CN114137032A - Resistivity measuring device and resistivity measuring method for sandstone model with large dynamic range - Google Patents
Resistivity measuring device and resistivity measuring method for sandstone model with large dynamic range Download PDFInfo
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Abstract
The invention relates to a resistivity measuring device and a resistivity measuring method for a sandstone model with a large dynamic range. The invention relates to a method for eliminating the error of zero drift by using extended Kalman filtering based on the application of the improved extended Kalman filtering in measuring the resistivity in a large dynamic range and by inhibiting the extended Kalman filtering of filtering divergence according to the norm of an innovation covariance matrix.
Description
Technical Field
The invention relates to the technical field of resistivity measurement, in particular to a large-dynamic-range sandstone model resistivity measurement device and method based on improved extended Kalman filtering.
Background
In oil production engineering, it is necessary to measure the variation values of a multi-path resistivity circuit with a large dynamic range of 500 ohms to 5 megaohms for a long time (1 week to 3 weeks). A128-path gating circuit and an 8-step automatic range circuit are designed, and a zero drift phenomenon inevitably occurs in a long-time measurement process. The zero drift phenomenon means that when a signal of an input port is short-circuited in an amplifying circuit, an output port can detect current. The method for suppressing zero drift mainly comprises two methods, one is a method utilizing capacitance compensation, the method is to design an automatic zero calibration circuit, store the voltage of a zero drift circuit into a capacitor by utilizing the capacitor in an integrating circuit, and then subtract the voltage of the capacitor by utilizing the actually measured voltage. Due to the aging of the capacitor, the voltage cannot be accurately stored. The second is to use kalman filtering, but kalman filtering can only solve the linearity problem, and filtering divergence is easily caused because the resistance value of the resistor changes greatly.
Disclosure of Invention
In order to solve the technical problems, the invention provides a device and a method for measuring resistivity of a sandstone model with a large dynamic range based on improved extended Kalman filtering, which is a method for eliminating errors of zero drift by using extended Kalman filtering for restraining filtering divergence according to norm of a new covariance matrix based on application of the improved extended Kalman filtering in measuring the resistivity with the large dynamic range.
In order to achieve the above object, the present invention adopts the following technical solutions.
The invention provides a resistivity measuring device for a sandstone model with a large dynamic range, which is used for constructing the sandstone model with the large dynamic range and measuring the internal resistance value of the sandstone model based on improved extended Kalman filtering.
Preferably, the circuit module comprises an 8-gear automatic range matching circuit and a 128-way gating circuit.
In any of the above technical solutions, it is preferable that the 128-way gating circuit is connected to a large sandstone model, and resistivity probes of the 128-way gating circuit are uniformly inserted into the sandstone model.
In any of the above technical solutions, preferably, the 128-way gating circuit is connected to the 8-gear automatic range matching circuit, the 8-gear automatic range matching circuit is connected to the data acquisition card, and the resistance value acquired by the 128-way gating circuit is transmitted to the PC through the data acquisition card.
In any of the above technical solutions, preferably, the circuit module is further provided with a differential amplification circuit for suppressing common mode interference in the measurement process.
The invention also provides a resistivity measuring method of the sandstone model with the large dynamic range, which adopts the resistivity measuring device of the sandstone model with the large dynamic range to construct the sandstone model and measure the internal resistance value of the sandstone model, and comprises the following steps:
uniformly inserting resistivity probes of 128-path gating circuits into a large sandstone model by using a prepared sandstone model;
secondly, an amplifying circuit is arranged in the circuit module, and the amplifying circuit adopts a differential amplifying circuit to inhibit common-mode interference;
thirdly, running a program through the PC, completely acquiring the 128 resistance value, and transmitting the resistance value to the PC through a data acquisition card;
and step four, removing errors generated by zero drift generated during resistance measurement by using an improved Kalman filtering algorithm.
In any of the above technical solutions, preferably, according to the first to fourth steps of the resistivity measurement method for the sandstone model with a large dynamic range, starting a PC program, constructing a kalman filtering model from 128 channels of acquired resistance signals by using a data acquisition card, and removing an error of zero drift, wherein the constructing of the kalman filtering model specifically includes:
establishing a state equation of the system based on the measurement of the resistance
X(k)＝f(k,X(k))+V(k)，
The measurement equation is
Z(k+1)＝h(k，X(k))+W(k)，
Wherein X (k) is a state vector of the measured potential, V (k) is process noise, Z (k) is an observed vector of the potential at time k, and W (k) is measurement noise.
