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CN112729603A - Discrete multipoint temperature measuring device and measuring method thereof - Google Patents

Discrete multipoint temperature measuring device and measuring method thereof Download PDF

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Publication number
CN112729603A
CN112729603A CN202011563541.7A CN202011563541A CN112729603A CN 112729603 A CN112729603 A CN 112729603A CN 202011563541 A CN202011563541 A CN 202011563541A CN 112729603 A CN112729603 A CN 112729603A
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temperature
layer
measurement
discrete
oil pipe
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吴木旺
林炳南
徐凤阳
毛敏
关利军
尚锁贵
梁豪
姜洪丰
高科超
李纪智
左翊寅
徐杨
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CNOOC China Ltd Hainan Branch
China France Bohai Geoservices Co Ltd
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CNOOC China Ltd Hainan Branch
China France Bohai Geoservices Co Ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01KMEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR
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    • G01K11/32Measuring temperature based upon physical or chemical changes not covered by groups G01K3/00, G01K5/00, G01K7/00 or G01K9/00 using changes in transmittance, scattering or luminescence in optical fibres
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    • G06NCOMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
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Abstract

The invention discloses a discrete multipoint temperature measuring device, comprising: an oil pipe; one end of the perforating gun is communicated with the oil pipe; a plurality of temperature measuring units which are arranged at intervals on the outer surface of the perforating gun; the first clamp is sleeved on the oil pipe and is close to the perforating gun; the temperature storage mechanism is arranged on the outer surface of the oil pipe and is fixed through the first clamp; the battery module is arranged outside the oil pipe, and one end of the battery module is connected with the temperature storage mechanism; and the second hoop is sleeved on the oil pipe and used for fixing the battery module. Through the surface at the perforating gun set up discrete temperature measurement mechanism, measure the temperature of different positions in the pit, it is accurate to measure, and convenient to use improves measurement of efficiency. The invention also provides a discrete multipoint temperature measuring method.

Description

Discrete multipoint temperature measuring device and measuring method thereof
Technical Field
The invention relates to a discrete multipoint temperature measuring device and a measuring method thereof, belonging to the field of downhole operation.
Background
In the process of oil and gas field exploration and development, the conventional temperature measurement technology has two types: single probe temperature measurement and fiber optic distributed temperature measurement.
A single probe temperature measurement often employs a storage thermometer comprising: the temperature probe, the signal acquisition and processing circuit and the battery power supply part only measure and record the temperature of the depth point of the probe. If the temperature of a plurality of depth points in a certain well section needs to be measured (time-temperature data, namely temperature profiles), a plurality of corresponding temperature instruments must be arranged for temperature measurement. This technical scheme has two drawbacks: (1) the temperature measuring points are limited by the length of the instrument, the depth interval of the temperature measuring points is large, and the application of temperature data is influenced. (2) And each temperature measuring point needs to be provided with a temperature instrument, so that the operation is complicated and the cost is high.
Optical fiber distributed temperature measurement (DTS) utilizes a Raman scattering effect (Raman scattering) and an Optical Time-Domain Reflectometry (OTDR for short) to acquire spatial temperature distribution information, thereby realizing temperature monitoring and signal transmission. During field construction, the optical fiber is clamped outside the oil (drill) pipe and is lowered into a target layer section. According to the technical scheme, the wellhead needs an optical fiber interrogator to realize the functions of injecting high-power narrow-pulse-width laser to the sensing optical fiber, collecting back scattering optical signals, processing data, outputting results and the like. There are two disadvantages: (1) the downhole target horizon is deep, typically 3000-4000 meters downhole, whereas the hydrocarbon producing interval is short, a few meters, tens of meters or tens of meters. The temperature of target intervals of dozens of meters or even several meters (oil and gas production intervals) is recorded by putting a sensing optical fiber of several kilometers into the target intervals. The acquisition/input ratio is low, the operation intensity of clamping the optical fiber of thousands of meters is high, and the operation is complex; (2) the cost is high, especially for the well exploration oil and gas well test, the drilling rig time is occupied, and the time efficiency is low; (3) the sensing optical fiber can be lowered into a target layer section only by penetrating through a wellhead production tree and an underground packer, and the optical fiber joint and the penetrating seal have leakage hidden danger, so that signal transmission faults are easily caused, the ground can not record underground temperature data, and secondary production faults are even caused.
