CN113806964A - Corrosion and scaling rate prediction method considering multi-factor coupling effect - Google Patents

Corrosion and scaling rate prediction method considering multi-factor coupling effect Download PDF

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CN113806964A
CN113806964A CN202111173727.6A CN202111173727A CN113806964A CN 113806964 A CN113806964 A CN 113806964A CN 202111173727 A CN202111173727 A CN 202111173727A CN 113806964 A CN113806964 A CN 113806964A
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曾德智
王熙
刘振东
孟可雨
赵春兰
董宝军
吴佳娟
袁海富
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Abstract

The invention discloses a corrosion and scaling rate prediction method considering multi-factor coupling effect, and belongs to the technical field of corrosion protection of oil and gas fields. The method is characterized in that: firstly, carrying out correlation analysis on collected work area corrosion and scaling parameters and determining main control factors; simulating a metal corrosion and scaling experiment through orthogonal design, and obtaining a regression equation of corrosion and scaling rate by combining a multiple regression analysis method; and finally, the regression equation and the regression coefficient are checked, the experiment expansion sample can be increased by reducing the horizontal interval of the main control factor, and the prediction precision is improved. According to the experiment of the influence of the main control factors on the corrosion and scaling rates, the method is combined with a multiple regression analysis method, the corrosion and scaling rates under a wider range of working conditions can be predicted, guidance is provided for field corrosion protection work, and safety accidents and economic losses are reduced.

Description

Corrosion and scaling rate prediction method considering multi-factor coupling effect
Technical Field
The invention belongs to the technical field of corrosion protection of oil and gas fields, and particularly relates to a corrosion and scaling rate prediction method considering multi-factor coupling effect.
Background
In the process of oil and gas field development, corrosive media such as carbon dioxide, hydrogen sulfide gas and the like seriously corrode production equipment, metal corrosion failure is caused, and meanwhile, the corrosion degree is aggravated under the coupling action of conditions such as temperature, pressure, flow velocity, pH value, scaling and the like. In order to avoid safety accidents and economic losses, experts and scholars predict corrosion and scaling rates, and currently, a plurality of methods for predicting the corrosion and scaling rates are provided, but main control factor analysis and scaling rate prediction aiming at work area parameters are often lacked in the prediction method, and the actual corrosion and scaling rates on the site cannot be accurately reflected, so that the establishment of a novel method for predicting the corrosion and scaling rates by considering the multi-factor coupling effect is of great significance.
At present, aiming at a corrosion and scaling prediction method, a corrosion prediction model of an acid gas field considering multiple factors and a parameter determination method (application publication number: CN112668206A), data are mainly obtained from the site to carry out multivariate regression analysis, the influence of five factors on the corrosion rate is considered to carry out the prediction of the corrosion rate, the regression model is checked, and finally the prediction model is output. However, the field data change is small, so that the prediction accuracy in a small-range working condition is high, when the influence factor value exceeds the range of a common operation working condition, the prediction accuracy is reduced, and the scaling rate is not predicted. ' A CO taking multiple factors into account2The corrosion prediction plate establishing method (application publication No. CN111177947A) mainly analyzes temperature, carbon dioxide partial pressure and chloride ion concentration and fits the functional relation between single factor and corrosion rate, and the influence of two factorsAnd the two-factor chart is drawn by nonlinear fitting, but the method does not give a mathematical model, and the prediction applicability of the corrosion rate is poor under the influence of more factors.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a corrosion and scaling rate prediction method considering multi-factor coupling effect, which screens main control factors of corrosion and scaling of a work area according to correlation coefficients, enlarges the value range of the main control factors, performs orthogonal test design, obtains a corrosion and scaling rate prediction equation under the influence of the main control factors, and provides a basis for corrosion protection work of an oil and gas field.
