CN111175336B - Method for measuring and calculating nuclear magnetic resonance two-phase flow sensor - Google Patents
Method for measuring and calculating nuclear magnetic resonance two-phase flow sensor Download PDFInfo
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Abstract
A method for measuring and calculating a nuclear magnetic resonance two-phase flow sensor comprises the steps of firstly, aiming at magnet design, determining the length of a pre-magnetized magnet A by analyzing the relationship between magnetization vectors and magnetization lengths of different flow rates and different water contents; study of Halbach Structure and target magnetic field intensity B 0 And uniformity P 1 Determining the parameters of the main measuring magnetic field B; target field homogeneity P by compensation magnet C 2 Determining the size of the bucking magnet C; secondly, aiming at coil design, firstly establishing a theoretical model for quantifying an FID signal and a coil, and analyzing the functional relation between the FID and the coil length under the influence of the flow velocity and the phase content rate of two-phase flow; and then researching structural parameter influence factors of the solenoid, such as wire diameter, number of turns, coil spacing, depth-height ratio and the like, determining structural parameters of the sectional type coil and completing the design of matching resonance parameters of the coil. Finally, determining the integral design of the structural parameters of the coil of the magnetic resonance two-phase flow sensor; the invention realizes more accurate measurement of the nuclear magnetic resonance sensor.
Description
Technical Field
The invention relates to the technical field of oil-water two-phase flow parameter measurement, in particular to a method for measuring and calculating a nuclear magnetic resonance two-phase flow sensor.
Background
In the process of oil exploitation, the produced fluid is mostly a mixture of oil and water two-phase flows, and the measurement difficulty of the produced fluid is far higher than that of a single-phase flow due to the variability and complexity of flow characteristics such as flow patterns, flow rates of various phases and the like, so that the two-phase flow measurement is still a great technical problem in the oil industry. Therefore, the research on the parameter measurement and calculation method of the oil-water two-phase flow has very important significance for the optimized exploitation of oil-gas wells, the effective protection of reservoir stratums, the improvement of recovery efficiency and the improvement of the economic benefit of the petroleum industry.
Most of the traditional two-phase flow measuring methods are contact type measuring methods, but because a measuring medium directly contacts the surface of a sensor, the problems of sensitivity reduction, accuracy deterioration and the like of the sensor are caused. The two-phase flow measuring technology based on the nuclear magnetic resonance principle has the advantages that the measuring result is not influenced by macroscopic physical characteristics, the limitation of the traditional measuring method can be effectively overcome, and the technology is a new direction in the field of two-phase flow research at present. In oil-water two-phase flow, the nuclear magnetic resonance phenomenon is the result of the interaction of electromagnetic waves and hydrogen element substances, an oil pipe is placed in a static magnetic field environment with specific strength, radio frequency pulses with corresponding frequency are applied to enable sample atomic nuclei in the pipeline to resonate, and the acquired echo signals are utilized to complete parameter information such as the structure, density distribution and the like of the two-phase flow substances. The magnetic resonance sensor has strict requirements on high uniformity of a magnetic field, high sensitivity of a radio frequency coil signal and high signal-to-noise ratio. For a magnet device, the magnet device has the function of generating a high-strength, uniform and stable main magnetic field, which is the primary condition for generating nuclear magnetic resonance, and the performance of the main magnet directly influences the sensitivity and precision of nuclear magnetic resonance measurement; for a coil system, when two separated coils work, the problems of mutual coupling, reduction of signal-to-noise ratio, energy transfer error and the like can occur, and the receiving and transmitting coils are combined into a whole, so that the high uniformity of a radio frequency magnetic field and the high sensitivity and the high signal-to-noise ratio of a received signal are difficult to simultaneously meet. Therefore, the optimization research of the magnetic resonance two-phase flow sensor is one of the hot spots and difficulties of NMR.
Disclosure of Invention
In order to solve the problems and difficulties in the prior art, the invention aims to provide a method for measuring and calculating a nuclear magnetic resonance two-phase flow sensor, which constructs an accurate nuclear magnetic resonance sensor structure model by introducing two-phase flow system parameters and optimizes and calculates various parameters aiming at a magnet and a coil device, fully analyzes and researches the effect and the precision influence of the sensor structure parameters on measurement signals, and improves the overall performance of the sensor.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for measuring and calculating a nuclear magnetic resonance two-phase flow sensor comprises the following steps:
the first step is as follows: the method comprises the following steps of determining the structural parameters of a magnet of the nuclear magnetic resonance two-phase flow sensor, wherein the magnet is formed by sequentially connecting a pre-magnetized magnet A, a measuring magnet B and a compensating magnet C on a coaxial line, and the method comprises the following specific steps:
1. determining the length of a pre-magnetized magnet A
(1) Determining the functional relationship among the flow velocity, the water content, the magnetization vector and the magnetization length according to the flow characteristics of the oil-water two-phase flow, wherein the expression is as follows:
where M is the actual magnetization vector, M 0 Is the vector of complete magnetization, x is the magnetization length, v is the average flow velocity of oil-water two-phase flow, T 1 The longitudinal relaxation time of the oil-water two-phase flow is related to the phase content a% of the oil-water two-phase flow, T 2 The transverse relaxation time of the oil-water two-phase flow;
(2) Obtaining a normalized magnetization vector according to equation (1)
Analyzing the magnetization vector M/M under different water contents a% and different flow velocities v 0 Characteristic relationship with magnetization length;
(3) According to M/M 0 Finding the magnetization vector M/M according to the curve diagram of the magnetization length 0 The corresponding magnetization length when approaching the maximum value of 1, thereby determining the length of the pre-magnetized magnet a;
2. measuring parameters of magnet B
(1) Establishing a magnetic field two-dimensional plane uniformity expression by adopting a Halbach magnet array
Wherein +>
Average static magnetic field strength, B, generated for a working space magnet max For a large field strength quantization value of the working range, B min Quantizing the value for the lower magnetic field strength in the working interval;
(2) Determining a discrete Halbach mathematical model, and respectively researching the magnetic field intensity B according to four parameters of an internal-external diameter ratio value R/R, the number N of assembly blocks, the shape of the blocks and a magnetic material 0 The following calculation model is obtained:
wherein: b is 0 Strength of static magnetic field generated for magnet, B r The residual magnetic flux density is R, the outer radius of the magnet, R, the inner radius and n, the number of the magnet blocks is calculated;
(3) Establishing a particle swarm optimization model according to a formula (2), wherein the shape of the blocks influences the error between the integral performance and the ideal structure of the discrete Halbach, and the magnetic material influences the residual magnetic flux density B r Influence of the number of building blocks N