In any of the above technical solutions, preferably, a kalman filtering model is constructed according to steps one to four of the resistivity measurement method for the sandstone model with a large dynamic range, and the extended kalman filtering process is adopted as follows:
the one-step prediction equation of state is
The prediction equation of covariance is
P(k+1|k)＝fx(k)P(k|k)fx′(k)+Q(k)，
Metrology prediction equation
Innovation covariance of
S(k+1)＝hx(k+1)P(k+1|k)hx′(k+1)+R(k+1)，
Gain of
The state update equation is
The covariance update equation is
The algorithm can be started and recurred only by giving a state initial value and a covariance matrix of a filtering estimation state vector; after the system reaches a steady state, predicting that covariance, innovation and gain all tend to minimum values; if the resistance is suddenly changed, the predicted value is not accurate any more, the innovation covariance is suddenly increased, but the gain cannot be changed, so that the filtering precision is reduced; because the calculation amount of the gain matrix K is large, the real-time performance is reduced due to recalculation of the gain matrix K, and the accuracy of a filtering value is improved by correcting a predicted value in one step;
after the filtering tends to be stable, the innovation matrix tends to be a minimum value, and whether the predicted value should be adjusted or not can be judged according to the size of the innovation matrix
||r(k+1)|＜λZmax|| (14)，
In the formula, ZmaxThe maximum value of the measurement error matrix is | | |, which is F-norm, and the value range of the lambda is [0.3,0.9 |)]；
When the innovation matrix satisfies the formula (14), the filtering is considered normal; when the resistance is not true, the resistance is considered to be changed greatly, the reliability of the measured value is high, the reliability of the one-step predicted value is low, and the one-step predicted value is corrected;
if not, indicating that the one-step predicted value X (k +1| k) is inaccurate, modifying X (k +1| k), and recalculating the state updating equation to obtain new X (k +1| k + 1);
the specific modification is as follows
In the formula, c1 is a correction for the predicted number of routes; c2 is the correction to the predicted resistance, r' (k +1) is the distance component of the innovation matrix at time k + 1; the value ranges of c1 and c2 are (0, 1), wherein c1 is selected to be 0.5, and c2 is selected to be 0.6; and obtaining a measurement data result with high precision after filtering.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
(1) according to the technical scheme, the differential amplifier circuit is utilized, so that common-mode interference can be inhibited;
(2) the invention provides the extended Kalman filtering for inhibiting the filtering divergence according to the norm of the innovation covariance matrix, and compared with the extended Kalman filtering, the prediction precision can be effectively improved;
(3) the application of the improved extended Kalman filter in large dynamic range resistivity can be used for other phenomena with zero drift.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 is a schematic structural diagram of a preferred embodiment of a resistivity measuring device for a sandstone model with a large dynamic range according to the invention;
figure 2 is a schematic diagram of the measurement principle of a preferred embodiment of the resistivity measuring device of the sandstone model with large dynamic range according to the invention;
fig. 3 is a schematic view of the kalman filtering result of the resistivity measuring apparatus for a sandstone model with a large dynamic range according to a preferred embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to overcome the technical problems that a resistivity circuit with a large dynamic range in oil extraction engineering has a zero drift phenomenon in a long-time measurement process and the like, the embodiment of the invention provides a resistivity measurement device and a resistivity measurement method for a sandstone model with a large dynamic range based on improved extended Kalman filtering, which are methods for eliminating the error of the zero drift by suppressing the extended Kalman filtering of filtering divergence according to the norm of an innovation covariance matrix based on the application of the improved extended Kalman filtering in measuring the resistivity with the large dynamic range.
The resistivity measuring device for the sandstone model with the large dynamic range, which is described in this embodiment, is used for constructing the sandstone model with the large dynamic range and is based on the improved extended kalman filter to measure the internal resistance value thereof, as shown in fig. 1, the resistivity measuring device comprises a large sandstone model with 128 paths of probes, a circuit module and a data acquisition card, wherein the large sandstone model is connected with a water injection well and an oil injection well, the circuit module is connected with the large sandstone model and the data acquisition card, and the data acquisition card is connected with a PC.
The circuit module of the resistivity measuring device for the sandstone model with the large dynamic range of the embodiment comprises an 8-gear automatic range matching circuit and a 128-channel gating circuit.
In the resistivity measuring device for the sandstone model with the large dynamic range, the 128-path gating circuit is connected with the large sandstone model, and the resistivity probes are uniformly inserted into the sandstone model.
In the resistivity measuring device for the sandstone model with the large dynamic range, the 128-path gating circuit is connected with the 8-gear automatic range matching circuit, the 8-gear automatic range matching circuit is connected with the data acquisition card, and the resistance value acquired by the 128-path gating circuit is transmitted to the PC through the data acquisition card.
In the resistivity measuring device for the sandstone model with the large dynamic range, the circuit module is also provided with a differential amplifying circuit for inhibiting common-mode interference in the measuring process.
