A Hybrid Monte Carlo Deep Penetration Calculation Method for Cased-Hole Density Logging

Abstract

The present invention belongs to the technical field of well logging, and specifically relates to a hybrid Monte Carlo deep penetration calculation method for cased-hole density logging. By constructing the same three-dimensional numerical model of the cased-hole density logging instrument and the formation in Monte Carlo software and a deterministic program; using the three-dimensional numerical model constructed in the deterministic program to obtain the importance map of the three-dimensional numerical model, and inputting it into the three-dimensional numerical model constructed in the Monte Carlo software as the guiding parameter for the importance of the weight window, so as to divide the important area and the unimportant area of the acquired energy spectrum, thereby realizing weighted sampling by energy group. By dividing the important area and the unimportant area, the simulation of the unimportant area by the program is avoided, the occupation of computer resources is reduced, and because more particles are added to simulate the important area, the simulation time when various environmental parameters change can be effectively shortened on the premise of ensuring the correctness and accuracy of the simulation results.

Description

Technical Field

[0001] The present invention belongs to the technical field of well logging, and particularly relates to a hybrid Monte Carlo deep penetration calculation method for cased-hole density logging. Background Art

[0002] Nuclear well logging is a method for determining the drilling geological profile and searching for oil and gas reservoirs based on the nuclear physical properties of rocks and media. It is known as one of the three major geophysical well logging techniques together with acoustic well logging and electrical well logging. Before well logging, nuclear well logging needs to pre-simulate the instrument. At present, the simulation methods in the field of nuclear well logging are mainly the diffusion theory method and the Monte Carlo method. The diffusion theory method contains a calculus equation with multiple variables, usually solved by numerical methods, and a unique analytical solution cannot be obtained. The Monte Carlo method is a numerical calculation method based on statistical probability. Its basic process is to establish a corresponding random sampling model for the problem raised, and obtain the solution of the problem through a large number of repeated experiments. The method for simulating particle transport is to use random numbers to track a large number of particles and record their trajectories.

[0003] In recent years, with the increase in the number of deep wells, the well trajectory has become more complex and the downhole operation difficulty has increased year by year. Under complex well conditions, it is difficult to obtain reservoir data through the open hole, and the operation risk cannot be effectively controlled. In response to this situation, some researchers have proposed the technology of cased-hole formation evaluation. However, due to the obstruction of the casing cement, the calculation resources required by the Monte Carlo method increase and the time consumption is too long, which cannot meet the efficiency requirements in the actual operation process. Specifically, it is reflected in:

[0004] 1. Particle transport simulation in the wellbore is a complex deep penetration problem. The traditional Monte Carlo method will simulate the trajectories of each particle and its secondary particles and store them in the computer. This leads to a large number of particle simulations, and the computational resources required for information storage and processing are high.

[0005] 2. The volume of the detector installed on the downhole instrument is small. After being doubly shielded by the casing and cement in the complex formation environment, the nuclear particles that can be counted by the detector are greatly weakened compared with a conventional well (open hole well), making it difficult to meet the accuracy requirements of the energy spectrum for density logging. How to ensure that the detector can obtain sufficient signals and verify their accuracy is a difficult point in nuclear detection in cased holes.

[0006] 3. The Monte Carlo simulation can only simulate a set of fixed environmental parameters each time. Simulating the continuously changing and parameter-rich downhole environment, such as: instrument position, wellbore size, casing size and material, formation lithology, formation porosity, well fluid type and saturation, formation fluid type and saturation, mud cake thickness and density, clay content, cement type, etc., requires a huge amount of time.

[0007] Therefore, it is necessary to study a hybrid Monte Carlo deep penetration calculation method for cased-hole density logging. On the premise of ensuring the correctness and accuracy of the simulation results, the simulation time when various environmental parameters change can be effectively shortened. Summary of the Invention

[0008] The object of the present invention is to provide a hybrid Monte Carlo deep penetration calculation method for cased-hole density logging, so as to solve the problem of low accuracy of detector energy spectrum counting caused by deep penetration problems, and improve the simulation efficiency of multiple environmental parameters in the post-casing environment.