The value relationship of (4), the influence of the value of the ratio of the inner to the outer diameter>
Using finite element simulation to comprehensively analyze the magnetic field intensity B 0 Two-dimensional plane uniformity P of magnetic field 1 The law of the change along with the parameters of the four magnets;
(4) According to the simulation analysis result, determining the restriction relation and the influence rule among the parameters, and finding out the magnetic field intensity B meeting the requirement 0 And the magnetic field two-dimensional plane uniformity P 1 The parameter with the highest uniformity, thereby determining each structural parameter of the measuring magnet B;
3. determining parameters of the bucking magnet C
(1) Study of three-dimensional axial magnetic field uniformity
Relationship to magnet length: wherein it is present>
For the average field strength in the axial z-direction, it can be concluded that the magnetic field homogeneity P increases infinitely with the magnet length 2 The axial magnetic field uniformity P is improved, but the length dimension of the magnet is limited in practice, so that the method of adding the compensation magnet C at the two ends of the measurement magnet B is provided 2 ；
(2) According to Maxwell equation of three-position static magnetic field and calculation formula of magnetic induction intensity of permanent magnet, obtaining uniformity P of compensation magnets C with different sizes to axial magnetic field by finite element static magnetic field simulation 2 Influence relationship of (1):
wherein B (x, y, z) is magnetic induction, H (x, y, z) is magnetic field intensity, J (x, y, z) is current density, the three vectors are all functional relations of vectors in all directions, and mu 0 Is the absolute permeability in vacuum, mu r For relative permeability, M P The polarization intensity of the permanent magnetic material;
(3) Comparing different structure sizes according to simulation analysisMagnet C to axial magnetic field uniformity P 2 Finding the magnet parameters with the highest optimization on the magnetic field uniformity and the smallest volume, thereby determining the size of the compensation magnet C;
finally determining the integral design of the magnet structure parameters of the magnetic resonance two-phase flow sensor according to the steps and the analysis result;
the second step: the method for determining the structural parameters of the coil of the nuclear magnetic resonance two-phase flow sensor comprises four steps as follows:
the first part of the steps are as follows:
1. establishing a theoretical model of a quantitative FID signal and a coil, determining a functional relation between a nuclear magnetic resonance receiving signal FID and the length of the coil, and solving the nuclear magnetic resonance receiving signal FID under different average flow velocities v and different water contents a%, wherein the expression is as follows:
wherein: s. the FID For quantizing the FID signal received by the coil, where M i0 ＝S i H I，i ，S i Is the saturation of the ith component, H, in the two-phase flow I，i Is the hydrogen index, L, of the ith component in the two-phase stream D Is the length of the coil, L M For the length of magnetization, T is the sampling time, c is the correction factor, T 1，i Is the spin lattice relaxation time, T, of the ith component 2，i Is the spin-spin relaxation time of the ith component;
2. analyzing FID signals S received by coils under models with different average flow velocities v and different water contents a% according to a formula (4) FID The rule of variation with the length of the coil;
3. by analysing the FID signal S received by the coil FID The corresponding coil length tends to be stable, so that the basic length parameter range of the detection coil is determined;
the second part of the steps are as follows:
1. establishing a theoretical model of coil performance and solenoid parameters, and determining an influence factor of coil sensitivity Bxy:
wherein, B 1 I is the radio frequency magnetic field intensity B generated by a unit current i in the coil 1 N is the number of turns of the coil, H/D is the ratio of the depth to the height of the pipe diameter, H is the height of the solenoid coil, D is the diameter of the coil, u 0 Vacuum magnetic conductivity;
2. establishing an equivalent model of coil resistance R under the skin effect and the proximity effect to obtain the following expression:
wherein R is coil Is the resistance value of an equivalent straight wire at radio frequency, epsilon is the enhancement factor of two adjacent turns of coils, R s The method is an equivalent resistance model, wherein l is the length of a lead used by a coil, d is the wire diameter of the coil, f is the resonance frequency of the coil, mu is the magnetic conductivity, and rho is the resistivity of a copper lead;
3. establishing relative signal-to-noise ratio SNR and sensitivity B under fixed pulse frequency xy And a resistance R s The response relationship of (a) is shown in formula 7; and (3) analyzing the influence rule of each parameter of the coil on the SNR (signal to noise ratio) by applying a particle swarm optimization algorithm in combination with finite element simulation:
wherein: b xy Is the sensitivity of the coil; k is a reaction radio frequency magnetic field B 1 Constant of homogeneity, v s For detecting the volume of the sample, N is the number of nuclear spins per unit volume, γ is the magnetic spin ratio of the atoms, h is Planckian, I is the spin quantum number of the nuclei, w 0 Is the precessional frequency of the nucleus, K B Is Boltzmann constant, R s Is the coil resistance, T is the temperature of the test sample; Δ f is the measured bandwidth;
4. according to the above influence factors and result analysis, the high sensitivity B is obtained xy And coil parameters of high signal-to-noise ratio (SNR);
the third part of the steps are as follows:
1. establishing a solenoid coil to generate a radio frequency magnetic field B 1 The theoretical model of (2) calculates the intensity of the radio frequency magnetic field generated by the coil, and the calculation formula is as follows:
wherein: mu.s 0 The magnetic field strength is vacuum magnetic conductivity, N is the number of turns of a coil, I is the current intensity of the coil, H is the height of a solenoid coil, R is the radius of the solenoid coil, and Z is the distance from any point of an axial space of the solenoid to a central point;
2. analysis of the RF magnetic field B by finite element magnetic field simulation according to equation (8) 1 And calculating the uniformity of the RF magnetic field in the target space
Is the average intensity of the radio frequency magnetic field;
3. by analyzing the change rule of the magnetic field intensity in the solenoid space, the result that the magnetic field intensity in the middle of the pipeline is high and gradually decreases towards the two ends is obtained. Therefore, a segmented coil structure with sparse middle and compact two ends is provided, and the purposes of weakening the magnetic field intensity of the middle section and enhancing the magnetic field intensity of the two ends are achieved by adjusting the space proportion of three segments of coils, so that the uniformity of the whole radio frequency magnetic field is improved;
the fourth step is as follows:
1. the resonance characteristic of a radio frequency system is researched, and various parameter values of a coil under a fixed frequency, including a resistor R, an inductance L and a capacitance C, are measured by using an impedance analyzer;
2. establishing RLC match response relationships according toCalculating to obtain various matching parameters of the coil quality factor according to the following expression, wherein Z is total impedance, W is frequency, and C m A capacitor, C, connected in series with the desired matching circuit t Connecting capacitors in parallel to the obtained matching circuit, wherein R is the actually measured coil resistance value, L is the coil inductance value, and j is a physical vector;
and finally determining the integral design of the coil structure parameters of the magnetic resonance two-phase flow sensor according to the steps and the analysis result.
