CN114818520B - A crude oil phase diagram fitting method and system based on trust region method - Google Patents
A crude oil phase diagram fitting method and system based on trust region method Download PDFInfo
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Abstract
本发明公开了一种基于信赖域方法的原油相图拟合方法及系统，该方法包括：获取原油原始状态方程参数及需要拟合的状态方程参数；根据原油原始状态方程参数及需要拟合的状态方程参数，选择拟合参数组合，并设置拟合参数界限；根据拟合参数组合，采用信赖域算法对原油原始相图进行拟合计算；输出拟合后的状态方程参数，根据原始相图与拟合相图结果进行对比；检查拟合对比结果，若不符合拟合要求，调整拟合参数重新拟合，本发明具有可实施性强，计算稳定性好，收敛速度快，拟合效果好，能够大大提高原油组分分析的精度。
The invention discloses a crude oil phase diagram fitting method and system based on a trust region method. The method comprises: obtaining original state equation parameters of crude oil and state equation parameters to be fitted; selecting a fitting parameter combination according to the original state equation parameters of crude oil and the state equation parameters to be fitted, and setting a fitting parameter limit; performing fitting calculation on the original phase diagram of crude oil by using a trust region algorithm according to the fitting parameter combination; outputting the fitted state equation parameters, and comparing the original phase diagram with the fitted phase diagram result; checking the fitting comparison result, and adjusting the fitting parameters to re-fit if the fitting requirement is not met. The invention has strong feasibility, good calculation stability, fast convergence speed, good fitting effect, and can greatly improve the accuracy of crude oil component analysis.
Description
Technical Field
The invention belongs to the technical field of oil and gas reservoir engineering, and particularly relates to a crude oil phase diagram fitting method and system based on a trust domain method.
Background
Reservoir fluids are complex mixtures containing many hydrocarbon components that can be distributed between a liquid phase and a gas phase at a given temperature and pressure, and a phase can be defined as a homogeneous portion of the system where the physical and chemical properties are identical, with a significant difference in properties between the different phases. The oil and gas reservoir P-T phase diagram shows the coexistence range of the temperature and pressure intervals and the phase states of the oil and gas reservoir complex fluid under different gas or liquid phase contents, and has a great number of applications in oil reservoir engineering, including oil and gas reservoir fluid phase state characteristic research, oil and gas reservoir type identification, high recovery ratio (EOR), separator design and the like, so that the calculation and fitting of the oil and gas reservoir P-T phase diagram are of great importance in the calculation and analysis of oil reservoir fluid.
The oil and gas reservoir P-T phase diagram (or phase envelope) is an envelope formed by a series of equiliquid phase lines, the equiliquid phase lines are phase characteristic lines formed by a series of (P, T) state points when the liquid phase mole fraction is a fixed value, the oil and gas reservoir P-T phase diagram calculation is to calculate the equiliquid phase lines under different liquid (or gas) contents of the specific component system fluid of the oil reservoir, in the range of 0.ltoreq.n g.ltoreq.1, a series of gas (liquid) phase mole fractions are given, a series of (P, T) state points are calculated, and the equiliquid phase lines corresponding to the liquid phase mole fraction can be obtained by plotting the state points.
At present, the main calculation method of the oil and gas reservoir P-T phase diagram (or the liquid-equal line) can be divided into two types, one is a univariate iteration method solved by a successive alternate iteration method, programming of the method is simple, initial value requirements are not high, algorithm stability is good, convergence speed is poor, the other is a multivariate iteration method for solving a nonlinear equation set by Newton-Raphson iteration, the convergence speed is high, the requirement on the initial value is severe, and the method can be diverged due to Jacobi matrix singular near a critical point.
In component combination or splitting and other component operations in the component analysis process, an empirical formula is generally adopted to calculate component properties to obtain new component characteristic parameters, and in the process, a certain error is generally generated in a P-T phase diagram of the oil and gas reservoir to cause the change of fluid phase state characteristics. However, in the current mainstream PVT analysis software, whether the PVTi software of the schlembeset company, the WinProp software of the CMG company or the special PVT analysis software PVTsim does not consider errors caused by the operations on the P-T phase diagram of the oil and gas reservoir, the consistency and accuracy of the subsequent phase analysis result cannot be ensured, and further, huge economic loss is brought to the exploitation of the oil reservoir to a certain extent.
In view of the above, a technical solution is needed that can overcome the shortcomings of the prior art, and can efficiently and stably calculate and fit a complex phase diagram of crude oil.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a crude oil phase diagram fitting method and a crude oil phase diagram fitting system based on a trust domain method, the invention adopts a combination method of an alternate iteration method and a Newton iteration method to efficiently and stably calculate a crude oil complex phase diagram, and a global convergence trust domain algorithm is adopted to fit the phase diagram, so that the global convergence can be ensured, the rapid convergence can be realized, and the accuracy of crude oil fluid analysis is effectively improved.