The technical problem to be solved by the invention is that the following technical scheme is adopted, and the corrosion and scaling rate prediction method considering the multi-factor coupling effect comprises the following steps:
the method comprises the following steps: collecting corrosion and scaling parameters of a work area and determining main control factors;
collecting corrosion and scaling parameters of a work area: the method comprises the following steps of (1) constructing a corrosion and scaling rate matrix A by using collected m corrosion and scaling rate influencing factors including influencing factors such as carbon dioxide partial pressure, temperature, flow velocity, chloride ion concentration, pH value, dissolved oxygen and bacteria, wherein the corrosion and scaling rate matrix A is as shown in a formula (1);
Figure BDA0003291309550000021
in the formula: a is a corrosion and scaling rate matrix; the front m columns are m collected corrosion and scaling rate influencing factors; a isijJ (j is more than or equal to 1 and less than or equal to m) th corrosion and scaling rate influence factor data in the ith group of data; column m +1 is reported as corrosion rate (fouling rate), mm/a (mg/m)2/h)；
Determining main control factors: calculating correlation coefficients of the collected m influencing factors with the corrosion rate and the scaling rate respectively; when the main control factor of the corrosion rate is analyzed, the corrosion rate data of the m +1 th column of the corrosion and scaling rate matrix A is taken and substituted into the formula (2) to obtain the relevant coefficient r of the corrosion ratei(m+1)(ii) a When the main control factor of the scaling rate is analyzed, the scaling of the m +1 th column of the corrosion and scaling rate matrix A is takenSubstituting the rate data into the formula (2) to obtain the scaling rate correlation coefficient ri(m+1)；
Figure BDA0003291309550000022
In the formula: r isi(m+1)Representing the influence correlation of each factor and the corrosion rate or the scaling rate for the corresponding correlation coefficient when substituting the corrosion rate data or the scaling rate data, wherein the correlation is stronger when the absolute value is larger;
absolute value | r of a coefficient relating corrosion to fouling ratei(m+1)Sorting the I from large to small, and selecting three factors with strongest correlation as main control factors;
step two: determining the variation ranges of the three main control factor values, performing a multi-factor and multi-level experiment by using an orthogonal design method, simulating metal corrosion and scaling in a high-temperature high-pressure kettle, calculating the corrosion rate and the scaling rate, and establishing a corrosion and scaling rate matrix V as shown in formula (3);
Figure BDA0003291309550000023
in the formula: v is a corrosion and scaling rate matrix obtained by an experiment; x is the number ofi1The ith group of data is the first main control factor; x is the number ofi2The ith group of data is the second main control factor; x is the number ofi3The ith group of data is the third main control factor; x is the number ofi4Corrosion rate of group i, mm/a; x is the number ofi5For group i fouling rates, mg/m2/h；
Step three: establishing a corrosion and scaling multiple regression model with a general formula as shown in a formula (4);
yi＝β0+β1zi1+β2zi2+β3zi3+β4zi4+β5zi5+τi (i＝1,2,...,n) (4)
when the model is a corrosion rate regression model, part of parameters in the formula (4) are shown as the formula (5);
Figure BDA0003291309550000031
in the formula: y isiCorrosion rate of group i, mm/a; beta is aj(j is more than or equal to 1 and less than or equal to 5) is a regression coefficient of the corrosion rate model; z is a radical ofij(j 1,2.. 5) converting the non-linear influence into an etch rate y in a regression modeliA linearization term of (a); tau isiIs a residual error;
when the scaling rate regression model is adopted, part of parameters in the formula (4) are shown as (6);
Figure BDA0003291309550000032
in the formula: y isiFor group i fouling rates, mg/m2/h；βj(j is more than or equal to 1 and less than or equal to 5) is a regression coefficient of the fouling rate model; z is a radical ofij(j 1,2.. 5) converting the non-linear influencing factors into fouling rate y in a regression modeliA linearization term of (a); tau isiIs a residual error;
step four: normally testing the data of the influence factors of the corrosion and scaling rate;