The resistivity measuring method of the sandstone model with the large dynamic range comprises the following steps:
uniformly inserting resistivity probes of 128-path gating circuits into a large sandstone model by using a prepared sandstone model;
secondly, an amplifying circuit is arranged in the circuit module, and the amplifying circuit adopts a differential amplifying circuit to inhibit common-mode interference;
thirdly, running a program through the PC, completely acquiring the 128 resistance value, and transmitting the resistance value to the PC through a data acquisition card;
and step four, removing errors generated by zero drift generated during resistance measurement by using an improved Kalman filtering algorithm.
A schematic diagram of the measurement principle of the resistivity measuring device for the sandstone model with a large dynamic range according to the embodiment is shown in fig. 2.
According to the first to fourth steps of the resistivity measurement method of the sandstone model with the large dynamic range, starting a PC program, constructing a Kalman filtering model by using 128 paths of collected resistance signals through a data acquisition card, and removing the error of zero drift, wherein the constructing of the Kalman filtering model specifically comprises the following steps:
establishing a state equation of the system based on the measurement of the resistance
X(k)＝f(k,X(k))+V(k)，
The measurement equation is
Z(k+1)＝h(k，X(k))+W(k)，
Wherein X (k) is a state vector of the measured potential, V (k) is process noise, Z (k) is an observed vector of the potential at time k, and W (k) is measurement noise.
Constructing a Kalman filtering model according to the first to fourth steps of the resistivity measurement method of the sandstone model with a large dynamic range, wherein the extended Kalman filtering process is as follows:
the one-step prediction equation of state is
The prediction equation of covariance is
P(k+1|k)＝fx(k)P(k|k)fx′(k)+Q(k)，
Metrology prediction equation
Innovation covariance of
S(k+1)＝hx(k+1)P(k+1|k)hx′(k+1)+R(k+1)，
Gain of
The state update equation is
The covariance update equation is
The algorithm can be started and recurred only by giving a state initial value and a covariance matrix of a filtering estimation state vector; after the system reaches a steady state, predicting that covariance, innovation and gain all tend to minimum values; if the resistance is suddenly changed, the predicted value is not accurate any more, the innovation covariance is suddenly increased, but the gain cannot be changed, so that the filtering precision is reduced; because the calculation amount of the gain matrix K is large, the real-time performance is reduced due to recalculation of the gain matrix K, and the accuracy of a filtering value is improved by correcting a predicted value in one step;
after the filtering tends to be stable, the innovation matrix tends to be a minimum value, and whether the predicted value should be adjusted or not can be judged according to the size of the innovation matrix
||r(k+1)||＜λ||Zmax|| (14)，
In the formula, ZmaxThe maximum value of the measurement error matrix is | | |, which is F-norm, and the value range of the lambda is [0.3,0.9 |)]；
When the innovation matrix satisfies the formula (14), the filtering is considered normal; when the resistance is not true, the resistance is considered to be changed greatly, the reliability of the measured value is high, the reliability of the one-step predicted value is low, and the one-step predicted value is corrected;
if not, indicating that the one-step predicted value X (k +1| k) is inaccurate, modifying X (k +1| k), and recalculating the state updating equation to obtain new X (k +1| k + 1);
the specific modification is as follows
In the formula, c1 is a correction for the predicted number of routes; c2 is the correction to the predicted resistance, r' (k +1) is the distance component of the innovation matrix at time k + 1; the value ranges of c1 and c2 are (0, 1), wherein c1 is selected to be 0.5, and c2 is selected to be 0.6; and obtaining a measurement data result with high precision after filtering.
According to the device and the method for measuring the resistivity of the sandstone model with the large dynamic range based on the improved extended Kalman filtering, a differential amplification circuit is utilized to suppress common-mode interference; the extended Kalman filtering for inhibiting the filtering divergence according to the norm of the innovation covariance matrix is provided, and compared with the extended Kalman filtering, the prediction precision can be effectively improved; the application of the extended Kalman filter based on the improvement in the large dynamic range resistivity can be used for other phenomena with zero drift.
The foregoing is merely illustrative of the preferred embodiments of the present invention and is not to be construed as limiting the scope of the invention; the above description is only for the specific embodiment of the present invention, and is not intended to limit the scope of the present invention; any modification, equivalent replacement, improvement and the like of the technical solution of the present invention by a person of ordinary skill in the art without departing from the design spirit of the present invention shall fall within the protection scope determined by the claims of the present invention.
Claims (8)
1. The resistivity measuring device for the sandstone model with the large dynamic range is characterized by comprising a large sandstone model with 128 paths of probes, a circuit module and a data acquisition card, wherein the large sandstone model is connected with a water injection well and an oil outlet well, the circuit module is connected with the large sandstone model and the data acquisition card, and the data acquisition card is connected with a PC (personal computer).