The invention relates to a parameter measuring and calculating method of a nuclear magnetic resonance two-phase flow sensor, which mainly comprises two steps, wherein in the first step, aiming at magnet design, the length of a pre-magnetized magnet A is determined by analyzing the relationship between magnetization vectors and magnetization lengths with different flow rates and different water contents; then by researching Halbach structure and target magnetic field intensity B 0 And uniformity P 1 Determining the size parameters of the main measuring field B by adopting a particle swarm optimization algorithm and combining finite element simulation; by using the principle of magnetic field superposition, the target magnetic field uniformity P is obtained by the compensation magnet C 2 Determining the optimal size of the compensation magnet C within the error tolerance; through the steps, the overall design of the magnetic structure parameters of the magnetic resonance two-phase flow sensor is finally determined. Secondly, aiming at coil design, firstly establishing a theoretical model for quantifying an FID signal and a coil, and fully analyzing the functional relation between the FID and the coil length under the influence of the phase content rate and the flow velocity of two-phase flow; then researching structural parameter influence factors of the solenoid including wire diameter, turns, coil spacing, depth-height ratio and the like, and establishing relative signal-to-noise ratio Sn and sensitivity B xy The response relation with the resistance R; finally aiming at the uniformity P of the radio frequency magnetic field 3 And (4) determining sectional type coil structure parameters and completing the matching resonance parameter design of the coil. Through the steps, the overall design of the coil structure parameters of the magnetic resonance two-phase flow sensor is finally determined. The parameter calculation method of the nuclear magnetic resonance two-phase flow sensor realizes more accurate measurement of the nuclear magnetic resonance sensor.
Drawings
FIG. 1 is a flow chart of a method for measuring and calculating a nuclear magnetic resonance two-phase flow sensor according to an embodiment of the present invention, wherein FIG. 1a is a flow chart of a step of determining structural parameters of a nuclear magnetic resonance magnet; FIG. 1b is a flow chart of the determination of structural parameters of the MRI coil in step two.
FIG. 2 is the variation rule of magnetization vector with magnetization length under different flow rates and different water contents in the present invention; wherein: FIG. 2 (a) shows a flow velocity of 0.1m/s, and FIG. 2 (b) shows a flow velocity of 0.3m/s.
Fig. 3 is a schematic diagram of a Halbach structure adopted by the magnet of the present invention.
In fig. 4, a is a change rule of the magnetic field strength in the Halbach structure according to the ratio of the inner diameter to the outer diameter; b is the change rule of the magnetic field intensity in the Halbach structure along with the discrete block array N.
Fig. 5 is a two-dimensional plane distribution diagram and a curve trend diagram of the magnetic field of the magnet B determined by the invention.
FIG. 6 is a graph showing the effect of compensating magnet configuration parameters on magnetic field strength and uniformity in accordance with the present invention; wherein: FIG. 6 (a) is a comparative schematic of an optimized sensor magnet configuration; fig. 6 (b) shows the influence of the magnets C with different structural parameters on the uniformity of the magnetic field.
FIG. 7 is the change rule of the quantized value of the FID signal along with the detection coil length under different average flow rates and water contents of the oil-water two-phase flow in the invention; FIG. 7 (a) shows a flow velocity of 0.1m/s, and FIG. 7 (b) shows a flow velocity of 0.3m/s.
FIG. 8 is a diagram of solenoid coil physical models and structural parameters, wherein: fig. 8 (a) is a physical model of a solenoid coil, and fig. 8 (b) is a parameter diagram of the coil structure.
FIG. 9 is a diagram showing performance analysis of coil sensitivity, signal-to-noise ratio, etc. under different coil parameters; wherein: FIG. 9 (a) is a graph of wire diameter, number of turns, and signal-to-noise ratio; FIG. 9 (b) is a graph showing the relationship between the wire diameter, the pitch, and the quality factor.
FIG. 10 is a graph showing the effect on magnetic field uniformity of a segmented coil structure over a conventional structure, in which: FIG. 10 (a) shows the variation of the magnetic field generated by the solenoid coil of the conventional structure along the axial direction (z-axis direction) of the pipe; FIG. 10 (b) shows the variation of the magnetic field generated by the segmented solenoid coil along the axial direction (z-axis direction) of the pipeline after optimization.
Fig. 11 is a schematic diagram of a circuit employing a parallel resonant circuit.
