CN113188613A - Multiphase flow measurement method and system based on uncertainty analysis - Google Patents
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Abstract
The invention discloses a multiphase flow measuring method and system based on uncertainty analysis. The method comprises the following steps: performing multi-element linear regression fitting on the equivalent flow and capacitance measurement values based on the cross-correlation time delay to obtain liquid phase flow and relative standard uncertainty thereof, and gas phase flow and standard uncertainty thereof; obtaining liquid phase flow and relative standard uncertainty thereof, and gas phase flow and standard uncertainty thereof by multivariate linear regression fitting based on the capacitance measurement value and the differential pressure measurement value; obtaining liquid phase flow and relative standard uncertainty thereof, and gas phase flow and standard uncertainty thereof by performing multiple linear regression fitting on equivalent flow based on differential pressure measurement values and cross-correlation time delays; and comparing the uncertainty obtained in different modes, and taking the gas-liquid flow and the uncertainty corresponding to the minimum uncertainty as quality indexes for measuring flow measurement. The invention can reduce the error of the measuring result and help the operation and maintenance personnel to know the accuracy of the measuring result.
Description
Technical Field
The invention relates to the technical field of oil-gas-water multiphase flow measurement in the oil and gas industry, in particular to a multiphase flow measurement method and a multiphase flow measurement system based on uncertainty analysis.
Background
During the research and application of multiphase flow testing, people tend to use the concept of error to assess the quality of a meter or an algorithm, and less deeply research is carried out on the uncertainty of measurement. This is mainly because the multiphase flow algorithm usually adopts empirical correlation and iterative algorithm, which results in complicated calculation of uncertainty. Meanwhile, the key parameters and specific algorithms necessary for uncertainty assessment are sometimes difficult to find from the open literature, which increases the difficulty of research to some extent. Because the measurement error can be calculated only under the condition that the true value is known, and the result has certain randomness, the source of the measurement error is difficult to trace, so that the research around the error has certain limitation, and the characteristics of different algorithms are difficult to compare deeply and meticulously.
The main document in the field of measurement uncertainty evaluation is "Guide to the expression of uncertainty in the measurement, GUM method" and its annex 1 "Propagation probability distribution by Monte Carlo method (MCM method). The above standards were jointly released in 2008 on behalf of 8 international organizations and adopted in 2012 by China. The starting point of the GUM method is that relevant information about the model input quantities is represented by their estimates and their associated standard uncertainties, which are "propagated" through the (linearized) model to provide estimates of the output quantities and their standard uncertainties. Furthermore, the GUM method is based on the central limit theorem, and the output quantity is assumed to be in a Gaussian distribution, so that the inclusion factor and the expansion uncertainty are obtained. Also, the GUM method takes into account the effect of correlation if the input quantities of the models are correlated.
The MCM method (monte carlo method), also called statistical simulation method, random sampling technique, is a method of solving problems using random numbers (or pseudo-random numbers). The monte carlo process operates as follows: fromA value is randomly generated in the probability density function for each input quantity and the corresponding output quantity value of the model at these input quantity values is calculated. This process is repeated a number of times, resulting in a total of M output magnitudes. According to the central limit theorem, the average value Y of the output magnitudes obtained in this way is in the order O (M) if a standard uncertainty of Y exists-1/2) Converges to the desired velocity of Y. Therefore, the Monte Carlo method has reasonable convergence.
However, the accuracy and applicability of the assessment for measuring multiphase flow uncertainty currently remains to be improved.
Disclosure of Invention
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and to provide a multiphase flow measurement method and system based on uncertainty analysis.
According to a first aspect of the present invention, a method of multiphase flow measurement based on uncertainty analysis is provided. The method comprises the following steps:
step S1: analyzing the oil-gas two-phase flow by using an online detection system, wherein the system is provided with a differential pressure type flowmeter and a high-frequency capacitance conductance detection element;
step S2: performing multi-element linear regression fitting on the equivalent flow and capacitance measurement values based on the cross-correlation time delay to obtain liquid phase flow and relative standard uncertainty thereof, and gas phase flow and standard uncertainty thereof;
step S3: obtaining liquid phase flow and relative standard uncertainty thereof, and gas phase flow and standard uncertainty thereof by multivariate linear regression fitting based on the capacitance measurement value and the differential pressure measurement value;
step S4: obtaining liquid phase flow and relative standard uncertainty thereof, and gas phase flow and standard uncertainty thereof by performing multiple linear regression fitting on equivalent flow based on differential pressure measurement values and cross-correlation time delays;
step S5: and comparing the uncertainty obtained in the steps S1, S2 and S3, and taking the gas-liquid flow corresponding to the minimum uncertainty and the corresponding uncertainty as quality indexes for measuring flow measurement.
According to a second aspect of the present invention, a multiphase flow measurement system based on uncertainty analysis is provided. The system comprises:
an online detection system: the system is used for analyzing oil-gas two-phase flow and is provided with a differential pressure type flowmeter and a high-frequency capacitance conductance detection element;
the first calculation unit: the method is used for obtaining liquid phase flow and relative standard uncertainty thereof, and gas phase flow and standard uncertainty thereof through linear fitting based on equivalent flow and capacitance measured values of cross-correlation time delay;
a second calculation unit: the device is used for obtaining the liquid phase flow and the relative standard uncertainty thereof, and the gas phase flow and the standard uncertainty thereof through linear fitting based on the capacitance measured value and the differential pressure measured value;
a third calculation unit: the equivalent flow based on the differential pressure measurement value and the cross-correlation time delay is subjected to linear fitting to obtain liquid phase flow and relative standard uncertainty thereof, and gas phase flow and standard uncertainty thereof;
a result output unit: and the uncertainty is used for comparing the uncertainty obtained by the first calculating unit, the second calculating unit and the third calculating unit, and the gas-liquid flow corresponding to the minimum uncertainty and the corresponding uncertainty are used as quality indexes for measuring flow measurement.