In a first aspect of the embodiment of the present invention, a crude oil phase diagram fitting method based on a trust domain method is provided, where the method includes:
Acquiring the original state equation parameters of crude oil and the state equation parameters to be fitted;
Selecting a fitting parameter combination according to the original state equation parameters of the crude oil and the state equation parameters to be fitted, and setting a fitting parameter limit;
according to the fitting parameter combination, fitting calculation is carried out on the crude oil original phase diagram by adopting a trust domain algorithm;
Outputting fitted state equation parameters, and comparing the state equation parameters with the fitted phase diagram results according to the original phase diagram;
And checking the fitting comparison result, and if the fitting comparison result does not meet the fitting requirement, adjusting fitting parameters to re-fit.
In a second aspect of the embodiment of the present invention, a crude oil phase diagram fitting system based on a trust domain method is provided, the system comprising:
The parameter acquisition module is used for acquiring the original state equation parameters of the crude oil and the state equation parameters to be fitted;
The selection module is used for selecting a fitting parameter combination according to the original state equation parameters of the crude oil and the state equation parameters to be fitted, and setting a fitting parameter limit;
the fitting calculation module is used for carrying out fitting calculation on the crude oil original phase diagram by adopting a trust domain algorithm according to the fitting parameter combination;
The comparison module is used for outputting the fitted state equation parameters and comparing the state equation parameters with the fitted phase diagram results according to the original phase diagram;
And the checking module is used for checking the fitting comparison result, and if the fitting comparison result does not meet the fitting requirement, adjusting the fitting parameters to re-fit.
In a third aspect of the embodiments of the present invention, a computer device is provided, including a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor implementing a crude oil phase diagram fitting method based on a trust domain method when executing the computer program.
In a fourth aspect of the embodiments of the present invention, a computer readable storage medium is presented, the computer readable storage medium storing a computer program which, when executed by a processor, implements a crude oil phase map fitting method based on a trust domain method.
The crude oil phase diagram fitting method and system based on the trust domain method provided by the invention are characterized by obtaining crude oil original state equation parameters and state equation parameters to be fitted, selecting fitting parameter combinations according to the crude oil original state equation parameters and the state equation parameters to be fitted, setting fitting parameter boundaries, carrying out fitting calculation on the crude oil original phase diagram by adopting the trust domain algorithm according to the fitting parameter combinations, outputting fitted state equation parameters, comparing the fitted state equation parameters with a fitted phase diagram result according to the original phase diagram, checking the fitted comparison result, and adjusting the fitting parameters to re-fit if the fitted comparison result does not meet the fitting requirement.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present application, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a crude oil phase diagram fitting method based on a trust zone method according to an embodiment of the invention.
Fig. 2 is a logarithmic transformation diagram of fitting parameters.
Fig. 3 is a flow chart of the isopipe line phase diagram calculation.
FIG. 4 is a flowchart for combining Wilson's equation and RR's equation to calculate initial points K i and T.
Fig. 5 is a flow chart of an alternate iterative solution.
FIG. 6 is a flow chart of the Newton-Raphson Newton iteration method acceleration solution.
Fig. 7 is a schematic diagram of the results of the isobologram and the original phase diagram after combining the original components.
Fig. 8 is a schematic diagram of the fitting result after the phase diagram fitting.
FIG. 9 is a schematic diagram of a crude oil phase diagram fitting system architecture based on a trust domain method according to an embodiment of the present invention.
Fig. 10 is a schematic diagram of a computer device according to an embodiment of the invention.
Detailed Description
The principles and spirit of the present invention will be described below with reference to several exemplary embodiments. It should be understood that these embodiments are presented merely to enable those skilled in the art to better understand and practice the invention and are not intended to limit the scope of the invention in any way. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
Those skilled in the art will appreciate that embodiments of the invention may be implemented as a system, apparatus, device, method, or computer program product. Accordingly, the present disclosure may be embodied in the form of entirely hardware, entirely software (including firmware, resident software, micro-code, etc.) or in a combination of hardware and software.
According to the embodiment of the invention, a crude oil phase diagram fitting method and system based on a trust domain method are provided.
The invention provides a complex equivalent liquid line phase diagram calculation method of a combined alternate direct solving algorithm and a Newton acceleration iteration algorithm, which solves the problems of poor convergence speed of the alternate direct solving algorithm, harsh requirement on the Newton acceleration iteration initial value and the like, and has the characteristics of high convergence speed, good calculation stability and the like; meanwhile, a trust domain algorithm with global convergence is adopted to fit a phase diagram, the phase diagram fitting firstly uses phase diagram critical points as characteristic points to determine a designated variable set of fitting points on an equal liquid line, then a corresponding state point (P-T) point set at the designated variable is accurately calculated in the equal liquid line phase diagram iteration process, further an error set between the fitted phase diagram and an equal liquid line curve on an original phase diagram is calculated, a Jacobian matrix of fitting parameters is calculated by a numerical derivation method, and therefore the equal liquid line phase diagram fitting problem is converted into a nonlinear minimum optimization problem of Levenberg-Marquardt, finally the phase diagram fitting is realized based on the trust domain algorithm.
The principles and spirit of the present invention are explained in detail below with reference to several representative embodiments thereof.