Detailed Description
The following is for diameter
The invention is described in detail by taking an oil pipe as an example and combining the attached drawings:
the invention relates to a parameter measuring and calculating method of a nuclear magnetic resonance two-phase flow sensor, which mainly comprises two steps, wherein in the first step, aiming at magnet design, the length of a pre-magnetized magnet A is determined by analyzing the relationship between magnetization vectors and magnetization lengths with different flow rates and different water contents; then by researching Halbach structure and target magnetic field intensity B 0 And uniformity P 1 Determining the size parameter of the main measuring field B by adopting a particle swarm optimization algorithm and combining finite element simulation; by using the principle of magnetic field superposition, the target magnetic field uniformity P is obtained by the compensation magnet C 2 Determining the optimal size of the compensation magnet C within the error tolerance; through the steps, the overall design of the magnetic structure parameters of the magnetic resonance two-phase flow sensor is finally determined. Secondly, aiming at coil design, firstly establishing a theoretical model of a quantitative FID signal and a coil, and fully analyzing the flow rate of two-phase flow and the functional relation between the FID and the length of the coil under the influence of phase content; then researching structural parameter influence factors of the solenoid, such as wire diameter, turns, coil spacing, depth-height ratio and the like, and establishing relative signal-to-noise ratio Sn and sensitivity B xy The response relation with the resistance R; finally aiming at the uniformity P of the radio frequency magnetic field 3 Problem, determining and completing sectional coil structure parametersAnd designing matching resonance parameters of the coil. Through the steps, the overall design of the coil structure parameters of the magnetic resonance two-phase flow sensor is finally determined. The parameter calculation method of the nuclear magnetic resonance two-phase flow sensor realizes more accurate measurement of the nuclear magnetic resonance sensor.
With reference to fig. 1, the present invention comprises the following steps in detail:
the first step is as follows: the method comprises the following steps of determining the structural parameters of a magnet of the nuclear magnetic resonance two-phase flow sensor, wherein the magnet is formed by sequentially connecting a pre-magnetized magnet A, a measuring magnet B and a compensating magnet C on a coaxial line to form a three-section Halbach cylinder array structure, and the method specifically comprises the following steps:
1. determining the length of a pre-magnetized magnet A
(1) Determining the functional relationship among the flow velocity, the water content, the magnetization vector and the magnetization length according to the flow characteristics of the oil-water two-phase flow, wherein the expression is as follows:
where M is the actual magnetization vector, M 0 Is the vector of complete magnetization, x is the magnetization length, v is the average flow velocity of oil-water two-phase flow, T 1 The longitudinal relaxation time of the oil-water two-phase flow is related to the phase content a% of the oil-water two-phase flow, T 2 The transverse relaxation time of the oil-water two-phase flow;
(2) Obtaining a normalized magnetization vector according to the calculation formula 1
Analyzing the magnetization vector M/M under different water content a% and different flow velocity v 0 Characteristic relationship with magnetization length;
(3) According to M/M 0 Plot of magnetization length against magnetization intensity vector M/M 0 The corresponding magnetization length when approaching the maximum value of 1, thereby determining the length of the pre-magnetized magnet a;
and (3) analyzing the change rule of the magnetization vector of the oil-water two-phase flow along with the magnetization length under different average flow velocities v and different water contents a% by combining the graph 2. FIG. 2 shows the magnetization vector as a function of the magnetization length for different average flow rates (0.1 m/s, 0.3 m/s) and different water contents (10%, 30%, 50%, 70%) of the oil-water mixture. Under a constant flow rate, the magnetization length to achieve complete magnetization becomes longer as the water content increases. Under the condition of a certain water content, the magnetization vector tends to be downward along with the increase of the flow speed. Further, at the same water content and flow rate, the magnetization vector gradually increases and stabilizes as the magnetization length increases. It can be seen that when the water content is less than 50% at a flow rate of 0.1m/s, the magnetization vector tends to be stable already when the magnetization length is in the range of 0.1-0.2 m; when the water content is less than 50% at a flow rate of 0.3m/s, the magnetization vector reaches a steady state when the magnetization length is in the range of 0.3 to 0.5 m. Therefore, the length of the pre-polarized magnet A is determined to be 0.3m by combining the effective utilization rate of the magnet aiming at the low flow rate and low water content state of the small pipe diameter.
2. Measuring parameters of magnet B
(1) Establishing a magnetic field two-dimensional plane uniformity expression by adopting a Halbach magnet array
Wherein->
To the working space average magnetic field strength, B max For a larger field strength quantization value of the working range, B min Quantizing the value for the lower magnetic field strength in the working interval;
(2) Determining a discrete Halbach mathematical model, and respectively researching the magnetic field intensity B according to four parameters of an internal-external diameter ratio value R/R, the number N of assembly blocks, the shape of the blocks and a magnetic material 0 The following calculation model is obtained:
wherein: b is 0 Strength of static magnetic field generated for magnet, B r The residual magnetic flux density is shown, R is the outer radius of the magnet, R is the inner radius, and n is the number of magnet blocks;
(3) Establishing a particle swarm optimization model according to a formula (2), wherein the shape of the blocks influences the error between the integral performance and the ideal structure of the discrete Halbach, and the magnetic material influences the residual magnetic flux density B r Influence of the number of building blocks N
In a relation of values of (a), the influence of the inner and outer diameter ratio value->
Using finite element simulation to comprehensively analyze the magnetic field intensity B 0 Two-dimensional plane uniformity of magnetic field P 1 The law of the change along with the parameters of the four magnets;
as shown in fig. 3, which is a schematic diagram of an ideal Halbach array, the discrete Halbach structure can be assembled in the shape of a single magnet, such as a square, a circle, or a sector. The sector is closest to the ideal state by finite element simulation method analysis. According to various performance parameters, namely, residual magnetism Br, coercive force Hc, intrinsic coercive force Hcj, maximum magnetic energy product W and Curie temperature Tc, given in the table 1, the neodymium iron boron with moderate cost performance is finally selected by combining with the analysis of actual requirements.
TABLE 1 comparison of the properties of various materials of different permanent magnets
TABLE 1
Fig. 4 (a) shows the simulation results of 8 sub-block Halbach arrays of 2 different sizes, respectively. The circular radiuses of the inner cavities are 15mm, and the outer radiuses are 20mm and 25mm respectively. I.e. the ratio of the inner diameter to the outer diameter is 3/4 and 3/5 respectively, and the obtained magnetic field strength is 0.165T and 0.301T respectively. Therefore, when the working area is constant, the strength of the magnetic induction increases as the thickness of the magnet increases, i.e., the inner-outer diameter ratio decreases. FIG. 4 (b) shows the magnetic induction distribution plots of 4,8 and 16 Halbach arrays of the same material and size, respectively, from the simulation results, it is shown that as the number N of the permanent magnet blocks increases (4, 8, 16), the magnetic induction and uniformity generated in the hollow region also increase (0.25T, 0.36T, 0.5T).