and (4) performing data normality check on the data in the corrosion and scaling rate matrix V in the step two by using SPSS, wherein the checked data comprises xi1、ln(xi1)、
Figure BDA0003291309550000033
xi3、
Figure BDA0003291309550000034
xi4、ln(xi2)、xi1xi2、xi5If the normal test is passed, carrying out the step five; if the normal test is not passed, expanding the sample data, and returning to the step two;
step five: calculating regression coefficients of the corrosion and scaling rate model;
the general formulas of the multiple regression models established in the step three are respectively carried into the formula (5) and the formula (6) to represent a corrosion rate model and a scaling rate model, and the regression coefficients of the two models are uniformly calculated according to the formula (7);
Figure BDA0003291309550000041
in the formula:
Figure BDA0003291309550000042
is to the regression coefficient betajAn estimated value of (d); z when corrosion rate model regression coefficient is calculatedij(j ═ 1,2.. 5) substituting parameters for formula (6), yiCorrosion rate of the ith group; z when the regression coefficient of the fouling rate model is calculatedij(j ═ 1,2.. 5) substituting parameters for formula (7), yiGroup i fouling rate;
step six: checking the regression model and the regression coefficient;
checking a regression model F: suppose that
Figure BDA0003291309550000043
Constructing a statistic F as shown in formula (8);
Figure BDA0003291309550000044
wherein:
Figure BDA0003291309550000045
in the formula: z when corrosion rate regression model is examinedij(j ═ 1,2.. 5) substituting parameters for formula (6),
Figure BDA0003291309550000046
the regression value of the ith group of corrosion rate is obtained, and F is the test statistic of a corrosion rate regression model; when examined by a regression model of fouling rate, zij(j ═ 1,2.. 5) substituting parameters for formula (7),
Figure BDA0003291309550000047
is as followsi groups of scaling rates, and F is a regression model test statistic of the scaling rates;
given significance level α1Looking up the table to obtain the critical value
Figure BDA0003291309550000048
When in use
Figure BDA0003291309550000049
Then the original hypothesis H is rejected0Indicating that the overall regression effect of the dependent variable and the independent variable is obvious, and performing a sixth step; otherwise, expanding the sample data and returning to the step two;
testing the significance t of the regression coefficient: suppose that
Figure BDA00032913095500000410
Construct statistics tjAs in equation (10);
Figure BDA00032913095500000411
Figure BDA0003291309550000051
in the formula: z in matrix Z when corrosion rate regression coefficients are examinedij(j ═ 1,2.. 5) substituting parameters for formula (6), tjRegression coefficients for corrosion rate
Figure BDA0003291309550000052
The test statistic of (a); z in matrix Z when scale rate regression coefficients are examinedij(j ═ 1,2.. 5) substituting parameters for formula (7), tjRegression coefficients for fouling rate
Figure BDA0003291309550000053
The test statistic of (a); u. ofjjIs the matrix Z as the jth row and jth column elements of formula (11);
when significance level a is given2Looking up the table to obtain the critical value
Figure BDA0003291309550000054
When all are
Figure BDA0003291309550000055
Then the original hypothesis H is rejected0Step seven is carried out, wherein the independent variable influence is obvious; if there is only one item tjFailed test, test
Figure BDA0003291309550000056
Corresponding zijWith any one of the other four zikIf the absolute value of the correlation coefficient between (k 1,2.. 5; k ≠ j) is greater than 0.7, the model will be used
Figure BDA0003291309550000057
Item elimination, step seven is carried out; otherwise, expanding the sample data and returning to the step two;
step seven: determining a corrosion and scaling rate prediction equation;
the corrosion rate prediction equation is formula (12);
Figure BDA0003291309550000058
in the formula: y is1Predicting the corrosion rate;
Figure BDA0003291309550000059
regression coefficient beta for corrosion ratejAn estimated value of (d); x1、X2、X3The first, second and third main control factors are respectively;
the fouling rate prediction equation is formula (13);
Figure BDA00032913095500000510
in the formula: y is2Predicting the scaling rate;
Figure BDA00032913095500000511
regression of fouling ratesCoefficient betajAn estimated value of (d); x1、X2、X3The first, second and third main control factors are respectively.