FIG. 1 is a schematic flow chart of a crude oil phase diagram fitting method based on a trust zone method according to an embodiment of the invention. As shown in fig. 1, the method includes:
step S1, acquiring crude oil original state equation parameters and state equation parameters to be fitted;
Step S2, selecting a fitting parameter combination according to the original state equation parameters of the crude oil and the state equation parameters to be fitted, and setting a fitting parameter limit;
step S3, fitting calculation is carried out on the crude oil original phase diagram by adopting a trust domain algorithm according to the fitting parameter combination;
S4, outputting fitted state equation parameters, and comparing the state equation parameters with the fitted phase diagram results according to the original phase diagram;
And S5, checking a fitting comparison result, and if the fitting comparison result does not meet the fitting requirement, adjusting fitting parameters to re-fit.
In order to more clearly explain the crude oil phase diagram fitting method based on the trust zone method, each step is described in detail below.
Step S1:
The method comprises the steps of obtaining crude oil original state equation parameters and state equation parameters to be fitted, wherein the state equation parameters mainly comprise critical parameters (P c,Tc,Vc,Zc), state equation coefficients (omega a,Ωb), physical characteristic parameters (eccentric factor omega c and volume correction coefficient Sshift), binary interaction coefficients kij and mole fractions (zi), and selecting a proper state equation to comprise a three-parameter PR or SRK state equation.
Step S2:
Selecting a suitable combination of fitting parameters and setting a limit of fitting parameters. The fitting parameters mainly select the state equation parameters of the combined component (the component with different properties from the original component), and the basic principle of the fitting state equation parameter selection is as follows:
1. mainly selecting critical parameters, state equation coefficients or physical characteristic parameters;
2. Binary correlation coefficients are not selected as much as possible;
3. The selection of mole fractions as fitting parameters is prohibited. The fit limit principle is that the larger the fit limit range is, the larger the change amount of the fit parameter is, the larger the heavy component fit parameter limit range can be set, and the light component fit parameter limit range can be relatively smaller.
Step S3:
Adopting a trust domain algorithm to carry out fitting calculation on the crude oil original phase diagram, the specific flow comprises the following steps:
S21, according to the fitting parameter combination, adopting a logarithmic transformation processing method, and equivalently processing the fitting parameter with constraint by using a first variable;
referring to fig. 2, a logarithmic transformation of the fitting parameters is illustrated. As shown in fig. 2, for each fitting parameter x, the variable S i can be used to equal, which can be achieved in one-to-one correspondence by;
After logarithmic transformation, the constraint boundary is removed, the fitting argument becomes S i, the objective function is lowered until convergence by iterating S i, and finally x is reversely calculated by using the relation between S i and x.
Step S22, carrying out phase diagram calculation on an equivalent liquid line by adopting an alternate iteration method and a Newton-Raphson iteration method to obtain a phase diagram of original component parameters;
step S23, calculating a phase diagram of the fitting component parameters by adopting a curve fitting method for calculating the distances between the characteristic points, and calculating fitting errors of the distances between the fitting component parameters and the characteristic points corresponding to the original component parameters;
Specifically, the fitting parameter x of the S i is reversely calculated through the constraint function, and is brought into a fitting state equation parameter to calculate a phase diagram of the equivalent liquid line, and the fitting error with the original phase diagram is calculated.
Step S24, calculating a jacobian matrix of the fitting error relative to the first variable by adopting a numerical value derivation method;
That is, a numerical derivation method is used to calculate the jacobian matrix of the fitting error with respect to the set of S i.
And S25, carrying out fitting calculation of the phase diagram by iteratively updating a first variable according to the jacobian matrix by adopting a trust domain algorithm.
And performing fitting calculation of the phase diagram by adopting a trust domain algorithm and performing iterative updating S i.
Specifically, the detailed flow of step S22 is as follows:
step S221, calculating a starting point value of an equivalent liquid quantity line phase diagram by adopting a simultaneous RR equation and Wilson formula method;
step S222, controlling the error within a certain range by adopting an alternating iteration method of accelerating the main characteristic value according to the initial point value of the liquid equivalent linear phase diagram;
step S223, converging the starting point value by adopting a Newton-Raphson iteration method according to the starting point value after the control error;
step S224, performing interpolation calculation on the next point to obtain an initial value of the next point;
Step S225, according to the initial value of each point, obtaining a phase diagram of the original component parameters.
