A method for azimuthal gamma density inversion of cement sheath in horizontal wells

Abstract

The present invention discloses a method for inverting the azimuthal gamma density of cement ring in a horizontal well. The method uses MCNP simulation software to establish a numerical calculation model of a horizontal well, introduces perturbation theory into the gamma ray detection process, establishes a cement ring spatial density sensitivity function library, and then divides the cement ring into multiple sectors. The cement ring spatial sensitivity function is spatially integrated in each sector to obtain the relative contribution of each cement ring sector to the detector gamma ray count, comprehensively considers the influence of casing eccentricity and cement ring azimuthal density change on the detector gamma ray count, establishes a cement ring azimuthal density calculation equation group and uses regularized Newton iteration method to obtain the optimal solution, and calculates the cement ring azimuthal density in combination with the cement ring density reference value. The present invention solves the problem that it is difficult to accurately evaluate the cement ring azimuthal density due to casing eccentricity and cement slurry settlement in a horizontal well, improves the calculation accuracy of the cement ring azimuthal density, and provides technical support for the evaluation of cementing quality in horizontal wells.

Description

Technical Field

[0001] The invention relates to the field of oil and gas development, and in particular to a method for azimuthal gamma density inversion of cement rings in horizontal wells. Background Art

[0002] Horizontal well technology has been widely used in the exploration and development of unconventional oil and gas reservoirs to increase the exposed area of ​​oil and gas reservoirs. Cementing is of great significance to the isolation of oil, gas and water layers. Determining cement density by gamma-ray attenuation is an important part of evaluating cementing effects. Compared with vertical well cementing, horizontal wells have problems such as casing eccentricity and cement slurry sedimentation due to the effect of casing gravity, which greatly affects gamma-ray detection and leads to uncertainty in cement ring azimuthal density evaluation.

[0003] At present, the evaluation of cement sheath density is mainly based on the detector's gamma-ray counts and cement density response, and the density parameters are directly calculated. However, due to the measurement errors of the logging instrument and the statistical nature of the gamma-ray counts, the azimuthal density of the cement sheath cannot be accurately monitored, making it difficult to meet the needs of on-site oil and gas evaluation. At the same time, due to the eccentricity of the casing in the horizontal well, the accuracy of the obtained cement density calculation formula is also difficult to guarantee. Therefore, it is urgent to propose a method for inverting the azimuthal gamma density of the cement sheath in horizontal wells to avoid the influence of the casing eccentricity on the gamma counts during cementing of the horizontal well and improve the calculation accuracy of the azimuthal density of the cement sheath. Summary of the invention

[0004] The purpose of the present invention is to introduce perturbation theory into the gamma ray detection process in view of the above-mentioned shortcomings. Based on the multi-detector gamma count information of the cement ring density measurement system, a method for inversion of the azimuthal gamma density of the cement ring in horizontal wells is proposed by combining the cement ring spatial sensitivity function and the regularized Newton iteration method. The influence of casing eccentricity and cement ring azimuthal density change on the detector gamma ray count is comprehensively considered, thereby improving the accuracy of cement ring azimuthal density calculation.

[0005] The present invention specifically adopts the following technical solutions:

[0006] A method for inversion of azimuthal gamma density of cement sheath in horizontal wells is based on a 137 The cement sheath density measurement system, which is composed of a Cs gamma source, a near detector and a plurality of far detectors arranged in a circumferential direction, specifically includes the following steps:

[0007] Step 1: According to the selected cement sheath density logging instrument parameters, the MCNP simulation software is used to establish a horizontal well numerical calculation model. At different casing eccentricity distances, the density of the medium outside the casing in the MCNP horizontal well numerical calculation model is changed, including the cement sheath density and the formation density. The perturbation theory is introduced into the gamma ray detection process to simulate the gamma count changes of each detector in the cement sheath density measurement system, and a cement sheath spatial density sensitivity function library is established;

[0008] The gamma count variation of each detector in the cement ring density measurement system is shown in formula (1):

[0009]

