CN114722610A - Horizontal well cement sheath azimuth gamma density inversion method - Google Patents
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Abstract
The invention discloses an azimuth gamma density inversion method for a horizontal well cement sheath. The method comprises the steps of establishing a horizontal well numerical calculation model by utilizing MCNP simulation software, introducing a perturbation theory into a gamma ray detection process, establishing a cement sheath space density sensitivity function library, dividing a cement sheath into a plurality of sectors, performing space integration on the cement sheath space sensitivity function in each sector respectively, obtaining the relative contribution of each cement sheath sector to the gamma ray counting of a detector, comprehensively considering the influence of casing eccentricity and cement sheath azimuth density change on the gamma ray counting of the detector, establishing a cement sheath azimuth density calculation equation set, solving an optimal solution by utilizing a regularization Newton iteration method, and calculating by combining a cement sheath density reference value to obtain the cement sheath azimuth density. The method solves the problem that the azimuth density of the cement sheath is difficult to accurately evaluate due to casing eccentricity and cement slurry sedimentation in the horizontal well, improves the calculation precision of the azimuth density of the cement sheath, and provides technical support for horizontal well cementation quality evaluation.
Description
Technical Field
The invention relates to the field of petroleum and natural gas development, in particular to a horizontal well cement sheath azimuth gamma density inversion method.
Background
The horizontal well technology is widely applied to exploration and development of unconventional oil and gas reservoirs, the exposed area of the oil and gas reservoirs is increased, and well cementation has important significance for isolation of oil, gas and water layers. The determination of cement density by gamma ray attenuation is an important part in the evaluation of well cementation effect. Compared with the vertical well cementing, the horizontal well has the problems of casing eccentricity, cement paste sedimentation and the like due to the action of casing gravity, so that the gamma ray detection is greatly influenced, and the uncertainty of the cement sheath azimuth density evaluation is caused.
At present, the density of the cement sheath is evaluated mainly based on gamma ray counting of a detector and cement density response, and density parameters are obtained for direct calculation. However, due to the measurement error of the logging instrument and the counting statistics of gamma rays, the azimuth density of the cement sheath cannot be accurately monitored, and the requirement of field oil and gas evaluation is difficult to meet. Meanwhile, the accuracy of the obtained cement density calculation formula is difficult to guarantee due to the fact that the casing in the horizontal well is eccentric. Therefore, a horizontal well cement sheath azimuth gamma density inversion method is needed to be provided, so that the influence of casing eccentricity on gamma counting during horizontal well cementing is avoided, and the calculation accuracy of the cement sheath azimuth density is improved.
Disclosure of Invention
Aiming at the defects, a perturbation theory is introduced into a gamma ray detection process, a horizontal well cement sheath orientation gamma ray density inversion method is provided based on multi-detector gamma counting information of a cement sheath density measurement system and by combining a cement sheath space sensitivity function and a regularized Newton iteration method, the influence of casing eccentricity and cement sheath orientation density change on detector gamma ray counting is comprehensively considered, and the accuracy of cement sheath orientation density calculation is improved.