Compared with the prior art, the invention has the advantages that the contribution proportion of the uncertainty is mastered by analyzing the uncertainty, and the contribution proportion changes along with the distribution change of the gas-liquid two-phase flow. In addition, the relationship between the relative error and the relative uncertainty was also studied, verifying that the uncertainty could be used to predict the error.
Other features of the present invention and advantages thereof will become apparent from the following detailed description of exemplary embodiments thereof, which proceeds with reference to the accompanying drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description, serve to explain the principles of the invention.
FIG. 1 is a schematic diagram of an oil-gas two-phase flow real-time on-line detection system according to one embodiment of the present invention;
FIG. 2 is a graph of experimental data distribution according to one embodiment of the present invention;
FIG. 3 is a flow chart of a capacitance + cross-correlation algorithm calculation according to one embodiment of the present invention;
FIG. 4 is a diagram illustrating the fitting effect of key parameters of the capacitance + cross-correlation algorithm according to an embodiment of the present invention, where FIG. 4(a) is a diagram illustrating the fitting effect of LVF and the distribution of standard uncertainty, and FIG. 4(b) is QtotFitting effect schematic diagram and standard uncertainty distribution;
FIG. 5 is a graph showing the standard uncertainty and error distribution of experimental data in a capacitance + cross-correlation algorithm, wherein FIG. 5(a) is a graph showing the standard uncertainty and error distribution of a liquid phase flow rate, and FIG. 5(b) is a graph showing the standard uncertainty and error distribution of a gas phase flow rate, according to an embodiment of the present invention;
FIG. 6 is a relative uncertainty composition and distribution plot of the liquid phase flow for the capacitance + cross-correlation algorithm, wherein FIG. 6(a) is the composition plot and FIG. 6(b) is the distribution plot, in accordance with one embodiment of the present invention;
FIG. 7 is a graph and plot of the relative uncertainty composition and distribution of gas phase flow for the capacitance + cross-correlation algorithm, where FIG. 7(a) is the composition graph and FIG. 7(b) is the distribution graph, according to one embodiment of the present invention;
FIG. 8 is a flow chart of a differential pressure + capacitance algorithm calculation according to one embodiment of the present invention;
FIG. 9 is a graph of gas phase virtual high flow Q in a differential pressure + capacitance algorithm, in accordance with one embodiment of the present inventiontpThe fitting effect graph of (1);
FIG. 10 is a graph showing the standard uncertainty and error distribution of experimental data in a differential pressure + capacitance algorithm, wherein FIG. 10(a) is a graph showing the standard uncertainty and error distribution of a liquid phase flow rate, and FIG. 10(b) is a graph showing the standard uncertainty and error distribution of a gas phase flow rate, according to one embodiment of the present invention;
FIG. 11 is a relative uncertainty composition and distribution plot of the differential pressure + capacitance algorithm liquid phase flow, wherein FIG. 11(a) is the composition plot and FIG. 11(b) is the distribution plot, in accordance with one embodiment of the present invention;
FIG. 12 is a graph and plot of the relative standard uncertainty composition and plot of the differential pressure + capacitance algorithm gas phase flow, where 12(a) is the composition graph and 12(b) is the plot, according to one embodiment of the present invention;
FIG. 13 is a graph of the change in probability density distribution when the volumetric liquid fraction LVF is converted to a Luoman number X in the differential pressure + capacitance algorithm, in accordance with one embodiment of the present invention; wherein FIG. 13(a) is a correspondence between a volume liquid fraction LVF and a Loma number X and a slope of a correlation curve; FIG. 13(b) is a probability density distribution of the volume fraction LVF and the Loma number X at a certain operating point;
FIG. 14 is a flow chart of a cross-correlation + differential pressure algorithm calculation according to one embodiment of the present invention;
FIG. 15 is a graph showing the standard uncertainty and error distribution of experimental data in the cross-correlation + differential pressure algorithm, wherein FIG. 15(a) is a graph showing the standard uncertainty and error distribution of the liquid phase flow rate, and FIG. 15(b) is a graph showing the standard uncertainty and error distribution of the gas phase flow rate, in accordance with one embodiment of the present invention;
FIG. 16 is a composition diagram and profile of the liquid phase flow of the cross-correlation + differential pressure algorithm according to one embodiment of the present invention, wherein FIG. 16(a) is the composition diagram and FIG. 16(b) is the profile;
FIG. 17 is a relative uncertainty composition and profile of the cross-correlation + differential pressure algorithm gas phase flow, wherein FIG. 17(a) is the composition and FIG. 17(b) is the profile, in accordance with one embodiment of the present invention;
FIG. 18 is a flow chart of a multi-sensory fusion algorithm calculation according to one embodiment of the present invention;
FIG. 19 is a graph illustrating the standard uncertainty and error distribution of experimental data in a multi-sensing fusion algorithm, wherein FIG. 19(a) is a graph illustrating the standard uncertainty and error distribution of liquid phase flow, and FIG. 19(b) is a graph illustrating the standard uncertainty and error distribution of gas phase flow, according to one embodiment of the present invention;
FIG. 20 is a relative uncertainty composition and distribution plot of the liquid phase flux for a multi-sensor fusion algorithm, wherein FIG. 20(a) is the composition plot and FIG. 20(b) is the distribution plot, in accordance with one embodiment of the present invention.