And further, determining the variation range of the main control factors, wherein the lower limit of the value of each main control factor is 0.5-0.8 times of the parameter data of the normal operation working condition of the work area, and the upper limit of the value of each main control factor is 1.2-2 times of the parameter data of the ultimate operation working condition of the work area.
Further, the method for calculating the corrosion rate and the scaling rate in the second step specifically comprises the following steps: orthogonal design n groups of experiments, before the experiments, 4 metal hanging pieces of the ith group are weighed and m is recorded1id(d is 1,2,3,4), after the experiment, the i-th group of 4 metal hanging pieces are dried by cold air, weighed and recorded2id(d ═ 1,2,3,4), and then the i-th group of 4 metal coupons were weighed after descaling and m was recorded3id(d ═ 1,2,3, 4); the corrosion rate v of each coupon of the set is obtained from equation (14)1id(d ═ 1,2,3,4), etch rate v of 4 coupons from the same group1id(d is 1,2,3,4) and the average value is recorded as the corrosion rate x of the corresponding group numberi4(ii) a Equation (15) yields the fouling rate v for each coupon of the set2id(d ═ 1,2,3,4), fouling rates v for 4 coupons in the same group were determined2id(d ═ 1,2,3,4) fouling rates x averaged for the corresponding groupsi5；
Figure BDA0003291309550000061
Figure BDA0003291309550000062
In the formula: i is the ith group in n groups of experiments; rho is the density of the metal pendant, g/cm3(ii) a A is the surface area of the metal pendant in cm2(ii) a t is experimental time, h; m is1idIs the initial mass of the metal hanging sheet, mg; m is2idThe mass of the metal hanging piece after the experiment is finished and dried by cold air is mg; m is3idMg is the mass of the metal hanging sheet after the rust and scale removal treatment; v. of1id(d ═ 1,2,3,4) for 4 coupon corrosion rates, mm/a, respectively; v. of2id(d-1, 2,3,4) is the fouling rate of 4 metal coupons, mg/m2/h。
And further, expanding the sample data in the fourth step, the sixth step and the seventh step, wherein the specific method is to reduce the horizontal spacing of the main control factors and increase an experimental data group during orthogonal test design.
Due to the adoption of the technical scheme, the invention has the following advantages:
(1) the method carries out correlation analysis on the influence factors of corrosion and scaling of the work area to obtain main control factors, designs multi-factor and multi-level metal corrosion and scaling experiments, and can effectively predict the corrosion and scaling rate under more complex working conditions and improve the applicability, wherein the designed working condition parameter range is larger than the actual operating working condition.
(2) The method considers corrosion and scaling at the same time, predicts the corrosion and scaling rate, is closer to the actual operation working condition of a work area, and provides guidance for avoiding corrosion and scaling damage.
Drawings
FIG. 1 is a flow chart of a corrosion and fouling prediction method that takes into account multi-factor coupling;
FIG. 2 shows the temperature xi1A normal test chart;
FIG. 3 shows ln (x)i1) A normal test chart;
FIG. 4 is
Figure BDA0003291309550000071
A normal test chart;
FIG. 5 shows the chloride ion concentration xi3A normal test chart;
FIG. 6 is
Figure BDA0003291309550000072
A normal test chart;
FIG. 7 is a graph of etch rate xi4A normal test chart;
FIG. 8 shows ln (x)i2) A normal test chart;
FIG. 9 is xi1xi2A normal test chart;
FIG. 10 is fouling rate xi5And (4) a normal test chart.
Detailed Description
The invention is described in detail below with reference to the drawings and the detailed description.