The invention specifically adopts the following technical scheme:
an azimuth gamma density inversion method for a horizontal well cement sheath adopts a single horizontal well cement sheath137The cement sheath density measuring system composed of the Cs gamma source, the near detector and the plurality of far detectors arranged along the circumferential direction specifically comprises the following steps:
step 1: according to selected parameters of a cement sheath density logging instrument, establishing a horizontal well numerical calculation model by using MCNP simulation software, changing the density of a medium outside a casing in the MCNP horizontal well numerical calculation model under different casing eccentric distances, wherein the density comprises the density of the cement sheath and the density of a stratum, introducing a perturbation theory into a gamma ray detection process, simulating to obtain the gamma counting variable quantity of each detector in a cement sheath density measurement system, and establishing a cement sheath space density sensitivity function library;
the gamma counting variable quantity of each detector in the cement sheath density measuring system is shown as a formula (1):
in the formula,. DELTA.N (r)R) The change in gamma ray count caused by the change in density of the medium, N (r)R) Gamma ray count of detector, psi (r) before change of medium densityS,r0E, Ω) is the position r0Flux of gamma photons, rSIs composed of137Position of Cs gamma source, E gamma photon energy, and Ω position r0Angle of scattering of (b), S (r)R,r0E, Ω) is the photon at position r0Probability of arriving at the detector after scattering, rRIn order to be able to locate the detector,
in order to be a function of the spatial sensitivity,
relative change of density of medium outside the sleeve;
step 4, changing the eccentric distance of a casing in the horizontal well numerical calculation model, only changing the density of a cement sheath of the horizontal well numerical calculation model under the condition of different casing eccentric distances, simulating to obtain gamma ray counts of each detector, obtaining the response relation between the gamma ray counts of each detector and the density of the cement sheath, then only changing the stratum density of the horizontal well numerical calculation model under the condition of different casing eccentric distances, simulating to obtain the gamma ray counts of each detector, and obtaining the response relation between the gamma ray counts of each detector and the stratum density;
Preferably, the circumferential far detector in the cement sheath density measurement system can be replaced by an array detector.
Preferably, in step 1, the cement sheath space density sensitivity function library includes cement sheath space sensitivity functions of all detectors in the cement sheath density measurement system at different casing eccentricity distances.
Preferably, in step 3, the stratum in the horizontal well numerical computation model is divided into a plurality of annular grid cells, and the radial width of each annular grid cell is set to 0.5cm, and the axial width of each annular grid cell is set to 0.5 cm.
Preferably, in the step 4, the density of the cement sheath of the horizontal well numerical calculation model is 1g/cm3Changing to 2.2g/cm3Each time increased by 0.2g/cm3(ii) a The stratum density of the horizontal well numerical calculation model is 1.8g/cm3Changing to 3g/cm3Each time increased by 0.2g/cm3。
Preferably, in the step 5, for each detector in the cement sheath density measurement system, after performing convolution calculation on the cement sheath spatial sensitivity function and each cement sheath sector density difference, multiplying the result by a reference value of a gamma ray count of the detector, so as to obtain a gamma ray count received by the detector as follows:
in the formula, n is the number of a detector in the cement sheath density measurement system; m is the total number of cement sheath sectors; i is the serial number of the cement sheath sector; n (r, x) is the gamma ray count of the detector when the eccentric distance of the sleeve is x and the source distance of the detector is r; n (r, x)refA reference value for counting gamma rays of the detector; w (theta)i) The relative contribution of the ith cement sheath sector to the detector gamma ray count; sca(x) The response relation between the gamma ray count of the detector and the density of the cement sheath is obtained; sf(x) Response relation between the gamma ray count of the detector and the formation density; Δ ρca(θi) The density difference of the ith cement sheath sector is the difference between the density of the ith cement sheath sector and the cement sheath density reference value;Δρfis the difference between the formation density and the reference value of the formation density;
based on the gamma ray counts actually received by each detector, a cement sheath orientation density calculation equation set is established, as shown in formula (3):
wherein the content of the first and second substances,
in the formula (I), the compound is shown in the specification,
the method comprises the steps of (1) providing a cement sheath sector density difference set which comprises density differences of all cement sheath sectors in a cement sheath; and x is the eccentric distance of the sleeve.
The invention has the following beneficial effects:
the invention starts from the interaction of gamma rays and media, introduces a perturbation theory into the detection process of the gamma rays, utilizes MCNP simulation software to establish a horizontal well numerical calculation model, changes the density of the media outside a sleeve in the horizontal well numerical calculation model under different sleeve eccentric distances, simulates to obtain the gamma counting variation of each detector in a cement sheath density measurement system, and establishes a cement sheath space density sensitivity function library.