More specifically, step S221 is described in detail:
Referring to fig. 3 and 4, which are respectively a flow chart of calculating an isopipe phase diagram and a flow chart of calculating initial points K i and T initial values by combining a Wilson formula and an RR equation, as shown in fig. 3 and 4, a detailed flow chart of calculating the initial point values of the isopipe phase diagram by adopting a combined RR equation and Wilson formula method is as follows:
Step A, setting the liquid content, pressure and initial temperature;
and step B, calculating a balance constant K i and an intermediate variable Q, dQ/dT by combining a Wilson formula and an RR equation, wherein,
Step B1, calculating a balance constant K i by using a Wilson formula:
wherein, p is pressure, T is temperature, p ci、Tci、ωi is critical pressure, critical temperature and eccentric factor of the ith component respectively;
Step B2, calculating intermediate variables Q, dQ/dT by combining the Wilson equation and the RR equation:
Wherein Nc is the total number of components, z i is the mole fraction of the ith component, F is the liquid content;
Step C, if Q or dQ/dT is not in the effective range, searching the temperature by adopting a dichotomy between a temperature T 1 meeting Q >0 and a temperature T 2 meeting Q <0, so that Q and dQ/dT are in the effective range;
And D, calculating the temperature T by adopting a Newton iterative algorithm:
more specifically, step S222 is described in detail:
Referring to FIG. 5, a flow chart is solved by an alternate iteration method, and as shown in FIG. 5, a detailed flow chart for controlling errors within a certain range by adopting an alternate iteration method of accelerating main eigenvalues is as follows:
Step A, setting the liquid content, pressure and initial temperature;
Step B, calculating a compression factor through a PR or SRK three-parameter state equation, and obtaining the loss of the component and the corresponding derivative according to the compression factor;
And C, calculating a balance constant K i by using a DEM main characteristic value acceleration method:
Wherein, Respectively the fugacity coefficient of the ith component in the liquid phase and the gas phase, and f i L、fi V is the fugacity of the ith component in the liquid phase and the gas phase, and the superscript n is an iteration step;
Step D, calculating the temperature by adopting Newton iterative algorithm
Wherein, The temperature of the n+1-th iteration step is the liquid content F.
More specifically, step S223 is described in detail:
referring to fig. 6, a flow chart of the acceleration solution of the Newton-Raphson Newton iteration method is shown, and as shown in fig. 6, a detailed flow chart of converging the starting point value by using the Newton-Raphson iteration method is as follows:
Step A, setting the liquid content, pressure and initial temperature;
Step B, calculating a state equation compression factor through a PR or SRK three-parameter state equation, and obtaining the fugacity and the corresponding derivative of the component according to the compression factor;
step C, establishing a Jacobian matrix, wherein,
Step C1, setting an iteration unknown quantity x= (ln K 1,ln K2,…,ln KNc, ln T, ln p);
Wherein K i (i is more than or equal to 1 and less than or equal to Nc) is the equilibrium constant of the ith component;
step C2, iterating the equation set:
Wherein, i is more than or equal to 1 and less than or equal to Nc, X i and y i are the mole fractions of the ith component in the liquid phase and the gas phase respectively, S= lnp 0 or lnT 0, when S= lnp 0, k=Nc+2, wherein, X k means the Nc+2 component of the variable X, and when S= lnT 0, k=Nc+1;
Step C3, jacobi matrix expression:
wherein, i is more than or equal to 1, j is less than or equal to Nc;
step D, newton iteration of nonlinear equation components:
Xn+1＝Xn-Jac-1g(Xn);
Where n is the iteration step and Jac is the Jacobi matrix generated in step C.
More specifically, step S224 interpolates the next point using linear interpolation or polynomial interpolation, wherein,
By linear interpolationAnd (3) withObtaining a linear interpolation estimation formula:
Wherein X is an iteration unknown quantity, X i is the ith quantity of the iteration unknown quantity, delta p is a pressure increment, and the same holds for the temperature T;
when polynomial interpolation is adopted, polynomial interpolation is carried out by utilizing the upper two points or the upper three points, and the calculation formula is as follows:
Where a im is the interpolation coefficient.
More specifically, in step S3, a trust domain algorithm is used to perform a fitting calculation on the raw phase diagram of the crude oil, including:
step A, according to the fitting error, converting a nonlinear fitting problem into a fitting error by adopting a trust domain algorithm:
wherein F (x) is a function consisting of the sum of squares of the error functions F (x);
F (x) second order Taylor expansion is written as:
Wherein,
Neglecting the second derivative, writing
Wherein J (x) is Jacobian matrix
Step B, iteratively calculating step sizes by using Levenberg_Marquardt:
Wherein h lm is the step size, μ is the radius of the confidence region, J k is the shorthand matrix of the Jacobian matrix of the kth iteration step f (x), I is the identity matrix;
Step C, obtaining the change of mu according to the evaluation function rho:
wherein the denominator is a predicted value of the gain, and the predicted value of the gain is solved by the following formula:
Wherein g is a gradient vector, J is a shorthand form of Jacobian matrix; and-g is positive, L (0) -L (h lm) is a positive value;
if the value of the evaluation function rho is larger than a first preset value, the corresponding L (h) iteration effect reaches the expected effect, and the next LM algorithm is close to the Gaussian Newton process by reducing mu;
If the control variable rho is smaller than a second preset value, the corresponding L (0) iteration effect does not reach the expected effect, and the iteration step is close to the maximum gradient descent direction by increasing the value of mu;
step D, judging and determining mu by comparing the evaluation function rho with a preset value epsilon 1,ε2 k+1
Wherein mu k+1 and mu k are the radius of the trust zone of mu k+1th and k-th iterations respectively, and tau 1 and tau 2 are the radius reduction coefficient and the radius increase coefficient of the trust zone respectively, which satisfy 0< tau 1<1,τ2 >1.
It should be noted that although the operations of the method of the present invention are described in a particular order in the above embodiments and the accompanying drawings, this does not require or imply that the operations must be performed in the particular order or that all of the illustrated operations be performed in order to achieve desirable results. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step to perform, and/or one step decomposed into multiple steps to perform.