The method comprises the following steps: collecting corrosion and scaling parameters of a certain work area, wherein 4 collected corrosion and scaling rate influence factors are temperature, carbon dioxide partial pressure and chloride ion concentration respectively, and 5 groups of data construct a statistical matrix A as shown in a formula (16);
Figure BDA0003291309550000073
in the formula: a is a corrosion and scaling rate matrix; the first column is temperature, deg.C; the second column is carbon dioxide partial pressure, MPa, and the third column is chloride ion concentration, mg/L; the fourth column is the flow velocity, m/s, the fifth column is the corrosion rate (fouling rate), mm/a (mg/m)2/h)；
When the main control factor of the corrosion rate is analyzed, the correlation coefficient | r is obtained by calculation15|＝0.692，|r25|＝0.3669，|r35|＝0.0714，|r450, |; when the main control factor of the scaling rate is adopted, the correlation coefficient | r is obtained by calculation15|＝0.6675，|r25|＝0.0607，|r35|＝0.0714，|r450, |; analyzing to obtain main control factors of temperature, carbon dioxide partial pressure and chloride ion concentration as corrosion and scaling rates;
step two: taking the 20# steel of the work area as a test pipe, according to the data collected in the step one, the temperature interval [40,55], the carbon dioxide partial pressure interval [0.3,0.6] and the chloride ion concentration interval [9000,11000], according to the method of claim 2, expanding the values of the main control factors, and establishing a corrosion and scaling rate V matrix as shown in a formula (4) through test design; the temperature interval of the first row is [30,60], the partial pressure interval of the carbon dioxide of the second row is [0.5,1], the concentration of the chloride ions of the third row is [5000,20000], 14 groups of data of corrosion and scaling rates are designed in an orthogonal mode, and a corrosion and scaling rate V matrix is established as a formula (17);
Figure BDA0003291309550000081
step three: establishing a corrosion and scaling multiple regression model with a general formula as shown in a formula (4); formula (5) represents a corrosion rate model, formula (6) represents a fouling rate model;
step four: normally testing the data of the influence factors of the corrosion and scaling rate;
and (4) performing data normality check on the data in the corrosion and scaling rate matrix in the step two by using SPSS software, wherein the checked data comprises xi1、ln(xi1)、
Figure BDA0003291309550000082
xi3、
Figure BDA0003291309550000083
xi4、ln(xi2)、xi1xi2、xi5Obtaining normal test graphs which are respectively shown in the graphs 2-10, and performing a fifth step by using the results of the normal test;
step five: calculating regression coefficients of the corrosion and scaling rate model;
and (3) substituting the data in the matrix V and the formula (5) into the formula (7) to obtain an estimated value of the regression coefficient of the corrosion rate prediction equation:
Figure BDA0003291309550000084
and (3) substituting the data in the matrix V and the formula (6) into the formula (7) to obtain an estimated value of the regression coefficient of the fouling rate prediction equation:
Figure BDA0003291309550000085
step six: checking the regression model and the regression coefficient;
checking a regression model F;
and (4) checking the corrosion rate model F: equation (8) gives the corrosion rate fsample statistic of 5.719, gives the significance level α of 0.05, and looks up the table to give the threshold F0.05When (5,8) ≥ 3.687, F ≥ Fα(5,8), the corrosion rate model passes the inspection;
fouling rate model F test: equation (8) gives a fouling rate fsample statistic of 8.365, gives a significance level α of 0.05, and looks up the critical value F0.05When (5,8) ≥ 3.687, F ≥ Fα(5,8), the fouling rate model passes the test;
checking a regression coefficient t;
carrying out regression coefficient t test on the corrosion rate model: equation (10) obtains t test statistic as t0＝-2.34，t1＝2.78，t2＝2.743，t3＝3.351，t4＝2.824，t5-2.707, where a threshold t is found by looking up the table, giving a significance level α of 0.050.05(8) 2.306 when | tj|≥t0.05(8) (j is more than or equal to 0 and less than or equal to 5) rejecting the original hypothesis H0Step seven is carried out, wherein the independent variable influence is obvious;