The method comprehensively considers the influence of the eccentricity of the casing and the change of the azimuth density of the cement sheath on the gamma counting of the multiple detectors, establishes a calculation equation set of the azimuth density of the cement sheath by combining the relative contribution of each cement sheath sector to the gamma ray counting of each detector in a cement sheath density measurement system, and performs multidimensional data inversion calculation on the azimuth density of the cement sheath and the eccentric distance of the casing by adopting a regularized Newton iteration method, thereby eliminating the influence of the eccentricity of the casing on the gamma counting of the detectors, improving the calculation precision of the azimuth density of the cement sheath in the cementing quality of the horizontal well and making up the defect of directly calculating the azimuth density of the cement sheath by using a density response formula.
Drawings
FIG. 1 is a horizontal well numerical calculation model using a cement sheath density measurement system;
FIG. 2 is a graph of the spatial sensitivity of the cement annulus at the near and far detectors with the casing centered; in the figure, fig. 2(a) is a spatial sensitivity distribution diagram of the cement sheath at the near detector when the casing is centered, and fig. 2(b) is a spatial sensitivity distribution diagram of the cement sheath at the far detector when the casing is centered.
FIG. 3 is a graph of the relative contribution of each cement sheath sector to the near and far detector gamma ray counts at different casing eccentricity distances; in the figure, fig. 3(a) is the relative contribution of each cement sheath sector to the near detector gamma ray count at different casing eccentricity, and fig. 3(b) is the relative contribution of each cement sheath sector to the far detector gamma ray count at different casing eccentricity.
FIG. 4 is a graph showing the effect of calculating the azimuthal density of a cement sheath of a horizontal well by using the method of the present invention.
In the figure, 1 is a borehole, 2 is a casing, 3 is a cement sheath, 4 is a formation, 5 is a cement sheath density logging instrument, and 6 is137A Cs source, 7 a W-Ni-Fe shield, 8 a near detector, and 9 a far detector.
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings:
a horizontal well cement sheath azimuth gamma density inversion method adopts a mode of combining one cement sheath azimuth gamma density inversion method137The cement sheath density measuring system comprises a Cs gamma source, a near detector and six far detectors which are uniformly arranged along the circumferential direction, and specifically comprises the following steps:
step 1: according to the selected parameters of the cement sheath density logging instrument, establishing a horizontal well numerical calculation model by using MCNP simulation software, wherein the horizontal well numerical calculation model comprises a borehole 1, a casing 2, a cement sheath 3, a stratum 4 and a cement sheath density logging instrument 5, and one cement sheath density logging instrument 5 is arranged in the cement sheath density logging instrument 5137 A Cs source 6, a near detector 8 and six far detectors 9 which are uniformly arranged along the circumferential direction,137tungsten-nickel-iron shields 7 are arranged between the Cs source 6 and the near detector 8 and between the near detector 8 and the far detector. The stratum in the horizontal well numerical calculation model is divided into a plurality of annular grid cells with the size of 0.5cm multiplied by 0.5 cm.
Under different casing eccentric distances, changing the density of a medium outside a casing in an MCNP horizontal well numerical calculation model, including cement sheath density and stratum density, introducing a perturbation theory into a gamma ray detection process, and simulating to obtain the gamma counting variable quantity of each detector in a cement sheath density measurement system, as shown in a formula (1):
in the formula,. DELTA.N (r)R) The change in gamma ray count caused by the change in density of the medium, N (r)R) Gamma ray count of detector, psi (r) before change of medium densityS,r0E, Ω) is the position r0Flux of gamma photons, rSIs composed of137The position of Cs gamma source, E gamma photon energy and omega position r0Scattering angle of (d), S (r)R,r0E, Ω) is the photon at position r0Probability of arriving at the detector after scattering, rRIn order to be able to locate the detector,
in order to be a function of the spatial sensitivity,
is the relative change in the density of the medium outside the casing.