Combining the simulation results to obtain the magnetic field intensity B through comprehensive analysis 0 、P 1 The law of the change of the parameters of the four magnets. The magnetic induction strength and uniformity of the Halbach array are mainly related to the shape and the number of blocks of the assembled magnet, the ratio of the inner diameter to the outer diameter, the performance of the permanent magnet material and the like. In determining the target intensity B 0 、P 1 The optimal solution meeting the result is obtained by synthesizing the change of a plurality of influence parameters, which is a typical electromagnetic field inversion problem applying a particle swarm optimization algorithm.
(4) According to the simulation analysis result, determining the restriction relation and the influence rule among the parameters, and finding out the magnetic field intensity B meeting the requirement 0 And P is 1 Determining the optimal parameters with high uniformity, thereby determining various structural parameters of the measuring magnet B;
in connection with fig. 5, for diameter
Considering that 16 magnets are difficult to assemble and easy to generate errors in actual processing, the sensor adopts an 8-block Halbach array made of neodymium iron boron (with residual magnetism of about 1.1T), and calculates analysis and simulation results according to the steps and the magnetic field intensity B 0 Target of =0.27T and consideration of P 1 The effective range and uniformity effect design optimizes the structure size of the magnet B. Finally, the length of the magnet B is determined to be 200mm, the outer radius is 40mm, and the inner radius is 30mm. The two-dimensional distribution and curve trend chart of the magnetic field plane is shown in fig. 5, and the magnetic field intensity is satisfied while the magnetic field uniformity is good.
3. Compensation magnet C parameter
(1) Study of three-dimensional axial magnetic field uniformity
The relationship to the length of the magnet. Wherein->
For the axial (z-direction) average field strength, it can be concluded that the field homogeneity P increases infinitely with the magnet length 2 The axial magnetic field uniformity P is improved, but the length dimension of the magnet is limited in practice, so that the method of adding the compensation magnet C at two ends of the measurement magnet B (with the length of 200 mm) is provided 2 ；
(2) Adding a compensating magnet C to the axial magnetic field uniformity P through finite element static magnetic field simulation analysis according to Maxwell equation of three-dimensional static magnetic field and magnetic induction calculation formula of permanent magnet 2 Influence relationship of (1):
b (x, y, z) is magnetic induction, H (x, y, z) is magnetic field intensity, J (x, y, z) is current density, and the three vectors are all in function of vectors in all directions. Wherein, mu 0 Is the absolute permeability in vacuum, mu r For relative permeability, M P The polarization intensity of the permanent magnetic material;
as described in detail with reference to fig. 6, the influence of the change in the compensation magnet C on the magnetic field strength was investigated on the basis of the holding magnet B. FIG. 6a is a schematic diagram of the original structure and the improved structure of the magnet, and FIG. 6b is a schematic diagram of the dimensional parameters of different magnets C versus the magnetic field uniformity P 2 The influence law of (2). Wherein, the axial length of the compensation magnet is 10mm and the radial thickness is 15mm in the graph (2), the axial length of the compensation magnet is 15mm and the radial thickness is 15mm in the graph (3), the axial length of the compensation magnet is 15mm and the radial thickness is 18mm in the graph (4), and it can be seen that the axial length and the radial thickness of the compensation magnet C are continuously changedRadial thickness and axial length dimensions, axial homogeneity P of the magnetic field 2 Improved and enhanced to various degrees.
(3) According to simulation analysis, comparing the axial magnetic field uniformity P of the magnets C with different structural sizes 2 Finding the magnet parameters with the highest optimization on the magnetic field uniformity and the smallest volume, thereby determining the size of the compensation magnet C;
through the analysis of the steps, the compensation magnet C and the axial uniformity P are determined 2 In increasing P 2 The volume of the magnet should be kept as small as possible in terms of diameter on the premise of uniformity
And an oil pipe, wherein the axial length of the finally determined compensating magnet C is 15mm, and the radial thickness of the finally determined compensating magnet C is 15mm.
And finally determining the overall design of the magnetic structure parameters of the magnetic resonance two-phase flow sensor according to the steps and the analysis result.