[0010] In the formula, ΔN(r R ) is the change in gamma-ray counts caused by the change in medium density, N(r R ) is the gamma-ray count of the detector before the medium density changes, ψ(r S ,r0,E,Ω) is the gamma photon flux at position r0, r S for 137 Cs is the position of the gamma source, E is the gamma photon energy, Ω is the scattering angle at position r0, S(r R ,r0,E,Ω) is the probability that a photon reaches the detector after being scattered at position r0, r R is the detector position, is the spatial sensitivity function, is the relative change of medium density outside the casing;

[0011] Step 2: The cement sheath in the horizontal well numerical calculation model is evenly divided into multiple cement sheath sectors. The density of each cement sheath sector together constitutes the cement sheath azimuthal density. For each detector in the cement sheath density measurement system, the cement sheath spatial sensitivity function is spatially integrated in each cement sheath sector to obtain the relative contribution of each cement sheath sector to the detector gamma-ray count.

[0012] Step 3, setting the medium density outside the casing in the horizontal well numerical calculation model according to the selected formation model, setting the cement ring density in the horizontal well numerical calculation model as the cement ring density reference value, setting the formation density as the formation density reference value, setting the casing in the horizontal well numerical calculation model in the center, simulating and obtaining the gamma ray counts of each detector in the cement ring density measurement system, and using them as the reference value of the gamma ray counts of each detector;

[0013] Step 4, changing the eccentric distance of the casing in the horizontal well numerical calculation model, under the condition of different casing eccentric distances, only changing the cement ring density of the horizontal well numerical calculation model, simulating the gamma ray counts of each detector, obtaining the response relationship between the gamma ray counts of each detector and the cement ring density, and then under the condition of different casing eccentric distances, only changing the formation density of the horizontal well numerical calculation model, simulating the gamma ray counts of each detector, obtaining the response relationship between the gamma ray counts of each detector and the formation density;

[0014] Step 5: Taking casing eccentricity and cement sheath azimuth density change as comprehensive factors causing the difference in gamma-ray counts of each detector in the cement sheath density measurement system, and combining the relative contribution of each cement sheath sector to the gamma-ray counts of each detector in the cement sheath density measurement system, a cement sheath azimuth density calculation equation group suitable for multiple detectors is established, and the regularized Newton iteration method is used to calculate the optimal solution of the cement sheath azimuth density in the cement sheath azimuth density calculation equation group, and the casing eccentricity distance x and the cement sheath sector density difference set are obtained. According to the density difference of each cement sheath sector and the cement sheath density reference value, the density of each cement sheath sector is calculated to obtain the cement sheath azimuthal density.

[0015] Preferably, the circumferential remote detector in the cement ring density measurement system can be replaced by an array detector.

[0016] Preferably, in step 1, the cement sheath spatial density sensitivity function library includes cement sheath spatial sensitivity functions of all detectors in the cement sheath density measurement system at different casing eccentricity distances.

[0017] Preferably, in step 3, the strata in the horizontal well numerical calculation model are divided into a plurality of annular grid elements, and the radial width of the annular grid elements is set to 0.5 cm and the axial width is set to 0.5 cm.

[0018] Preferably, in step 4, the cement sheath density of the horizontal well numerical calculation model is 1 g / cm 3 Change to 2.2g / cm 3 , increase by 0.2g / cm each time 3 ; The formation density of the horizontal well numerical calculation model is 1.8g / cm 3 Change to 3g / cm 3 , increase by 0.2g / cm each time 3 .