For a clearer explanation of the above crude oil phase diagram fitting method based on the trust zone method, a specific example will be described below, however, it should be noted that this example is only for better explaining the present invention and is not meant to limit the invention unduly.
In the complex phase diagram fitting process of crude oil, since the phase diagram calculation is complex and needs to be solved in an iterative way, fitting parameters (state equation parameters) cannot be directly derived and a numerical method is adopted, and n+1 (n is the number of fitting parameters) phase diagram calculations need to be carried out for each iteration, so that more phase diagram calculations are involved in the phase diagram fitting, and the phase diagram needs to be calculated with high efficiency.
Secondly, the phase diagram fitting also involves arbitrary transformation of fitting parameters, so that phase diagram calculation under any fitting parameter combination must be able to be stably calculated and accurately solved. Meanwhile, the calculation of the crude oil complex phase diagram is complex, and a very small fitting parameter change amount can possibly cause great result change, so that a method capable of ensuring global convergence and fast convergence is needed.
The crude oil phase diagram fitting method based on the trust domain method mainly comprises the following two aspects of efficiently and stably calculating a crude oil complex phase diagram by adopting a combination method of an alternate iteration method and a Newton iteration method, fitting the phase diagram by adopting a global convergence trust domain algorithm, and concretely comprises the following steps:
S01, selecting initialization parameters, namely initializing fitting parameters x0, initializing reliability region radius mu 0＝τmax{aii, judging threshold value 0< epsilon 1＜ε2 <1, radius expansion ratio 0< tau 1＜1＜τ2 and convergence accuracy
S02, calculating a fitting phase diagram and an original phase diagram respectively, and solving an error of the fitting point, wherein the error is specifically as follows:
s021, calculating a critical point, wherein the critical point is used as a main special point on the phase diagram, plays a key role in the fitting of the liquid-level line phase diagram, and mainly adopts a method of HEIDEMANN for direct solving.
S022, selecting fitting points on the equipotential lines, wherein the state points (P, T) on the equipotential lines are obtained by iterative solution based on the previous state point, and when fitting, a single-variable iteration method with the pressure being a designated variable temperature as an iteration variable is adopted, and a fitting point set on the equipotential lines is calculated by a method of calculating an incomplete phase diagram, wherein the designated pressure is P di＝i(Pc-Psc)/N.
S023, calculating liquid lines such as phase diagrams mainly adopts a method combining an alternate iteration method and a Newton-Raphson iteration method.
S0231, initializing a starting point pressure P0, an initial iteration step dp and an initial temperature guess T0;
s0232, calculating the starting point of the isopipe:
a) The temperature T0 of the starting point P0 and the initial value of the phase equilibrium constant Ki0 are calculated by combining the RR equation and the Wilson equation;
b) According to the initial value calculated in a), adopting an alternating iteration method of accelerating the main characteristic value to enable the error to be within a certain range;
c) According to the initial value calculated in b), using Newton-Raphson iterative method to accelerate the calculation of temperature (T) 0 and phase equilibrium constant (K i)0 values and their first derivatives to the initial pressure (P) 0 at the initial point (P) 0;
d) The first point specified pressure (P) 1 is calculated from the iteration step (dp) 1 and the specified pressure P di, and the initial value of (T) 1,(Ki)1 is interpolated from the derivative of (T) 0,(Ki)0 and (P) 1.
S0233, carrying out Newton-Raphson iterative calculation on the kth point according to the initial value calculated by the last point, if the iteration fails, turning to S0234, otherwise turning to S0235:
S0234, if the iteration fails, adopting an alternate iteration method to recalculate, and accelerating convergence through Newton-Raphson, if the iteration continues to fail, turning to S0235, otherwise turning to S0236;
S0235, decreasing the step-down step (dp) k, recalculating the specified pressure (P) k, interpolating the initial value of the estimate (T) k,(Ki)k, and moving to S0233 for the kth point iterative calculation.
S0236, judging whether (dp) k is smaller than the set threshold value or (P) k reaches the vicinity of the threshold point, if one of them is satisfied, skipping out the liquid amount line calculation, otherwise, proceeding to S0237.
S0237, determining the step-down step length (dp) k+1 of k+1 points according to the iteration number of the kth point, calculating the designated pressure (P) k+1 of the k+1 points, interpolating to estimate the initial value of the next iteration (T) k+1,(Ki)k+1, and turning to S0233 to continue calculation. S024, calculating the error of each fitting point according to the calculation results of the original phase diagram and the fitting phase diagram
S03, calculating Jacobi matrix of fitting point error relative to fitting parameter x according to step S02 by using numerical value derivation methodWherein the method comprises the steps ofFirst order gradient descent directionIf it isThen exit, else continue.
S04, calculating a second-order approximate hessian matrix about the fitting parameter x
S05, according to the formulaThe iteration step h lm is calculated using a gaussian solution.
S06, calculating x new＝xk+hlm by using the formulaCalculating the evaluation function ρ, if ρ >0, going to S07, otherwise going to S08.
S07, comparing the evaluation function ρ with a preset value ε 1,ε2 to determine the radius of the trusted regionAnd updating the parameter x k+1＝xk+hlm, returning to the step S02 to perform the next iterative calculation.