[0009] To achieve the above object, the present invention adopts the following technical solutions:

[0010] A hybrid Monte Carlo deep penetration calculation method for cased-hole density logging includes the following steps:

[0011] S1. Obtain the environmental parameters of the cased-hole density logging instrument and the formation it measures;

[0012] S2. Based on the environmental parameters of the cased-hole density logging instrument and the formation it measures obtained in S1, construct a three-dimensional numerical model of the cased-hole density logging instrument and the formation in the Monte Carlo software and the deterministic program respectively;

[0013] S3. Use the three-dimensional numerical model constructed in the deterministic program in S2 to obtain the importance map of the three-dimensional numerical model;

[0014] S4. Input the importance map obtained in S3 into the three-dimensional numerical model constructed in the Monte Carlo software in S2 as a guiding parameter for the importance of the weight window, so as to divide the important area and the unimportant area of the collected energy spectrum, thereby realizing weighted sampling by energy group, obtaining the simulation error and operation efficiency and outputting.

[0015] Further, in the deterministic program, the steps of constructing the three-dimensional numerical model of the cased-hole density logging instrument and the formation include:

[0016] According to the environmental parameters of the cased-hole density logging instrument and the formation it measures obtained in S1, set up the collected environmental parameters, set the source strength, energy distribution, and emission direction of the instrument; set the database for particle deterministic calculation, that is, the reaction cross-section library of elements; set the detector position, conjugate source size and number;

[0017] In the Monte Carlo software, the steps of constructing the three-dimensional numerical model of the cased-hole density logging instrument and the formation include:

[0018] Based on the environmental parameters of the cased density logging tool obtained from S1 and the formation it measures, set up the collected environmental parameters, set the source strength, energy distribution, and emission direction of the tool; divide the weight window and make the following settings: set the input data storage area, upper weight window boundary, lower weight window boundary, and survival weight, set the weight window bias to sample particles by energy group according to particle energy, set the energy spectrum collection to collect by weight, read the current weight of each particle and perform weighted accumulation into the detector results of each event simulation.

[0019] Furthermore, the weight window division uses the parallel geometric body method in Monte Carlo to divide the weight window.

[0020] Further, the steps of obtaining the importance map of the three-dimensional numerical model in S3 include:

[0021] 3.1. In the deterministic program, according to the formation, wellbore, tool, and detector positions, perform discrete grid division on the XYZ axes to obtain discrete energy intervals;

[0022] 3.2. Use the discrete ordinate method SN to perform finite element difference calculation on the discrete grid to obtain the importance map of the three-dimensional numerical model by photon energy group; the photon energy group refers to obtaining discrete energy intervals using the discrete ordinate method.

[0023] Furthermore, the solution steps of using the discrete ordinate method SN to perform finite element difference calculation on the discrete grid in S3.2 include:

[0024] S3.2.1. Define the SN equation for each energy group as:

[0025] LΨ = MSφ + q (1)

[0026] L is the differential transport operator; M is the discrete operator; S is the scattering cross-section matrix; q is the conjugate source; φ is the angular flux at discrete angles; ψ is the angular flux vector at discrete angles.

[0027] S3.2.2. Convert the SN equation to obtain the conjugate equation:

[0028] L * φ * = MS * φ * + q * (2)

[0029] S3.2.3. Apply the operator D, where φ = Dψ, and rearrange the terms to convert the conjugate equation into the form of a traditional linear system, Ax = b,

[0030] (I - DL -1 MS) = DL -1 q (3)

[0031] Based on the traditional wavefront solution method, solve for L -1 v, where v is the iteration vector; among them, for the selection of the q conjugate source, the forward weighted consistency conjugate-driven importance sampling method FW-CADIS method or CADIS method is adopted;

[0032] When the detector is a single detector, the CADIS method is adopted, and the conjugate flux φ is established based on the single detector * The relationship with the detector response R, and obtain the importance map of the numerical three-dimensional model by photon energy group; when the detector is a multi-detector, the FW-CADIS method is adopted, and according to the response function σ of the detector * (E), obtain the importance map of the numerical three-dimensional model by photon energy group.