Disclosure of Invention
The invention designs and develops a discrete type multi-point temperature measuring device, measures the temperatures of different underground positions by arranging a discrete type temperature measuring mechanism on the outer surface of a perforating gun, has accurate measurement and convenient use, and improves the measuring efficiency.
The invention also designs and develops a discrete multipoint temperature measuring method, the underground temperature of the target well section is collected through a pre-distributed temperature measuring mechanism, the output layer is determined through a BP neural network, the measuring efficiency is high, the fixed-point measurement can be realized, and the purpose is strong.
The technical scheme provided by the invention is as follows:
a discrete multi-point temperature measurement device comprising:
an oil pipe;
one end of the perforating gun is communicated with the oil pipe;
a plurality of temperature measuring units which are arranged at intervals on the outer surface of the perforating gun;
the first clamp is sleeved on the oil pipe and is close to the perforating gun;
the temperature storage mechanism is arranged on the outer surface of the oil pipe and is fixed through the first clamp;
the battery module is arranged outside the oil pipe, and one end of the battery module is connected with the temperature storage mechanism;
and the second hoop is sleeved on the oil pipe and used for fixing the battery module.
Preferably, the temperature measuring unit includes a plurality of temperature sensors.
Preferably, the temperature sensors are arranged on the outer surface of the perforating gun at equal intervals along the axial direction and the radial direction.
A discrete multipoint temperature measuring method using the discrete multipoint temperature measuring device comprises the following steps:
step one, determining the number and the spacing of temperature measurement units according to the length of a well section to be measured, and programming a temperature storage mechanism;
fixing a steel pipe temperature sensor outside the perforating gun, then putting the steel pipe temperature sensor into the well, butting the steel pipe temperature sensor with the temperature acquisition unit, and fixing the steel pipe temperature sensor outside the oil pipe to obtain the assembled discrete multipoint temperature measuring device;
step three, sending the discrete multipoint temperature measuring device into each preset test layer, and carrying out acquisition and test work;
and step four, determining a production layer and a non-production layer through the BP neural network.
Preferably, the step four of determining the productive layer and the non-productive layer through the BP neural network includes:
step 1, acquiring the length L of a test well section and measuring adjacent temperature according to a sampling periodDistance d between units, measured temperature T of each temperature measuring unitiThe pressure P of each measuring node and the depth h of each measuring node are normalized;
step 2, determining the input layer vector of the three-layer BP neural network as x ═ x1,x2,x3,x4,x5}; wherein x is1For testing the length coefficient, x, of the well section2For the spacing coefficient, x, between adjacent temperature-measuring cells3For measuring temperature coefficient, x, of each temperature measuring unit4For the pressure coefficient, x, of each measurement node5The depth coefficient of each measurement node is obtained;
step 3, mapping the input layer to a middle layer, wherein a vector y of the middle layer is { y ═ y1,y2,…,ym}; m is the number of hidden nodes;
and 4, obtaining an output layer vector o ═ o1,o2}; wherein o is1For the measurement zone as a production zone signal, o2The measurement zone is a non-production zone signal.
Preferably, the number m of the intermediate layer nodes satisfies:
Figure BDA0002859952460000031
wherein n is the number of nodes of the input layer, and p is the number of nodes of the output layer.
Preferably, the normalization is performed by the following formula:
Figure BDA0002859952460000032
wherein x isjFor parameters in the input layer vector, XjRespectively are measurement parameters n and T1、T2、v,j=1,2,3,4;XjmaxAnd XjminRespectively, a maximum value and a minimum value in the corresponding measured parameter.
Preferably, the empirical formula for the fluid production of each test zone is:
Figure BDA0002859952460000033
wherein,
Figure BDA0002859952460000034
for base fluid production, T, of each test layeriIs the test temperature of the ith test layer,
Figure BDA0002859952460000035
is the initial temperature of the ith test layer, c is the speed of light, λ is the wavelength of the signal light, f is the frequency of the fiber sensor, σ is the Boltzmann constant, ε is the Raman frequency shift of the sensing fiber, PiIs the test pressure of the ith test layer, P0Is the static pressure of the ith test layer.