FIG. 21 is a multi-sensor fusion algorithm gas phase flow relative uncertainty composition diagram and profile, wherein FIG. 21(a) is the composition diagram and FIG. 21(b) is the profile, in accordance with one embodiment of the present invention.
Detailed Description
Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that: the relative arrangement of the components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless specifically stated otherwise.
The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses.
Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate.
In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
The invention firstly simplifies three common gas-oil two-phase flow algorithms (capacitance + cross correlation, cross correlation + differential pressure and differential pressure + capacitance algorithms) in a laboratory properly, obtains an analytical expression of the uncertainty of the gas and liquid flow standards by a GUM method, and obtains a numerical solution of the uncertainty by simulating by using an MCM method. The analysis verifies that the results obtained by the two methods are basically the same, so that the correctness and feasibility of the two methods are theoretically verified. Subsequently, the invention traces the source of the uncertainty of each algorithm, and researches the contribution ratio of each sensor (such as Venturi differential pressure, ECT capacitance and electrical cross-correlation time delay) to the final uncertainty and the change of the contribution ratio along with the distribution of gas-liquid two-phase flow. In addition, the invention also researches the relation between the relative error and the relative uncertainty, and verifies the useful conclusion that the uncertainty can be used for predicting the error. Finally, the invention provides a multi-sensor fusion method for multiphase flow measurement based on uncertainty analysis, and compared with any existing algorithm, the method has lower relative error and relative standard uncertainty, enables the distribution of the error and the uncertainty to be more uniform, and can effectively improve the accuracy and the application range of the multiphase flow measurement.
The uncertainty assessment of both GUM method and MCM method includes three stages of formula establishment, propagation and summarization. The establishment of the formula can be divided into two steps of establishing a mathematical model and analyzing uncertainty sources. Mathematical models of different flow algorithms will be described in detail below, while the source and spread of uncertainty generally follow the following laws.
1) Sources of uncertainty
The method of assessing the uncertainty of each input quantity criterion can be divided into a class a assessment based on repeated readings and a class B assessment based on other available information. The algorithm related to the embodiment of the invention is to obtain intermediate variables by performing least square fitting on the measurement signals, and then integrate different intermediate variables to obtain the gas-liquid two-phase flow. Thus, embodiments of the present invention are directed to algorithms where uncertainty in the input is derived from a multiple linear regression fit.
Standard statistical model of multiple linear regression specifies YiIs xijIs added to the random noise term, expressed as:
where ei is the random error, with: e (E)i)＝0，Var(ei)＝σ2，Cov(ei，ej)＝0，i≠j。
With matrix notation, equation (1) can be written as:
Yn×1＝Xn×pβp×1+en×1(2)
wherein: e (e) 0, Σee＝σ2I。
It can be shown that the least squares estimation of the coefficient beta
And its covariance matrix
Respectively as follows:
in the formula, σ2Is the error eiSquare expectation of (a), can prove2The unbiased estimate of (c) is:
in summary, the standard statistical model considers that the independent variable X is not random, but is a fixed variable that can be accurately controlled and observed, while the dependent variable Y has a constant variance σ due to the effect of the error e2. Fitting coefficient beta and its standard uncertainty
The specific expression of (2) can be derived from the formulas (3) to (5).
2) Propagation of uncertainty
The measurement model is expressed as:
Y＝f(X)＝f(X1，…，XN)(6)
the estimated value of the output quantity is:
y＝f(x1，…，xN)(7)
synthetic target of measured estimated value yQuasi-uncertainty uc(y) is calculated as:
equation (8) is the propagation rate of uncertainty, where u (x)i，xj) Is an input quantity xiAnd xjCovariance, Σ, betweenxIs the corresponding covariance matrix. If the input quantity xiAnd xjAll are coefficients obtained by multivariate linear fitting, then
For sensitivity factors, it is usual to measure the function f at xiThe partial derivative of the position is obtained,
is the corresponding sensitivity coefficient row vector. When the measurement model is complicated and inconvenient to calculate by partial derivatives,
it can also be obtained by numerical calculation methods or experimental measurements.
The invention is described in further detail below with reference to the figures and the specific embodiments.
Referring to fig. 1, the oil-gas two-phase flow real-time online detection system of the embodiment includes a fluid mixing module 1, a high-frequency capacitance/conductance detection module 2, a differential pressure type flow meter module 3, a data processing module 4, and a display module 5. Oil-gas two-phase flow sequentially flows through a mixing module 1, a high-frequency capacitance/conductance detection module 2 and a differential pressure type flowmeter module 3. The data processing module 4 receives the signals of the high-frequency capacitance/conductance detection module 2 and the differential pressure type flowmeter module 3 for analysis and processing, and the respective flow of the oil-gas phases is obtained through calculation. The display module 5 outputs and displays the result of the data acquisition processing module 4. The detection system utilizes the characteristic that the density of gas is far lower than that of oil, and the dielectric constant/conductivity of the oil is far higher than that of the gas, so that the volume gas fraction LVF is directly obtained as far as possible, and mutual coupling among errors is avoided; meanwhile, the oil-gas two-phase flow is detected on line in real time by using non-separation, non-radiation and non-invasive detection technologies (such as time series cross-correlation analysis, differential pressure type flow meters and capacitance/conductance detection elements).