The second step is that: the method for determining the structural parameters of the coil of the nuclear magnetic resonance two-phase flow sensor comprises four steps as follows:
the first part of the steps are as follows:
1. and establishing a theoretical model of the quantitative FID signal and the coil, and determining the functional relation between the nuclear magnetic resonance receiving signal FID and the coil length. Obtaining nuclear magnetic resonance receiving signals FID under different average flow velocities v and different water contents, wherein the expression is as follows:
wherein: s. the FID For quantizing the FID signal received by the coil, where M i0 ＝S i H I，i ，S i Is the saturation of the ith component, H, in a two-phase flow I，i Is the hydrogen index, L, of the ith component in the two-phase stream D Is the length of the coil, L M For the length of magnetization, T is the sampling time, c is the correction factor, T 1，i Is the spin lattice relaxation time, T, of the ith component 2，i Is the spin-spin relaxation time of the ith component;
2. analyzing the quantitative FID signal S received by the coil under the models with different average flow velocities v and different water contents a% according to the formula (4) FID The rule of the change along with the length of the coil;
3. quantitative FID signal S received by analysis coil FID The corresponding coil length tends to be stable, so that the basic length parameter range of the detection coil is determined;
referring to FIG. 7, the water contents are 10%, 30%, 50%, and 70%, respectively, and the average flow rates are 0.1m/s and 0.3m/s, respectively. At the same water cut and flow rate, the FID signal gradually increases and stabilizes as the detector coil length increases. At the same flow rate, the FID signal increases with increasing water cut. At the same water content, the FID signal decreases with increasing flow rate. For lower average flow velocity and lower water content, when the length of the coil of the detector is in the range of 0.4-0.6m, the FID signal tends to be stable;
the second part of the steps are as follows:
1. establishing a theoretical model of coil performance and solenoid parameters, and determining coil sensitivity B xy The influence factor of (c): the distance g, the number of turns N, the wire diameter D and the pipe diameter ratio H/D;
wherein, B 1 I is the radio frequency magnetic field intensity B generated by a unit current i in the coil 1 N is the number of turns of the coil, H/D is the ratio of the depth to the height of the pipe diameter, H is the height of the solenoid coil, D is the diameter of the coil, u 0 Is a vacuum magnetic permeability. FIG. 8 is a schematic diagram of a solenoid model and the physical parameters involved;
2. establishing an equivalent model of coil resistance R under the skin effect and the proximity effect to obtain the following expression:
wherein R is coil Is the resistance value of an equivalent straight wire at radio frequency, epsilon is the enhancement factor of two adjacent turns of coils, R s For the equivalent resistance model, l is the length of the wire used by the coil, d is the wire diameter of the coil, f is the resonance frequency of the coil, mu is the magnetic permeability, and rho is the resistivity of the copper wire. The coil is an enameled copper wire, and the skin effect of the metal conductor under the high-frequency condition is considered
The wire diameter should be greater than or equal to twice the skin depth;
3. establishing relative signal-to-noise ratio SNR and sensitivity B under fixed pulse frequency xy And a resistance R s The response relationship of (c) is shown in formula 7; analyzing the influence rule of each parameter of the coil on the SNR by applying a particle swarm optimization algorithm and combining finite element simulation;
wherein: b is xy Is the sensitivity of the coil; k is a reaction radio frequency magnetic field B 1 Constant of homogeneity, v s For detecting the volume of the sample, N is the number of nuclear spins per unit volume, γ is the magnetic spin ratio of the atoms, h is Planckian, I is the spin quantum number of the nuclei, w 0 Is the precession frequency of the nucleus, K B Is Boltzmann constant, R s Is the coil resistance, T is the temperature of the test sample; Δ f is the measured bandwidth;
in the process of designing the solenoid radio frequency coil, the above parameters are mutually restricted and influence, which is a typical particle swarm optimization problem. The higher the SNR, given the magnetic field B0 and the particular sample conditions, the larger the magnetic field produced per unit current, the lower the radio frequency resistance of the coil. In short, the main optimization direction is to obtain the best relative signal-to-noise ratio by maximizing the coil sensitivity and minimizing the effective resistance. For obtaining high-quality images, the transmitting coil is required to have high energy conversion speed and high efficiency, and the radio frequency field is required to be highly uniform so as to ensure that the excited biological samples obtain uniform excitation strength; for the receiving coil, it is essential that the sensitivity of the detection is high to ensure a sufficient signal-to-noise ratio.
With reference to FIG. 9 (a), the diameter of the coil is controlled between 0.6mm and 1.5mm in the process of manufacturing the coil of the small-diameter nuclear magnetic resonance multiphase flow sensor in a static magnetic field B 0 In a static magnetic field environment of 100mt, the proton resonance frequency is 4MHz. Considering the coil driving transmitting power and the current carrying capacity, an enameled copper wire is selected according to 2.5-3A per square millimeter, the influence rule of the number of turns of the coil on the signal-to-noise ratio under different wire diameters is researched, as shown in fig. 9 (a), when the wire diameter is 0.5mm, the quantized signal-to-noise ratio of the number of turns between 25-30 turns reaches the maximum; when the wire diameter is 1mm, the quantized signal-to-noise ratio reaches the maximum between 10 and 15 turns. When the wire diameter is 1.5mm, the quantized signal-to-noise ratio reaches the maximum between 5 and 10 turns.
With reference to fig. 9 (b), at a certain line diameter d, as the coil pitch p increases, the resistance and the inductance of the coil gradually decrease, and the Q value of the quality factor tends to increase and decrease due to the influence of the skin effect and the proximity effect. As can be seen from the figure, the value of the coil quality factor reaches a maximum for different wire diameters d when the pitch p equals 1 wire diameter, i.e. g = d.
4. According to the above influence factors and result analysis, the high sensitivity B is obtained xy And high signal-to-noise ratio SNR. Through the above steps, calculation and analysis are carried out for the diameter
An oil pipe, wherein the diameter of the adopted wire is determined to be 1mm, and the number of turns is 15;
the third part of steps are as follows:
1. establishing a solenoid coil to generate a radio frequency magnetic field B 1 Calculating the radio frequency generated by the coilThe magnetic field intensity is calculated according to the following formula:
wherein: mu.s 0 The magnetic field strength is vacuum magnetic conductivity, N is the number of turns of a coil, I is the current intensity of the coil, H is the height of a solenoid coil, R is the radius of the solenoid coil, and Z is the distance from any point of an axial space of the solenoid to a central point;
referring to fig. 8, the solenoid coil can be seen as being composed of a plurality of coaxial circular coils with the same radius, and when the length of the solenoid and the number of turns of the coil are known, the current flowing into the solenoid coil is constant, and the current density of the coil per unit length can be calculated. And (3) completing the integration of Z' on the solenoid coil with the height H to obtain the magnetic induction intensity of any point p on the axis.