According to the gamma counting variable quantity of each detector obtained through simulation, a cement sheath space density sensitivity function library is established, the cement sheath space density sensitivity function library comprises cement sheath space sensitivity functions of all the detectors in the cement sheath density measuring system under different sleeve eccentric distances, and the distribution condition of the cement sheath space sensitivity of each detector can be obtained according to the cement sheath space sensitivity functions, as shown in fig. 2.
And 2, uniformly dividing the cement sheath in the horizontal well numerical calculation model into six cement sheath sectors, wherein the densities of the six cement sheath sectors jointly form the azimuth density of the cement sheath, and performing spatial integration on the space sensitivity functions of the cement sheath in each cement sheath sector by combining the space sensitivity functions of the cement sheath of each detector in a cement sheath space density sensitivity function library aiming at each detector in the cement sheath density measurement system to obtain the relative contribution of each cement sheath sector to the gamma ray counting of the detector, as shown in fig. 3.
And 3, setting the density of a medium outside a casing in a horizontal well numerical calculation model according to the selected stratum model, setting the density of a cement sheath in the horizontal well numerical calculation model as a cement sheath density reference value and the stratum density as a stratum density reference value, centering the casing in the horizontal well numerical calculation model, simulating to obtain the gamma ray count of each detector in the cement sheath density measurement system, and using the gamma ray count as a reference value of each detector.
Step 4, changing the eccentric distance of the casing in the horizontal well numerical calculation model, and enabling the density of the cement sheath of the horizontal well numerical calculation model to be 1g/cm under the condition of different casing eccentric distances3Changing to 2.2g/cm3Each time increased by 0.2g/cm3And simulating to obtain the gamma ray count of each detector in the cement sheath density measurement system, and obtaining the response relation between the gamma ray count of each detector and the cement sheath density.
Then under the condition of different casing eccentric distances, the stratum density of the horizontal well numerical calculation model is controlled to be 1.8g/cm3Changing to 3g/cm3Each time increased by 0.2g/cm3And simulating to obtain the gamma ray count of each detector in the cement sheath density measurement system, and obtaining the response relation between the gamma ray count of each detector and the formation density.
in the formula, n is the number of a detector in the cement sheath density measurement system; m is the total number of the cement sheath sectors, and m is 6 in the embodiment; i is the serial number of the cement sheath sector; n (r, x) is the gamma ray count of the detector when the eccentric distance of the sleeve is x and the source distance of the detector is r; n (r, x)refA reference value for counting gamma rays of the detector; w (theta)i) The relative contribution of the ith cement sheath sector to the detector gamma ray count; sca(x) The response relation between the gamma ray count of the detector and the density of the cement sheath is obtained; sf(x) Counting the response relation between the gamma rays of the detector and the density of the stratum; Δ ρca(θi) Density difference of the ith cement sheath sector; Δ ρfIs the difference between the formation density and the reference formation density value.
And (3) counting the gamma rays actually received by each detector in the cement sheath density measurement system, and establishing a cement sheath azimuth density calculation equation set as shown in a formula (3):
wherein the content of the first and second substances,
in the formula (I), the compound is shown in the specification,
is a set of density difference values of cement sheath sectors, and x is casing offsetThe heart distance; in this embodiment, n is 1,2, 3.
Calculating the optimal solution of the azimuth density of the cement sheath in the cement sheath azimuth density calculation equation set by utilizing a regularized Newton iteration method to obtain a sleeve eccentric distance x and a cement sheath sector density difference value set
Cement sheath sector density difference set
Including the difference value Deltarho of the density of each cement sheath sectorca(θi) And calculating the density of each cement sheath sector according to the difference of the density of each cement sheath sector and by combining the density reference value of the cement sheath to obtain the azimuth density of the cement sheath.