The raw data used in the present invention are from gas-oil two-phase experiments of 9, 12 and 2020, which are 20 groups, and have a gauge pressure of 0.3MPa, and the distribution is shown by the small circle in fig. 2. The solid line on the right side of fig. 2 represents a contour of capacitance, the dotted line represents a contour of cross-correlation equivalent flow rate, and the dotted line represents a contour of differential pressure equivalent flow rate. It can be seen that by finding the intersection point of any two contour lines, the corresponding gas-liquid two-phase flow can be found from fig. 2. Therefore, theoretically, three algorithms of capacitance + cross correlation, differential pressure + capacitance, cross correlation and differential pressure can be selected, and the calculation flows of the three algorithms are described in detail below.
1) Capacitance + cross-correlation algorithm
The basic calculation flow of the capacitance + cross correlation algorithm is shown in fig. 3. As can be seen from FIG. 3, the total volume flow Q required for calculating the gas and liquid flow ratestotAnd the volume fraction LVF were both obtained by unary linear fitting.
Wherein the average capacitance
The capacitance between four groups of counter electrodes of ECT is selected to be averaged to obtain:
and the average time delay is obtained by averaging the time delay signals between the two adjacent electrodes through the double-layer ECT eight pairs:
then the equivalent flow rate QthCalculated by the following formula:
a represents the transverse section of the ductCross-sectional area, L, represents the spacing between the two layers of ECT.
Then, the average capacitances are respectively measured
Positive equivalent flow rate QthAs dependent variable y, LVF and Q are respectively used at the same timetotIs used as an independent variable x to perform unary linear fitting:
y＝β0+β1x(9)
According to the calculation flow of the capacitance + cross-correlation algorithm in fig. 3 and the formula (9), the estimated value LVF of the volume liquid fraction LVF0Need to pass through intermediate variables
Calculated to obtain the total volume flow QtotEstimated value of Qtot0Need to pass through an intermediate variable Qth0And (4) calculating according to the following calculation formulas:
when dependent variable y0When known, x can be derived0The standard uncertainty of (c) is:
simplifying to obtain:
in the formula
Volume liquid fraction LVF0The distribution of the standard uncertainty is shown in the right graph of FIG. 4(a), and the total volume flow Qtot0The standard uncertainty distribution of (a) is shown in the right graph of FIG. 4 (b). As can be seen from FIG. 4 and equation (12), the calibration curve is obtained by unary linear fitting, and the uncertainty of the fitted value obtained on the calibration curve is related to the difference in addition to the parameters n and p
It is related. When fitting point x0And
the closer together, the less measurement uncertainty. This, in turn, can be used as a basis for selecting measurement points when initially fitting the calibration curve, i.e. selecting the mean value of the X-coordinates of the respective measurement points
Should be as close as possible to the fitting point x to be measured in the future0。
Obtaining an estimated value LVF of the volume liquid content LVF0And standard uncertainty u (LVF)0) And total volumetric flow rate QtotEstimated value of Qtot0And standard uncertainty u (Q)tot0) Then, the liquid phase flow rate Ql0And its relative standard uncertainty urel(Ql0) The calculation can be made as follows:
ql0＝Qtot0LVF0(13)
the gas phase flow rate and its corresponding standard uncertainty can be calculated with reference to equations (13) and (14), and will not be described herein.
The gas and liquid flow prediction effect of the capacitance + cross-correlation algorithm is shown in fig. 5. The figure respectively shows the numerical simulation result of the MCM method (Monte Carlo method) and the theoretical derivation result of the GUM method, the length of a line segment represents the standard uncertainty of an estimated value, and the vertical distance from a point to a central black line reflects the error of the point. As can be seen from fig. 5, the capacitance-cross-correlation algorithm has a poor prediction effect on the liquid phase flow rate and a good prediction effect on the gas phase flow rate, and is particularly obvious under the working condition of the atmospheric air volume. As can also be seen in fig. 5, there is a certain link between error and uncertainty: the longer the line segment corresponding to the uncertainty is, the greater the possibility that the point deviates from the central black line is; meanwhile, if the average value of the uncertainty is larger, the average value of the error is generally larger. Therefore, the standard uncertainty corresponding to the estimated value can predict the point error to a certain extent, thereby providing guidance for practical application.
The relative uncertainty composition and distribution of the liquid phase flow for the capacitance-cross correlation algorithm is shown in fig. 6. As can be seen from fig. 6(a), in the relative uncertainty of the liquid phase flow of the capacitance-cross-correlation algorithm, the component introduced by cross-correlation and the component introduced by capacitance are similar. At the same time, the liquid phase flow rate QlUnder certain conditions, along with the gas phase flow rate QgThe component introduced by the cross-correlation gradually decreases and the component introduced by the capacitance gradually increases, resulting in a relative uncertainty u in the liquid phase flowrel(Ql) Showing a tendency to decrease first and then increase. And with QlIncrease of (2) relative uncertainty u of the liquid phase flowrel(Ql) Presenting a monotonically decreasing trend. Thus, the relative uncertainty u of the liquid phase flow of the capacitance-cross correlation algorithmrel(Ql) The contour lines of (a) are shown in FIG. 6 (b).