2. Analysis of the RF magnetic field B by finite element magnetic field simulation according to equation (8) 1 And calculating the uniformity of the RF magnetic field in the target space
Is the average intensity of the radio frequency magnetic field;
3. by analyzing the change rule of the magnetic field intensity in the solenoid space, the result that the magnetic field intensity in the middle of the pipeline is high and gradually decreases towards the two ends is obtained. Therefore, a sectional type (sparse in the middle and compact at two ends) coil structure is provided, and the purposes of weakening the magnetic field intensity in the middle section and enhancing the magnetic field intensity at two ends are achieved by adjusting the space proportion of three sections of coils, so that the uniformity of the whole radio frequency magnetic field is improved;
with reference to fig. 10, in a certain detection range, as the number of turns of the coil is continuously increased and the coverage area is larger, the uniform range of the obtained radio frequency magnetic field is higher and higher, but if the uniform range of the magnetic field is desired to be improved, the length and the number of turns of the coil cannot be increased at one step, infinite increase of the resistance of the coil is caused, and the signal to noise ratio is greatly reduced, so that a magnetic field combination compensation mode is adopted, and a winding mode of sparse and dense combination is utilized, and the number of turns and the length of the coil are not reducedUnder the condition of changing, the uniformity of the magnetic field is improved by adjusting the coil structure. As can be seen from fig. 10, the radio frequency magnetic field generated by the optimized coil structure tends to be stable relative to the magnetic field generated by the original structure, the variation range is reduced, the overall uniformity P3 is improved, and the error allowable range of the magnetic resonance apparatus is satisfied. Thus aiming at the diameter
And the oil pipe adopts a winding mode of density combination to improve the uniformity of a magnetic field on the basis of ensuring the optimal signal-to-noise ratio under the condition that the number of turns and the length of the front part of coils are not changed. The parameters finally determined are: the wire diameter is 1mm, the number of turns is 16, the middle part has 8 turns, the turn interval is 1mm, the two ends have 4 turns respectively, and the turn interval is 0.5mm.
The fourth step is as follows:
1. the resonance characteristics of the radio frequency system are studied. Firstly, measuring various parameter values of a coil under a fixed frequency by using an impedance analyzer, wherein the parameter values comprise a resistor R, an inductance L and a capacitance C;
2. and establishing an RLC matching response relation, and calculating to obtain various matching parameters of the coil quality factor according to the following expression. Wherein Z is total impedance, W is frequency, C m Capacitors, C, connected in series with the desired matching circuit t Connecting capacitors in parallel to the obtained matching circuit, wherein R is the actually measured coil resistance value, L is the coil inductance value, and j is a physical vector;
with reference to FIG. 11, a schematic diagram of a resonant matching circuit used in the coil, a magnetic resonance power amplification system and the like in this studyThe characteristic impedance of the axial cable is 50 Ω, and the resonance frequency and the larmor resonance frequency are kept coincident. According to the above calculation formula 9 and circuit analysis, Z is made equal to 50 Ω, and theoretical parameters such as inductance, capacitance, and complementary resistance required for designing an antenna can be determined. During the matching and tuning process of the radio frequency coil, an eddy current effect is generated due to the action of the magnet, so that the alternating current resistance and the alternating current inductance of the coil are changed. Therefore, the radio frequency coil needs to be in an actual working position in the processes of measuring coil parameters, matching and tuning, the total impedance is kept to be 50 omega, and C is adjusted m And C t Is such that the resonance frequency of the matching circuit reaches the larmor resonance frequency point of the magnetic resonance system.
And finally determining the integral design of the coil structure parameters of the magnetic resonance two-phase flow sensor according to the steps and the analysis result.
Claims (1)
1. A method for measuring and calculating a nuclear magnetic resonance two-phase flow sensor is characterized by comprising the following steps:
the first step is as follows: the method comprises the following steps of determining the structural parameters of a magnet of the nuclear magnetic resonance two-phase flow sensor, wherein the magnet is formed by sequentially connecting a pre-magnetized magnet A, a measuring magnet B and a compensating magnet C on a coaxial line, and the method comprises the following specific steps:
1. determining the length of a pre-magnetized magnet A
(1) Determining the functional relationship among the flow velocity, the water content, the magnetization vector and the magnetization length according to the flow characteristics of the oil-water two-phase flow, wherein the expression is as follows:
where M is the actual magnetization vector, M 0 Is the complete magnetization vector, x is the magnetization length, v is the average flow velocity of the oil-water two-phase flow, T 1 The longitudinal relaxation time of the oil-water two-phase flow is related to the phase content a% of the oil-water two-phase flow, T 2 The transverse relaxation time of the oil-water two-phase flow;
(2) Obtaining a normalized magnetization vector according to equation (1)
Analyzing the magnetization vector M/M under different water content a% and different flow velocity v 0 A characteristic relationship with magnetization length;
(3) According to M/M 0 Plot of magnetization length against magnetization intensity vector M/M 0 The corresponding magnetization length when approaching the maximum value of 1, thereby determining the length of the pre-magnetized magnet a;
2. measuring parameters of magnet B
(1) Establishing a magnetic field two-dimensional plane uniformity expression by adopting a Halbach magnet array
Wherein->
Average static magnetic field strength, B, generated for a working space magnet max For a larger field strength quantization value of the working range, B min A quantized value of the magnetic field strength in a lower working interval is obtained;
(2) Determining a discrete Halbach mathematical model, and respectively researching the magnetic field intensity B according to four parameters of an internal-external diameter ratio value R/R, the number N of assembly blocks, the shape of the blocks and a magnetic material 0 The following calculation model is obtained:
wherein: b is 0 Strength of static magnetic field generated for magnet, B r The residual magnetic flux density is shown, R is the outer radius of the magnet, R is the inner radius, and n is the number of magnet blocks;
(3) Establishing a particle swarm optimization model according to a formula (2), wherein the shape of the blocks influences the error between the integral performance and the ideal structure of the discrete HalbachThe magnetic material influencing the residual magnetic flux density B r Influence of the number of building blocks N
The value relationship of (4), the influence of the value of the ratio of the inner to the outer diameter>
Using finite element simulation to comprehensively analyze the magnetic field intensity B 0 Two-dimensional plane uniformity P of magnetic field 1 The law of the change along with the parameters of the four magnets;