S08, ρ.ltoreq.0 indicates that the function value is changing toward an ascending rather than descending trend (contrary to the goal of optimization), at which time it should not go to the next point, but should "step in place", i.e., the original parameter x k+1＝xk is retained and the convergence radius μ k+1＝τ1μk is reduced, returning to step S02 for re-iterative calculation.
Taking an oilfield as an example, the oilfield crude oil contains 41 components, and the PR3 state equation is adopted for calculation. Since the number of components cannot meet the requirements of crude oil analysis and simulation calculation, the components need to be combined, the original 41 components are combined into 8 components by a mole average method in the calculation example, and the results of the liquid equivalent line phase diagram and the original phase diagram after the combination are shown in fig. 7. As can be seen from the comparison of the combined phase diagram with the original phase diagram, the combined phase diagram and the original phase diagram have large differences, and the phase diagram fitting must be performed on the combined state equation parameters.
1) And selecting original state equation parameters of the crude oil with 41 components, and taking the combined state equation parameters of 8 components as fitting component data.
2) A suitable combination of fitting parameters was selected, 7 combined and additive components were selected as shown in table 1, and their critical temperatures Tc and critical pressures Pc were fitted for a total of 14 fitting parameters.
3) And adopting a trust domain algorithm to perform fitting calculation on the crude oil original phase diagram.
4) The fitting results are shown in fig. 8, and the fitting parameter changes are shown in table 1.
Table 1 amount of fitting parameter change
| Fitting component | Equation of state parameters | Before fitting numerical value | Post-fitting numerical values | Variation of |
| N2-C1 | Pc | 666.6859 | 669.166 | 1.00372 |
| C2-C3 | Pc | 669.2124 | 671.916 | 1.00404 |
| IC4-C6 | Pc | 489.4524 | 487.659 | 0.996336 |
| C7-C10 | Pc | 400.4859 | 397.415 | 0.992332 |
| C11-C20 | Pc | 269.5295 | 262.181 | 0.972736 |
| C21-C35 | Pc | 174.657 | 171.437 | 0.981564 |
| C36+ | Pc | 53.46961 | 52.9732 | 0.990716 |
| N2-C1 | Tc | 342.3557 | 341.039 | 0.996154 |
| C2-C3 | Tc | 598.7472 | 587.932 | 0.981937 |
| IC4-C6 | Tc | 837.0256 | 839.838 | 1.00336 |
| C7-C10 | Tc | 1047.36 | 1040.33 | 0.993288 |
| C11-C20 | Tc | 1275.265 | 1276.17 | 1.00071 |
| C21-C35 | Tc | 1527.03 | 1559.54 | 1.02129 |
| C36+ | Tc | 1874.806 | 1874.9 | 1.00005 |
Having described the method of an exemplary embodiment of the present invention, a crude oil phase diagram fitting system based on a trust zone method of an exemplary embodiment of the present invention is next described with reference to fig. 9.
The implementation of the crude oil phase diagram fitting system based on the trust zone method can be referred to the implementation of the method, and the repetition is not repeated. The term "module" or "unit" as used below may be a combination of software and/or hardware that implements the intended function. While the means described in the following embodiments are preferably implemented in software, implementation in hardware, or a combination of software and hardware, is also possible and contemplated.
Based on the same inventive concept, the invention also provides a crude oil phase diagram fitting system based on a trust zone method, as shown in fig. 9, the system comprises:
the parameter obtaining module 910 is configured to obtain an original state equation parameter of crude oil and a state equation parameter to be fitted;
The selection module 920 is configured to select a fitting parameter combination according to the crude oil original state equation parameter and the state equation parameter to be fitted, and set a fitting parameter limit;
The fitting calculation module 930 is configured to perform fitting calculation on the crude oil original phase diagram by adopting a trust domain algorithm according to the fitting parameter combination;
the comparison module 940 is configured to output the fitted state equation parameter, and compare the fitted state equation parameter with the fitted phase diagram result according to the original phase diagram;
And the checking module 950 is configured to check the fitting comparison result, and if the fitting requirement is not met, adjust the fitting parameters to re-fit.
It should be noted that while several modules of a crude oil phase map fitting system based on a trust zone method are mentioned in the above detailed description, this partitioning is merely exemplary and not mandatory. Indeed, the features and functions of two or more modules described above may be embodied in one module in accordance with embodiments of the present invention. Conversely, the features and functions of one module described above may be further divided into a plurality of modules to be embodied.
Based on the foregoing inventive concept, as shown in fig. 10, the present invention further proposes a computer device 1000, including a memory 1010, a processor 1020, and a computer program 1030 stored in the memory 1010 and executable on the processor 1020, where the processor 1020 implements the crude oil phase diagram fitting method based on the trust domain method when executing the computer program 1030.
Based on the foregoing inventive concept, the present invention proposes a computer readable storage medium storing a computer program which, when executed by a processor, implements the aforementioned crude oil phase map fitting method based on a trust domain method.