scaling rate model regression coefficient ttest: equation (10) obtains t test statistic as t0＝-2.795，t1＝-1.73，t2＝-2.719，t3＝2.357，t4＝2.786，t5Given a significance level α of 0.05, 3.007, the critical value t was found by looking up the table0.05(8) 2.306, except for t1All the z is obtained by checking and calculating by combining the formula (6)i1And zikAbsolute values of correlation coefficients of (k 2,3,4,5) are 0.3126, 0.813, 0.3019, 0.1334, and zi1＝xi1And zi3＝xi1xi2If the absolute value of the correlation coefficient is 0.813 and greater than 0.7, the correlation coefficient is rejected
Figure BDA0003291309550000091
Item, go to step seven;
step seven: determining a corrosion and scaling rate prediction equation;
the corrosion rate prediction equation is expressed as a formula (18);
Figure BDA0003291309550000092
secondly, the scaling rate prediction equation is expressed as a formula (19);
Figure BDA0003291309550000093
the basic method and main features of the present invention have been described above. It will be understood by those skilled in the art that while the present invention has been described in detail with reference to the preferred embodiments thereof, the present invention is susceptible to modification of part of the features of the invention and equivalents thereof without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is defined by the claims and their equivalents.

Claims (4)

1. A corrosion and scaling rate prediction method considering multi-factor coupling effect is characterized by comprising the following specific steps:
the method comprises the following steps: collecting corrosion and scaling parameters of a work area and determining main control factors;
collecting corrosion and scaling parameters of a work area: the method comprises the following steps of (1) constructing a corrosion and scaling rate matrix A by using collected m corrosion and scaling rate influencing factors including influencing factors such as carbon dioxide partial pressure, temperature, flow velocity, chloride ion concentration, pH value, dissolved oxygen and bacteria, wherein the corrosion and scaling rate matrix A is as shown in a formula (1);
Figure FDA0003291309540000011
in the formula: a is a corrosion and scaling rate matrix; the front m columns are m collected corrosion and scaling rate influencing factors; a isijJ (j is more than or equal to 1 and less than or equal to m) th corrosion and scaling rate influence factor data in the ith group of data; column m +1 is reported as corrosion rate (fouling rate), mm/a (mg/m)2/h)；
Determining main control factors: calculating correlation coefficients of the collected m influencing factors with the corrosion rate and the scaling rate respectively; when the main control factor of the corrosion rate is analyzed, the corrosion rate data of the m +1 th column of the corrosion and scaling rate matrix A is taken and substituted into the formula (2) to obtain the relevant coefficient r of the corrosion ratei(m+1)(ii) a When the main control factor of the scaling rate is analyzed, the scaling rate data of the m +1 th column of the corrosion and scaling rate matrix A is taken and substituted into a formula(2) Obtaining the scaling rate correlation coefficient ri(m+1)；
Figure FDA0003291309540000012
In the formula: r isi(m+1)Representing the influence correlation of each factor and the corrosion rate or the scaling rate for the corresponding correlation coefficient when substituting the corrosion rate data or the scaling rate data, wherein the correlation is stronger when the absolute value is larger;
absolute value | r of a coefficient relating corrosion to fouling ratei(m+1)Sorting the I from large to small, and selecting three factors with strongest correlation as main control factors;
step two: determining the variation ranges of the three main control factor values, performing a multi-factor and multi-level experiment by using an orthogonal design method, simulating metal corrosion and scaling in a high-temperature high-pressure kettle, calculating the corrosion rate and the scaling rate, and establishing a corrosion and scaling rate matrix V as shown in formula (3);
Figure FDA0003291309540000013
