CN110634534A - Chemical process parameter sensitivity determination method based on extended Fourier amplitude analysis - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 41
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- 238000004458 analytical method Methods 0.000 title claims abstract description 18
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Abstract
The invention discloses a chemical process parameter sensitivity determination method based on extended Fourier amplitude analysis, which belongs to the field of chemical process parameter sensitivity determination and comprises the following steps: determining input variables and distributions; establishing a reaction system model; fourier decomposition and model conversion; sobol decomposition and amplitude calculation; and (5) carrying out variance decomposition and analysis on a calculation result. The method is used for theoretical derivation and model establishment based on system intrinsic dynamics characteristics, a Sobol algorithm is added, the accuracy of the model is improved to a great extent, researchers and engineering technicians can solve corresponding problems by using results of various parameter sensitivity coefficients and influence rules on system safety, and the method has important application and popularization values for determining the safe operation range of the chemical process and guaranteeing the safe operation of chemical equipment.
Description
Technical Field
The invention belongs to the field of chemical process parameter sensitivity determination, and particularly relates to a chemical process parameter sensitivity determination method based on extended Fourier amplitude analysis.
Background
In the chemical process, it is very important to divide the safe operation and thermal runaway limits of the reaction system, i.e. to determine the safe operation domain, especially when the operation parameters change near the parameter sensitive critical value, the small change of the parameters will cause the sharp change of the temperature. The parameter sensitivity analysis method helps to theoretically reveal the safe operating range of the reactor, so that adverse effects caused by different operating parameter changes can be avoided in the reactor design and before operation.
Since the complexity of a chemical reaction system, especially the system state, is quite sensitive to changes in operating conditions, design parameters and operating parameters affecting the process of the chemical reaction system are manifold. The prior predictions about safety critical criteria mostly adopt a local sensitivity analysis method or even simple direct data fitting, often break away from the intrinsic kinetics of the reaction, and ignore the interaction between the operation variables. The agent model technology with higher computational efficiency and the global sensitivity analysis capable of screening important parameters have become the key research content of the multi-parameter nonlinear system. The global sensitivity analysis method is based on a numerical solution method, has unique advantages in the aspects of importance measurement, model orthogonal decomposition and the like, and is considered to be capable of effectively solving the difficult problem of high-dimensional complex model establishment.
For nonlinear complex change law analysis, a method based on model output result variance decomposition is one of the best choices, and representative methods are a Sobol algorithm and a Fourier amplitude analysis method. In terms of combining calculation accuracy and calculation time, a fourier amplitude analysis (FAST) based method is considered as a very efficient variance-based calculation method, but has the disadvantages of large calculation amount, low high-order sensitivity calculation accuracy and the like. The Extended Fourier Amplitude (EFAST) method is a quantitative global sensitivity analysis method improved on the FAST method after combining the advantages of the Sobol method, and has the characteristics of robustness, lower sample number and high calculation efficiency.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a chemical process parameter sensitivity determination method based on extended Fourier amplitude analysis, which is reasonable in design, overcomes the defects of the prior art and has a good effect.
In order to achieve the purpose, the invention adopts the following technical scheme:
a chemical process parameter sensitivity determination method based on extended Fourier amplitude analysis is sequentially carried out according to the following steps:
step 1: determining input variables and distributions;
comprehensively analyzing a reaction system to be investigated, identifying relevant variables and determining a variable fluctuation range;
step 2: establishing a reaction system model;
according to the characteristics of a reaction system, establishing a one-dimensional/two-dimensional and quasi-homogeneous/heterogeneous model, establishing a material balance and energy balance equation, and establishing an algebraic relation among the temperature of a reactor, the temperature of a cooling medium and the conversion rate by combining reaction kinetics and thermodynamic parameters: y ═ f (X) is a functional expression, and X ═ X (X)1,x2,x3…,xn) Inputting variables for n dimensions, wherein each variable has a probability density function;
and step 3: fourier decomposition and model conversion;
introducing a function with common independent parameters into each parameter in the model, and defining an integer frequency for each parameter to enable the model to become a periodic function of the independent parameters;
and 4, step 4: sobol decomposition and amplitude calculation;
adding a decomposition model thought of a Sobol method, calculating the amplitude of parameters by Fourier transform, converting sampling values into values of each function through a conversion function, and respectively calculating the contribution of each input variable to the total variance of an output result by considering the coupling effect among the parameters;
and 5: carrying out variance decomposition and calculation result analysis;
by individual and combined parametersThe function of (2) calculates the total variance of the model output, parameter xiThe direct contribution to the model output total variance and the indirect contribution to the model output variance through the interaction between the parameters can be represented by a total sensitivity index, and the total sensitivity index of each parameter is obtained through normalization processing.