The crude oil phase diagram fitting method and system based on the trust domain method provided by the invention are characterized by obtaining crude oil original state equation parameters and state equation parameters to be fitted, selecting fitting parameter combinations according to the crude oil original state equation parameters and the state equation parameters to be fitted, setting fitting parameter boundaries, carrying out fitting calculation on the crude oil original phase diagram by adopting the trust domain algorithm according to the fitting parameter combinations, outputting fitted state equation parameters, comparing the fitted state equation parameters with a fitted phase diagram result according to the original phase diagram, checking the fitted comparison result, and adjusting the fitting parameters to re-fit if the fitted comparison result does not meet the fitting requirement.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It should be noted that the foregoing embodiments are merely illustrative embodiments of the present invention, and not restrictive, and the scope of the invention is not limited to the embodiments, and although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that any modification, variation or substitution of some of the technical features of the embodiments described in the foregoing embodiments may be easily contemplated within the scope of the present invention, and the spirit and scope of the technical solutions of the embodiments do not depart from the spirit and scope of the embodiments of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. A crude oil phase diagram fitting method based on a trust zone method, which is characterized by comprising the following steps:
Acquiring the original state equation parameters of crude oil and the state equation parameters to be fitted;
Selecting a fitting parameter combination according to the original state equation parameters of the crude oil and the state equation parameters to be fitted, and setting a fitting parameter limit;
according to the fitting parameter combination, fitting calculation is carried out on the crude oil original phase diagram by adopting a trust domain algorithm;
Outputting fitted state equation parameters, and comparing the state equation parameters with the fitted phase diagram results according to the original phase diagram;
checking the fitting comparison result, and if the fitting comparison result does not meet the fitting requirement, adjusting fitting parameters to re-fit;
according to the fitting parameter combination, a trust domain algorithm is adopted to carry out fitting calculation on the crude oil original phase diagram, and the method comprises the following steps:
according to the fitting parameter combination, adopting a logarithmic transformation processing method, and equivalently processing fitting parameters with constraint by using a first variable;
Carrying out phase diagram calculation on the liquid equivalent line by combining an alternating iteration method and a Newton-Raphson iteration method to obtain a phase diagram of the original component parameters;
Calculating a phase diagram of the fitting component parameters by adopting a curve fitting method for calculating the distances between the characteristic points, and calculating fitting errors of the distances between the fitting component parameters and the characteristic points corresponding to the original component parameters;
calculating a jacobian matrix of the fitting error relative to the first variable by adopting a numerical value derivation method;
and according to the jacobian matrix, adopting a trust domain algorithm, and carrying out fitting calculation of the phase diagram by iteratively updating the first variable.
2. The method of claim 1, wherein the phase diagram of the original component parameters is obtained by performing an isoliquid line phase diagram calculation using an alternating iterative method in combination with a Newton-Raphson iterative method, comprising:
calculating a starting point value of an equivalent liquid quantity line phase diagram by adopting a simultaneous RR equation and a Wilson formula method;
according to the initial point value of the liquid equivalent linear phase diagram, an alternating iteration method of accelerating a main characteristic value is adopted to control the error within a certain range;
according to the starting point value after the control error, adopting a Newton-Raphson iteration method to converge the starting point value;
performing interpolation calculation on the next point to obtain an initial value of the next point;
and obtaining a phase diagram of the original component parameters according to the initial value of each point.
3. The method of claim 2, wherein calculating the starting point value of the isobologram using the simultaneous RR equation and Wilson equation method comprises:
Step A, setting the liquid content, pressure and initial temperature;
and step B, calculating a balance constant K i and an intermediate variable Q, dQ/dT by combining a Wilson formula and an RR equation, wherein,
Step B1, calculating a balance constant K i by using a Wilson formula:
wherein, p is pressure, T is temperature, p ci、Tci、ωi is critical pressure, critical temperature and eccentric factor of the ith component respectively;
Step B2, calculating intermediate variables Q, dQ/dT by combining the Wilson equation and the RR equation:
Wherein Nc is the total number of components, z i is the mole fraction of the ith component, F is the liquid content;
Step C, if Q or dQ/dT is not in the effective range, searching the temperature by adopting a dichotomy between a temperature T 1 meeting Q >0 and a temperature T 2 meeting Q <0, so that Q and dQ/dT are in the effective range;
And D, calculating the temperature T by adopting a Newton iterative algorithm:
4. A method according to claim 3, wherein the error is controlled within a certain range by using an alternating iterative method of acceleration of main eigenvalues according to the starting point value of the isobar line phase diagram, comprising:
Step A, setting the liquid content, pressure and initial temperature;
Step B, calculating a state equation compression factor through a PR or SRK three-parameter state equation, and obtaining the fugacity and the corresponding derivative of the component according to the compression factor;
And C, calculating a balance constant K i by using a DEM main characteristic value acceleration method:
Wherein, Respectively the fugacity coefficient of the ith component in the liquid phase and the gas phase, and f i L、fi V is the fugacity of the ith component in the liquid phase and the gas phase, and the superscript n is an iteration step;
Step D, calculating the temperature by adopting Newton iterative algorithm
Wherein, The temperature of the n+1-th iteration step is the liquid content F.