[0019] Preferably, in step 5, for each detector in the cement sheath density measurement system, the cement sheath spatial sensitivity function is convolved with the density difference of each cement sheath sector, and then multiplied by a reference value of the detector gamma ray count to obtain the gamma ray count received by the detector:

[0020]

[0021] Where n is the detector number in the cement ring density measurement system; m is the total number of cement ring sectors; i is the sequence number of cement ring sectors; N(r,x) is the gamma ray count of the detector when the casing eccentricity distance is x and the detector source distance is r; N(r,x) ref is the reference value of the detector gamma-ray count; w(θ i ) is the relative contribution of the ith cement ring sector to the detector gamma-ray counts; S ca (x) is the response relationship between the detector gamma ray count and cement ring density; S f (x) is the response relationship between the detector gamma-ray count and the formation density; Δρ ca (θ i ) is the density difference of the ith cement sheath sector, that is, the difference between the density of the ith cement sheath sector and the cement sheath density reference value; Δρ f is the difference between the formation density and the reference value of formation density;

[0022] Based on the gamma-ray counts actually received by each detector, the cement sheath azimuthal density calculation equation group is established, as shown in formula (3):

[0023]

[0024] in,

[0025]

[0026] In the formula, is the density difference set of cement sheath sectors, including the density difference of each cement sheath sector in the cement sheath; x is the eccentricity distance of the casing.

[0027] The present invention has the following beneficial effects:

[0028] The present invention starts from the interaction between gamma rays and media, introduces perturbation theory into the detection process of gamma rays, uses MCNP simulation software to establish a horizontal well numerical calculation model, and simulates the gamma count changes of each detector in the cement annulus density measurement system by changing the density of the medium outside the casing in the horizontal well numerical calculation model at different casing eccentricity distances, and establishes a cement annulus spatial density sensitivity function library.

[0029] The present invention comprehensively considers the influence of casing eccentricity and cement sheath azimuthal density change on multi-detector gamma counts, combines the relative contribution of each cement sheath sector to the gamma ray counts of each detector in the cement sheath density measurement system, establishes a cement sheath azimuthal density calculation equation group, and uses the regularized Newton iteration method to perform multi-dimensional data inversion calculation on the cement sheath azimuthal density and casing eccentricity distance, thereby eliminating the influence of casing eccentricity on the detector gamma counts, improving the calculation accuracy of cement sheath azimuthal density in horizontal well cementing quality, and making up for the deficiency of directly using the density response formula to calculate the cement sheath azimuthal density. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a numerical calculation model for horizontal wells using cement sheath density measurement system;

[0031] Figure 2 The distribution diagram of the spatial sensitivity of cement sheath at near and far detectors when the casing is centered; Figure 2 (a) is the spatial sensitivity distribution diagram of the cement sheath near the detector when the casing is centered. Figure 2 (b) is the spatial sensitivity distribution diagram of the cement annulus at the far detector when the casing is centered.

[0032] Figure 3 is the relative contribution of each cement sheath sector to the gamma-ray counts of near and far detectors at different casing eccentricity distances; in the figure, Figure 3 (a) is the relative contribution of each cement sheath sector to the near-detector gamma-ray counts at different casing eccentricity distances. Figure 3 (b) The relative contribution of each cement ring sector to the gamma-ray counts of the far detector at different casing eccentricity distances.

[0033] Figure 4 The figure is a rendering of the effect of using the present invention to calculate the azimuthal density of cement sheath in a horizontal well.

[0034] In the figure, 1 is the wellbore, 2 is the casing, 3 is the cement ring, 4 is the formation, 5 is the cement ring density logging instrument, 6 is 137 Cs source, 7 is a tungsten-nickel-iron shield, 8 is a near detector, and 9 is a far detector. DETAILED DESCRIPTION

[0035] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments:

[0036] A method for inversion of azimuthal gamma density of cement sheath in horizontal wells is based on a 137 The cement sheath density measurement system, which consists of a Cs gamma source, a near detector and six far detectors evenly arranged along the circumference, specifically includes the following steps:

[0037] Step 1: According to the selected cement sheath density logging instrument parameters, use MCNP simulation software to establish a horizontal well numerical calculation model, such as Figure 1 As shown, the horizontal well numerical calculation model includes a wellbore 1, a casing 2, a cement ring 3, a formation 4 and a cement ring density logging instrument 5. The cement ring density logging instrument 5 is provided with a 137 The cement ring density measurement system consists of a Cs source 6, a near detector 8 and six far detectors 9 evenly arranged along the circumference. 137 A tungsten-nickel-iron shield 7 is provided 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 elements with a size of 0.5 cm×0.5 cm.