Relative uncertainty in gas phase flow for capacitance-cross correlation algorithmThe degree of formation and distribution is shown in fig. 7. As can be seen from fig. 7(a), in the relative uncertainty of the gas-phase flow of the capacitance-cross-correlation algorithm, the component introduced by the cross-correlation is much larger than the component introduced by the capacitance, so the gas-phase flow uncertainty urel(Qg) Is dominated by the cross-correlation component. At the same time, the liquid phase flow rate QlUnder certain conditions, along with the gas phase flow rate QgIs increased, the components introduced by the cross-correlation and by the capacitance are both gradually reduced, resulting in a relative uncertainty u of the gas-phase flowrel(Qg) Presenting a monotonically decreasing trend. And with QlIncrease of gas phase flow relative uncertainty urel(Qg) But also exhibits a monotonically decreasing trend. Thus, the relative uncertainty u of the gas phase flow of the capacitance-cross correlation algorithmrel(Qg) At a low liquid phase flow rate QlLow gas phase flow rate QgThe contour line of the maximum value (c) is shown in FIG. 7 (b).
2) Differential pressure + capacitance algorithm
The calculation flow of the differential pressure + capacitance algorithm is shown in fig. 8, and the estimated value LVF of the volume liquid fraction LVF thereof0And its standard uncertainty u (LVF)0) The calculation method of (2) is completely the same as the capacitance + cross-correlation algorithm. After obtaining LVF0The algorithm then transforms it to X as follows0：
The formula of uncertainty of the synthetic standard according to the linear measurement model includes:
according to the research results of Murdock, Bizon and forest tiger, etc., the gas phase imaginary high coefficient
And Loma number
There is a linear relationship between:
φg＝β0+β1X(17)
the left and right sides of the above formula are multiplied by QgThe method comprises the following steps:
in the formula QtpThe gas phase virtual high flow can be calculated by the venturi differential pressure Δ p according to the following formula:
in the above formula, A represents the cross-sectional area of the pipe, ρgDenotes the gas phase density, plDenotes the density of the liquid phase, CdRepresenting the outflow coefficient of the venturi, epsilon representing the coefficient of expansion of the compressible fluid, CdAnd the value of epsilon can be chosen by ISO 5167-4.
The invention utilizes the formula (18) to correct the gas phase virtual high flow QtpThe fitting was performed and the effect of the fitting is shown in fig. 9. The fitting method considers the gas phase virtual high flow QtpStandard uncertainty u (Q) oftp) Is constant, the value thereof can be calculated with reference to the formula (5), and the coefficient
And its corresponding covariance matrix
The calculation may be performed with reference to equation (3) and equation (4), respectively. These parameters will be used in the calculation of the gas-liquid two-phase flow and its standard uncertainty.
Note that equation (18) can be written as Qtp＝Qg(β0+β1X)＝QgφgCan also be written as
So that the gas phase virtual height coefficient phi is obtainedgAnd liquid phase imaginary height coefficient philAnd its corresponding standard uncertainty u (phi)g) And u (phi)l) According to the formula Qg＝Qtp/φgAnd
and calculating the volume flow of the gas phase and the liquid phase.
Wherein the gas phase virtual height coefficient phigThe uncertainty of (d) can be calculated according to the following equation:
if Q is ignoredtpAnd phigCorrelation between, relative uncertainty u of gas phase flowrel(Qg) The calculation can be performed according to the uncertainty synthesis formula of the linear measurement model:
relative uncertainty u of liquid phase flowrel(Ql) Similar processing can be performed with reference to formula (20) and formula (21).
The gas and liquid flow prediction effect of the differential pressure + capacitance algorithm is shown in fig. 10, which respectively shows the numerical simulation result of the MCM method (monte carlo method) and the theoretical derivation result of the GUM method. It can be seen from fig. 10 that the MCM method result and the GUM method result of the differential pressure + capacitance algorithm substantially coincide with each other, but there is still a certain difference, and the reason for this difference will be finally analyzed below. As can be seen from fig. 10, the differential pressure + capacitance algorithm has a better prediction effect on the liquid flow rate, and is particularly obvious under the working condition of large liquid amount. Meanwhile, the prediction effect of the algorithm on the gas phase flow is stable and ideal, but the prediction effect of the algorithm under the working condition of large air volume is poor.
The relative uncertainty make-up and distribution of the differential pressure + capacitance algorithm liquid phase flow is shown in fig. 11. As can be seen in fig. 11(a), the components introduced by differential pressure and capacitance are substantially similar in the relative uncertainty of the liquid phase flow for the differential pressure + capacitance algorithm. At the same time, the liquid phase flow rate QlUnder certain conditions, along with the gas phase flow rate QgThe component introduced by differential pressure gradually decreases and the component introduced by capacitance gradually increases, resulting in a relative uncertainty u of the liquid phase flowrel(Ql) Showing a tendency to decrease slightly before increasing. And with QlIncrease of (2) relative uncertainty u of the liquid phase flowrel(Ql) Presenting a monotonically decreasing trend. Thus, the relative uncertainty u of the liquid phase flow of the differential pressure + capacitance algorithmrel(Ql) The flow rate is maximum at a low liquid phase flow rate and a high gas phase flow rate, and the contour lines thereof are as shown in FIG. 11 (b).