5. A method according to claim 3, wherein converging the start point values using a Newton-Raphson iteration method comprises:
Step A, setting the liquid content, pressure and initial temperature;
Step B, calculating a state equation compression factor through a PR or SRK three-parameter state equation, and obtaining the fugacity and the corresponding derivative of the component according to the compression factor;
step C, establishing a Jacobian matrix, wherein,
Step C1, setting an iteration unknown quantity x= (lnK 1,lnK2,…,lnKNc, lnT, lnp);
Wherein K i (i is more than or equal to 1 and less than or equal to Nc) is the equilibrium constant of the ith component;
step C2, constructing an iterative equation set:
Wherein, i is more than or equal to 1 and less than or equal to Nc, X i and y i are the mole fractions of the ith component in the liquid phase and the gas phase respectively, S= lnp 0 or lnT 0, when S= lnp 0, k=Nc+2, wherein, X k means the Nc+2 component of the variable X, and when S= lnT 0, k=Nc+1;
step C3, establishing a Jacobi matrix:
wherein, i is more than or equal to 1, j is less than or equal to Nc;
and D, carrying out Newton iteration solution on the nonlinear equation set:
Xn+1＝Xn-Jac-1g(Xn);
Where n is the iteration step and Jac is the Jacobi matrix generated in step C.
6. The method of claim 5, wherein interpolating the next point to obtain an initial value for the next point comprises:
interpolation calculation is carried out on the next point by adopting linear interpolation or polynomial interpolation, wherein,
By linear interpolationAnd (3) withObtaining a linear interpolation estimation formula:
Wherein X is an iteration unknown quantity, X i is the ith quantity of the iteration unknown quantity, delta p is a pressure increment, and the same holds for the temperature T;
when polynomial interpolation is adopted, polynomial interpolation is carried out by utilizing the upper two points or the upper three points, and the calculation formula is as follows:
wherein a im is a polynomial interpolation coefficient.
7. The method of claim 1, wherein fitting the raw phase map of the crude oil using a trust domain algorithm comprises:
Step A, according to the fitting error, recording an error function as f (x), and converting a nonlinear fitting problem into a fitting error by adopting a trust domain algorithm:
wherein F (x) is a function consisting of the sum of squares of the error functions F (x);
F (x) second order Taylor expansion is written as:
Wherein,
Neglecting the second derivative, writing
Wherein J (x) is Jacobian matrix
Step B, iteratively calculating step sizes by using Levenberg_Marquardt:
Wherein h lm is the step size, μ is the radius of the confidence region, J k is the shorthand matrix of the Jacobian matrix of the kth iteration step f (x), I is the identity matrix;
Step C, obtaining the change of mu according to the evaluation function rho:
wherein the denominator is a predicted value of the gain, and the predicted value of the gain is solved by the following formula:
Wherein g is a gradient vector, J is a shorthand form of Jacobian matrix; and-g is positive, L (0) -L (h lm) is a positive value;
if the value of the evaluation function rho is larger than a first preset value, the corresponding L (h) iteration effect reaches the expected effect, and the next LM algorithm is close to the Gaussian Newton process by reducing mu;
If the control variable rho is smaller than a second preset value, the corresponding L (0) iteration effect does not reach the expected effect, and the iteration step is close to the maximum gradient descent direction by increasing the value of mu;
step D, judging and determining mu by comparing the evaluation function rho with a preset value epsilon 1,ε2 k+1
Wherein mu k+1 and mu k are the radius of the trust zone of mu k+1th and k-th iterations respectively, and tau 1 and tau 2 are the radius reduction coefficient and the radius increase coefficient of the trust zone respectively, which satisfy 0< tau 1<1,τ2 >1.
8. A crude oil phase map fitting system based on a trust zone method, the system comprising:
The parameter acquisition module is used for acquiring the original state equation parameters of the crude oil and the state equation parameters to be fitted;
The selection module is used for selecting a fitting parameter combination according to the original state equation parameters of the crude oil and the state equation parameters to be fitted, and setting a fitting parameter limit;
the fitting calculation module is used for carrying out fitting calculation on the crude oil original phase diagram by adopting a trust domain algorithm according to the fitting parameter combination;
The comparison module is used for outputting the fitted state equation parameters and comparing the state equation parameters with the fitted phase diagram results according to the original phase diagram;
the checking module is used for checking the fitting comparison result, and if the fitting comparison result does not meet the fitting requirement, the fitting parameters are adjusted to be fitted again;
the fitting calculation module is specifically configured to:
according to the fitting parameter combination, adopting a logarithmic transformation processing method, and equivalently processing fitting parameters with constraint by using a first variable;
Carrying out phase diagram calculation on the liquid equivalent line by combining an alternating iteration method and a Newton-Raphson iteration method to obtain a phase diagram of the original component parameters;
Calculating a phase diagram of the fitting component parameters by adopting a curve fitting method for calculating the distances between the characteristic points, and calculating fitting errors of the distances between the fitting component parameters and the characteristic points corresponding to the original component parameters;
calculating a jacobian matrix of the fitting error relative to the first variable by adopting a numerical value derivation method;
and according to the jacobian matrix, adopting a trust domain algorithm, and carrying out fitting calculation of the phase diagram by iteratively updating the first variable.
9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the method of any of claims 1 to 7 when executing the computer program.
10. A computer readable storage medium, characterized in that the computer readable storage medium stores a computer program which, when executed by a processor, implements the method of any of claims 1 to 7.
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