[0033] Furthermore, the method for the CADIS method to obtain the importance map of the numerical three-dimensional model by photon energy group includes the following steps:

[0034] Establish the relationship between the conjugate flux φ * and the detector response R based on the response function of the detector:

[0035]

[0036] where r is the particle position vector; E is the particle energy; q is the particle source; V s is the source volume size; V d is the detector volume size, and d represents integration within the detector volume;

[0037] Based on q * (r,E) = σ * (E)g(r), where g(r) = 1 means entering the detector; substituting into equation (4) gives:

[0038]

[0039] where, is the biased source; φ * (r,E) is the conjugate flux; R is the detector response; calculate the importance map according to the following formula based on the conjugate flux to be used as the lower boundary of the Monte Carlo weight window:

[0040]

[0041] Furthermore, the FW-CADIS method, the method for obtaining the importance map of the numerical three-dimensional model by photon energy group, includes the following steps:

[0042] In the FW-CADIS method, according to the response function σ of the detector* (E), to obtain Equation (7):

[0043]

[0044] The importance spectrum of each sub-photon energy group can be determined using Equation (7).

[0045] Furthermore, the implementation method of S4 includes the following steps:

[0046] S4.1: Extract the importance spectrum of the sub-photon energy group in S3.2. According to the principle of the Cartesian coordinate system, starting from the origin of the coordinates, read the weights of the discrete grid from bottom to top and from left to right, and store them in the storage area of the input data;

[0047] S4.2: Determine whether the particle splits, roulette, or is killed based on the particle weight, so as to guide more particles that contribute to the detector count to be simulated at the required positions, and reduce the continuous simulation of particles in unimportant areas;

[0048] S4.3: According to the accumulated deposition energy spectrum in the detector, count the deposition energy of each event for each channel value, calculate the average value and standard deviation to obtain the statistical error of a single event, and output the simulation accuracy, time consumption of each channel value, as well as the count statistical error and efficiency of the total count.

[0049] The present invention belongs to the technical field of logging, and specifically relates to a hybrid Monte Carlo deep penetration calculation method for cased-hole density logging. By constructing the same three-dimensional numerical model of the post-casing density logging instrument and the formation in the Monte Carlo software and the deterministic program; using the three-dimensional numerical model constructed in the deterministic program, the importance spectrum of the three-dimensional numerical model can be obtained by sub-photon groups, and it is input into the three-dimensional numerical model constructed in the Monte Carlo software as a guiding parameter for the importance of the weight window, so as to divide the important area and unimportant area of the collected energy spectrum, thereby realizing weighted sampling by energy group. By dividing the important area and unimportant area, the simulation of the unimportant area by the program is avoided, the occupation of computer resources is reduced, and because more particles are added to simulate in the important area, the simulation time when various environmental parameters change can be effectively shortened on the premise of ensuring the correctness and accuracy of the simulation results.

[0050] In addition, in the process of obtaining the importance map of the numerical three-dimensional model of the photon energy group spectrum, based on the characteristics of the detector response, the response result is established as the relationship between the conjugate flux and the source term. According to the different numbers of detectors of specific instruments, different acceleration strategies are used. That is, the CADIS method corresponds to local optimization, the optimization of a single detector; while FW-CADIS corresponds to global optimization, that is, the optimization of multiple detectors can be set. Through different acceleration methods, the conjugate source can be determined. Thus, the three-dimensional numerical model can be meshed according to the Cartesian coordinate system using the Sn discrete ordinate method, and the conjugate flux can be calculated. It obtains a shorter simulation time and higher accuracy within the same time, which has important reference significance for the density logging method after casing.