The invention has the following beneficial effects: according to the requirements of the interval of the logging points and the logging length, a batch of temperature probes at different depths and different interval distances are distributed in advance, and underground temperature data of a target well section is measured and recorded. The method is particularly suitable for exploration and development well testing.
According to the discrete multipoint temperature measuring method provided by the invention, the underground temperature of the target well section is collected through the pre-distributed temperature measuring mechanism, and the output layer is determined through the BP neural network, so that the measuring efficiency is high, the fixed-point measurement can be realized, the operation risk is small, and the purpose is strong.
Drawings
Fig. 1 is a schematic structural diagram of a discrete multipoint temperature measuring device according to the present invention.
Fig. 2 is a schematic circuit diagram of a discrete multipoint temperature measuring device according to the present invention.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.
As shown in fig. 1-2, the present invention provides a discrete type multipoint temperature measuring device, comprising: the perforating gun 220, the plurality of temperature measuring units 230, the elastic clips 210, the first collar 150, the temperature storage mechanism 140, the oil pipe 130, the battery module 120 and the second collar 110.
One end of the perforating gun 220 is communicated with the oil pipe 130, a plurality of temperature measuring units 230 are fixedly arranged on the outer surface of the perforating gun 220 and are arranged at intervals, and the first clamp 150 is sleeved on the oil pipe 130 and is close to the perforating gun 220. A temperature storage mechanism 140 is fixedly arranged on the outer surface of the oil pipe 130, the temperature storage mechanism 140 is fixed by a first clamp 150, the temperature storage mechanism 150 is fixed on the oil pipe, the battery module 120 is arranged on the outer surface of the oil pipe 130, the battery module 120 is fixed on the outer surface of the oil pipe 130 by a second clamp 110, the battery module 120 is electrically connected with the temperature storage mechanism 140 to supply power to the storage mechanism 140, and the plurality of temperature measurement units 230 are electrically connected with the temperature storage mechanism 140 to transmit the measured temperature to the temperature storage mechanism 140.
In the present invention, it is preferable that the temperature measuring unit 230 is a temperature sensor, and a plurality of temperature sensors are arranged on the outer surface of the perforating gun 220 at intervals along the axial direction and the radial direction to form a discrete multi-point temperature measuring mechanism.
And selecting the temperature probes according to specific operation requirements, considering probe intervals and probe quantity, and installing the temperature probes on a standard acquisition short section. After the acquisition program is compiled, the oil drill pipe or the perforating gun is clamped at the outer side of the oil drill pipe or the perforating gun), and the oil drill pipe is lowered to a preset depth along with the test pipe column. After the test is finished, the data of the memory in the acquisition nipple are played back along with the test pipe column taking-out device (the temperature probe and the acquisition nipple).
The present invention also provides a method for measuring a discrete multipoint temperature measuring device, using the discrete multipoint temperature measuring device, and comprising:
step one, determining the number and the spacing of temperature measurement units according to the length of a well section to be measured, and programming a temperature storage mechanism;
fixing a steel pipe temperature sensor outside the perforating gun, then putting the steel pipe temperature sensor into the well, butting the steel pipe temperature sensor with the temperature acquisition unit, and fixing the steel pipe temperature sensor outside the oil pipe to obtain the assembled discrete multipoint temperature measuring device;
step three, sending the discrete multipoint temperature measuring device into each preset test layer, and carrying out acquisition and test work;
and step four, determining a production layer and a non-production layer through the BP neural network.
In the invention, as an optimization, a three-layer BP neural network is selected as a neural network model, and the specific establishing and training processes of the neural network are as follows:
step 1, establishing a BP neural network model;
the BP network system structure adopted by the invention is composed of three layers, wherein the first layer is an input layer, n nodes are provided in total, n detection signals representing the working state of the equipment are correspondingly provided, and the signal parameters are provided by a data preprocessing module. The second layer is a hidden layer, and has m nodes, and is determined by the training process of the network in a self-adaptive mode. The third layer is an output layer, p nodes are provided in total, and the output is determined by the response actually needed by the system.