[0038] Under different casing eccentricity distances, the density of the medium outside the casing in the MCNP horizontal well numerical calculation model, including the cement sheath density and the formation density, is changed. The perturbation theory is introduced into the gamma-ray detection process, and the gamma count changes of each detector in the cement sheath density measurement system are simulated, as shown in formula (1):

[0039]

[0040] In the formula, ΔN(r R ) is the change in gamma-ray counts caused by the change in medium density, N(r R ) is the gamma-ray count of the detector before the medium density changes, ψ(r S ,r0,E,Ω) is the gamma photon flux at position r0, r S for 137 Cs is the gamma source position, E is the gamma photon energy, Ω is the scattering angle at position r0, S(r R ,r0,E,Ω) is the probability that a photon reaches the detector after being scattered at position r0, r R is the detector position, is the spatial sensitivity function, is the relative change of the density of the medium outside the casing.

[0041] According to the gamma count variation of each detector obtained by simulation, a cement annulus spatial density sensitivity function library is established. The cement annulus spatial density sensitivity function library includes the cement annulus spatial sensitivity functions of all detectors in the cement annulus density measurement system at different casing eccentricity distances. According to the cement annulus spatial sensitivity function, the distribution of cement annulus spatial sensitivity at each detector can be obtained, such as Figure 2 shown.

[0042] Step 2: The cement sheath in the horizontal well numerical calculation model is evenly divided into six cement sheath sectors. The densities of the six cement sheath sectors together constitute the cement sheath azimuthal density. For each detector in the cement sheath density measurement system, the cement sheath spatial sensitivity function of each detector in the cement sheath spatial density sensitivity function library is combined. By spatially integrating the cement sheath spatial sensitivity function in each cement sheath sector, the relative contribution of each cement sheath sector to the detector gamma-ray count is obtained, as shown in Fig. Figure 3 shown.

[0043] Step 3, setting the medium density outside the casing in the horizontal well numerical calculation model according to the selected formation model, and setting the cement ring density in the horizontal well numerical calculation model to the cement ring density reference value, and the formation density to the formation density reference value, setting the casing in the horizontal well numerical calculation model in the center, simulating the gamma ray counts of each detector in the cement ring density measurement system, and using them as the reference value of the gamma ray counts of each detector.

[0044] Step 4: Change the eccentric distance of the casing in the horizontal well numerical calculation model. Under different casing eccentricity conditions, the cement sheath density of the horizontal well numerical calculation model is changed from 1 g / cm 3 Change to 2.2g / cm 3 , increase by 0.2g / cm each time 3 , the gamma-ray counts of each detector in the cement sheath density measurement system are simulated, and the response relationship between the gamma-ray counts of each detector and the cement sheath density is obtained.

[0045] Then, under different casing eccentricity conditions, the formation density of the horizontal well numerical calculation model was changed from 1.8 g / cm 3 Change to 3g / cm 3 , increase by 0.2g / cm each time 3 , the gamma-ray counts of each detector in the cement sheath density measurement system are simulated, and the response relationship between the gamma-ray counts of each detector and the formation density is obtained.

[0046] Step 5: Taking casing eccentricity and cement sheath azimuthal density change as comprehensive factors causing the difference in gamma-ray counts of each detector in the cement sheath density measurement system, and combining the relative contribution of each cement sheath sector to the gamma-ray counts of each detector in the cement sheath density measurement system, the gamma-ray counts received by each detector in the cement sheath density measurement system can be obtained by convolving the cement sheath spatial sensitivity function with the density difference of each cement sheath sector and multiplying it by the reference value of the gamma-ray counts of each detector, that is, the gamma-ray counts received by each detector are:

[0047]

[0048] Wherein, n is the number of the detector in the cement ring density measurement system; m is the total number of cement ring sectors, and in this embodiment, m=6; i is the sequence number of the cement ring sector; N(r,x) is the gamma ray count of the detector when the casing eccentricity distance is x and the detector source distance is r; N(r,x) ref is the reference value of the detector gamma-ray count; w(θ i ) is the relative contribution of the ith cement ring sector to the detector gamma-ray counts; S ca (x) is the response relationship between the detector gamma ray count and cement ring density; S f (x) is the response relationship between the detector gamma-ray count and the formation density; Δρ ca (θ i ) is the density difference of the i-th cement ring sector; Δρ f It is the difference between the formation density and the formation density reference value.