in the formula: v is a corrosion and scaling rate matrix obtained by an experiment; x is the number ofi1The ith group of data is the first main control factor; x is the number ofi2The ith group of data is the second main control factor; x is the number ofi3The ith group of data is the third main control factor; x is the number ofi4Corrosion rate of group i, mm/a; x is the number ofi5For group i fouling rates, mg/m2/h；
Step three: establishing a corrosion and scaling multiple regression model with a general formula as shown in a formula (4);
yi＝β0+β1zi1+β2zi2+β3zi3+β4zi4+β5zi5+τi(i＝1,2,...,n) (4)
when the model is a corrosion rate regression model, part of parameters in the formula (4) are shown as the formula (5);
Figure FDA0003291309540000021
in the formula: y isiCorrosion rate of group i, mm/a; beta is aj(j is more than or equal to 1 and less than or equal to 5) is a regression coefficient of the corrosion rate model; z is a radical ofij(j 1,2.. 5) converting the non-linear influence into an etch rate y in a regression modeliA linearization term of (a); tau isiIs a residual error;
when the scaling rate regression model is adopted, part of parameters in the formula (4) are shown as (6);
Figure FDA0003291309540000022
in the formula: y isiFor group i fouling rates, mg/m2/h；βj(j is more than or equal to 1 and less than or equal to 5) is a regression coefficient of the fouling rate model; z is a radical ofij(j 1,2.. 5) converting the non-linear influencing factors into fouling rate y in a regression modeliA linearization term of (a); tau isiIs a residual error;
step four: normally testing the data of the influence factors of the corrosion and scaling rate;
and (4) performing data normality check on the data in the corrosion and scaling rate matrix V in the step two by using SPSS, wherein the checked data comprises xi1、ln(xi1)、
Figure FDA0003291309540000023
xi3、
Figure FDA0003291309540000024
xi4、ln(xi2)、xi1xi2、xi5If the normal test is passed, carrying out the step five; if the normal test is not passed, expanding the sample data, and returning to the step two;
step five: calculating regression coefficients of the corrosion and scaling rate model;
the general formulas of the multiple regression models established in the step three are respectively carried into the formula (5) and the formula (6) to represent a corrosion rate model and a scaling rate model, and the regression coefficients of the two models are uniformly calculated according to the formula (7);
Figure FDA0003291309540000031
in the formula:
Figure FDA0003291309540000032
is to the regression coefficient betajAn estimated value of (d); z when corrosion rate model regression coefficient is calculatedij(j ═ 1,2.. 5) substituting parameters for formula (6), yiCorrosion rate of the ith group; z when the regression coefficient of the fouling rate model is calculatedij(j ═ 1,2.. 5) substituting parameters for formula (7), yiGroup i fouling rate;
step six: checking the regression model and the regression coefficient;
checking a regression model F: suppose H0:
Figure FDA0003291309540000033
Constructing a statistic F as shown in formula (8);
Figure FDA0003291309540000034
wherein:
Figure FDA0003291309540000035
in the formula: z when corrosion rate regression model is examinedij(j ═ 1,2.. 5) substituting parameters for formula (6),
Figure FDA00032913095400000311
the regression value of the ith group of corrosion rate is obtained, and F is the test statistic of a corrosion rate regression model; when examined by a regression model of fouling rate, zij(j ═ 1,2.. 5) substituting parameters for formula (7),
Figure FDA0003291309540000036
f is the fouling rate regression model test statistic for the ith group of fouling rates;
given significance level α1Looking up the table to obtain the critical value
Figure FDA0003291309540000037
When in use
Figure FDA0003291309540000038
Then the original hypothesis H is rejected0Indicating that the overall regression effect of the dependent variable and the independent variable is obvious, and performing a sixth step; otherwise, expanding the sample data and returning to the step two;
testing the significance t of the regression coefficient: suppose H0:
Figure FDA0003291309540000039
Construct statistics tjAs in equation (10);
Figure FDA00032913095400000310
Figure FDA0003291309540000041