The mathematical model of the network is:
inputting a layer vector: x ═ x1,x2,…,xn)T
Intermediate layer vector: y ═ y1,y2,…,ym)T
Outputting a layer vector: z is (z)1,z2,…,zp)T
In the invention, the number of nodes of the input layer is n equals to 5, the number of nodes of the output layer is p equals to 2, and the number of nodes of the hidden layer m is estimated by the following formula:
Figure BDA0002859952460000061
the 5 parameters of the input layer are respectively expressed as: x is the number of1For testing the length coefficient, x, of the well section2For the spacing coefficient, x, between adjacent temperature-measuring cells3For measuring temperature coefficient, x, of each temperature measuring unit4For the pressure coefficient, x, of each measurement node5The depth coefficient of each measurement node is obtained;
the data acquired by the sensors belong to different physical quantities, and the dimensions of the data are different. Therefore, before data is input into the artificial neural network, the data needs to be normalized to a value between 0 and 1.
The normalized formula is:
Figure BDA0002859952460000062
wherein x isjFor parameters in the input layer vector, XjRespectively, measurement parameters are as follows: l, d, Ti、Pi、h,j=1,2,3,4,5;XjmaxAnd XjminRespectively, a maximum value and a minimum value in the corresponding measured parameter.
Specifically, the length L of the well section is tested, and after normalization, a length coefficient x of the test well section is obtained1
Figure BDA0002859952460000063
Wherein L isminAnd LmaxRespectively measuring the minimum value and the maximum value of the length of the well section;
specifically, the distance d between adjacent temperature measurement units is normalized to obtain the distance coefficient x between adjacent temperature measurement units2
Figure BDA0002859952460000064
Wherein d isminAnd dmaxThe minimum value and the maximum value of the distance between the adjacent temperature measurement units are respectively;
specifically, the measured temperature of each temperature measuring unit is normalized to obtain the measured temperature coefficient x of each temperature measuring unit3
Figure BDA0002859952460000065
Wherein, TiminAnd TimaxIs the minimum sum of the measured temperatures of the temperature measuring unitsA maximum value;
specifically, the pressure at each measurement node is normalized to obtain a pressure coefficient x at each measurement node4
Figure BDA0002859952460000066
Wherein, PiminAnd PimaxRespectively the minimum value and the maximum value of the pressure of each measuring node;
specifically, the depth h coefficient x of each measurement node is obtained by normalizing the depth of each measurement node5
Figure BDA0002859952460000071
Wherein h isminAnd hmaxRespectively the minimum value and the maximum value of the depth of each measuring node;
output layer vector o ═ o1,o2The two parameters of are respectively expressed as: o1For the measurement zone as a production zone signal, o2The measurement zone is a non-production zone signal.
In another embodiment, the empirical calculation of fluid production for each production zone is:
Figure BDA0002859952460000072
wherein,
Figure BDA0002859952460000073
for base fluid production, T, of each test layeriIs the test temperature of the ith test layer,
Figure BDA0002859952460000074
is the initial temperature of the ith test layer, c is the speed of light, λ is the wavelength of the signal light, f is the frequency of the fiber optic sensor, σ is the Boltzmann constant, and ε is the transmissionRaman frequency shift amount, P, of optical fiberiIs the test pressure of the ith test layer, P0Is the static pressure of the ith test layer.
Wherein λ is2For the second correction coefficient, Ti2Is the test temperature of the molten steel in the second heating stage.
And 2, training the BP neural network.
After the BP neural network node model is established, the training of the BP neural network can be carried out. And obtaining a training sample according to historical experience data of the product, and giving a connection weight between the input node i and the hidden layer node j and a connection weight between the hidden layer node j and the output layer node k.
Training method
Each subnet adopts a separate training method; when training, firstly providing a group of training samples, wherein each sample consists of an input sample and an ideal output pair, and when all actual outputs of the network are consistent with the ideal outputs of the network, the training is finished; otherwise, the ideal output of the network is consistent with the actual output by correcting the weight; the input samples for each subnet training are shown in table 1:
Figure BDA0002859952460000075
Figure BDA0002859952460000081
when the system is designed, the system model is a network which is only initialized, the weight needs to be learned and adjusted according to data samples obtained in the using process, and therefore the self-learning function of the system is designed. Under the condition that learning samples and quantity are specified, the system can carry out self-learning so as to continuously improve the network performance, and output samples after each subnet is trained are shown in a table 2:
TABLE 2
Figure BDA0002859952460000082
And 3, acquiring and transmitting the operation parameters of each unit and inputting the operation parameters into a neural network to obtain a signal of the measuring layer as a production layer and a signal of the measuring layer as a non-production layer.