[0049] Based on the gamma-ray counts actually received by each detector in the cement sheath density measurement system, the cement sheath azimuthal density calculation equation group is established, as shown in formula (3):

[0050]

[0051] in,

[0052]

[0053] In the formula, is the density difference set of cement sheath sectors, x is the casing eccentricity distance; in this embodiment, the value range of n is n=1,2,3,...,7.

[0054] The regularized Newton iteration method is used to calculate the optimal solution of the cement sheath azimuth density in the cement sheath azimuth density calculation equation group, and the casing eccentricity distance x and the cement sheath sector density difference set are obtained. Cement ring sector density difference collection The density difference Δρ of each cement sheath sector is included in ca (θ i ), according to the difference of density of each cement ring sector and the reference value of cement ring density, the density of each cement ring sector is calculated to obtain the azimuthal density of cement ring.

[0055] Figure 4It is an effect diagram of calculating the azimuthal density of cement sheath in horizontal wells by using the present invention, wherein the first track is a depth track, the second track is a set value of the azimuthal density of cement sheath in the numerical calculation model of horizontal wells (set according to the selected formation model), the third track is a casing eccentricity distance curve and a gamma ray counting curve of a near detector, the fourth track is a gamma ray counting curve of a far detector (N1 to N6 correspond to the first far detector to the sixth far detector), the fifth to tenth tracks are used to compare the calculated value and the set value of the azimuthal density of cement sheath at each far detector, and the eleventh track is an imaging result of the azimuthal density of cement sheath.

[0056] Depend on Figure 4 It can be seen that the present invention avoids the influence of instrument measurement errors on the monitoring of cement sheath azimuthal density, solves the problem that the cement sheath azimuthal density is difficult to accurately evaluate due to casing eccentricity and cement slurry settlement in horizontal wells, realizes accurate monitoring of cement sheath azimuthal density, and provides technical support for horizontal well cementing quality evaluation and oil and gas resource development.