Fig. 4 is an effect diagram for calculating the azimuth density of the cement sheath of the horizontal well by using the method of the present invention, wherein the 1 st track is a depth track, the 2 nd track is a set value (set according to a selected stratum model) of the azimuth density of the cement sheath in a numerical calculation model of the horizontal well, the 3 rd track is a casing eccentricity distance curve and a gamma ray counting curve of a near detector, the 4 th track is a gamma ray counting curve of a far detector (N1-N6 correspond to a first far detector to a sixth far detector), the 5 th track to the 10 th track are used for comparing the calculated value and the set value of the azimuth density of the cement sheath at each far detector, and the 11 th track is an imaging result of the azimuth density of the cement sheath.
According to the method, the influence of instrument measurement errors on the cement sheath azimuth density monitoring is avoided, the problem that the cement sheath azimuth density is difficult to accurately evaluate due to casing eccentricity and cement slurry sedimentation in the horizontal well is solved, the cement sheath azimuth density is accurately monitored, and technical support is provided for horizontal well cementing quality evaluation and oil gas resource development.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.
Claims (6)
1. An azimuth gamma density inversion method for a horizontal well cement sheath adopts a single horizontal well cement sheath137The cement sheath density measuring system is characterized by comprising a Cs gamma source, a near detector and a plurality of far detectors arranged along the circumferential direction, and the cement sheath density measuring system specifically comprises the following steps:
step 1: according to selected parameters of a cement sheath density logging instrument, establishing a horizontal well numerical calculation model by using MCNP simulation software, changing the density of a medium outside a casing in the MCNP horizontal well numerical calculation model under different casing eccentric distances, wherein the density comprises the density of the cement sheath and the density of a stratum, introducing a perturbation theory into a gamma ray detection process, simulating to obtain the gamma counting variable quantity of each detector in a cement sheath density measurement system, and establishing a cement sheath space density sensitivity function library;
the gamma counting variable quantity of each detector in the cement sheath density measuring system is shown as a formula (1):
in the formula,. DELTA.N (r)R) The change in gamma ray count due to a change in density of the medium, N (r)R) Gamma ray count of detector, psi (r) before changing density of mediumS,r0E, Ω) is the position r0Flux of gamma photons, rSIs composed of137Position of Cs gamma source, E gamma photon energy, and Ω position r0Scattering angle of (d), S (r)R,r0E, Ω) is the photon at position r0Probability of arrival at the detector after scattering, rRIn order to be able to locate the detector,
in order to be a function of the spatial sensitivity,
relative change of density of medium outside the sleeve;
step 2, uniformly dividing a cement sheath in a horizontal well numerical calculation model into a plurality of cement sheath sectors, wherein the density of each cement sheath sector jointly forms the azimuth density of the cement sheath, and performing spatial integration on a cement sheath spatial sensitivity function in each cement sheath sector aiming at each detector in a cement sheath density measurement system to obtain the relative contribution of each cement sheath sector to the gamma ray counting of the detector;
step 3, setting the density of a medium outside a casing in a horizontal well numerical calculation model according to the selected stratum model, setting the density of a cement sheath in the horizontal well numerical calculation model as a cement sheath density reference value and the stratum density as a stratum density reference value, centrally setting the casing in the horizontal well numerical calculation model, simulating to obtain the gamma ray count of each detector in the cement sheath density measurement system, and using the gamma ray count as a reference value of each detector;
step 4, changing the eccentric distance of a casing in the horizontal well numerical calculation model, only changing the density of a cement sheath of the horizontal well numerical calculation model under the condition of different casing eccentric distances, simulating to obtain gamma ray counts of each detector, obtaining the response relation between the gamma ray counts of each detector and the density of the cement sheath, then only changing the stratum density of the horizontal well numerical calculation model under the condition of different casing eccentric distances, simulating to obtain the gamma ray counts of each detector, and obtaining the response relation between the gamma ray counts of each detector and the stratum density;
step 5, the eccentricity of the casing and the variation of the azimuthal density of the cement sheath are taken as comprehensive factors causing the gamma ray count difference of each detector in the cement sheath density measurement system, a cement sheath azimuthal density calculation equation set suitable for multiple detectors is established by combining the relative contribution of each cement sheath sector to the gamma ray count of each detector in the cement sheath density measurement system, the optimal solution of the azimuthal density of the cement sheath in the cement sheath azimuthal density calculation equation set is calculated by utilizing a regularized Newton iteration method, and the eccentric distance x of the casing and the density difference set of the cement sheath sector are obtained
According to the cementAnd calculating the density of each cement sheath sector by combining the density difference of the sheath sectors and the density reference value of the cement sheath to obtain the azimuth density of the cement sheath.