[0051] In summary, the simulation matching method of the present invention solves the problems of high computer resource occupation, low simulation efficiency and low accuracy caused by density logging after casing. Brief Description of the Drawings

[0052] Figure 1 It is a simplified model of the scenario of the density gamma instrument in the environment after casing;

[0053] Figure 2 It is a schematic diagram of the process from weight window meshing to Geant4 accelerated simulation;

[0054] Figure 3 Schematic diagram of the weight window sampling method;

[0055] Figure 4 Schematic diagram of the multi-energy group processing method;

[0056] Figure 5 It is a comparison chart of the simulation results of ordinary Monte Carlo (ANALOG) and the simulation results (CADIS) accelerated by the method of this embodiment. Among them, (a) is the simulation result of ordinary Monte Carlo (ANALOG), and (b) is the simulation result (CADIS) accelerated by the method of this embodiment. Detailed Description of the Specific Embodiment

[0057] The present invention will be described in detail below in combination with the Monte Carlo software Geant4, the drawings and the embodiments.

[0058] As Figure 1 shown, compensated density logging irradiates the formation with gamma rays emitted by the Cs137 source, interacts with the formation element nuclei, and measures the gamma attenuation between the detector and the source to obtain its count rate, and then the density of the lithology can be determined. However, in the measurement of the formation through the casing, due to the increased shielding effect of the casing and the cement sheath, the detector count rate is reduced, that is, the accuracy of the energy spectrum capture spectrum is reduced, thus affecting the accuracy of obtaining the density and lithology.

[0059] To solve the problem of low accuracy of counting results caused by deep penetration in the measurement of the post-casing density instrument. Based on the Monte Carlo software (Geant4), this embodiment implants the method and proposes a quantitative evaluation method for the cementing cement in the environment of cased-hole density logging, including the following steps:

[0060] S1. Obtain the environmental parameters of the post-casing density logging instrument and the formation it measures.

[0061] S2. Based on the environmental parameters of the post-casing density logging instrument and the formation it measures obtained in S1, construct three-dimensional numerical models of the post-casing density logging instrument and the formation in the Monte Carlo software and the deterministic program respectively.

[0062] The steps of constructing the three-dimensional numerical model of the post-casing density logging instrument and the formation in the deterministic program include:

[0063] According to the environmental parameters of the post-casing density logging instrument and the formation it measures obtained in S1, set up the collected environmental parameters, set the instrument to emit gamma particles at 0.662 MeV and 45° obliquely upward.

[0064] Set the database for deterministic calculation of particles, that is, the reaction cross-section library of elements.

[0065] Set the detector position, conjugate source size and number.

[0066] The steps of constructing the three-dimensional numerical model of the post-casing density logging instrument and the formation in the Monte Carlo software include:

[0067] Set up the parameter environment of the collected data, set the emission source intensity of the instrument to 0.662 MeV, and emit gamma particles at 45° obliquely upward.

[0068] Based on the ParallelGeometry method in Geant4, divide the weight window, that is, perform grid division; set the WeightWindowStore to be used to input the grid weights in different energy groups calculated by the SN discrete ordinate method.

[0069] Set the WeightWindowAlgorithm to set the upper weight window boundary, lower weight window boundary and survival weight, and determine the maximum particle splitting factor.

[0070] In the WeightWindowBiasing method, perform particle sampling according to the particle energy into energy groups to input the weights of different energy intervals into the corresponding parallel geometric grids.

[0071] In the G4EnergeDeposition energy spectrum collection method, a method of setting weights is adopted. The current weight of each particle is read and weighted and accumulated into the detector results of each event simulation to complete particle transport.

[0072] S3. Use the three-dimensional numerical model constructed in the S2 deterministic program to obtain the importance map of the three-dimensional numerical model. The detailed steps include:

[0073] 3.1. In the deterministic program, according to the formation, wellbore, instrument, and detector positions, discrete grid division is performed on the XYZ axes to obtain discrete energy intervals. In this embodiment, the discrete grid formed after grid division has the same structure as the discrete grid formed by grid division in Monte Carlo.

