat storage, etc. Therefore, the minimum injection flow rate requirement can be calculated based on the enthalpy rise of the safety injection coolant after it is injected into the core. In addition, bypass flow and corrections to meet the requirement of preventing boron crystallization in the core need to be considered.

[0040] The total core heat Q = residual fission energy + decay heat + metal heat storage;

[0041] The enthalpy rise of the safety injection coolant = the enthalpy value of the gas phase at the reactor outlet * the gas phase fraction at the outlet + the enthalpy value of the liquid phase at the reactor outlet * the liquid phase fraction at the outlet - the enthalpy value of the liquid phase at the reactor inlet;

[0042] (Note 1: The inlet is pure liquid phase, that is, the liquid phase fraction at the inlet is 100%).

[0043] (Note 2: The gas phase fraction at the outlet is determined based on the bypass flow and the requirement of preventing boron crystallization in the core. For example, if the required liquid phase fraction at the outlet to prevent boron crystallization in the core is 10%, then the gas phase fraction at the outlet can be determined to be 90% and the liquid phase fraction at the outlet is 10%);

[0044] The injection flow rate requirement = the total core heat Q / the enthalpy rise of the safety injection coolant.

[0045] Step 2: Determine the maximum design parameter range of the safety injection system

[0046] The design parameters of the safety injection system mainly include geometric structures such as the shape, height, inner diameter of each structural equipment, and state parameters such as water inventory and pressure. The maximum design parameter range of the safety injection system is determined based on engineering experience and the limitations of the actual plant. For example, if the designed length, width, and height of the plant cannot exceed 10 meters, then parameters such as the shape and height of the equipment cannot exceed this space limitation. For example, the height of the equipment cannot exceed 10 meters.

[0047] Step 3: Sort out the trigger and input logic of each equipment in the safety injection system

[0048] According to the design requirements, sort out the trigger and input logic of the safety injection system. If the trigger parameters of the equipment cannot be determined, these trigger parameters can be used as uncertain design parameters for design optimization analysis together.

[0049] The trigger and input logic of the safety injection system can be a "signal" for the safety injection to be put into operation determined by other methods. For example, when the primary loop pressure is lower than 10 MPa (for example, the actual pressure value varies depending on the reactor), trigger the injection signal of the passive core makeup tank. When the pressure further drops to 6 MPa, trigger the injection signal of the accumulator safety injection tank. When the pressure drops to 3 MPa, trigger the injection signal of the passive refueling water tank. Here, "when the system pressure is lower than a certain pressure, the safety injection is put into operation" is the trigger and input logic of the safety injection system.

[0050] Step 4: Construct a rapid calculation method for the injection flow rate of the safety injection system

[0051] During the coolant injection process of the safety injection system such as the passive core makeup tank, accumulator safety injection tank, and passive refueling water tank, it follows the basic fluid flow law, which is single-phase or two-phase liquid flow based on the pressure difference. Therefore, the injection driving head of each device in the safety injection system can be calculated, and combined with the resistance coefficient of the injection pipeline, the Darcy formula can be used to calculate the injection flow rate of each device in the safety injection system, in the form shown in Equation (1):

[0052] ΔP = R·q 2 (1)

[0053] In the formula, ΔP represents the total driving head, R represents the injection pipeline resistance coefficient of the safety injection system, and q represents the injection flow rate.

[0054] Step 5: Determine the length of the Markov chain

[0055] Determine the length of the Markov chain to be constructed in the uncertainty quantification, and the length is not less than 10,000;

[0056] The core of the Bayesian calibration method is the Bayesian formula. The typical total probability Bayesian formula is shown in Equation (2-1). When applied to model uncertainty quantification, it can be expressed as:

[0057]

[0058] In the formula, x —— a vector composed of n important parameters or sub-model uncertainty deviations; R c The definition of is shown in Equation (2-7), which represents a vector of the differences between k observed experimental data and calculated values. In Equation (2-1), since P(R c ) is not a function of x, it can be regarded as a normalization multiplier. Therefore, the above formula can be expressed as:

[0059] P(x|R c ) ∝ P(x)P(R c |x)(2-2)

[0060] In Equation (2-2), P(x) represents the prior information of important parameters or sub-model uncertainty. Generally, it is assumed that its distribution follows a normal distribution, that is, x ~ N(μ x , C x ), and when the parameters are independent of each other, it can be expressed as Therefore, P(x) can be expressed in the following form:

[0061]

[0062] In Equation (2-2), P(R c|x) represents the likelihood function. As can be known from the previous discussion, it generally follows a normal distribution R c ~N(μ tot ,σ tot 2 ). At this time, the likelihood function is:

[0063]

[0064] In the formula: μ tot The mean of the residuals between the experimental measurement values and the model calculation values; σ tot The standard deviation of the residuals between the experimental values and the calculated values. Generally speaking, σ tot mainly includes three parts, namely the experimental measurement error σ e , the model deviation σ ε and the error σ s introduced by using the surrogate model, which can be expressed as:

[0065] σ tot =σ e +σ ε +σ s (2-5)

[0066] When it is difficult to obtain the uncertainty standard deviations of the experimental measurement error and the model deviation, the maximum likelihood estimation method can be used to estimate the values of μ tot and σ tot , as follows:

[0067]

[0068] It can be calculated that the values of μ tot and σ tot are as follows:

[0069]

[0070] When there are few experimental data, the denominator terms in equations (2-8) and (2-9) need to be changed to (k-1). Substituting equations (2-3) and (2-4) into equation (2-2), the value of the posterior probability can be expressed as:

[0071]

[0072] Since μ x and C x are unknown quantities to be solved, equation (2-10) cannot be used for explicit calculation. The MCMC algorithm can be applied to this situation. Common Monte Carlo algorithms developed based on Markov chains include the Metropolis algorithm, the Gibbs algorithm, etc.

[170] , and these algorithms all have sufficient engineering applications. The Metropolis algorithm is used in the paper. The implementation steps of this algorithm combined with Bayes' formula are as follows:

[0073] 1) Given the prior mean μ of the parameter uncertainty x 0 , and the covariance matrix C is given;

[0074] 2) For times t = 1, 2,..., loop the following process

[0075] a. Randomly draw the uncertain mean μ' of the new time from the normal distribution N[μ (t-1) , C];

[0076] b. Calculate the acceptance probability

[0077] c. Generate a random number u from the uniform distribution U(0, 1), and compare the magnitudes of α and u:

[0078] If α ≥ u, then accept the transfer, i.e., μ (t) = μ';

[0079] If α < u, then do not accept the transfer, i.e., μ (t) = μ (t-1) ;

[0080] In the actual application process, it is very important to give the initial values of μ 0 and C in the above first step, especially the given value of the variance C. If the given value of C is less than the actual value, it will lead to an excessive number of samples required for the pre-burning period and the steady calculation period of the Markov chain, thereby greatly increasing the calculation cost. If the given value of C is greater than the actual value, it will lead to difficulty in the transfer of the Markov chain, making the calculation results inaccurate. Therefore, giving appropriate initial values is very important for this algorithm.

[0081] Step 6: Determine the initial state and transition matrix of the Markov chain

[0082] Step 7: For each node in the Markov chain, execute Steps 8 to 11 until the length of the Markov chain reaches the length of the Markov chain determined in Step 5;

[0083] Step 8: Draw samples of the Markov chain as the design parameter values of each device;

[0084] Based on the transition matrix determined in Step 6, use the random sampling method to draw the design parameter values of each device (devices include: passive core makeup water tank, accumulator injection tank, passive refueling water tank, etc. in the injection system) in the current state. These design parameter values are all the design parameters determined in Steps 2 and 3.

[0085] The design parameters include: geometric structures such as the shape, height, inner diameter, etc. of each structural device, as well as state parameters such as water filling volume and pressure; and the "trigger parameters" mentioned in step 3 (for example, when the pressure drops to 10 MPa to trigger the passive core makeup tank, the trigger parameter is the trigger pressure);

[0086] Step 9: Use the rapid flow calculation method constructed in step 4 to calculate the injection flow value of the safety injection system under the current design state;

[0087] Step 10: Compare the calculated flow value with the minimum flow requirement, and based on Bayesian theory, judge whether the Markov chain accepts the transfer;

[0088] Compare the injection flow value of the safety injection system calculated in step 9 with the minimum injection flow requirement determined in step 1, compare the differences between the two injection flows, calculate the variance of the two injection flow data, and calculate the transfer probability in the Markov chain Monte Carlo algorithm based on Bayesian theory to judge whether the current Markov chain accepts the transfer.

[0089] Step 11: Increment the length of the current Markov chain by one;

[0090] Step 12: Conduct a statistical analysis on the Markov chain to obtain the uncertainty distribution intervals of each parameter.

[0091] When the Markov chain is constructed, conduct a statistical analysis (such as frequency histogram, hypothesis testing method, orthogonal sequence method, etc.) on the Markov chain corresponding to each design parameter to obtain the uncertainty distribution intervals of all design parameters determined in step 2 and step 3. This interval is the interval of the safety injection system equipment that makes the injection flow of the safety injection system meet the minimum required flow, that is, the optimal value range for the design of the safety injection system equipment.

[0092] For example, as Figure 2 shown, the two Markov chains are the Markov chains of the "height" and "water filling volume" of the passive core makeup tank designed.