2. The horizontal well cement sheath azimuth gamma density inversion method according to claim 1, characterized in that a circumferential far detector in the cement sheath density measurement system can be replaced by an array detector.
3. The horizontal well cement sheath orientation gamma density inversion method according to claim 1, wherein in the step 1, the cement sheath space density sensitivity function library comprises cement sheath space sensitivity functions of all detectors in the cement sheath density measurement system under different casing eccentricity distances.
4. The horizontal well cement sheath azimuth gamma density inversion method of claim 1, wherein in the step 3, the stratum in the horizontal well numerical computation model is divided into a plurality of annular grid cells, the radial width of each annular grid cell is set to be 0.5cm, and the axial width of each annular grid cell is set to be 0.5 cm.
5. The horizontal well cement sheath azimuth gamma density inversion method of claim 1, wherein in the step 4, the cement sheath density of the horizontal well numerical computation model is 1g/cm3Changing to 2.2g/cm3Each time increased by 0.2g/cm3(ii) a The stratum density of the horizontal well numerical calculation model is 1.8g/cm3Changing to 3g/cm3Each time increased by 0.2g/cm3。
6. The horizontal well cement sheath azimuth gamma density inversion method according to claim 1, wherein in the step 5, for each detector in the cement sheath density measurement system, after performing convolution calculation on the cement sheath space sensitivity function and each cement sheath sector density difference, multiplying the result by a reference value of a detector gamma ray count to obtain the gamma ray count received by the detector as follows:
in the formula, n is the number of a detector in the cement sheath density measurement system; m is the total number of cement sheath sectors; i is the serial number of the cement sheath sector; n (r, x) is the gamma ray count of the detector when the eccentric distance of the sleeve is x and the source distance of the detector is r; n (r, x)refA reference value for counting gamma rays of the detector; w (theta)i) The relative contribution of the ith cement sheath sector to the gamma ray count of the detector; sca(x) The response relation between the gamma ray count of the detector and the density of the cement sheath is obtained; sf(x) Counting the response relation between the gamma rays of the detector and the density of the stratum; Δ ρca(θi) Density difference of the ith cement sheath sector; Δ ρfIs the difference between the formation density and the reference value of the formation density;
based on the gamma ray counts actually received by each detector, a cement sheath orientation density calculation equation set is established, as shown in formula (3):
wherein the content of the first and second substances,
in the formula (I), the compound is shown in the specification,
and x is the eccentric distance of the casing.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115522913A (en) * | 2022-09-30 | 2022-12-27 | 中国石油大学(华东) | Gamma logging fast forward modeling method and system for high-inclination horizontal well |
| CN115992692A (en) * | 2023-03-23 | 2023-04-21 | 中海油田服务股份有限公司 | Cement ring thickness measuring method and device, electronic equipment and storage medium |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115522913A (en) * | 2022-09-30 | 2022-12-27 | 中国石油大学(华东) | Gamma logging fast forward modeling method and system for high-inclination horizontal well |
| US11940590B1 (en) * | 2022-09-30 | 2024-03-26 | China University Of Petroleum(East China) | Fast forward method and system for gamma-ray logging of highly-deviated and horizontal wells preliminary class |
| CN115992692A (en) * | 2023-03-23 | 2023-04-21 | 中海油田服务股份有限公司 | Cement ring thickness measuring method and device, electronic equipment and storage medium |
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