[0074] 3.2. Use the discrete ordinate method SN to perform finite element difference calculation on the discrete grid to obtain the importance map of the three-dimensional numerical model by photon energy group; specifically:

[0075] S3.2.1. Define the SN equation for each energy group as:

[0076] LΨ=MSφ+q (1)

[0077] L is the differential transport operator; M is the discrete operator; S is the scattering cross-section matrix; q is the conjugate source; φ is the angular flux at discrete angles; ψ is the angular flux vector at discrete angles.

[0078] S3.2.2. Convert the SN equation to obtain the conjugate equation:

[0079] L * φ * =MS * φ * +q * (2)

[0080] S3.2.3. Apply the operator D, where φ = Dψ, and rearrange the terms to convert the conjugate equation into the form of a traditional linear system, Ax = B,

[0081] (I - DL -1 MS)=DL -1 q (3)

[0082] Based on the traditional wavefront solution method, solve for L -1 v, where v is the iteration vector; for the selection of the q conjugate source, the forward weighted consistent conjugate-driven importance sampling method FW-CADIS method or CADIS method is adopted.

[0083] When the detector is a single detector, the CADIS method is adopted, and the conjugate flux φ *Relationship with the detector response R, importance map of the numerical three-dimensional model obtained by photon energy group; when the detector is a multi-detector, the FW-CADIS method is adopted, and according to the response function σ of the detector * (E), importance map of the numerical three-dimensional model obtained by photon energy group.

[0084] In this embodiment, the method for the CADIS method to obtain the importance map of the numerical three-dimensional model by photon energy group includes the following steps:

[0085] Establish the adjoint flux φ based on the response function of the detector * Relationship with the detector response R:

[0086]

[0087] where r is the particle position vector; E is the particle energy; q is the particle source; V s is the source volume size; V d is the detector volume size;

[0088] Based on q * (r,E) = σ * (E)g(r), where g(r) = 1 means entering the detector; substituting into Equation (4) gives:

[0089]

[0090] where, is the biased source; φ * (r,E) is the adjoint flux; R is the detector response;

[0091] Calculate the importance map according to the adjoint flux according to the following formula, and its calculation method is as follows:

[0092]

[0093] The FW-CADIS method, the method for obtaining the importance map of the numerical three-dimensional model by photon energy group, includes the following steps:

[0094] In the FW-CADIS method, according to the response function σ of the detector * (E), Equation (7) is obtained:

[0095]

[0096] The importance map of each photon energy group can be determined by using Equation (7).

[0097] S4. Take the importance map obtained in S3 as the importance map for Monte Carlo, and input it into the weight window program of the three-dimensional numerical model constructed by S2 in the Monte Carlo software Geant4 to run in parallel, so as to use it as a guiding parameter for the importance of the weight window, divide the important area and unimportant area of the acquired energy spectrum, thereby realizing weighted sampling by energy group, collecting the weighted deposited energy spectrum, obtaining the simulation error and operation efficiency, and outputting. The specific operations are as follows:

[0098] S4.1. Extract the importance map of the photon energy group in S3.2. According to the principle of the Cartesian coordinate system, starting from the origin of coordinates, read the importance of the discrete grid from bottom to top and from left to right, and store it in the weight window memory WeightWindowStore of S1.2.

[0099] S4.2. Set the upper weight window boundary, lower weight window boundary and survival weight according to the weight window method WeightWindowAlgorithm of S1.3. Judge whether the particle splits, roulette or is killed according to the particle weight, so as to guide more particles that contribute to the detector count to be simulated at the required positions, and reduce the continuous simulation of particles in the unimportant area.