The trained artificial neural network is solidified in the chip, so that the hardware circuit has the functions of prediction and intelligent decision making, and intelligent hardware is formed.
Simultaneously acquired by sensors
Figure BDA0002859952460000083
Normalizing the parameters to obtain initial input vector of BP neural network, and calculating to obtain initial output vector
Figure BDA0002859952460000084
And step four, monitoring the output quantity condition of the measuring layer.
And judging the output condition of the measuring layer in the (i + 1) th cycle according to the sampling signals of the length of the collecting and testing well section, the distance between the adjacent temperature measuring units, the measuring temperature of each temperature measuring unit, the pressure of each measuring node and the depth of each measuring node in the ith cycle to obtain the output condition.
And judging the working states of the motor and the power converter in the (i + 1) th cycle according to the height between the solar photovoltaic system and the top of the automobile in the (i) th cycle, the temperature in the cab, the ambient temperature and the sampling signal of the running speed of the automobile, and adjusting the output level of the fan and the working state of the heating mechanism.
According to the requirements of the interval of the logging points and the logging length, a batch of temperature probes at different depths and different interval distances are distributed in advance, and underground temperature data of a target well section is measured and recorded. The method is particularly suitable for exploration and development well testing.
The discrete temperature measurement system mainly comprises a temperature storage short section (one) and a temperature acquisition unit (a plurality of), and the instrument string connection adopts a single-core structure.
The whole system communication adopts a master-slave mode, the temperature storage short section is a master, the temperature acquisition units are slaves, different addresses are allocated to the temperature acquisition units, the temperature storage short section successively accesses the temperature acquisition units according to configuration information, the accessed temperature acquisition units transmit data to the temperature storage short section, and the temperature storage short section stores the data in FLASH after arranging the data.
The whole system is divided into a USB communication mode and a measurement mode, and is in the USB communication mode after being plugged with a USB line to connect a computer, and at the moment, FLASH data, configuration instruments and the like can be read. When the battery pack is plugged, the instrument works in a measurement mode, and the instrument starts to acquire and store data of each temperature acquisition unit according to the configuration information.
The temperature storage short section mainly comprises a USB interface, a TBUS bus interface, FLASH storage, a battery pack and other parts;
the USB interface mainly completes communication between the storage battery short section and a computer, and comprises instrument configuration, FLASH data reading and the like, the USB interface part only works after a USB line is plugged, and does not work in a measurement mode, and the USB interface part also comprises an independent 3.3V power supply for the interface chip to work. The system adopts a single-core mode, supplies power and transmits data on one line, and therefore comprises a receiving circuit and a loading circuit, the loading circuit loads address information sent by the MCU to the TBUS, and the receiving circuit receives data information on the TBUS. An inductive isolation is also included between the stack and the TBUS due to the low internal resistance of the stack.
The FLASH storage adopts nonvolatile storage, and even when the underground battery power is exhausted or other faults occur, the stored data cannot be lost as long as the FLASH chip is not damaged.
The storage battery short section also comprises bus control, voltage measurement and current measurement. The bus control is used for controlling whether power is supplied to the temperature acquisition unit or not; the USB voltage is lower than the voltage of the battery pack, and the working state of the instrument and the consumption of the electric quantity of the battery are monitored through voltage measurement and current measurement. In addition, the device also comprises a buzzing information indication, and after the battery pack is switched on, different information is prompted by different sounds of the buzzer to simply confirm whether the working state of the device is normal.
The temperature acquisition unit comprises a TBUS bus interface, a temperature measurement circuit and a 3.3V power supply. And the TBUS bus interface is used for finishing communication with the storage pup joint. The principle is the same as that of a storage battery short joint, and the difference is that the storage battery short joint receives addresses and sends data.
The sensor measurement comprises a PT1000 temperature sensor and an A/D conversion part, wherein the A/D conversion is controlled by an MCU (microprogrammed control unit), and the MCU reads A/D data according to an A/D time sequence.