in the formula: z in matrix Z when corrosion rate regression coefficients are examinedij(j ═ 1,2.. 5) substituting parameters for formula (6), tjRegression coefficients for corrosion rate
Figure FDA0003291309540000042
The test statistic of (a); z in matrix Z when scale rate regression coefficients are examinedij(j ═ 1,2.. 5) substituting parameters for formula (7), tjRegression coefficients for fouling rate
Figure FDA0003291309540000043
The test statistic of (a); u. ofjjIs the matrix Z as the jth row and jth column elements of formula (11);
when significance level a is given2Looking up the table to obtain the critical value
Figure FDA0003291309540000044
When all are
Figure FDA0003291309540000045
Then the original hypothesis H is rejected0Step seven is carried out, wherein the independent variable influence is obvious; if there is only one item tjFailed test, test
Figure FDA0003291309540000046
Corresponding zijWith any one of the other four zikIf the absolute value of the correlation coefficient between (k 1,2.. 5; k ≠ j) is greater than 0.7, the model will be used
Figure FDA0003291309540000047
Item elimination, step seven is carried out; otherwise, expanding the sample data and returning to the step two;
step seven: determining a corrosion and scaling rate prediction equation;
the corrosion rate prediction equation is formula (12);
Figure FDA0003291309540000048
in the formula: y is1Predicting the corrosion rate;
Figure FDA0003291309540000049
regression coefficient beta for corrosion ratejAn estimated value of (d); x1、X2、X3The first, second and third main control factors are respectively;
the fouling rate prediction equation is formula (13);
Figure FDA00032913095400000410
in the formula: y is2Predicting the scaling rate;
Figure FDA00032913095400000411
regression coefficient beta for fouling ratejAn estimated value of (d); x1、X2、X3The first, second and third main control factors are respectively.
2. The method for predicting the corrosion and scaling rate considering the multi-factor coupling effect as claimed in claim 1, wherein in the second step, the variation range of the main control factors is determined, the lower limit of the value of each main control factor is 0.5-0.8 times of the parameter data of the normal operation condition of the work area, and the upper limit of the value of each main control factor is 1.2-2 times of the parameter data of the ultimate operation condition of the work area.
3. The method for predicting corrosion and fouling rates according to claim 1, wherein the method for calculating corrosion and fouling rates in step two comprises: orthogonal design n groups of experiments, before the experiments, 4 metal hanging pieces of the ith group are weighed and m is recorded1id(d is 1,2,3,4), after the experiment, the i-th group of 4 metal hanging pieces are dried by cold air, weighed and recorded2id(d ═ 1,2,3,4), and then the i-th group of 4 metal coupons were weighed after descaling and m was recorded3id(d ═ 1,2,3, 4); the corrosion rate v of each coupon of the set is obtained from equation (14)1id(d ═ 1,2,3,4), etch rate v of 4 coupons from the same group1id(d is 1,2,3,4) and the average value is recorded as the corrosion rate x of the corresponding group numberi4(ii) a Equation (15) yields the fouling rate v for each coupon of the set2id(d ═ 1,2,3,4), fouling rates v for 4 coupons in the same group were determined2id(d ═ 1,2,3,4) fouling rates x averaged for the corresponding groupsi5；
Figure FDA0003291309540000051
Figure FDA0003291309540000052
In the formula: i is the ith group in n groups of experiments; rho is the density of the metal pendant, g/cm3(ii) a A is the surface area of the metal pendant in cm2(ii) a t is experimental time, h; m is1idIs the initial mass of the metal hanging sheet, mg; m is2idThe mass of the metal hanging piece after the experiment is finished and dried by cold air is mg; m is3idMg is the mass of the metal hanging sheet after the rust and scale removal treatment; v. of1id(d ═ 1,2,3,4) for 4 coupon corrosion rates, mm/a, respectively; v. of2id(d-1, 2,3,4) is the fouling rate of 4 metal coupons, mg/m2/h。
4. The method according to claim 1, wherein the sample data is expanded in the fourth, sixth and seventh steps by reducing the horizontal spacing of the main control factors and adding the experimental data set during orthogonal test design.
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