[0093] By conducting a statistical analysis (such as frequency histogram) on this Markov chain, statistical quantities such as the distribution map or classification type of all points can be obtained, as Figure 3 shown. The 95% confidence intervals of the "height" and "water filling volume" of the passive core makeup tank can be obtained. For example, by conducting a statistical analysis on the Markov chain, it is determined that the "height" (left figure) of the passive core makeup tank follows a normal distribution with a mean of 3 meters and a standard deviation of 0.5 meters. Then its 95% confidence interval is "mean ± two standard deviations", that is, the 95% confidence interval of the "height" of the core makeup tank is (2, 4) meters, so the design range of the "height" of the passive core makeup tank is (2, 4) meters.

Claims

1. An optimization method for the emergency core cooling system of a nuclear reactor based on inverse quantization, characterized in that, It includes the following steps: Step 1: Determine the minimum injection flow rate requirement; Step 2: Determine the maximum design parameter range of the emergency injection system; Step 3: Sort out the triggering and input logic of each device in the emergency injection system; Step 4: Construct a rapid calculation method for the injection flow rate of the emergency injection system; Step 5: Determine the length of the Markov chain; Step 6: Determine the initial state and transition matrix of the Markov chain Step 7: For each node in the Markov chain, execute Steps 8 to 11 until the length of the Markov chain reaches the length of the Markov chain determined in Step 5; Step 8: Extract samples of the Markov chain as the design parameter values of each device; Step 9: Use the rapid flow rate calculation method constructed in Step 4 to calculate the injection flow rate value of the emergency injection system in the current design state; Step 10: Compare the calculated flow rate value with the minimum flow rate requirement, and based on Bayesian theory, judge whether the Markov chain accepts the transfer; Step 11: Increment the current length of the Markov chain by one; Step 12: Conduct a statistical analysis of the Markov chain to obtain the uncertainty distribution interval of each parameter.

2. The optimization method of the nuclear reactor safety injection system based on inverse quantization according to claim 1, characterized in that: In the aforementioned Step 1, The total core heat Q = residual fission energy + decay heat + metal heat storage; The enthalpy rise of the emergency injection coolant = enthalpy value of the gas phase at the reactor outlet * gas phase fraction at the outlet + enthalpy value of the liquid phase at the reactor outlet * liquid phase fraction at the outlet - enthalpy value of the liquid phase at the reactor inlet; The injection flow rate requirement = total core heat Q / enthalpy rise of the emergency injection coolant.

3. The optimization method of the nuclear reactor safety injection system based on reverse quantization according to claim 1, wherein: In Step 2, the design parameters of the emergency injection system include the shape, height, inner diameter, water inventory, and pressure of each structural device. The maximum design parameter range of the emergency injection system is determined based on engineering experience and the limitations of the actual plant.

4. The optimization method of the nuclear reactor safety injection system based on inverse quantization according to claim 1, characterized in that: In Step 4, the coolant injection process of the emergency injection system such as the passive core makeup tank, accumulator injection tank, and passive refueling water tank follows the basic fluid flow law, which is single-phase or two-phase liquid flow based on the pressure difference. By calculating the injection driving head of each device in the emergency injection system and combining with the resistance coefficient of the injection pipeline, the injection flow rate of each device in the emergency injection system is calculated using the Darcy formula, in the form shown in Equation (1): ΔP = R·q 2 (1) In the formula, ΔP represents the total driving head, R represents the resistance coefficient of the injection pipeline of the emergency injection system, and q represents the injection flow rate.

5. The optimization method of the nuclear reactor safety injection system based on inverse quantization according to claim 1, characterized in that: In Step 5, determine the length of the Markov chain to be constructed in uncertainty quantification, and the length is not less than 10,000.

6. The optimization method of the nuclear reactor safety injection system based on inverse quantization according to claim 1, characterized in that: In Step 8, based on the transition matrix determined in Step 6, use the random sampling method to extract the design parameter values of each device in the current state. The devices include the emergency injection system such as the passive core makeup tank, accumulator injection tank, and passive refueling water tank. These design parameter values are all the design parameters determined in Steps 2 and 3. The design parameters include the shape, height, inner diameter, water inventory, and pressure of each structural device, as well as the "trigger parameters" mentioned in Step 3.

7. The optimization method of the nuclear reactor safety injection system based on inverse quantization according to claim 1, characterized in that: In Step 10, compare the injection flow rate value of the emergency injection system calculated in Step 9 with the minimum injection flow rate requirement determined in Step 1, compare the differences between the two injection flow rates, calculate the variance of the two injection flow rate data, and calculate the transfer probability in the Markov chain Monte Carlo algorithm based on Bayesian theory to judge whether the current Markov chain accepts the transfer.

8. The optimization method of the nuclear reactor safety injection system based on inverse quantization according to claim 1, characterized in that: When the Markov chain is constructed in step 12, statistical analysis is performed on the Markov chains corresponding to each design parameter to obtain the uncertainty distribution intervals of all design parameters determined in steps 2 and 3. This interval is the equipment interval of the safety injection system that enables the injection flow rate of the safety injection system to meet the minimum required flow rate, that is, the optimal value range for the design of the safety injection system equipment.

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