In the present invention, preferably, the 3.3V power supply provides an operating power supply for the operation of the temperature acquisition unit.
While embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable in various fields of endeavor to which the invention pertains, and further modifications may readily be made by those skilled in the art, it being understood that the invention is not limited to the details shown and described herein without departing from the general concept defined by the appended claims and their equivalents.

Claims (8)

1. A discrete multipoint temperature measurement device, comprising:
an oil pipe;
one end of the perforating gun is communicated with the oil pipe;
a plurality of temperature measuring units which are arranged at intervals on the outer surface of the perforating gun;
the first clamp is sleeved on the oil pipe and is close to the perforating gun;
the temperature storage mechanism is arranged on the outer surface of the oil pipe and is fixed through the first clamp;
the battery module is arranged outside the oil pipe, and one end of the battery module is connected with the temperature storage mechanism;
and the second hoop is sleeved on the oil pipe and used for fixing the battery module.
2. The discrete multi-point temperature measurement device according to claim 1, wherein the temperature measurement unit includes a plurality of temperature sensors.
3. The discrete multi-point temperature measurement device of claim 2, wherein the temperature sensors are equally spaced axially and radially on the exterior surface of the perforating gun.
4. A discrete multipoint temperature measuring method using the discrete multipoint temperature measuring device according to any one of claims 1 to 3, comprising:
step one, determining the number and the spacing of temperature measurement units according to the length of a well section to be measured, and programming a temperature storage mechanism;
fixing a steel pipe temperature sensor outside the perforating gun, then putting the steel pipe temperature sensor into the well, butting the steel pipe temperature sensor with the temperature acquisition unit, and fixing the steel pipe temperature sensor outside the oil pipe to obtain the assembled discrete multipoint temperature measuring device;
step three, sending the discrete multipoint temperature measuring device into each preset test layer, and carrying out acquisition and test work;
and step four, determining a production layer and a non-production layer through the BP neural network.
5. The discrete multipoint temperature measurement method according to claim 4, wherein the step four of determining the production layer and the non-production layer through the BP neural network comprises:
step 1, acquiring the length L of a test well section, the distance d between adjacent temperature measurement units and the measurement temperature T of each temperature measurement unit according to a sampling periodiThe pressure P of each measuring node and the depth h of each measuring node are normalized;
step 2, determining the input layer vector of the three-layer BP neural network as x ═ x1,x2,x3,x4,x5}; wherein x is1For testing the length coefficient, x, of the well section2For adjacent temperature measurementCoefficient of spacing between cells, x3For measuring temperature coefficient, x, of each temperature measuring unit4For the pressure coefficient, x, of each measurement node5The depth coefficient of each measurement node is obtained;
step 3, mapping the input layer to a middle layer, wherein a vector y of the middle layer is { y ═ y1,y2,…,ym}; m is the number of hidden nodes;
and 4, obtaining an output layer vector o ═ o1,o2}; wherein o is1For the measurement zone as a production zone signal, o2The measurement zone is a non-production zone signal.
6. The discrete multipoint temperature measurement method according to claim 5, wherein the number m of intermediate layer nodes satisfies:
Figure FDA0002859952450000021
wherein n is the number of nodes of the input layer, and p is the number of nodes of the output layer.
7. The discrete multipoint temperature measurement method according to claim 6, wherein said normalization is performed by the formula:
Figure FDA0002859952450000022
wherein x isjFor parameters in the input layer vector, XjRespectively are measurement parameters n and T1、T2、v,j=1,2,3,4;XjmaxAnd XjminRespectively, a maximum value and a minimum value in the corresponding measured parameter.
8. The discrete multi-point temperature measurement method of claim 7, wherein the empirical formula for the fluid production of each production zone is:
Figure FDA0002859952450000023
wherein,
Figure FDA0002859952450000024
for base fluid production, T, of each test layeriIs the test temperature of the ith test layer,
Figure FDA0002859952450000025
is the initial temperature of the ith test layer, c is the speed of light, λ is the wavelength of the signal light, f is the frequency of the fiber sensor, σ is the Boltzmann constant, ε is the Raman frequency shift of the sensing fiber, PiIs the test pressure of the ith test layer, P0Is the static pressure of the ith test layer.
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