[0100] As Figure 3 shown, the particle weight is judged when the particle runs to the weight window boundary. If the particle weight is higher than the upper boundary of the weight window, a splitting operation is performed; if the particle is lower than the lower boundary of the weight window, a roulette is performed, and a killing or survival operation is performed. The particles that survive after the roulette return as the survival weight. Therefore, more particles can be concentrated in the important area for simulation, and the number of particles in the unimportant area is reduced, and the simulation results are not affected at the same time. Therefore, according to the importance, the number of particles is selectively controlled, so as to achieve the purpose of increasing the number of samples at the target counting position. This improves the accuracy of the target count, thus solving the problems of high time consumption and deep penetration in the source-detector Monte Carlo calculation.

[0101] As Figure 4 shown, weight windows of different energy groups are set in the parallel geometry. During the particle transport process, according to the weight of its energy group, the particles are sampled during the weight window biasing process. Then, the particle annihilation or splitting is controlled by the weight window algorithm. By recording the position, energy and weight of the particles during Step-to-Event-to-Run, the weighted deposited energy spectrum can be output at the end of the simulation. The process of collecting weighted particles into the histogram is as Figure 4 shown.

[0102] S4.3. According to the deposited energy spectrum accumulated in the detector, calculate the average value and standard deviation of the deposited energy count for each event at each channel value to obtain the statistical error of a single event, and output the simulation accuracy, time consumption of each channel value, as well as the counting statistical error and efficiency of the total count.

[0103] In this embodiment, a comparison is made between the results of ordinary Monte Carlo (ANALOG) and the accelerated simulation energy spectrum (CADIS). As Figure 5 (a), Figure 5 (b) shows, in the Monte Carlo simulation with the same number of simulated particles, the CADIS method shows better smoothness than ANALOG in the figure. It can be seen from the energy spectra of different detectors at near and far source distances that the energy spectrum of the far-source-distance detector fluctuates more, which is due to the more serious attenuation of gamma particles transmitted to the far source distance. After using the CADIS method, smoother and correct results are achieved for both near and far source distance detectors, indicating the feasibility of the method for accelerating density logging simulation based on hybrid Monte Carlo in the present invention.

[0104] It should be noted that the above embodiments are only a part of the embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the described embodiments without creative efforts fall within the scope of protection of the present invention.

Claims

1. A hybrid Monte Carlo deep penetration calculation method for cased-hole density logging, characterized in that It includes the following steps: S1. Obtain the environmental parameters of the casing density logging tool and the formation it measures; S2. Based on the environmental parameters of the casing density logging tool and the formation obtained in S1, construct a three-dimensional numerical model of the casing density logging tool and the formation in Monte Carlo software and a deterministic program respectively; S3. Use the three-dimensional numerical model constructed in the deterministic program in S2 to obtain the importance map of the three-dimensional numerical model; the steps of obtaining the importance map of the three-dimensional numerical model in S3 include: 3.

1. In the deterministic program, perform discrete grid division on the XYZ axes according to the formation, wellbore, instrument, and detector positions to obtain discrete energy intervals; 3.

2. Use the discrete ordinate method SN to perform finite element difference calculation on the discrete grid to obtain the importance map of the three-dimensional numerical model by photon energy group; the photon energy group refers to obtaining discrete energy intervals using the discrete ordinate method; S4. Input the importance map obtained in S3 into the three-dimensional numerical model constructed in the Monte Carlo software in S2 as the guiding parameter for the importance of the weight window, and use the parallel geometry method in Monte Carlo to divide the weight window to divide the important and unimportant regions for collecting the energy spectrum, so as to achieve weighted sampling by energy group, obtain the simulation error and operation efficiency, and output.

2. A hybrid Monte Carlo deep penetration calculation method for cased-hole density logging according to claim 1, characterized in that In the deterministic program, the steps of constructing a three-dimensional numerical model of the casing density logging tool and the formation include: According to the environmental parameters of the casing density logging tool and the formation obtained in S1, set up the collected environmental parameters, set the source strength, energy distribution, and emission direction of the instrument; set the database for particle deterministic calculation, that is, the reaction cross-section library of elements; set the detector position, conjugate source size, and number; In the Monte Carlo software, the steps of constructing a three-dimensional numerical model of the casing density logging tool and the formation include: According to the environmental parameters of the casing density logging tool and the formation obtained in S1, set up the collected environmental parameters, set the source strength, energy distribution, and emission direction of the instrument; divide the weight window and make the following settings: set the input data storage area, upper weight window boundary, lower weight window boundary, and survival weight, set the weight window bias to perform particle sampling by energy group according to particle energy, set the energy spectrum collection to collect by weight, read the current weight of each particle and perform weighted accumulation into the detector results of each event simulation.