[0057] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for inversion of azimuthal gamma density of cement sheath in horizontal wells, using a 137 The cement ring density measurement system consists of a Cs gamma source, a near detector and a plurality of far detectors arranged in the circumferential direction, and is characterized in that: The specific steps include: Step 1: According to the selected cement sheath density logging instrument parameters, the MCNP simulation software is used to establish a horizontal well numerical calculation model. At different casing eccentricity distances, the density of the medium outside the casing in the MCNP horizontal well numerical calculation model is changed, including the cement sheath density and the formation density. The perturbation theory is introduced into the gamma ray detection process to simulate the gamma count changes of each detector in the cement sheath density measurement system, and a cement sheath spatial density sensitivity function library is established; The gamma count variation of each detector in the cement ring density measurement system is shown in formula (1): In the formula, ΔN(r R ) is the change in gamma-ray counts caused by the change in medium density, N(r R ) is the gamma-ray count of the detector before the medium density changes, ψ(r S ,r0,E,Ω) is the gamma photon flux at position r0, r S for 137 Cs is the position of the gamma source, E is the gamma photon energy, Ω is the scattering angle at position r0, S(r R ,r0,E,Ω) is the probability that a photon reaches the detector after being scattered at position r0, r R is the detector position, is the spatial sensitivity function, is the relative change of medium density outside the casing; Step 2: The cement sheath in the horizontal well numerical calculation model is evenly divided into multiple cement sheath sectors. The density of each cement sheath sector together constitutes the cement sheath azimuthal density. For each detector in the cement sheath density measurement system, the cement sheath spatial sensitivity function is spatially integrated in each cement sheath sector to obtain the relative contribution of each cement sheath sector to the detector gamma-ray count. Step 3, setting the medium density outside the casing in the horizontal well numerical calculation model according to the selected formation model, setting the cement ring density in the horizontal well numerical calculation model as the cement ring density reference value, setting the formation density as the formation density reference value, setting the casing in the horizontal well numerical calculation model in the center, simulating and obtaining the gamma ray counts of each detector in the cement ring density measurement system, and using them as the reference value of the gamma ray counts of each detector; Step 4, changing the eccentric distance of the casing in the horizontal well numerical calculation model, under the condition of different casing eccentric distances, only changing the cement ring density of the horizontal well numerical calculation model, simulating the gamma ray counts of each detector, obtaining the response relationship between the gamma ray counts of each detector and the cement ring density, and then under the condition of different casing eccentric distances, only changing the formation density of the horizontal well numerical calculation model, simulating the gamma ray counts of each detector, obtaining the response relationship between the gamma ray counts of each detector and the formation density; Step 5: Taking casing eccentricity and cement sheath azimuth density change as comprehensive factors causing the difference in gamma-ray counts of each detector in the cement sheath density measurement system, and combining the relative contribution of each cement sheath sector to the gamma-ray counts of each detector in the cement sheath density measurement system, a cement sheath azimuth density calculation equation group suitable for multiple detectors is established, and the regularized Newton iteration method is used to calculate the optimal solution of the cement sheath azimuth density in the cement sheath azimuth density calculation equation group, and the casing eccentricity distance x and the cement sheath sector density difference set are obtained. According to the density difference of each cement sheath sector, the density of each cement sheath sector is calculated in combination with the cement sheath density reference value to obtain the cement sheath azimuth density; In step 5, for each detector in the cement sheath density measurement system, the cement sheath spatial sensitivity function is convolved with the density difference of each cement sheath sector, and then multiplied by the reference value of the detector gamma ray count to obtain the gamma ray count received by the detector: Where n is the detector number in the cement ring density measurement system; m is the total number of cement ring sectors; i is the sequence number of cement ring sectors; N(r,x) is the gamma ray count of the detector when the casing eccentricity distance is x and the detector source distance is r; N(r,x) ref is the reference value of the detector gamma-ray count; w(θ i ) is the relative contribution of the ith cement ring sector to the detector gamma-ray counts; S ca (x) is the response relationship between the detector gamma ray count and cement ring density; S f (x) is the response relationship between the detector gamma-ray count and the formation density; Δρ ca (θ i ) is the density difference of the i-th cement ring sector; Δρ f is the difference between the formation density and the reference value of formation density; Based on the gamma-ray counts actually received by each detector, the cement sheath azimuthal density calculation equation group is established, as shown in formula (3): in, In the formula, is the density difference set of cement sheath sectors, and x is the casing eccentricity distance.

2. A method for azimuthal gamma density inversion of cement sheath in a horizontal well according to claim 1, characterized in that: The circumferential remote detector in the cement ring density measurement system can be replaced by an array detector.

3. A method for azimuthal gamma density inversion of cement sheath in a horizontal well according to claim 1, characterized in that: In the step 1, the cement sheath spatial density sensitivity function library includes cement sheath spatial sensitivity functions of all detectors in the cement sheath density measurement system at different casing eccentricity distances.

4. A method for azimuthal gamma density inversion of cement sheath in a horizontal well according to claim 1, characterized in that: In the step 3, the strata in the horizontal well numerical calculation model are divided into a plurality of annular grid elements, and the radial width and axial width of the annular grid elements are set to 0.5 cm and 0.5 cm, respectively.

5. The method for azimuthal gamma density inversion of cement sheath in a horizontal well according to claim 1, characterized in that: In step 4, the cement sheath density of the horizontal well numerical calculation model is changed from 1 g / cm 3 Change to 2.2g / cm 3 , increase by 0.2g / cm each time 3 ; The formation density of the horizontal well numerical calculation model is 1.8g / cm 3 Change to 3g / cm 3 , increase by 0.2g / cm each time 3 .

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