Differential pressure + capacitance algorithm the relative uncertainty make-up and distribution of gas phase flow is shown in fig. 12. As can be seen from FIG. 12(a), in the relative uncertainty of the differential pressure + capacitance algorithm gas phase flow, the component introduced by the capacitance is much larger than the component introduced by the differential pressure, so the gas phase flow uncertainty urel(Qg) Is dominated by the capacitance component. At the same time, at a liquid phase flow rate QlUnder certain conditions, along with the gas phase flow rate QgThe component introduced by the capacitance decreases slightly and then increases gradually, while the component introduced by the differential pressure decreases gradually, resulting in a relative uncertainty u of the gas-phase flowrel(Qg) It also shows a tendency of slightly decreasing and then increasing. And with QlIncrease of gas phase flow relative uncertainty urel(Qg) But also exhibits a substantially monotonically decreasing trend. Thus, the differential pressure + capacitance algorithm relative uncertainty u of the gas phase flowrel(Qg) At a low liquid phase flow rate QlHigh gas phase flow rate QgThe contour line of the maximum value (c) is shown in FIG. 12 (b).
As can be seen from fig. 11(b) and 12(b), the matching effect of the GUM and MCM results in the differential pressure + capacitance algorithm is not very good. After the analysis, it can be found that this is caused by the fact that when the formula (15) is used for converting the volume liquid content LVF into the loma number X, the probability density distribution of X deviates from the gaussian distribution, and the effect is shown in fig. 13 (b). The relationship between the volume liquid fraction LVF and the logma number X and the slope of the correlation curve are shown in fig. 13(a), and it can be seen that the LVF ranges from 0 to 1, and X ranges from 0 to + ∞. Therefore, the larger the LVF is, the larger the corresponding curve slope dX/dLVF is, and the increase of X caused by positive disturbance of the LVF is always larger than the decrease of X caused by negative disturbance of the LVF, so that X has the characteristic of right deviation. Meanwhile, the larger the LVF is, the more serious the X right deviation is, and it is obvious from FIG. 13(b) that the expected MCM result of X is larger than the GUM result thereof. A right shift in X will further cause the gas and liquid flow to deviate from the Gaussian distribution, resulting in MCM results deviating from GUM results. The inclusion interval in this case shall be subject to the results given in the MCM method.
3) Cross-correlation + differential pressure algorithm
The flow of calculation of the cross-correlation + differential pressure algorithm is shown in FIG. 14, with a volume flow QtotEstimated value of Qtot0And its standard uncertainty u (Q)tot0) The calculation method of (1) is identical to the capacitance + cross-correlation algorithm, and the virtual high flow Q istpCoefficient of (2)
Covariance matrix
And u (Q)tp) The calculation method is completely the same as the differential pressure + capacitance algorithm. Obtaining an estimate Q of the total volumetric flowtot0The algorithm then transforms Ql＝Qtot-QgSubstituting into equation (18), the reduction is:
in the same way, if Q is equalg＝Qtot-QlSubstituting into equation (18) can obtain a table of liquid phase flowThe expression is as follows:
taking the flow rate of the gas phase as an example,
and
can be simplified according to equation (8).
The standard uncertainties referred to in equations (24) and (25) may both be derived from a multivariate linear fit to obtain a covariance matrix
And the standard uncertainty u (y) of the dependent variable y.
In solving for gas phase flow QgStandard uncertainty u (Q) ofg) When, special attention should be paid to
And
the correlation between them.
In the formula:
standard uncertainty u (Q) of liquid phase flowl) Similar processing can be performed with reference to equations (24) to (27) based on equation (23).
The gas and liquid flow prediction effect of the cross-correlation + differential pressure algorithm is shown in fig. 15, and as can be seen from fig. 15, the cross-correlation + differential pressure algorithm has a very stable prediction effect on the liquid flow, has very high prediction precision, and is particularly obvious under the working condition of large liquid amount. However, the prediction effect of the algorithm on the gas flow is very unstable, and the prediction accuracy of the algorithm is rapidly reduced along with the reduction of the gas flow, so that the prediction effect of the algorithm is very good under the working condition of large gas flow, and the performance of the algorithm is very poor under the working condition of small gas flow. Therefore, the algorithm is more suitable for running under the working condition of large flow.
The relative uncertainty make-up and distribution of the liquid phase flow for the cross-correlation + differential pressure algorithm is shown in fig. 16. As can be seen in fig. 16(a), the components introduced by differential pressure and the components introduced by cross-correlation are similar in the standard uncertainty of the liquid phase flow for the cross-correlation + differential pressure algorithm. At the same time, at a liquid phase flow rate QlUnder certain conditions, the components introduced by differential pressure and cross-correlation do not follow the gas phase flow QgIs varied to result in a relative uncertainty u of the liquid phase flowrel(Ql) Substantially independent of gas phase flow QgAnd (4) changing. And with QlIncrease of (2) relative uncertainty u of the liquid phase flowrel(Ql) Presenting a monotonically decreasing trend. And with QlThe relative uncertainty of the liquid phase flow rate shows a monotonically decreasing trend. Thus, the relative uncertainty u of the liquid phase flow of the cross-correlation + differential pressure algorithmrel(Ql) The contour lines of (a) are shown in FIG. 16 (b).
The cross-correlation + differential pressure algorithm gas phase flow relative uncertainty make-up and distribution is shown in fig. 17. As can be seen from fig. 17(a), in the relative uncertainty of the gas-phase flow rate in the cross-correlation + differential pressure algorithm, the component introduced by the cross-correlation is much larger than the component introduced by the capacitance, and therefore the gas-phase flow rate uncertainty urel(Qg) Is dominated by the cross-correlation componentAnd (4) leading. At the same time, the liquid phase flow rate QlUnder certain conditions, along with the gas phase flow rate QgBoth the components introduced by the cross-correlation and the differential pressure decrease rapidly, resulting in a relative uncertainty u of the gas phase flowrel(Qg) Showing a tendency to decrease rapidly. And with QlIncrease of gas phase flow relative uncertainty urel(Qg) And is substantially invariant. Thus, the relative uncertainty u of the gas phase flow for the cross-correlation + differential pressure algorithmrel(Qg) The contour lines of (a) are shown in FIG. 17 (b).