The invention has the following beneficial technical effects:
compared with the existing chemical process parameter sensitivity determination method, the method has the advantages that theoretical derivation and model establishment are carried out based on the intrinsic dynamic characteristics of the system, the overall parameter sensitivity of the complex chemical process is determined, the idea of overall parameter sensitivity analysis is introduced into a chemical process model, the improvement is carried out on the basis of a FAST method, and a Sobol algorithm is added, so that the model precision is improved to a great extent, the internal relation among the operation parameters and the influence rule of the internal relation on the system safety key parameters, particularly the high-order influence rule of the internal relation can be obtained through analysis, and the occurrence of dangerous results such as thermal runaway and the like is avoided; researchers and engineering technicians can solve corresponding problems by using results of the sensitivity coefficients of all parameters and the rule of influence on system safety, overcome the defects that the traditional sensitivity analysis method is separated from reaction intrinsic dynamics, ignores interaction among variables and the like, and have important application and popularization values for determining the safe operation range of the chemical process and guaranteeing the safe operation of chemical equipment; can provide scientific guidance and guarantee for the safe and stable operation of the chemical process.
The method mainly calculates the parameter sensitivity of the chemical reaction process through expanded Fourier amplitude analysis, further determines the safe operation area of the reaction system, avoids the occurrence of risks such as runaway and the like, and can be applied to various reaction systems such as batch type/continuous type, parallel and series reaction and the like.
Drawings
FIG. 1 is a flow chart of a chemical process parameter sensitivity determination method based on extended Fourier amplitude analysis.
FIG. 2 is a schematic diagram of the sensitivity index of a global parameter of a certain coupling process.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
the EFAST method is a variance-based quantitative global sensitivity analysis method, i.e., it is considered that the sensitivity of the model output result can be reflected by the variance of the model result. The method separates the sensitivity of the model into sensitivity of individual parameter independent action and sensitivity of interaction between individual parameters.
The specific technical scheme is as follows:
1. establishing a reaction model: establishing an energy and material balance equation according to different reaction kinetic characteristics, establishing a reactor model by combining equipment properties and heat transfer of a cooling medium, and establishing a reactor model by using basic operation parameters including initial concentration C0Initial feed temperature T0The cooling medium temperature Tc, the reactor parameters (length, diameter and other parameters that may be present, such as stirring, internals, etc.), the catalyst parameters (diameter, density, porosity, etc.), the operating pressure P and other transfer coefficients, etc., the different processes are separately modeled on the basis of the main influencing variables.
2. And (3) global parameter sensitivity analysis calculation: according to the reaction model y ═ f (x)1,x2,x3…,xn)(xiThe ith parameter representing the model) and performing chemical process parameter sensitivity analysis by using an EFAST global sensitivity analysis method, firstly searching in a multidimensional space of the parameters by using a proper search curve, introducing a function with common independent parameters into each parameter in the model, defining an integer frequency for each parameter to enable the model to be a periodic function of the independent parameters, adding a decomposition model thought of a Sobol method, and calculating the amplitude of the parameter by using Fourier transform, wherein the larger the amplitude, the more sensitive the parameter is. According to the parameter sensitivity analysis result, the influence of the uncertainty of the input parameters on the system output can be calculated, the sensitivity index of each order and the total sensitivity index of each operation parameter are quantitatively calculated, the direct and indirect influence of each parameter change on the model result is further obtained, and finally, the main parameter change rule influencing the system safety parameters is identified.