(4) According to the simulation analysis result, the restriction relation and the influence rule among the parameters are determined, and the magnetic field intensity B meeting the requirement is found 0 And the magnetic field two-dimensional plane uniformity P 1 The parameter with the highest uniformity, thereby determining each structural parameter of the measuring magnet B;
3. determining parameters of bucking magnet C
(1) Study of three-dimensional axial magnetic field uniformity
Relationship to magnet length: wherein +>
For the average field strength in the axial z-direction, it can be concluded that the field homogeneity P increases infinitely with the magnet length 2 The axial magnetic field uniformity P is improved by adding the compensation magnets C at two ends of the measurement magnet B 2 ；
(2) According to Maxwell equation of three-position static magnetic field and calculation formula of magnetic induction intensity of permanent magnet, obtaining uniformity P of compensation magnets C with different sizes to axial magnetic field by finite element static magnetic field simulation 2 Influence relationship of (c):
B(x，y，z)＝μ 0 ·μ r ·H+μ 0 ·M P
wherein B (x, y, z) is magnetic induction, H (x, y, z) is magnetic field intensity, J (x, y, z) is current density, the three vectors are all functional relations of vectors in all directions, and mu 0 Is the absolute permeability in vacuum, mu r For relative permeability, M P The polarization intensity of the permanent magnetic material;
(3) According to simulation analysis, comparing the axial magnetic field uniformity P of the magnets C with different structural sizes 2 Finding the magnet parameters with the highest optimization on the magnetic field uniformity and the smallest volume, thereby determining the size of the compensation magnet C;
finally determining the integral design of the magnet structure parameters of the magnetic resonance two-phase flow sensor according to the steps and the analysis result;
the second step: the method for determining the structural parameters of the coil of the nuclear magnetic resonance two-phase flow sensor comprises four steps as follows:
the first part of the steps are as follows:
1. establishing a theoretical model of a quantitative FID signal and a coil, determining a functional relation between a nuclear magnetic resonance receiving signal FID and the length of the coil, and solving the nuclear magnetic resonance receiving signal FID under different average flow velocities v and different water contents a%, wherein the expression is as follows:
wherein: s. the FID For quantizing the FID signal received by the coil, where M i0 ＝S i H I，i ，S i Is the saturation of the ith component, H, in a two-phase flow I，i Is the hydrogen index, L, of the ith component in a two-phase flow D Is the length of the coil, L M For the magnetization length, t is the sampling time, c is the correction systemNumber, T 1，i Is the spin lattice relaxation time, T, of the ith component 2，i Is the spin-spin relaxation time of the ith component;
2. analyzing FID signals S received by coils under models with different average flow velocities v and different water contents a% according to a formula (4) FID The rule of the change along with the length of the coil;
3. by analysing the FID signal S received by the coil FID The corresponding coil length tends to be stable, so that the basic length parameter range of the detection coil is determined;
the second part of the steps are as follows:
1. establishing a theoretical model of coil performance and solenoid parameters, and determining an influence factor of coil sensitivity Bxy:
wherein, B 1 I is the radio frequency magnetic field intensity B generated by a unit current i in the coil 1 N is the number of turns of the coil, H/D is the ratio of depth to height of the tube diameter, H is the height of the solenoid coil, D is the diameter of the coil, u 0 Vacuum magnetic conductivity;
2. establishing an equivalent model of coil resistance R under the skin effect and the proximity effect, and obtaining the following expression:
wherein R is coil Is the resistance value of an equivalent straight wire at radio frequency, epsilon is the enhancement factor of two adjacent turns of coils, R s The method is an equivalent resistance model, wherein l is the length of a lead used by a coil, d is the wire diameter of the coil, f is the resonance frequency of the coil, mu is the magnetic conductivity, and rho is the resistivity of a copper lead;
3. establishing relative signal-to-noise ratio SNR and sensitivity B under fixed pulse frequency xy And a resistance R s The response relationship of (a) is shown in formula 7; analyzing the relative confidence of each parameter pair of the coil by applying a particle swarm optimization algorithm and combining finite element simulationLaw of influence of noise ratio SNR:
wherein: b is xy Is the sensitivity of the coil; k is a reaction radio frequency magnetic field B 1 Constant of homogeneity, v S For detecting the volume of the sample, N is the number of nuclear spins per unit volume, γ is the magnetic spin ratio of the atoms, h is Planckian, I is the spin quantum number of the nuclei, w 0 Is the precession frequency of the nucleus, K B Is Boltzmann constant, R s Is the coil resistance, T is the temperature of the test sample; Δ f is the measured bandwidth;
4. according to the above influence factors and result analysis, B satisfying high sensitivity is obtained xy And coil parameters of high signal-to-noise ratio (SNR);
the third part of the steps are as follows:
1. establishing a solenoid coil to generate a radio frequency magnetic field B 1 The theoretical model of (2) calculates the intensity of the radio frequency magnetic field generated by the coil, and the calculation formula is as follows:
wherein: mu.s 0 The magnetic field strength is vacuum magnetic conductivity, N is the number of turns of a coil, I is the current intensity of the coil, H is the height of a solenoid coil, R is the radius of the solenoid coil, and Z is the distance from any point of an axial space of the solenoid to a central point;
2. analysis of the radio frequency magnetic field B by finite element magnetic field simulation according to equation (8) 1 And calculating the uniformity of the RF magnetic field in the target space
Is the average intensity of the radio frequency magnetic field;
3. by analyzing the change rule of the magnetic field intensity in the solenoid space, the result that the magnetic field intensity in the middle of the pipeline is high and gradually decreases towards the magnetic fields at two ends is obtained, so that a coil structure with sparse middle and compact and sectional type at two ends is provided, and the purposes of weakening the magnetic field intensity in the middle section and enhancing the magnetic field intensity at two ends are achieved by adjusting the space proportion of three sections of coils, so that the uniformity of the whole radio frequency magnetic field is improved;
the fourth step is as follows:
1. the resonance characteristic of a radio frequency system is researched, and various parameter values of a coil under a fixed frequency, including a resistor R, an inductance L and a capacitance C, are measured by using an impedance analyzer;
2. establishing an RLC matching response relation, and calculating to obtain various matching parameters of the coil quality factor according to the following expression, wherein Z is total impedance, W is frequency, and C is m A capacitor, C, connected in series with the desired matching circuit t Connecting capacitors in parallel to the obtained matching circuit, wherein R is the actually measured coil resistance value, L is the coil inductance value, and j is a physical vector;
and finally determining the integral design of the coil structure parameters of the magnetic resonance two-phase flow sensor according to the steps and the analysis result.
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