4) Multi-sensor fusion method
The calculation flow of the multi-sensor fusion algorithm is shown in FIG. 18, and the basic idea is to calculate the uncertainty and flow rate of the three algorithms respectively, then take the serial number of the minimum uncertainty in the three algorithms, and then take the gas-liquid flow rate Q corresponding to the serial numbertp1And the corresponding uncertainty is output as a final result.
The gas and liquid flow prediction effect of the multi-sensing fusion algorithm is shown in fig. 19, and as can be seen from fig. 19, the multi-sensing fusion algorithm has a very stable prediction effect on the liquid flow and very ideal precision, especially under the working condition of large liquid amount. Meanwhile, the prediction effect of the algorithm on the gas phase flow is very stable, the accuracy is ideal, and especially under the working condition of large air volume. Therefore, the multi-sensing fusion algorithm has lower relative uncertainty than the three conventional algorithms and lower relative error than the three conventional algorithms, so that the conclusion that the uncertainty analysis can be used for guiding the error of the improved algorithm is proved to a certain extent. Thus, multi-sensing fusion methods based on uncertainty analysis can be used in practice to improve the accuracy of the meter.
The relative uncertainty composition and distribution of the multi-sensory fusion algorithm is shown in fig. 20. As can be seen in fig. 20(a), the uncertainty of the differential pressure + capacitance algorithm and the cross-correlation + differential pressure algorithm are similar in magnitude for the relative uncertainty of the liquid phase flow, whereas the uncertainty of the capacitance + cross-correlation algorithm is not advantageous. At the same time, the liquid phase flow rate QlUnder certain conditions, along with the gas phase flow rate QgThe uncertainty of the differential pressure + capacitance algorithm is gradually increased, and the uncertainty of the differential pressure-cross correlation algorithm is gradually reduced, so that the liquid phase uncertainty of the multi-sensor fusion algorithm is essentially an organic combination of the differential pressure + capacitance algorithm under a low-flow working condition and the cross correlation + differential pressure algorithm under a high-flow working condition. And with QlThe liquid phase flow relative uncertainty of all three algorithms shows a monotonically decreasing trend, and therefore the contour of the uncertainty of the liquid phase flow is shown in fig. 20 (b).
The relative uncertainty make-up and distribution of the multi-sensing fusion algorithm gas phase flow is shown in FIG. 21. As can be seen from fig. 21(a), the uncertainty of the differential pressure + capacitance algorithm and the capacitance + cross-correlation algorithm are similar in magnitude for the relative uncertainty of the gas phase flow, while the uncertainty of the cross-correlation + differential pressure algorithm is not advantageous. At the same time, the liquid phase flow rate QlUnder certain conditions, along with the gas phase flow rate QgThe uncertainty of the differential pressure + capacitance algorithm is gradually increased, and the uncertainty of the capacitance + cross-correlation algorithm is gradually decreased, so that the gas phase uncertainty of the multi-sensor fusion algorithm is essentially an organic combination of the differential pressure + capacitance algorithm under a low-flow working condition and the capacitance + cross-correlation algorithm under a high-flow working condition. And with QlThe gas phase flow relative uncertainty of all three algorithms shows a tendency to decrease monotonically to some extent, so the contour of the uncertainty of the liquid phase flow is shown in fig. 21 (b).
In this context, uncertainty means the degree of uncertainty in the measured value, due to the presence of measurement errors, which is an indicator for characterizing the quality of the measurement result. The smaller the uncertainty is, the closer the measurement result is to the measured true value is, the higher the quality is, the higher the level is, and the higher the use value is; the greater the uncertainty, the lower the quality of the measurement and the lower the level, the lower its value of use.
In summary, the invention firstly simplifies three common gas-oil two-phase flow algorithms of a laboratory multiphase flow measuring device, and obtains a mathematical model between the input quantity and the output quantity of the laboratory multiphase flow measuring device through theoretical derivation. Meanwhile, uncertainty of different conventional flow algorithms is analyzed by using a GUM method and an MCM method respectively, and correctness and feasibility of the two methods are verified theoretically. Meanwhile, the invention also obtains the following important conclusions:
1) the flow uncertainty is obviously different under different gas and liquid flow combinations, and the uncertainty given by different algorithms has obvious difference in both value and distribution. This difference in distribution can provide the basis for multi-sensory fusion: if the multiphase flowmeter is provided with a plurality of flow calculation methods, the flow prediction result of the algorithm with the minimum uncertainty is only required to be given under a certain gas and liquid flow.
2) The uncertainty contribution ratios of the individual sensors differ significantly from one algorithm to the next. The conclusion helps to reveal the deep differences among different algorithms and provides guidance for the development of the algorithms and the selection of sensors in the future.
3) The uncertainty may predict to some extent the magnitude of the error. Therefore, the research uncertainty can also help the operation and maintenance personnel to know the accuracy of the metering result, thereby providing help for production decision.