2. The high dynamic range sandstone model resistivity measuring device of claim 1 wherein the circuit module comprises an 8-step automatic range matching circuit and a 128-way gating circuit.
3. The high dynamic range sandstone model resistivity measuring device of claim 2, wherein the 128-way gating circuit is connected with a large sandstone model, and a resistivity probe of the 128-way gating circuit is uniformly inserted into the sandstone model.
4. The resistivity measuring device for the sandstone model with the large dynamic range of claim 3, wherein the 128-way gating circuit is connected with an 8-way automatic range matching circuit, the 8-way automatic range matching circuit is connected with a data acquisition card, and the resistance value acquired by the 128-way gating circuit is transmitted to a PC (personal computer) through the data acquisition card.
5. The large dynamic range sandstone model resistivity measuring device of claim 2, wherein the circuit module is further provided with a differential amplifying circuit for suppressing common mode interference during the measurement process.
6. A method for measuring resistivity of a sandstone model with a large dynamic range by adopting the resistivity measuring device of the sandstone model with the large dynamic range as claimed in any one of claims 1 to 5, and constructing the sandstone model to measure the internal resistance value thereof, is characterized by comprising the following steps:
uniformly inserting resistivity probes of 128-path gating circuits into a large sandstone model by using a prepared sandstone model;
secondly, an amplifying circuit is arranged in the circuit module, and the amplifying circuit adopts a differential amplifying circuit to inhibit common-mode interference;
thirdly, running a program through the PC, completely acquiring the 128 resistance value, and transmitting the resistance value to the PC through a data acquisition card;
and step four, removing errors generated by zero drift generated during resistance measurement by using an improved Kalman filtering algorithm.
7. The resistivity measurement method for the sandstone model with the large dynamic range of claim 6, wherein according to the first to fourth steps of the resistivity measurement method for the sandstone model with the large dynamic range, a PC program is started, 128 paths of acquired resistance signals are acquired through a data acquisition card, a Kalman filtering model is constructed, errors of zero drift are removed, and the constructing of the Kalman filtering model specifically comprises the following steps: establishing a state equation of the system based on the measurement of the resistance
X(k)＝f(k,X(k))+V(k)，
The measurement equation is
Z(k+1)＝h(k，X(k))+W(k)，
Wherein X (k) is a state vector of the measured potential, V (k) is process noise, Z (k) is an observed vector of the potential at time k, and W (k) is measurement noise.
8. The resistivity measurement method for the sandstone model with the large dynamic range of claim 7, wherein a Kalman filtering model is constructed according to the first to fourth steps of the resistivity measurement method for the sandstone model with the large dynamic range, and the expanded Kalman filtering process is adopted as follows:
the one-step prediction equation of state is
The prediction equation of covariance is
P(k+1|k)＝fx(k)P(k|k)fx′(k)+Q(k)，
Metrology prediction equation
Innovation covariance of
S(k+1)＝hx(k+1)P(k+1|k)hx′(k+1)+R(k+1)，
Gain of
The state update equation is
The covariance update equation is
The algorithm can be started and recurred only by giving a state initial value and a covariance matrix of a filtering estimation state vector; after the system reaches a steady state, predicting that covariance, innovation and gain all tend to minimum values; if the resistance is suddenly changed, the predicted value is not accurate any more, the innovation covariance is suddenly increased, but the gain cannot be changed, so that the filtering precision is reduced; because the calculation amount of the gain matrix K is large, the real-time performance is reduced due to recalculation of the gain matrix K, and the accuracy of a filtering value is improved by correcting a predicted value in one step;
after the filtering tends to be stable, the innovation matrix tends to be a minimum value, and whether the predicted value should be adjusted or not is judged according to the size of the innovation matrix
||r(k+1)||＜λ||Zmax|| (14)，
In the formula, ZmaxThe maximum value of the measurement error matrix is | | |, which is F-norm, and the value range of the lambda is [0.3,0.9 |)]；
When the innovation matrix satisfies the formula (14), the filtering is considered normal; when the resistance is not true, the resistance is considered to be changed greatly, the reliability of the measured value is high, the reliability of the one-step predicted value is low, and the one-step predicted value is corrected;
if not, indicating that the one-step predicted value X (k +1| k) is inaccurate, modifying X (k +1| k), and recalculating the state updating equation to obtain new X (k +1| k + 1);
the specific modification is as follows
In the formula, c1 is a correction for the predicted number of routes; c2 is the correction to the predicted resistance, r' (k +1) is the distance component of the innovation matrix at time k + 1; the value ranges of c1 and c2 are (0, 1), wherein c1 is selected to be 0.5, and c2 is selected to be 0.6; and obtaining a measurement data result with high precision after filtering.
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