3. A hybrid Monte Carlo deep penetration calculation method for cased-hole density logging according to claim 1, characterized in that The solution steps of using the discrete ordinate method SN to perform finite element difference calculation on the discrete grid in S3.2 include: S3.2.

1. Define the SN equation for each energy group as: LΨ=MSφ+q (1) L is the differential transport operator; M is the discrete operator; S is the scattering cross-section matrix; q is the conjugate source; φ is the angular flux at discrete angles; ψ is the angular flux vector at discrete angles; S3.2.

2. Convert the SN equation to obtain the conjugate equation: L * φ * = MS * φ * +q * (2) S3.2.

3. Apply the operator D, where φ=Dψ, and rearrange the terms to convert the conjugate equation into the form of a traditional linear system, Ax=b, (I-DL -1 MS) = DL -1 q (3) Based on the traditional wavefront solution method, solve for L -1 v, where v is the iteration vector; for the selection of the q conjugate source, use the forward-weighted consistency conjugate-driven importance sampling method FW-CADIS method or CADIS method; When the detector is a single detector, the CADIS method is adopted to establish the conjugate flux φ based on the single detector * The relational expression with the detector response R is used to obtain the importance map of the numerical three-dimensional model by photon energy group; when the detector is a multi-detector, the FW-CADIS method is adopted, and according to the response function σ * (E) of the detector, the importance map of the numerical three-dimensional model is obtained by photon energy group.

4. A hybrid Monte Carlo deep penetration calculation method for cased-hole density logging according to claim 3, characterized in that, The method of using the CADIS method to obtain the importance map of the numerical three-dimensional model by photon energy group includes the following steps: Establish the conjugate flux φ based on the response function of the detector * Relationship with the detector response R: where r is the particle position vector; E is the particle energy; q is the particle source; V s is the source volume size; V d is the detector volume size, and d represents integration within the detector volume; Based on q * (r, E) = σ * (E)g(r), where g(r) = 1 indicates entry into the detector; substituting into Equation (4) gives: wherein, is a bias source; φ * (r, E) is a conjugate flux; R is a detector response; an importance spectrum is calculated according to the conjugate flux by the following formula as the lower boundary of the Monte Carlo weight window:

5. A hybrid Monte Carlo deep penetration calculation method for cased-hole density logging according to claim 3, characterized in that, The FW-CADIS method, a method for obtaining an importance map of a numerical three-dimensional model by photon energy groups, includes the following steps: In the FW-CADIS method, according to the response function σ of the detector * (E), Equation (7) is obtained as follows: σ d (E) is the response function of the detector. Using Equation (7), the importance spectrum of each sub-photon energy group can be determined.

6. A hybrid Monte Carlo deep penetration calculation method for cased-hole density logging according to claim 1, characterized in that, The implementation method of S4 includes the following steps: S4.

1. Extract the importance map of the photon energy groups in S3.

2. Starting from the coordinate origin, read the weights of the discrete grids from bottom to top and from left to right according to the Cartesian coordinate system principle, and store them in the storage area of the input data; S4.

2. Determine whether the particle splits, undergoes roulette, or is killed according to the particle weight, so as to guide more particles that contribute to the detector count to be simulated at the required positions, and reduce the continuous simulation of particles in unimportant regions; S4.

3. According to the cumulative deposited energy spectrum in the detector, count the deposited energy of each event for each channel value, calculate the average value and standard deviation to obtain the statistical error of a single event, and output the simulation accuracy, time consumption of each channel value, as well as the counting statistical error and efficiency of the total count.

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