4) An uncertainty analytic solution obtained through theoretical derivation is basically the same as an uncertainty numerical solution obtained through Monte Carlo method simulation, and therefore correctness and feasibility of the two methods are theoretically verified. With the help of statistical and simulation software, the Monte Carlo method can be directly used for solving more complex nonlinear fitting and iterative algorithm in practical problems, thereby ensuring the expandability and practicability of the algorithm. The analytical solution can be used for verifying the numerical simulation result under specific or simplified conditions, so that the reliability of the simulation result is ensured.
The present invention may be a system, method and/or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions embodied therewith for causing a processor to implement various aspects of the present invention.
The computer readable storage medium may be a tangible device that can hold and store the instructions for use by the instruction execution device. The computer readable storage medium may be, for example, but not limited to, an electronic memory device, a magnetic memory device, an optical memory device, an electromagnetic memory device, a semiconductor memory device, or any suitable combination of the foregoing.
Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer-readable program instructions.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen in order to best explain the principles of the embodiments, the practical application, or improvements made to the technology in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein. The scope of the invention is defined by the appended claims.
Claims (10)
1. A multiphase flow measurement method based on uncertainty analysis comprises the following steps:
step S1: analyzing the oil-gas two-phase flow by using an online detection system, wherein the system is provided with a differential pressure type flowmeter and a high-frequency capacitance conductance detection element;
step S2: performing multi-element linear regression fitting on the equivalent flow and capacitance measurement values based on the cross-correlation time delay to obtain liquid phase flow and relative standard uncertainty thereof, and gas phase flow and standard uncertainty thereof;
step S3: obtaining liquid phase flow and relative standard uncertainty thereof, and gas phase flow and standard uncertainty thereof by multivariate linear regression fitting based on the capacitance measurement value and the differential pressure measurement value;
step S4: obtaining liquid phase flow and relative standard uncertainty thereof, and gas phase flow and standard uncertainty thereof by performing multiple linear regression fitting on equivalent flow based on differential pressure measurement values and cross-correlation time delays;
step S5: and comparing the uncertainty obtained in the steps S2, S3 and S4, and taking the gas-liquid flow corresponding to the minimum uncertainty and the corresponding uncertainty as quality indexes for measuring flow measurement.
2. The method of claim 1, wherein in step S2, the liquid phase flow rate Ql0And its relative standard uncertainty urel(Ql0) Calculated according to the following formula:
Ql0＝Qtot0LVF0
wherein, LVF0Is an estimate of the volume liquid fraction LVF, Qtot0Is the total volume flow QtotEstimated value of urel(.) represent the corresponding relative standard uncertainty.
3. The method according to claim 1, wherein in step S3, the gas phase flow rate QgAnd its relative standard uncertainty urel(Qg) Expressed as:
Qg＝Qtp/φg
wherein Q istpDenotes a gas phase virtual high flow, urel(Qtp) Is QtpThe relative standard uncertainty of (a), the value of which is obtained by linear fitting; phi is agIs the gas phase imaginary high coefficient, urel(φg) Is phigRelative standard uncertainty of (d).
4. The method of claim 3, wherein in step S4, the gas phase streamQuantity QgAnd its standard uncertainty u (Q)g) Expressed as:
wherein the content of the first and second substances,
where ρ isgDenotes the gas phase density, plDenotes the density of the liquid phase, beta1And beta0Is a coefficient of multiple linear regression, QtpRepresenting a gas phase virtual high flow.
5. The method of claim 1, wherein the standard statistical model of multiple linear regression specifies YiIs xijIs added to the random noise term, expressed as:
wherein eiIs a random error having: e (E)i)＝0，Var(ei)＝σ2，Cov(ei，ej)＝0，i≠j。
6. The method of claim 1, wherein the differential pressure flow meter is a venturi differential pressure flow meter.
7. The method according to claim 1, wherein the online detection system comprises a fluid mixing module, a high-frequency capacitance/conductance detection module, a differential pressure type flowmeter module, a data processing module and a display module, wherein the oil-gas two-phase flow sequentially flows through the mixing module, the high-frequency capacitance conductance detection module and the differential pressure type flowmeter module, the data processing module is used for receiving signals of the high-frequency capacitance conductance detection module and the differential pressure type flowmeter module for analysis and processing, the respective flow rates of the oil-gas two phases are obtained through calculation, and the display module is used for outputting and displaying the result of the data acquisition and processing module.
8. A multiphase flow measurement system based on uncertainty analysis, comprising:
an online detection system: the system is used for analyzing oil-gas two-phase flow and is provided with a differential pressure type flowmeter and a capacitance conductance detection element;
the first calculation unit: the device is used for obtaining the liquid phase flow and the relative standard uncertainty thereof, and the gas phase flow and the standard uncertainty thereof through linear fitting based on the capacitance measured value;
a second calculation unit: the device is used for obtaining the liquid phase flow and the relative standard uncertainty thereof, and the gas phase flow and the standard uncertainty thereof through linear fitting based on the capacitance measured value and the differential pressure measured value;
a third calculation unit: the method is used for obtaining liquid phase flow and relative standard uncertainty thereof, and gas phase flow and standard uncertainty thereof through linear fitting based on equivalent flow and differential pressure measured values of cross-correlation time delay;
a result output unit: and the uncertainty is used for comparing the uncertainty obtained by the first calculating unit, the second calculating unit and the third calculating unit, and the gas-liquid flow corresponding to the minimum uncertainty and the corresponding uncertainty are used as quality indexes for measuring flow measurement.
9. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 7.
10. A computer device comprising a memory and a processor, on which memory a computer program is stored which is executable on the processor, characterized in that the steps of the method of any of claims 1 to 7 are implemented when the processor executes the program.
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