The parameter sensitivity determination method based on extended Fourier amplitude analysis comprises 5 steps, as shown in FIG. 1, and specifically comprises the following steps:
step 1: determining input variables and distributions;
comprehensively analyzing a reaction system to be investigated, identifying relevant variables and determining a variable fluctuation range;
step 2: establishing a reaction system model;
according to the characteristics of a reaction system, establishing a one-dimensional/two-dimensional and quasi-homogeneous/heterogeneous model, establishing a material balance and energy balance equation, and establishing an algebraic relation among the temperature of a reactor, the temperature of a cooling medium and the conversion rate by combining reaction kinetics and thermodynamic parameters: y ═ f (X) is a functional expression, and X ═ X (X)1,x2,x3…,xn(ii) a Wherein x isiThe ith parameter representing the model) is an n-dimensional input variable, each variable having a probability density function;
and step 3: fourier decomposition and model conversion;
introducing a function with common independent parameters into each parameter in the model, and defining an integer frequency for each parameter to enable the model to become a periodic function of the independent parameters;
and 4, step 4: sobol decomposition and amplitude calculation;
adding a decomposition model thought of a Sobol method, calculating the amplitude of a parameter by Fourier transform, converting a sampling value into a value of each function by a conversion function, considering the coupling effect among the parameters and calculating the contribution of each input variable to the total variance of an output result, wherein the larger the amplitude is, the more sensitive the parameter is;
and 5: carrying out variance decomposition and calculation result analysis;
calculating the total variance of the model output as a function of the individual and combined parameters, parameter xiThe direct contribution to the model output total variance and the indirect contribution to the model output variance through the interaction between the parameters can be represented by a total sensitivity index, and the total sensitivity index of each parameter is obtained through normalization processing.
Taking a certain coupling reaction process as an example, the method of the invention examines the influence rule of different parameters (including temperature, concentration, pressure, airspeed, cooling medium and the like) on system safety parameters (reaction heat and the like), a pseudo-homogeneous two-dimensional model is used to combine with the heat transfer of the cooling medium to establish a reactor model, and a global sensitivity analysis method is adopted, and the result is shown in an attached figure 2.
Taking the reaction heat with large influence on the system safety risk as an example, as can be seen from fig. 2, the variable first-order sensitivity ordering is as follows from large to small: space velocity, temperature, methane flow, pressure, oxygen flow; and the order of magnitude of the sum considering the high order effects is: temperature, space velocity, methane flow, pressure, oxygen flow.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.
Claims (1)
1. A chemical process parameter sensitivity determination method based on extended Fourier amplitude analysis is characterized by comprising the following steps: the method comprises the following steps:
step 1: determining input variables and distributions;
comprehensively analyzing a reaction system to be investigated, identifying relevant variables and determining a variable fluctuation range;
step 2: establishing a reaction system model;
according to the characteristics of a reaction system, establishing a one-dimensional/two-dimensional and quasi-homogeneous/heterogeneous model, establishing a material balance and energy balance equation, and establishing an algebraic relation among the temperature of a reactor, the temperature of a cooling medium and the conversion rate by combining reaction kinetics and thermodynamic parameters: y ═ f (X) is a functional expression, and X ═ X (X)1,x2,x3…,xn) Inputting variables for n dimensions, wherein each variable has a probability density function;
and step 3: fourier decomposition and model conversion;
introducing a function with common independent parameters into each parameter in the model, and defining an integer frequency for each parameter to enable the model to become a periodic function of the independent parameters;
and 4, step 4: sobol decomposition and amplitude calculation;
adding a decomposition model thought of a Sobol method, calculating the amplitude of parameters by Fourier transform, converting sampling values into values of each function through a conversion function, and respectively calculating the contribution of each input variable to the total variance of an output result by considering the coupling effect among the parameters;
and 5: carrying out variance decomposition and calculation result analysis;
calculating the total variance of the model output as a function of the individual and combined parameters, parameter xiThe direct contribution to the model output total variance and the indirect contribution to the model output variance through the interaction between the parameters can be represented by a total sensitivity index, and the total sensitivity index of each parameter is obtained through normalization processing.
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| CN116305593A (en) * | 2023-05-23 | 2023-06-23 | 西安交通大学 | Global sensitivity analysis method with strong portability |
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